GB2640582A

GB2640582A - Determining a value of an electric power flow characteristic of an electric power grid

Info

Publication number: GB2640582A
Application number: GB2405896.8A
Authority: GB
Inventors: Aula Janne; Destino Giuseppe
Original assignee: Reactive Technologies Ltd
Current assignee: Reactive Technologies Ltd
Priority date: 2024-04-26
Filing date: 2024-04-26
Publication date: 2025-10-29
Also published as: WO2025224216A1; GB202405896D0

Abstract

A power grid comprises at least one power unit to consume electric power from and/or provide electric power to the grid. A power change by the power unit causes a change in value of a first parameter of electric power flow in the grid. A method of determining the value comprises: 102 correlating a particular power change with at least one value of the first parameter at a first grid location and at least one value of the first parameter at a second grid location; 104 determining a difference between the value of the parameter at the first and second grid locations; and 106 determining, based on the difference, a value of the electric power flow characteristic of the electric power grid. The value may indicate the difference in impedance between the power unit and the first and second grid locations. The first parameter may indicate the phase of AC electricity in the grid. The value may be indicative of grid inertia.

Description

DETERMINING A VALUE OF AN ELECTRIC POWER FLOW CHARACTERISTIC OF AN ELECTRIC POWER GRID

Technical Field

The present invention relates to a method, apparatus, and system for determining a value of an electric power flow characteristic of an electric power grid.

Background

An electricity distribution network or electric power grid distributes electric power from generators or providers of electrical power to consumers of electrical power. A grid operator may be tasked with maintaining proper operation of an electric power grid. To this end, it is useful for grid operators to determine or otherwise be provided with values of one or more electric power flow characteristics of the grid. These can provide an insight to the state of operation of the grid and can accordingly be used to inform repair or optimisation of the configuration and/or operation of the grid, as needed, for example.

Summary

According to a first aspect of the present invention, there is provided a computer-implemented method of determining a value of an electric power flow characteristic of an electric power grid, the grid comprising at least one power unit configured to consume electric power from and/or provide electric power to the electric power grid, a change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit causing a change in value of a first parameter of electric power flow in the electric power grid, the method comprising: a) correlating a particular change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit with at least one value of the first parameter at a first grid location and at least one value of the first parameter at a second grid location; b) determining a difference between the at least one value of the first parameter at the first grid location and the at least one value of the first parameter at the second grid location; and c) determining, based on the determined difference, a value of the electric power flow characteristic of the electric power grid.

Optionally, the value of the electric power flow characteristic is indicative of a difference between a first impedance between the at least one power unit and the first grid location and a second impedance between the at least one power unit and the second grid location.

Optionally, the first parameter is indicative of a phase of AC electricity flowing in the electric power grid.

Optionally, determining the value of the electric power flow characteristic is further based on one or both of a value of grid inertia at the first grid location and a value of grid inertia at the second grid location.

Optionally, the value of the electric power flow characteristics is indicative of at least one of: grid inertia at the first grid location; grid inertia at the second grid location; a proportion of the particular change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit experienced at the first grid location; and a proportion of the particular change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit experienced at the second grid location.

Optionally, there are a plurality of second grid locations, and the method comprises performing steps a) to c) for each one of the plurality of second grid locations.

Optionally, there are a plurality of first grid locations, and the method comprises performing steps a) to c) for each combination of first and second grid locations.

Optionally, the method comprises identifying, based on the determined value or values of the electric power flow characteristic, a particular operational state of the electric power grid.

Optionally, the method comprises: inputting data representing the determined value or values of the electric power flow characteristic into a trained machine learning model, the trained machine learning model having been trained to map input data representing one or more values of the electric power flow characteristic onto one of a plurality of operational states of the electric power grid, thereby to identify the particular operational state of the electric power grid based on the determined value or values of the electric power flow characteristic.

Optionally, the method comprises training the machine learning model to provide the trained machine learning model, where training the machine learning model comprises: providing training data sets, each training data set comprising one or more values of the electric power flow characteristic and a corresponding ground truth operational state of the electric power grid; and adjusting one or more parameters of the machine learning model to minimize a difference between, for each training data set, the ground truth operational state of the electric power grid and the operational state of the electric power grid onto which the one or more values of the electric power flow characteristic is mapped by the machine learning model. Optionally, the method comprises: d) performing steps a) to c) to determine a first value of the electric power flow characteristic corresponding to a first time; e) performing steps a) to c) to determine a second value of the electric power flow characteristic corresponding to a second time, later than the first time; f) determining a difference value representing a difference between the first value of the electric power flow characteristic and the second value of the electric power flow characteristic.

Optionally, there are a plurality of second grid locations, and the method comprises performing steps d) to 0 for each one of the plurality of second grid locations.

Optionally, are a plurality of first grid locations, and the method comprises performing steps d) to 0 for each combination of first and second grid locations, thereby to determine a difference value for each combination.

Optionally, the method comprises identifying, based on the determined difference value or values, a particular change in operational state of the electric power grid.

Optionally, the method comprises: inputting data representing the difference value or values into a trained machine learning model, the trained machine learning model having been trained to map input data representing one or more such difference values onto a particular one of a plurality of changes in operational state of the electric power grid, thereby to identify the particular change in operational state of the electric power grid based on the determined difference value or difference values.

Optionally, the method comprises training the machine learning model to provide the trained machine learning model, where training the machine learning model comprises: providing training data sets, each training data set comprising one or more said difference values and a corresponding ground truth change in operational state of the electric power grid; and adjusting one or more parameters of the machine learning model to minimize a difference between, for each training data set, the ground truth operational state of the electric power grid and the change in operational state of the electric power grid onto which the one or more difference values is mapped by the machine learning model.

Optionally, a particular operational state represents a particular topology of electrical connections between grid locations in the electric power grid.

Optionally, the first parameter is indicative of a voltage phase angle of AC electricity flowing in the electric power grid.

Optionally, the difference is indicative of an amplitude of a difference between the voltage phase angle at the first grid location and the voltage phase angle at the second grid location.

Optionally, the first parameter is indicative of a magnitude of voltage of the electricity fl owing in the electric power grid.

Optionally, the difference is indicative of an amplitude of a difference between voltage magnitude at the first grid location and voltage magnitude at the second grid location.

Optionally, the method comprises: determining the at least one value of the first parameter at the first grid location and/or the at least one value of the first parameter at the second grid location.

Optionally, determining the at least one value of the first parameter at a particular grid location comprises: correlating each one of a plurality of sets of at least one first value of the first parameter at the particular grid location with a respective change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit; averaging the plurality of sets of at least one first value; and determining the at least one value of the first parameter at the particular grid location based on the average of the plurality of sets of at least one first value.

Optionally, the first grid location comprises a first plurality of sublocations in the grid and/or the second grid location comprises a second plurality of sublocations in the grid, and determining the at least one value of the first parameter at a particular grid location comprises: for each of the plurality of sublocations of the particular grid location, correlating the particular change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit with at least one value of the first parameter at the sublocation, thereby to obtain a plurality of sets of at least one value of the first parameter, each set corresponding to a respective sublocation; averaging the plurality of sets of at least one value of the first parameter; and determining the at least one value of the first parameter at the particular grid location based on the average of the plurality of sets of at least one value of the first parameter.

Optionally, determining the at least one value of the voltage phase angle at a particular grid location comprises accumulating changes in measured voltage phase angle measured at the particular grid location.

Optionally, the method comprises: causing the at least one power unit to perform the particular change in consumption of electric power from or provision of electric power to the electric power grid.

Optionally, the method comprises: obtaining change data generated by at least one data generating device respectively associated with the at least one power unit, the change data being indicative of the particular change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit; and based on the obtained change data, correlating the particular change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit with the at least one value of the first parameter at the first grid location and the at least one value of the first parameter at a second grid location.

Optionally, the grid comprises a plurality of power units, each power unit being configured to consume electric power from and/or provide electric power to the electric power grid, a change in consumption of electric power from or provision of electric power to the electric power grid by each power unit causing a respective change in value of the first parameter, each power unit having a different grid location, and the method comprises: performing steps a) to c) for a particular change in consumption of electric power from or provision of electric power to the electric power grid by at least one first power unit of the plurality of power units, to determine a third value of the electric power flow characteristic corresponding to the at least one first power unit; performing steps a) to c) for a particular change in consumption of electric power from or provision of electric power to the electric power grid by at least one second power unit of the plurality of power units, to determine a fourth value of the electric power flow characteristic corresponding to the at least one second power unit; and determining a fifth value of the electric power flow characteristic, or a value of a further electric power flow characteristic of the electric power grid, based on the third value and the fourth value.

According to a second aspect of the present invention, there is provided apparatus configured to perform the method according to the first aspect.

According to a third aspect of the present invention, there is provided a system comprising the apparatus according to the second aspect and a plurality of measurement devices, each measurement device configured to measure a value of the first parameter at a respective different grid location.

According to a fourth aspect of the present invention, there is provided a computer program comprising instructions which, when executed by a computing system, cause the computing system to perform a method according to the first aspect. Further features and advantages of the invention will become apparent from the following description of preferred embodiments of the invention, given by way of example only, which is made with reference to the accompanying drawings.

Brief Description of the Drawings

Figure 1 is a flow diagram illustrating a method according to an example; Figure 2 is a schematic diagram illustrating an electric power grid according to

an example;

Figure 3A is a graph illustrating plots of power imbalance, grid frequency, and voltage phase angle, as a function of time, where the phase angle is sampled at a rate of 50 Hz, according to an example; Figure 3B is a graph illustrating a plot of two voltage waveforms having different frequencies, according to an example; Figure 3C is a graph illustrating plots of grid frequency, voltage phase angle, unwrapped voltage phase angle, and total or accumulated voltage phase angle, as a function of time, where the phase angles are sampled at a rate of 50 Hz, according to an example; Figure 4 is a schematic diagram illustrating a model of an electric power grid including a plurality of grid locations, according to an example; Figure 5A is a graph illustrating a plot of each of the following as a function of time, at a first time, according to an example: the consumption/provision of power by a power unit to/from the electric power grid, a correlated change in voltage phase angle at a first grid location, a correlated change in voltage phase angle at a second grid location, a correlated difference between the voltage phase angle at the first grid location and the second grid location, and a correlated difference between the voltage phase angle at the second grid location and the first grid location, where the phase angles are sampled at a rate of 50 Hz; Figure 5B is a graph illustrating a plot of each of the following as a function of time, at the first time, according to an example: the consumption/provision of power by a power unit to/from the electric power grid, a correlated change in voltage phase angle at a further first grid location, a correlated change in voltage phase angle at a further second grid location, a correlated difference between the voltage phase angle at the further first grid location and the further second grid location, and a correlated difference between the voltage phase angle at the further second grid location and the further first grid location, where the phase angles are sampled at a rate of 50 Hz; Figure 6 is a schematic diagram illustrating the amplitude of voltage phase angle difference between each of the grid locations of Figure 4 and each other of the grid locations of Figure 4, according to an example; Figure 7A is a schematic diagram illustrating a machine learning model according to an example; Figure 7B is a schematic diagram illustrating further steps of the method according to an example; Figure 8A is a graph illustrating a plot of each of the following as a function of time, at a second time different to the first time of Figures 5A and 5B, according to an example: the consumption/provision of power by a power unit from/to the electric power grid, a correlated change in voltage phase angle at the first grid location, a correlated change in voltage phase angle at the second grid location, a correlated difference between the voltage phase angle at the first grid location and the second grid location, and a correlated difference between the voltage phase angle at the second grid location and the first grid location, where the phase angles are sampled at a rate of 50 Hz; Figure 8B is a graph illustrating each of the following, according to an example: the consumption/provision of power by a power unit from/to the electric power grid, the correlated difference between the voltage phase angle at the first grid location and the second grid location of Figure 5A, the correlated difference between the voltage phase angle at the first grid location and the second grid location of Figure 8A, and the difference between those two correlated differences; Figure 9 is a schematic diagram illustrating the amplitude of the change of the voltage phase angle difference between the first time and the second time, for each combination of the grid locations of Figure 4 with each other of the grid locations of Figure 4, according to an example; Figure 10 is a schematic drawing illustrating a machine learning model according to another example; Figure 11 is a schematic diagram illustrating a system according to an example; and Figure 12 is a schematic diagram illustrating an apparatus according to an example.

Detailed Description

Referring to Figure 1, there is illustrated a method of determining a value of an electric power flow characteristic of an electric power grid, according to an example. As described in more detail below with reference to Figures 2 to 4, the grid 200 comprises a at least one power unit 219 configured to consume electric power from and/or provide electric power to the electric power grid 200. As described in more detail below with reference to Figures 3A-3C, 5A, 5B, and 8A, a change in consumption of electric power from or provision of electric power to the electric power grid 200 by the at least one power unit 219 causes a respective change in a value of a first parameter (e.g. voltage phase angle) of electric power flow in the electric power grid 200. In broad overview, the method comprises: a) correlating a particular change P, 502, 512, 502' in consumption of electric power from or provision of electric power to the electric power grid 200 by the at least one power unit 219 with at least one value PZ9, PZ1, PZ9', 504, 414, 504' of the first parameter at a first grid location Z9, Z1 and at least one value PZ13, PZ18, PZ13', 506, 516, 506' of the first parameter at a second grid location Z13, Z18; b) determining a difference PZ9-Z13, PZ1-Z18, 508, 518, 508' between the at least one value PZ9, PZ1, PZ9', 504, 414, 504' of the first parameter at the first grid location Z9, Z1 and the at least one value PZ13, PZ18, PZ13', 506, 516, 506' of the first parameter at the second grid location Z13, Z18; and c) determining, based on the determined difference PZ9-Z13, PZ1-Z18, 508, 518, 508', a value of the electric power flow characteristic of the electric power grid 200 (e.g. an amplitude of the difference PZ9-Z13, PZ1-Z18, 508, 518, 508' itself, or another characteristic derived from the difference).

The inventors have appreciated that by determining a difference between values of the first parameter at first and second grid locations, a value of an electric power flow characteristic can be determined that relates not only to the grid locations but to the electrical connections between grid locations in the electric power grid. For example, a value of such a characteristic may indicate an operational state of the grid, such as a current topology of the grid, or otherwise allow for such an operational state to be derived. A value of such a characteristic may therefore, for example, provide useful insight to grid operators to inform operation of the grid, such as repair or optimisation of the configuration and/or operation of the grid, as needed.

Correlating the at least one value of the first parameter at each grid location with the particular change in power consumption/provision by the at least one power unit helps ensure that the values of the first parameter used in determining the difference are those resulting from the particular power change (e.g. whose grid location, magnitude and/or waveform may be known), as opposed to other power changes that may occur in the electric power grid (e.g. whose grid location, magnitude and/or waveform may be unknown). Accordingly, a meaningful value of the electric power flow characteristic can be reliably and accurately determined.

As mentioned, the method is for determining a value of an electric power flow characteristic of an electric power grid 200. Referring now to Figure 2, there is illustrated an electric power grid 200 according to an example.

Supply of electricity from providers such as power stations, to consumers, such as domestic households and businesses, typically takes place via an electricity distribution network or electric power grid 200. In the example of Figure 2, the electric power grid (hereinafter 'grid') 200 comprises a transmission grid 202 and a distribution grid 204.

The transmission grid 202 is connected to power generators 206, which may be nuclear plants or gas-fired plants, for example, from which it transmits large quantities of electrical energy at very high voltages (typically of the order of hundreds of kV), over power lines such as overhead power lines, to the distribution grid 204. These power generators 206 may also include larger-scale wind farms and/or solar farms.

The transmission grid 202 is linked to the distribution grid 204 via a transformer 208, which converts the electric supply to a lower voltage (typically of the order of 50kV) for distribution in the distribution grid 204.

The distribution grid 204 is connected via substations 210 comprising further transformers for converting to still lower voltages to local networks which provide electric power to power consuming devices connected to the electric power grid 200.

The local networks may include networks of domestic consumers, such as a city network 212, that supplies power to domestic appliances within private residences 213 that draw a relatively small amount of power in the order of a few kW. Private residences 213 may also use electric vehicles, battery storage, heat pumps, air conditioning devices and photovoltaic devices 215 to provide relatively small amounts of power for consumption either by appliances at the residence or for provision of power to the grid. The local networks may also include industrial premises such as a factory 214, in which larger appliances operating in the industrial premises draw larger amounts of power in the order of several kW to MW. The local networks may also include networks of smaller power generators such as battery storage, solar and wind farms 216 that provide power to the electric power grid.

Although, for conciseness, only one transmission grid 202 and one distribution grid 204 are shown in Figure 2, in practice a typical transmission grid 202 supplies power to multiple distribution grids 204 and one transmission grid 202 may also be interconnected to one or more other transmission grids 202.

Electric power flows in the electric power grid 200 as alternating current (AC), which flows at a system frequency, which may be referred to as a grid frequency (typically 50 or 60 Hz, depending on country). The grid 200 may include one or more direct current (DC) interconnects 217 that provide a DC connection between the electric power grid 200 and other electric power grids. Typically, the DC interconnects 217 connect to the typically high voltage transmission grid 202 of the electrical power grid 200. The DC interconnects 217 provide a DC link between the various electric power grids, such that the electric power grid 200 defines an area which operates at a given, synchronised, grid frequency that is not affected by changes in the grid frequency of other electric power grids. For example, the UK transmission grid is connected to the Synchronous Grid of Continental Europe via DC interconnects.

The electric power grid 200 may comprise one or more measurement devices 220 for measuring a value of a first parameter of electric power flow in the electric power grid 200. For example, the measurement device 220 may comprise a phasor measurement unit (PMLT), which may be configured to measure one or more of a frequency, voltage, current, power, reactive power, and phase angle of electricity flowing in the electric power grid (such as a voltage phase angle of AC electricity flowing in the electric power grid). As another example, the measurement device 220 may comprise an extensible measurement unit (XMU), which may be configured to collect voltage data from the grid and apply signal processing to determine one or more of a frequency, voltage, and voltage angle of electricity flowing in the electric power grid. As another example, the measurement device 220 may comprise other types of measurement devices such as a Power Meter or a Digital Fault Recorder (DFR). A DFR may be configured to sample and record first parameter values including but not limited to harmonics, frequency, and voltage levels of electricity flowing in the electric power grid. For example, a DFR may sample data captured by, for example, protection relays of the grid. Other measurement devices may be used, such as measurement devices configured to measure a synchrophasor and/or a Point on Wave of electricity flowing in the electric power grid. Other measurement devices may be used.

The grid 200 comprises at least one (in this example a plurality of) power units 219. Each power unit 219 is configured to consume electric power from and/or provide electric power to the electric power grid 200. For example, each of the power generators 206, residences 213, photovoltaic devices 215, factory 214, and wind farms 216 may be an example of a power unit 219. Indeed, in examples, any device or other grid asset, or combination or subset of such grid assets, that consume electric power from and/or provide electric power to the electric power grid 200, may be a power unit 219.

In some examples, the at least one power unit 219 may comprise a dedicated power modulator, which may be controllable to consume power from and/or provide power to the grid, for example at relatively large magnitudes (such as a few or a few tens of Mega Watts), and for example with a particular waveform. For example, the power unit 219 may be controllable by a computing system 205 associated with the electric power grid 200, for example over wired and/or wireless means, to perform a particular change in consumption and/or provision of electric power to the grid 200 in this way. A particular power unit 219 may, for example, only consume power from the grid, may only provide power to the grid, or may both consume power from the grid and provide power to the grid 200. For example, a particular power unit 202 may consume power from the grid 200 during some times, and at other times may provide power to the grid 200. As mentioned above, in examples, any device or other grid asset, or combination or subset of such grid assets, that consume electric power from and/or provide electric power to the electric power grid 200, may be a power unit 219. In some examples, the at least one power unit 219 may be associated with a data generating device 218 configured to generate sets of event data. For example, each set of generated event data may indicate i) a change in consumption of electric power from or provision of electric power to the electric power grid 200 by the associated power unit 219 and ii) a time of the change. For example, each set of event data may indicate i) an amplitude of a change in consumption of electric power from or provision of electric power to the electric power grid 200 by the associated power unit 219 and ii) a time of the change. For example, the event data may include the amplitude of the change, for example in the form of an amplitude value. The time of the change may be the time at which the change occurred, for example in the form of a timestamp associated with the change. As another example, the event data may include a series of values of power consumed or provided by the associated power unit 219 as a function of time over a time period including a change in the power consumed or provided by the associated power unit. In examples, the change may be measured by the data generating device 218 and/or may be a change that the data generating device 218 has controlled the associated power unit 219 to make. In examples, each data generating device 218 may be configured to determine that a change in provision or consumption of power by the associated power unit 219 has occurred, and, responsive to the determination, generate event data indicating i) the change and ii) the time of the change. In examples, each data generating device 218 may be configured to send the sets of event data to a computing system 205. For example, the data generating devices 218 may send the event data to the computing system 205 over wired and/or wireless means.

A change in consumption of electric power from or provision of electric power to the electric power grid 200 by the at least one power unit 219 causes a change in value of a first parameter of electric power flow in the electric power grid 200. For example, the value of the first parameter may be indicative of a frequency of AC electricity in the grid 200, and/or a phase of AC electricity in the grid, for example a voltage phase angle of AC electricity flowing in the grid.

For example, regarding grid frequency, a change in consumption of electric power from or provision of electric power to the electric power grid 200 by the at least one power unit 219 causes a change in the balance between power generation and power consumption in the grid 200. The grid frequency may depend on the rate at which spinning generators (such as turbines) in the grid are rotating. When consumption increases relative to generation, the relative load on the power generators increases, which can reduce the rate at which the spinning power generators rotate, which can in turn reduce the grid frequency. Conversely, when consumption decreases relative to generation, the relative load on the power generators decreases, which can increase the rate at which the spinning power generators rotate, which can in turn increase the grid frequency. Accordingly, a change in consumption/provision by the at least one power unit 219 causes a change in a value of the grid frequency. More specifically, as is known per se, power imbalance AP can be related to the grid frequency/. through the swing equation: f (r) = fo +fofri AP (s) ds (1) w-herefo is the nominal grid frequency (which is e.g. 50 Hz for the UK national grid), FT is the grid inertia, the time dependence of the frequency is denoted by T, and the time dependence of the power imbalance is denoted by s. Accordingly, the grid frequency is proportional to the integral of the power imbalance.

As another example, regarding phase angle, the grid frequency is the first time derivative of the phase angle of the AC electricity flowing in the grid 200, for example the voltage phase angle. Accordingly, a change in grid frequency corresponds to a change in the phase angle. More specifically, as is known per se, the grid frequencylis related to the phase angle cp as follows: co,(t) = 2ff Tot f (z)di + 0 (2) where B is a constant phase angle offset, and the time dependence of the phase angle is denoted by 1. Accordingly, the phase angle is proportional to the integral of the grid frequency (which in turn is proportional to the integral of power imbalance).

Figure 3A illustrates the relationship between power imbalance, grid frequency, and phase angle, according to an example. Referring to Figure 3A, there is a plot 302 of power imbalance as a function of time t. In this example, the power imbalance plot has the form cos(t). For plot 302, positive values on the y axis correspond to, for example, the provision of power by a power unit 219 to the grid, and negative values on the y axis correspond to, for example, the consumption of power by the power unit 219 from the grid. Figure 3A also includes a plot 304 of the grid frequency as a function of time t. For plot 304, positive values on the y axis correspond to grid frequencies above the nominal grid frequency (e.g. 50Hz), and negative values on the y axis correspond to grid frequencies below the nominal grid frequency (e.g. 50Hz). That is, the plot 304 illustrates the deviation of frequency from a nominal value (e.g. 50Hz). The changes in grid frequency of plot 304 are caused by the changes in power imbalance of plot 302. Specifically, in this example, the plot 304 has the form of sin(t), which is the integral of the power imbalance waveform cos(t) (see also equation (1) above). When the power imbalance 302 is positive, the frequency 304 increases, and when the power imbalance 302 is negative, the frequency 304 decreases. Figure 3A also includes a plot 306 of the phase angle as a function of time t, sampled at a rate of 50 Hz. For plot 306, the y axis values correspond to the phase angle relative to an initial phase angle of 0. That is, the plot 306 illustrates the deviation of phase angle from an initial phase angle of 0. The changes in phase angle of plot 306 are caused by the changes in frequency of plot 304, and hence in turn by the changes in power imbalance of plot 302. Specifically, in this example, the plot 306 has the form of -cos(t), which is the integral of the frequency waveform sin(t) (see also equation (2) above). When the frequency 304 is positive, the phase angle 306 increases, and when the frequency 304 is negative, the phase angle 306 decreases.

Figure 3B illustrates how a change in frequency may relate to a change in phase angle, according to an example. Referring to Figure 3B, there are illustrated two AC voltage waveforms 308, 310, with different frequencies. In Figure 3B, the y axis represents voltage IT, and the x axis represents time. The frequency of a first, nominal, waveform 308 is the nominal grid frequency.fo (such as 50 Hz in the UK). The frequency of the second waveform 310 is higher than the frequency of the first waveform 308. At a first time /0, the phase angle of the first waveform 302 and the second waveform 304 are the same, in particular, zero. A second time ti is separated from the first time to by the period of the first waveform, i.e. by 1/lo, (which in the UK would be 20 ms). At the second time t1, the phase angle of the first waveform 308 is still 0, but the phase angle of the second waveform 310 is 22.5 degrees. A third time 12 is separated from the second time tr by the period of the first waveform, i.e. by 1/fo, (which in the UK would be 20 ms). At the third time t2, the phase angle of the first waveform 308 is still 0, but the phase angle of the second waveform 310 is 45 degrees. The phase angle at time 12 is larger than the phase angle at tr, due to addition of the phase shift between times to and ti (22.5 degrees), with the phase shift between 1; and /2(22.5 degrees). When the grid frequency is above the nominal frequency, the phase will increase, and when the grid frequency is below the nominal frequency, the phase will decrease. In this example, the phase angle is sampled at a rate of f° (e.g. 50 Hz for the UK), that is, the phase angle is sampled with a sampling interval of 1/fo (e.g. 20 ms for the UK). By determining the phase angle every 1/lo (such as every 20 ms for the UK), or every fraction of 1/fo, or every integer multiple of 1/fo, for example, the phase angle (e.g. voltage phase angle) of AC electricity flowing in the grid 200 at a particular grid location as a function of time can be determined.

In some instances, there may be a discontinuity in the phase angle as a function of time, caused by the phase angle passing through +/-180 degrees i.e. +/-it radians, for example. Accordingly, in examples, a phase unwrapping operation may be applied to the determined phase angle, thereby to produce an unwrapped phase angle, which will not have such discontinuities. As one example, a phase unwrapping operation may be performed to determine the unwrapped phase angle, as follows: The change c4 = (pt. p<< 1between the phase yoti at a particular sample time ti and the phase coti_i at a previous sample time /24 (e.g. a time 20ms immediately previous to the particular sample time) may be determined. If the change co c, is between -180 and +180 degrees (i.e. -it and +7c radians) then the unwrapped phase at the particular sample time t, may be taken as the phase coti at the particular sample time th If the change yo; is higher than +180 degrees (+7c radians), then the unwrapped phase may be taken as cpti -360 degrees (i.e. cot. -27c radians). If the change (pit'i is lower than -degrees err radians), then the unwrapped phase may be taken as yoti + 360 degrees (i.e. cpti + 27c radians). It will be appreciated that, in the above, it is assumed that the phase angle does not pass through +180 degrees (or -180 degrees) more than once per sampling interval. The sampling rate of the phase angle may be set such that the phase angle does not pass through +180 degrees (or -180 degrees) more than once per sampling interval. It will also be appreciated that phase unwrapping need not necessarily be used. For example, where there is no discontinuity, for example because there are only small changes in phase angle, phase unwrapping need not be applied and/or may not be used.

As alternative to determining the phase angle (unwrapped or otherwise) in the way described above, the total or absolute phase angle (that is, the total phase accumulated from an arbitrary starting time) may be used, and may be determined at any time. For example, in Figure 3B, where the total phase of the waveform 308 at time to is 0, the total phase of the waveform 308 at time t, would be 360 degrees, and the total phase of the waveform 308 at time 12 would be 720 degrees. For example, in Figure 3B, where the total phase of the waveform 310 at time to is 0, the total phase of the waveform 310 at time tr would be 382.5 degrees, and the total phase of the waveform 304 at time 12 would be 765 degrees.

Figures 3C illustrates plots of frequency 320, phase angle 322, unwrapped phase angle 324, and total phase angle 326 as a function of time (provided in the form of a timestamp), according to an example. In this example, the phase angles are sampled at a rate of 50 Hz. In this example, a step change in power balance (not shown) occurs just after the time 12:30:12. Specifically, this is a step reduction in power provided to the grid by a power unit 219, such as might occur when a power generator suffers a fault and stops generating power. This causes the frequency 320 to reduce below 50 Hz. This in turn causes the phase angle 322 and the unwrapped phase angle 324 to reduce. Regarding the phase angle 322, when the phase angle 322 reaches -7E radians, there is a discontinuity, and the phase angle goes to +ir radians.

This happens twice in the phase angle 322 of Figure 3C. However, in the unwrapped phase angle 324, the discontinuities have been removed and the unwrapped phase angle reduces in a continuous manner. The total phase angle 326 increases throughout (which will be the case whether or not the frequency is above or below the nominal frequency). Although not visible in the plot 326, the rate of change of the total phase angle (and hence the value of the total phase angle at any given time) is dependent on the frequency, and hence the change in frequency (caused by the power balance change) will cause a respective change in the total phase angle at any given time.

As is evident from the above, a change in power consumption/provision by the at least one power unit 219 causes a change in value of the phase angle (e.g. voltage phase angle) at a given location in the grid 200. In particular, a change in power consumption/provision by the at least one power unit 219 causes a corresponding change in the grid frequency, which causes a corresponding change in the phase angle (be that unwrapped phase angle, total phase angle, or otherwise). Other examples of how the voltage phase angle at a particular grid location may change as a result of a change in power consumption/provision by the at least one power unit 219 are described in more detail below with reference to Figures SA, 5B, 8A, and 8B.

It will be appreciated that the phase angle (e.g. voltage phase angle) need not necessarily be determined at 20 ms (or multiple or fraction thereof) intervals and can be determined at any particular point in time, for example relative to the most recent zero-crossing of the voltage having a positive slope (provided that, where needed, discontinuities between successive values are removed by applying a suitable unwrapping operation). Further, it will be appreciated that, rather that expressing phase angle relative to the most recent cycle start point (i.e. the most recent zero-crossing of the voltage having a positive slope), equally phase angle may be expressed as the total or absolute phase angle (that is, the total accumulated phase angle from an arbitrary start point, such as to in Figure 3A, at a particular time).

The grid 200 may be associated with a computing system 205. The computing system 205 may be configured to perform the method of any of the examples described herein with reference to Figure L In some examples, the measurement devices 220 may send one or more measured values of the first parameter to the computing system 205, for example over a computer network such as the Internet. In some examples, the at least one power unit 219 may be in communication with the computing system 205. For example, the computing system 205 may control the power unit 219 to perform a particular power change, or the power unit 219 may perform a particular power change and send information about the particular power change (such as time, magnitude, and/or waveform) to the computing system 205.

Referring now to Figure 4, there is illustrated a model 400 of an electric power grid. For example, the model 400 may be of the grid 200 (or of a grid of the type) according to any of the examples described above with reference to Figure 2. Behaviour in the model 400 is, accordingly, a model of the behaviour that would be experienced in a corresponding electric power grid, for example the grid 200 (or a grid of the type) according to any of the examples described above with reference to Figure 2. In this example, the model 400 represents the UK electric power grid. The model 400 is used herein to demonstrate and illustrate various features of examples of the present invention.

As represented in Figure 4, the model 400 of the grid comprises a plurality of nodes or zones Z1 to Z33, as well as connections between the zones. Each zone Z1 to Z33 represents an aggregation of one or more generators (not shown) that provide power to the grid 200 and/or one or more consumers (not shown) that consume power from the grid 200 in a particular location or area of the grid corresponding to the zone.

Each zone Zl to Z33 is therefore associated with a respective different grid location in the grid. Each zone is connected to one or more others of the zones Z1 to Z33. The connections between the zones represent electrical connections, such as transmission lines, between the zones Z1 to Z33. The generators and/or consumers may be according to any of the examples described above with reference to Figure 2.

As an example, the model 400 may represent a transmission grid, with each zone Z1 to Z33 representing aggregated generators and consumers in an area corresponding to the respective zone Z1 to Z33, and each connection between the zones Zl to Z31 representing a respective transmission line between the areas. Each area represented by respective zones Z1 to Z33 may comprise one or more distribution grids and one or more local networks for distributing electrical energy at relatively lower voltage, for example as described above. In examples, each zone Z1 to Z31 may be modelled as a high-voltage busbar with the aggregated generators and consumers in the area corresponding to the respective zone Z1 to Z33, and electrically connected to other zones as shown. In examples, the model 400 may represent other types of electric power grid.

As shown, the modelled grid comprises at least one power unit 219 (only one is shown in Figure 2) configured to consume electric power from and/or provide electric power to the grid. The at least one power unit 219 may be according to any of the examples described above with reference to Figure 2. In the example of Figure 4, one power unit 219 is shown, and the power unit 219 is part of (that is, located in) zone Z24.

As shown, the modelled grid includes at least one measurement device 220 for measuring a value of the first parameter of electric power flow in the electric power grid 200. Although only one measurement device 220 is shown in Figure 4, there may be a measurement device at each of a plurality of grid locations in the grid. For example, there may be a measurement device at each of the zones Zl to Z33 (or some subset of the plurality of zones Z1 to Z33). In examples, the measurement device 220 may be according to any of the examples described above with reference to Figure 2. The model also includes a computing system 205 associated with the grid, which may be according to any of the examples described above with reference to Figure 2.

Returning now to the method of Figure 1, as mentioned, the method comprises, in step 102, correlating a particular change in consumption of electric power from or provision of electric power to the electric power grid 200 by the at least one power unit 219 (e.g. located at Z24 in Figure 4) with at least one value of the first parameter at a first grid location (e.g. Z9) and at least one value of the first parameter at a second grid location (e.g. Z13).

In some examples, the method may comprise determining the at least one value of the first parameter at the first grid location and the at least one value of the first parameter at the second grid location. For example, these may be obtained by the computing system 205 from a database of stored values of the first parameter at different locations. In some examples, determining these values may comprise measuring the at least one value of the first parameter at the first grid location and measuring the at least one value of the first parameter at the second grid location. For example, this may be performed by a respective measuring device 220 located at each respective grid location. As described above, each measuring device 220 may transmit their respective measured data to the computing system 205. In examples, each value may be provided or otherwise associated with a time at which the value was measured.

As mentioned above with reference to Figure 3C, in some cases the voltage phase angle at a particular grid location may pass through +/-180 degrees. In this case, in order to keep track of the change in voltage phase angle as a function of time, the changes in voltage phase angle may be accumulated, such as by applying a phase unwrapping operation to the measured voltage phase angle data. Accordingly, in examples where the first parameter is the voltage phase angle, determining the at least one value of the first parameter at a particular grid location may comprise accumulating changes in measured voltage phase angle measured at the particular grid location. Alternatively, as mentioned, the absolute or total voltage phase angle may be used.

In examples, correlating the particular change in power consumption/provision of the power unit 219 (e.g. located at Z24) with the at least one value of the first parameter at a given grid location Z9, Z13 may comprise determining one or more values of the first parameter at the given grid location Z9, Z13 that occur at the same time as the particular power change.

For example, the computer system 205 may be in communication with the at least one power unit 219. The method may comprise causing the at least one power unit 219 to perform the particular power change. For example, the computer system 205 may control or otherwise cause the at least one power unit 219 to perform the particular change, for example at a certain time. The computer system 205 may then identify one or more values of the first parameter at the given grid location Z9, Z13 occurring at (e.g. measured at) the certain time, thereby to correlate the one or more values of the first parameter at the given grid location with the particular change As another example, the power unit 219 may send information on the particular change in power that it has performed (e.g. including a time of the particular change) to the computing system 205. The computing system 205 may then identify one or more values of the first parameter occurring at (e.g. measured at) the time of the change, thereby to correlate the one or more values of the first parameter with the particular change. In some examples, the computing system 205 may obtain change data generated by at least one data generating device 218 respectively associated with the at least one power unit 219, for example as described above. The change data may be indicative of the particular change, and the values of the first parameter at a given location Z9, Z13 may be correlated with the particular change based on the obtained change data. In some examples, the computing system 205 may obtain the change data directly from the data generating device 218. In other examples, the computing system 205 may obtain the change data from a database storing the change data. In these examples, the method may comprise obtaining change data generated by at least one data generating device 218 respectively associated with the at least one power unit 219, the change data being indicative of the particular change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit 219; and based on the obtained change data, correlating the particular change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit 219 with the at least one value of the first parameter at the first grid location Z9 and the at least one value of the first parameter at a second grid location Z13. This may, for example, allow for the particular power change to be provided by power changes that may have anyway been occurring the in electric power grid. This may, in turn, reduce the need for a dedicated power modulator, or the need to control a power unit 219 to perform the power change.

In some examples, correlating the particular change in power consumption/provision by the power unit 219 with the at least one value of the first parameter at a given grid location Z9, Z13 may comprise matching a waveform of the particular change to a waveform of a plurality of values of the first parameter. For example, the particular power change may have a waveform of a particular shape, and the correlation may comprise identifying a resultant waveform in the plurality of values of the first parameter. For example, as mentioned above, the phase angle is the time integral of the time integral of the power imbalance. Accordingly, the correlation may comprise identifying a waveform in the one or more values of the first parameter having a shape corresponding to the time integral of the time integral of the power change waveform. For example, as described above with reference to Figure 3A, where the power imbalance waveform is cos(t), the phase angle waveform may be cos(t). As another example, the power change may have a the waveform sin(t), and hence the resultant phase angle may have a waveform of -sin(t). I this case, the correlation may comprise identifying the resultant -sin(t) waveform in the plurality of values of the first parameter. In some examples, the correlation may comprise fitting the waveform of the particular shape (e.g. e.g. -sin(t)) to the plurality of values of the first parameter. In some examples, the at least one value of the first parameter may be a single value of the first parameter. For example, a peak (or trough) of the particular power change may be correlated with a minimum (or maximum) of the plurality of values of the first parameter. For example, in the example of the values of the first parameter having a waveform of -sin(t), a sine function (such as asin(REIS)1 where Q, R, S and 11 are fitting parameters) may be fitted to a plurality of values of the first parameter, and the at least one value of the first parameter may be taken as the amplitude (e.g. parameter Q) of the fitted sine function. Other examples are possible.

In some examples, the at least one value of the first parameter at a particular grid location may be relative to a reference location in the grid 200. For example, the at least one value of the first parameter at the first grid location and the at least one value of the first parameter at the second grid location may both be relative to the same particular reference location in the grid 200. For example, the at least one value of the first parameter at the first grid location may be provided by the voltage phase angle at the first grid location less the voltage phase angle at the reference location, and the at least one value of the first parameter at the second grid location may be provided by the voltage phase angle at the second grid location less the voltage phase angle at the reference location. For example, the reference location may be zone Z1, or for example a power plant connected to zone Z1, or any location in the grid. Any reference location in the grid can be used.

In some examples, the at least one value of the first parameter at a particular grid location correlated with the particular power change may be determined by averaging over a plurality of sets of at least one first value of the first parameter at the particular grid location. For example, this averaging may be performed over multiple repetitions or cycles of the particular power change by the power unit 219. For example, where the waveform of the power change is a sine wave, each of a plurality of cycles of the waveform may be correlated with a respective set of at least one first value of the first parameter at the particular grid location. The method may then comprise averaging the plurality of sets of at least one first value and determining the value of the at least one first parameter at the particular grid location based on the average of the plurality of sets of at least one first value. For example, the at least one value of the first parameter may correspond to the values of the first parameter as a function of time averaged over multiple cycles. As another example, the at least one value of the first parameter may correspond to an average amplitude of the waveform of the values of the first parameter over multiple cycles. Other examples are possible.

In any case, performing averaging may allow for the values of the first parameter (and hence the value of the electric power flow characteristic) to be reliably determined, even when relatively small power changes are being used. Other examples are possible.

As mentioned above with reference to Figure C, in some cases the voltage phase angle at a particular grid location may pass through +/-180 degrees. In this case, in order to keep track of the change in voltage phase angle as a function of time, the changes in voltage phase angle may be accumulated, such as by applying a phase unwrapping operation to the measured voltage phase angle data, or by using absolute or total phase angle. Accordingly, in some examples, determining the at least one value of the first parameter, and in particular the voltage phase angle, at a particular grid location may comprise accumulating changes in measured voltage phase angle measured at the particular grid location.

Figure 5A illustrates a particular change in power P provided to and consumed from the modelled grid by the power unit 219, located at zone Z24, as a function of time, according to an example. In this example, the power provided/consumed by the power unit 219 has a sine waveform, with a peak-to-peak amplitude of 10 MW, and a frequency of 0.2 Hz. In the graph of Figure SA, the left-hand y-axis corresponds to power.

Figure SA also illustrates a plot of values of voltage phase angle as a function of time at two grid locations Z9, Z13 of the modelled grid of Figure 4, according to an example. In this example, the phase angles are sampled at a rate of 50 Hz. In this example, in each case, unwrapped voltage phase angles are used. In this example, in each case, the voltage phase angles are relative to the voltage phase angle at a reference location, in this example, a power plant (not shown) connected to zone Z1. Specifically, the plot labelled PZ9 is a plot of values of voltage phase angle at the first grid location Z9 relative to the values of voltage phase angle at the reference grid location, as a function of time, and the plot labelled PZ 13 is a plot of values of voltage phase angle at the second grid location Z13 relative to the values of voltage phase angle at the reference grid location, as a function of time. Further, for each plot PZ9, PZ13, the voltage phase angle values have the respective average voltage phase angle value of the plot, PZ9, PZ13 removed.

As can be seen in Figure 5A, in this example, the particular change in power P causes respective changes in the values of the voltage phase angles at the first and second grid locations Z9, Z13 relative to the reference location. That is, in this example, when the power provision increases, the voltage phase angle at both grid locations Z9, Z13 relative to the reference location increases, and vice versa. Indeed, the waveform of the voltage phase angle at both locations relative to the reference location matches the waveform of the particular power change. Accordingly, for example, the particular power change P may be correlated with the values of the voltage phase angle at the first grid location Z9 and the second location Z13 relative to the reference location. As another example, a peak 502 in the particular change in power P may be correlated with a peak value 506 of the voltage phase angle at the first grid location Z9 relative to the reference location and a peak value 504 of the voltage phase angle at the second grid location Z13 relative to the reference location. It is noted here that the amplitude of the sine waveforms of the two plots PZ9 and PZ13 are different. Specifically, the amplitude (e.g. peak value 504) of the plot PZ13 is larger than the amplitude (e.g. peak value 506) of the plot PZ9. As explained in more detail below, this is due to differences in the impedance between the power unit 219 located at zone Z24 and each of the first and second grid locations Z9, Z13, and/or the grid inertia in each of the first and second grid locations Z9, Z13.

Figure 5A shows the voltage phase angle in plots Z9, Z13 relative to the reference location for illustrative purposes and to allow easier visual appreciation of the correspondence between power change and voltage phase angle. However, it will be appreciated that, as above for e.g. Figures 3A to 3C, the voltage phase angle at a particular grid location itself; rather than voltage phase angle relative to a reference location, may be the first parameter determined at a particular time and/or as a function of time. For example, any of the phase angle, the unwrapped phase angle, or the absolute or total phase angle described above, as well as other first parameters, may be used.

As mentioned, the method comprises, in step 104, determining a difference between the at least one value of the first parameter at the first grid location Z9 and the at least one value of the first parameter at the second grid location Z13.

In some examples, determining the difference may comprise subtracting one or more values of the first parameter at the first grid location Z9 from a respective one or more values of the first parameter at the second grid location Z13 (or vice versa). For example, there may be a time series of values of each of the voltage phase angle at the first grid location Z9 and the voltage phase angle at the second grid location Z13. Determining the difference may comprise subtracting the former from the latter (or vice versa). This may result in a new time series of values representing the difference between the values of the first parameter at the first grid location Z9 and the values of the first parameter at the second grid location Z13. It is noted that this difference will be the same whether or not the voltage phase angles values are relative to those of a reference grid location. This is because the reference grid location voltage phase angle values are cancelled out when the difference between the values at the first grid location and the values at the second grid location is calculated. Figure 5A illustrates a plot labelled 'PZ9-Z13' that is the result of subtracting the plot labelled PZ13 from the plot labelled PZ9. Figure 5A also illustrates a plot labelled TZ13-Z9' that is the result of subtracting the plot labelled PZ9 from the plot labelled PZ13. Both of these difference plots 'PZ9-Z13' and 'PZ13-Z9' have a sine waveform. In some examples, determining the difference may comprise determining an amplitude (e.g. peak value 508) of the difference between the values of the first parameter at the first grid location Z9 and the values of the first parameter at the second grid location Z13. For example, determining the difference may comprise fitting a waveform (such as a sine waveform) to the plot labelled 'PZ9-Z13' or the plot labelled tZ13-Z9', and determining an amplitude (e.g. peak value 508) of the plot based on the fitting. In this case, the difference between the at least one value of the first parameter at the first grid location Z9 and the at least one value of the first parameter at the second grid location Z13 may be the amplitude (e.g. peak value 508) of the plot PZ9-Z13. As explained in more detail below, this difference is due to (and hence indicative of) differences in the impedance (that is, the grid impedance) between the power unit 219 located at zone Z24 and each of the first and second grid locations Z9, Z13, and/or the grid inertia in each of the first and second grid locations Z9, Z13.

It is noted that, as mentioned above, although in the example of Figure 5A (and also Figures 5B, 8A and 8B) the difference plots (e.g. PZ9-Z13 and PZ13-Z9 as per Figure 5A) are determined from a difference in voltage phase angles at the first grid location and the second grid location, the same difference plots (e.g. PZ9-Z13 and PZ13-Z9 as per Figure 5A) would be obtained from the difference in absolute or total voltage phase angle at the first grid location and the second grid location. In other words, the subtraction of the absolute or total voltage phase angles at one grid location from the absolute or total voltage phase angles at another grid location will result in the difference plots PZ9-Z13 and PZ13-Z9. This is because the accumulation of the voltage phase angle over successive measurement periods is present in the voltage phase angle at both grid locations, and hence is removed when the subtraction is performed. Accordingly, in examples, determining the difference between the at least one value of the first parameter at the first grid location Z9 and the at least one value of the first parameter at the second grid location Z13 may comprise determining the difference between at least one value of the absolute or total voltage phase angle at the first grid location and at least one value of the absolute or total voltage phase angle at the second grid location.

As mentioned, the method comprises, in step 106, determining, based on the determined difference, a value of the electric power flow characteristic of the electric power grid.

In some examples, the value of the electric power flow characteristic may be the difference determined in step 104. For example, in the example of Figure 5A, the value of the electric power flow characteristic may be the amplitude (e.g. peak value 508) of the plot PZ9-Z13. As described in more detail below, in some examples, other electric power flow characteristics may be derived based on this difference, but nonetheless the difference determined in step 104 may itself provide a useful electric power flow characteristic. For example, as described in more detail below, the value of such a characteristic may be indicative of a difference between a first impedance between the at least one power unit 219 and the first grid location Z9 and a second impedance between the at least one power unit 219 and the second grid location Z13. A value of such a characteristic may therefore be indicative of a topology of the grid, which may be useful information for grid operators in monitoring the operation state of the grid.

In order to illustrate the utility of the difference determined in step 104 in examples where the first parameter is voltage phase angle, a mathematical model of voltage in the grid 200 is developed. The waveform of AC voltage V at grid location locations i and j in the grid as a function of time t may be given by: I/Kt) = Ahsin(cph(t)) Vi(t) = Ai sin (cp (t)) where A, is the amplitude of the waveform at grid location i and (pi(t) is the voltage phase angle at time t at the grid location t; and Ai is the amplitude of the waveform at grid location j and yoiN is the voltage phase angle at time t at the grid location j. Here, the grid location i may be, for example, any one of Zones Z1 to Z33 of the model 400 of Figure 4, and the grid location] may be any other one of the zones Z1 to Z33 of the model of Figure 4. As a specific example, r may correspond to zone Z9, and j may correspond to zone Z13, as per the example illustrated in Figure 5A. As is known, phase is the time integral of frequency. Accordingly, the voltage phase angle yo (t) and (pj 10 may be written as: (so i(t) = 27t Tot fi(u)dt + Oh (5) c fa) = 2g fot ff(r)d-c + Of (6) where/ is the local grid frequency at grid location i and! is the local grid frequency at grid location I each of which frequencies are dependent on time (the time dependence of the frequencies being denoted by t), O is a constant phase angle offset at grid location i and Of is a constant phase angle offset at grid location j. Accordingly, the phase angle difference cpi (t) between the voltage phase angle qii(t) at grid location I and the voltage phase angle p1(t) at grid location/ can be written as: vii(t) = (Mt) -(pi(t) = + 2 for(fi(r) h CO) dr (7) where Ou = Oi - Based on the swing equation, which as is known per se relates power imbalance, grid frequency, and grid inertia, the frequency f at grid location i and the frequency! at grid location/ can be written as: =fo+fa 211,AP i(s) ds (8) ti(r) = fo + fo K) AP (s) ds 2H I 1 (9) whereto is the nominal grid frequency (which is e.g. 50 Hz for the UK national grid), H, is the local inertia at grid location i, H, is the local inertia at grid location! OP; (s) is the local power imbalance at grid location i, and APJ(s) is the local power imbalance at grid location j, each of which power imbalances are dependent on time (the time dependence of the power imbalances being denoted by s). It is noted here that, in general, grid inertia is a measure of the amount of kinetic energy stored in the electric power grid and influences the rate at which the frequency of the grid changes in response to a change in balance of power provision and consumption in the grid.

The grid inertia depends on the number and type of both generators and loads connected to the grid. For example, spinning generation such as in nuclear or fossil fuel power stations generally contribute to the grid inertia whereas renewable energy production methods like wind and solar generally do not. Additionally, large rotating power consumption machines such as used in factories generally contribute to inertia whereas typical domestic consumption, such as loading laptop batteries, generally does not. Due to the different mix of generators and loads in different areas of the electrical power grid, different areas of the electrical power grid can have different inertia values. The rate of change of grid frequency for a given change in power balance in a grid area with high inertia is less than it is in a grid area with low inertia.

In any case, substituting equations 8 and 9 into equation 7 results in the following: o (t) = 61,j + rrfo fo 0 H fa I l Pi(s) -a13-(s) ds) di (10) i Further, in the case of a power unit 219 located at a particular grid location in performing a particular change in consumption of power from and/or provision of power to the grid, the local power imbalance aPi(s) at grid location i and the local power imbalance APi(s) at grid location j can be written as: APi(s) = AQi(s) + Mi(s, Znii) ( II) APJ(s) = AQ (s) + (s, Z,,,j) (12) where AQi(s) is the ambient local power imbalance at grid location i, AQi(s) is the ambient local power imbalance at grid location j (that is, in each case, the local power imbalance that may exist in the local area not including the power imbalance in the local area resulting from the particular change in power by the power unit 219). Mi(s,Z",i) is the local power imbalance at grid location i resulting from the particular change in power by the power unit 219 (in other words, the change in power by the power unit 219 as experienced at the grid location i), which is a function of the impedance Zmi between the grid location in of the power unit 219 and the grid location i. Similarly, Mi(s,Z,"") is the local power imbalance at grid location j resulting from the particular change in power by the power unit 219 (in other words, the change in power by the power unit 219 as experienced at the grid location j), which is a function of the impedance 4,1 between the grid location in of the power unit 219 and the grid location j. Inserting equations (11) and (12) into equation (10) results in the following: (pip) = Bii + Tri t T 1 1 o L I -aQi(s)--Agi(s) 0 0 Hi Hi 1 1 +-HiMi(s, -H Mf(s, Zrui)dsdi (13) The local ambient power imbalance AQi(s), aQi(s) can be dealt with in a number of ways. For example, it some situations it may be assumed that the local ambient power imbalance may be small or negligible, in which case the associated terms in equation (13) can be ignored and treated as zero. As another example, the local ambient power imbalance at each grid location may be considered a random variable. In this case, averaging equation (13) over multiple cycles of a particular power change (or averaging over multiple instances of a given particular power change), for example as described above, will cause the terms associated with the local ambient power imbalance in equation (13) to tend to zero, in which case the associated terms in equation (13) can be ignored and treated as zero. In either case, (or in other examples where the local ambient power imbalance can be treated as zero), equation 13 may be rewritten as: (14) c0 (t) = 9 * ± TC 1 1 s, Z,ni)dscit io f Zmi) TT/ M j Further, Mi (s, Z,"1) and Mf (s,Z,,,i) may be re-written as: Mi(S, Zmi) = Bi(Zmi)p(s) (15) Mi(s, Z mi) = 13j(Z",j)p(s) (16) where p(s) is the waveform of the particular change in power by the power unit 219 located at the grid location m, Bi(Z,,i) is the amplitude of the particular change in power by the power unit 219 as experienced at the grid location i (which is a function of the impedance Zmi between the grid location m of the power unit 219 and the grid location i), and BAZ,"j) is the amplitude of the particular change in power by the power unit 219 as experienced at the grid location j (which is a function of the impedance Z,,,j between the grid location 111 of the power unit 219 and the grid location j). Substituting equations (15) and (16) into equation (14) results in the following: j(t) = Oti + fon-(B (Z,",) -H. -1 co BJ (Z"I)) p(s)dscli 0 0 (17).

The constant phase angle difference Bif can be taken to be constant during the particular power change of waveform p(s). This term can be dealt with in a number of different ways. For example, the value of Bij may be determined as the value of Ty(t) at a time when p(s) is zero. As another example, where p(s) is symmetrical with respect to power provision and consumption (e.g. as per the example sine power waveform P in Figure 5A), the value of Bij can be determined as the mean value of (pi j(t) over a period of the power waveform p(s). In such cases, the constant phase angle difference Oij can be subtracted from ririd(t) thereby to remove from equation (17). Other examples are possible, such as determining coo(() based on an amplitude of the phase difference waveform (e.g. plot PZ9-Z13) as opposed to the absolute value of (pip), in which case the constant phase angle difference Oji will automatically be removed from equation (17). In any case, after removing the constant phase angle difference 8, , equation 17 becomes the following: Tii(t) = 1 1 I, .1 r fr (-HiBi(Znii) H. p(s)dscit 0 0 (18).

The waveform p(s) is known. For example, this may be the particular power change that the power unit 219 may have been controlled to make by the computing system 205, or which the power unit 219 (or a data generating device 218 associated therewith) may have communicated to the computing system 205. It is noted that this waveform need not necessarily be a sine wave, and could for example be a step function, for example corresponding to a power unit 219 turning on at a certain time, or any waveform. Moreover, the nominal grid frequencyfo is known. Accordingly, the j value of the term (1 -B,(Z",r) -H. -B-(Zinj -) can be determined directly from a f it I determination of the phase angle difference (so id(t) (derived from the voltage phase angle at each grid location i, j). As an example, where the waveform of the particular power change (and hence the resulting waveform of yoid(t)) is sinusoidal, a determination of the amplitude of (pip) may provide for a direct determination of the value of this term. As another example, where the waveform of the particular power change (and hence the resulting waveform of yoid(t)) is a step function, a determination of the magnitude of the step increase in coy(t) may provide for a direct determination of the value of this tent This term is itself an electric power flow characteristic of the grid, and as above a value of this electric power flow characteristic can be determined.

As above, B, is a function of the impedance Zmi between the power unit 219 and the first grid location i and B1 is a function of the impedance Zmi between the power unit 219 and the second grid location j. Accordingly, in examples where value of the electric power flow characteristic is the value of the abovementioned term in equation 18, the value of the electric power flow characteristic is indicative of a difference between a first impedance Zmi between the at least one power unit 219 and the first grid location i and a second impedance Z"ii between the at least one power unit 219 and the second grid location/ In some examples, determining the value of the electric power flow characteristic may be based on one or both of a value of grid inertia Hi at the first grid location i and a value of grid inertia Ili at the second grid location]. For example, the inertia Hi in the first grid location and the inertia 111 in the second grid location] may be known (and/or may be assumed to be the same at both grid locations, and/or may be assumed to be some constant value). In this case the value of the quantity (Bi(Z,,j) -BAZ,,J)) may be calculated directly. If it is assumed that B, and B, only depend on the respective impedances (or it is assumed that other contributions are negligible), then this quantity (Bi(Zmi) -Bi(Z,,j)) (which is another example of an electric power flow characteristic) may directly represent the difference between the first impedance Zmi between the at least one power unit 219 and the first grid location i and the second impedance Znij between the at least one power unit 219 and the second grid location]. In either case, this term or quantity can be interpreted as an 'electrical distance' between the first grid location i and the second grid location j relative to the location of the at least one power unit. As an example, referring to Figure 4, it can be seen that grid locations (zones) Z9 and Z13 are relatively electrically close to one another, indeed they are directly connected to one another by an electrical connection. In this case, it would be expected that the difference in impedance between the power unit 219 (at zone Z24) and the respective grid locations Z9 and Z13 would be relatively small. And indeed, as can be seen from the plot PZ9-PZ13 in Figure 5A, the amplitude of the phase angle difference plot PZ9-PZ13 is relatively small. On the other hand, referring again to Figure 4, it can be seen that grid locations (zones) Z1 and Z18 are relatively electrically distant from one another. Specifically, Z18 is only two electrical connections away from Z24 (where the power unit 219 is located), whereas Z1 is at least 5 electrical connections away from Z24. In this case, it would be expected that the difference in impedance between the power unit 219 (at zone Z24) and the respective grid locations Z1 and Z18 would be relatively large. This is shown in Figure 5B. Referring to Figure 5B, there are shown plots that are similar to those shown in Figure 5A, except the voltage phase angle plots PZ1 and PZ18 are for voltage phase angle at grid locations (zones) Z1 and Z18 relative to the reference location, respectively, and the voltage phase angle difference plots PZ1-Z18 and PZ18-Z1 represent the difference between the voltage phase angle plots PZ1 and PZ18, and PZ18 and PZ1, respectively. Here again, the voltage phase angles are sampled at a rate of 50 Hz. The particular power change P, having a peak value 512, is the same as that in Figure SA. In the example of Figure 5B, the amplitude 514 of the phase angle difference plot PZ18 is relatively large, and the amplitude 516 of the phase angle difference plot PZI is relatively small. Accordingly, the amplitude 518 of the phase angle difference plots PZ1-Z18 and PZ18-Z1 is relatively large. This reflects that the difference in impedance between the power unit 219 (at zone Z24) and the respective grid locations Zl and Z18 is relatively large, as above.

As can be seen from these examples, the value of the above-mentioned electric power flow characteristic (e.g. the term or quantity mentioned above) can be indicative of the topology of the grid 200, 400. For example, as above, a relatively large value of the abovementioned term or quantity is indicative that the first and second grid locations have a relatively large difference in impedance relative to the location of the at least one power unit 219 (and hence may be relatively electrically distant from one another, that is, the difference in the number of electrical connections by which each is separated from the at least one power unit may be relatively large), whereas a relatively small value of the abovementioned term or quantity is indicative that the first and second grid locations have a relatively small difference in impedance relative to the location of the at least one power unit 219 (and hence may be relatively electrically close to one another, that is, the difference in the number of electrical connections by which each is separated from the at least one power unit may be relatively small). As such, this term or quantity can be indicative of a current topology or operational state of the grid 200, 400. For example, it may be known that in a particular operational state, e.g. when grid is operating with a particular topology, the value of the electric power flow characteristic will be at a particular value. If the determined value of the electric power flow characteristic is the particular value, then it may be determined that the grid is in the particular operational state. However, if the determined value of the electric power flow characteristic is different from, for example deviates above a threshold amount from, the particular value, then it may be determined that the grid is not in the particular operational state. For example, from this is may be determined that the grid is in an 'abnormal' operational state, which may prompt a grid operator to investigate the cause.

As other examples, as can be seen from equation (18) and the above discussion, the value of the electric power flow characteristics may be indicative of at least one of: grid inertia Hi at the first grid location /; grid inertia Hi at the second grid location]; a proportion B1 of the particular change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit 219 experienced at the first grid location.1, and a proportion B7 of the particular change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit 219 experienced at the second grid location j. For example, as can be seen from equation (18), if any three of these parameters are known, then the fourth may be determined directly from the amplitude of yo ip). As another example, any one of these parameters can be determined by using simultaneous equations based on the amplitude of (pi j(t) determined for different combinations of i and j and/or different locations in of the at least on power unit 219. Other examples are possible.

In examples, there may be a plurality of second grid locations 1, and the method may comprise performing steps 102 to 106 of Figure 1 for each one of the plurality of second grid locations/ For example, a particular power change by the at least one power unit 219 may be correlated with each of at least one value of the first parameter (e.g. voltage phase angle) at a first grid location i, at least one value of the first parameter at one second grid location ji and at least one value of the first parameter at another second grid location 12, for example in the manner described above. The method may then comprise determining a first difference between the at least one value of the first parameter at the first grid location i, and the at least one value of the first parameter at one second grid location ft and a second difference between the at least one value of the first parameter at the first grid location i and at least one value of the first parameter at the another second grid location j2. The method may then comprise determining a value of a first electric power flow characteristic based on the first difference, and a value of a second electric power flow characteristic based on the second difference. For example, the value of the first electric power flow characteristic may be the voltage phase angle difference, or a term or quantity from equation (18) as described above, relating to the first grid location and the one second grid location, and the second electric power flow characteristic may be the voltage phase angle difference, or a term or quantity from equation (18) as described above, relating to the first grid location and the another second grid location. This may be done for any number of second grid locations. This may allow for a more granular picture of an operational state of the grid, such as a current topology of the grid, to be determined. For example, the values of the electric power flow characteristics may indicate the electrical distance of each of the plurality of second grid locations from the location of the at least one power unit 219 relative to the first grid location.

In a similar way, in some examples, there may be a plurality of first grid locations i, and the method may comprise performing steps 102 to 106 of Figure 1 for each combination of first grid locations i and second grid locations j. This may provide a matrix of values of electric power flow characteristics for different combinations of first grid locations i and second grid locations j. Accordingly, this may provide for a yet more granular picture of an operational state of the grid, such as a current topology of the grid, to be determined. Referring to Figure 6, there is a plot of the value of the amplitude of the voltage phase difference q) iii(t) (an example of an electric power flow characteristic) for all the combinations of grid locations (zones) Z1 to Z33 in the grid 400 of Figure 4 (and based on the power unit 219 performing the particular power change being located at zone Z24). The plot is in the form of a matrix where the value of the voltage phase difference amplitude is represented by the shading of the respective matrix element. In the example of Figure 6, a convention is adopted whereby a particular element represents the voltage phase difference coi,j(t) where the row is represented by i and the column is represented by j. For example, the element in row Z1 and column Z18, the value is negative, whereas for the element in row Z18 and column Z1, the value is the same but positive, for example. The value of the voltage phase difference amplitude is zero for elements on the diagonal of the matrix. In Figure 6, larger positive values are represented by blacker shading, larger negative values are represented by whiter shading, and smaller values are represented by grey shading. As can be seen in Figure 6, those combinations which have the largest difference in impedance or electrical distance relative to zone Z24 generally have the blackest (or whitest) element. For example, the element in row Z23 and column Z1 is particularly dark (or equivalently, the element in row Z1 and column Z23 is particularly white), as zone Z1 is directly connected to zone Z24 whereas zone Z23 is at its closest five electrical connections away from zone 24. On the other hand, the element in row Z23 and column Z25A (or equivalently in row Z25A and column Z23) is a middling grey shading (indicating a value close to zero), as zones Z23 and Z25A are directly connected to one another. This matrix of values may therefore itself represent an operational state of the grid, for example, a current topology of the grid 400.

In some examples, the method comprises identifying, based on the determined value or values of the electric power flow characteristic, a particular operational state of the electric power grid. In examples, a particular operational state may represent a particular topology of electrical connections between grid locations (zones) in the electric power grid. For example, one or more determined values of an electric power flow characteristic (such as the matrix of values of Figure 6) may be compared to a respective one or more values (such as a particular matrix of values) that are known to represent a particular operational state of the grid, and if the one or more values match (or are within some threshold difference from one another), it may be determined that the grid currently has the particular operational state (such as a particular grid topology). In some examples, if the one or more values do not match (e.g. are outside some threshold difference from one another), it may be determined that the grid has an operational state other than the particular operational state. For example, the particular operational state could represent a 'normal' operational state of the grid (such as a 'normal' grid topology), and the operational state other than the particular state may represent an 'abnormal' operational state of the grid (such as an 'abnormal' grid topology). In some examples, there may be a plurality of known sets of one or more values (e.g. a plurality of matrices) each set corresponding to a respective different operational stage of the grid. For example, each set may correspond to a respective different topology of the grid (that is, a respective different combination of electrical connections between the grid locations of the grid). Determining the operational state may comprise determining whether the determined one or more values match a particular known set (or determining which of the known sets the determined one or more values is closest to and/or within a certain range of). The current operational state of the grid may then be determined as the operational state associated with the matched known set (or the known set that is closest to and/or within the certain range of the determined one or more values).

In some examples, the operational state of the grid may be determined using a trained machine learning model. For example, referring to Figure 7A, there is illustrated a trained machine learning model 704. For example, the trained machine learning model may be a trained neural network, such as a deep neural network, although other examples are possible. The trained machine learning model 704 may have been trained to map input data 702 representing one or more values of the electric power flow characteristic onto one 706 of a plurality of operational states of the electric power grid 200. For example, the input data 702 may be a column vector formed from each of the phase angle difference amplitude values of a matrix of phase angle difference amplitude values, for example as per the matrix shown in Figure 6. In examples, the trained machine learning model 704 may classify the input data 702 to a particular one of any number of possible operational states that the trained machine learning model 704 has been trained to classify into. For example, there may be two operational states (e.g. 'normal' and abnormal'), or there may be a more complex distribution of operational states (e.g. there may be an operational state associated with each of the electrical connections between zones in the grid 400 of Figure 4, where each operational state may represent a different one of the electrical connections between zones in the grid 400 of Figure 4 being down or otherwise nonoperational). Accordingly, in examples, an input of a matrix of determined values of the electric power flow characteristic (e.g. as per Figure 6) into the trained machine learning model 704 may result in an output operational state indicating that a particular one of the connections (e.g. transmission line) of the grid 400 of Figure 4 is down (or an output operational state indicating that none of the connections is down). In examples, the method may comprise training the machine learning model 704 to provide the trained machine learning model 704. For example, training the machine learning model 704 may comprise providing training data sets (not shown).

For example, there may be many, for example tens or hundreds or thousands of training data sets. Each training data set may comprise one or more values of the electric power flow characteristic and a corresponding ground truth operational state of the electric power grid. For a given set, the ground truth operational state represents the operational state that is known to have been prevailing when the one or more values of the electric power flow characteristic were determined. Training the machine learning model may then comprise adjusting one or more parameters of the machine learning model (such as weights of neurons of a neural network) to minimize a difference between, for each training data set, the ground truth operational state of the electric power grid and the operational state of the electric power grid onto which the one or more values of the electric power flow characteristic is mapped by the machine learning model 704. Accordingly, once the machine learning model 704 is trained, inputting data 702 representing one or more values of the electric power flow characteristic into the trained machine learning model 704 will result in the trained machine learning model 704 outputting the particular one 706 of the plurality of operational states to which those determined one or more values of the electric power flow characteristic corresponds.

Accordingly, in examples, the method may comprise inputting data 702 representing the determined value or values of the electric power flow characteristic into the trained machine learning model 704, thereby to identify the particular operational state 706 of the electric power grid based on the determined value or values of the electric power flow characteristic. For example, identifying the particular operational state 706 may comprise obtaining the output 706 of the machine learning model 704 that is output on the basis of the input of the determined value or values of the electric power flow characteristic 702 into the trained machine learning model 702. Using the trained machine learning model 704 may allow for a flexible way to determine a current operational state of the grid, which need not rely on a hard-coded algorithm. For example, through its training, the machine learning model 704 may be able to classify the determined one or more values into a particular operational state based on subtle patterns or nuances in those values which it has learned, and which might otherwise be missed or difficult to account for in a hard-coded classification algorithm.

In some of the examples described above, a current or static operational state of the grid may be determined. However, it may also be useful to determine changes in an operational state of the grid. For example, where the operational state is a grid topology, it may be useful to dynamically determine that the grid topology has changed, and for example dynamically determine the way in which the grid topology has changed. For example, it may be useful to be able to dynamically determine or otherwise infer that a particular connection (e.g. transmission line) between two grid locations (zones) has gone down or otherwise become non-operational.

Accordingly, and referring to Figure 7B, in some examples, the method may comprise: in step 712, performing steps 102 to 106 of the method of Figure 1 to determine a first value of the electric power flow characteristic corresponding to a first time; in step 714 performing steps 102 to 106 of the method of Figure 1 to determine a second value of the electric power flow characteristic corresponding to a second time, later than the first time; and in step 716, determining a difference value representing a difference between the first value of the electric power flow characteristic and the second value of the electric power flow characteristic.

For example, the plots of Figure 5A described above may correspond to determining a first value 508 of the electric power flow characteristic at a first time. Specifically, for example, the first value of the electric power flow characteristic may be the amplitude 508 of the voltage phase angle difference plot PZ13-Z9. However, referring now to Figure 8A, the plots labelled P, PZ9', PZ13', PZ13-Z9', PZ9-Z13', and the amplitudes 502', 504', 506' and 508' are the same as those the plots labelled P, PZ9, PZ13, PZ13-Z9, PZ9-Z13, and the amplitudes 502, 504, 506 and 508 of Figure 5A, except at a later, second time, when the electrical connection between zone Z9 and Z13 is non-operational. As can be seen from a comparison of Figures 5A and 8A, the plot PZ13' at the second time is essentially the same as the plot PZ13 at the first time. This is because, as can be seen from Figure 4, losing the electrical connection between zones Z9 and Z13 would not significantly affect the impedance between zone Z24 (where the power unit 219 is located) and zone Z13. However, the plot PZ9' at the second time is substantially different to the plot PZ9 at the first time, specifically its amplitude 506' is significantly lower. This is because, as can be seen from Figure 4, losing the electrical connection between zones Z9 and Z13 would significantly affect (specifically, increase) the impedance between zone Z24 (where the power unit 219 is located) and zone Z9, because this connection is part of an electrical path between zones Z24 and Z9.

Referring to Figure 8B, there is illustrated again the plot P of the particular power change by the power unit 219 as a function of time, as well as the plot PZ9-Z13 of the difference between voltage phase angles at zones Z9 and Z13 as a function of time relative to the first time, and the plot PZ19-Z13' of the first difference between voltage phase angles at zones Z9 and Z13 as a function of time relative to the second time. Also shown in Figure 8B is a plot 802 of the difference between PZ9-Z13 and PZ19-Z13'. As can be seen, this plot 802 has an amplitude 808. This amplitude may be taken as the difference value representing a difference between the first value of the electric power flow characteristic at the first time (e.g. the amplitude 508) and the second value of the electric power flow characteristic at the second time (e.g. the amplitude 508'). This difference value 808, and in particular that it is relatively large, is indicative of the loss of the electrical connection between zones Z9 and Z13 between the first time and the second time. Accordingly, this difference value represents a change in the operational state in the grid between the first time and the second time, and in particular the loss of the electrical connection between zones Z9 and Z13 between the first time and the second time.

The process of determining a difference value may be repeated for all combinations of the grid locations (zones) Z1-Z31 for which the value of the first parameter is determined. Specifically, in examples, there may be a plurality of second Grid locations, and the method may comprise performing steps 712 to 716 for each one of the plurality of second grid locations. Similarly, there may be a plurality of first grid locations, and the method may comprise performing steps 712 to 716 for each combination of first and second grid locations, thereby to determine a difference value for each combination. This may provide a matrix of difference values for different combinations of first grid locations i and second grid locations /. Accordingly, this may provide for a granular picture of a change in operational state of the grid, such as a change in grid topology of the grid, to be determined. Referring to Figure 9, there is a plot of the difference value for the first time and the second time for all the combinations of grid locations (zones) Z1 to Z33 in the grid 400 of Figure 4 (and based on the power unit 219 performing the particular power change being located at zone Z24). The plot is in the form of a matrix where the difference value (also referred to as the voltage angle difference amplitude change) is represented by the shading of the respective matrix element. In the example of Figure 9, larger difference values are represented by blacker shading, and smaller difference values are represented by whiter shading. The difference values are zero along the diagonal of the matrix in Figure 9. As may be appreciated from Figure 9, the largest difference value is for the combination of Z9 and Z13. This is because it is the electrical connection that connects zones Z9 and Z13 that has become non-operational between the first time and the second time, and hence the greatest change in impedance is between zones Z9 and Z13. Further, the difference values for the combination of Z9 with each of Z1, Z2, Z4 to Z6, Z12 and Z14 to Z33 are also relatively large (although not as large as for Z13 with Z9) and the difference values for the combination of Z9 with each of Z3 and Z7 to Z11 is relatively small. This is because, due to the particular topology of the grid 400 of Figure 4, the connection between Z9 and Z13 affects the impedance between Z9 with each of Z3 and Z7 to Z11 a relatively small amount, but affects the impedance between Z9 with each of with each of Z1, Z2, Z4 to Z6, Z12 and Z14 to Z33 a relatively large amount. This matrix of values may therefore itself represent a change in operational state of the grid, for example, a change in topology of the grid 400. In particular, as is evident from the above, the matrix of values itself indicates the particular change in topology of the grid that has occurred, that is, the loss of the electrical connection between zones Z9 and Z13. In some examples, the method may comprise identifying, based on the determined difference value or values, a particular change in operational state of the electric power grid. Again, for example, the particular change in operational state may be a particular change in a topology of electrical connections in the electric power grid. In examples, identifying the particular change in operational state of the grid may comprise analysing the determined difference value of values to determine is there has been a change. For example, the or each determined difference value may be compared to a threshold, and if the difference value is above the threshold, then it may be determined that a change in operational state has occurred in respect of the grid locations (zones) associated with that difference value. For example, based on a particular difference vale being larger than a threshold, it may be determined that an electrical connection between the two grid locations (zones) associated with the difference value has or may have become non-operational. As another example, identifying a particular change in operational state of the grid may comprise analysing a plurality of difference values (such as the difference values of the matrix of Figure 9) to determine the largest difference value. For example, the largest difference value may be determined, and accordingly it may be determined that a change in operational state has occurred in respect of the grid locations (zones) associated with this difference value. For example, it may be determined that an electrical connection between the two grid locations (zones) associated with the largest difference value has or may have become non-operational. For example, in the example of Figure 9, the largest difference value is associated with grid locations (zones) Z9 and Z13, and hence it may be determined that the electrical connection between zones Z9 and Z13 has become non-operational. Other examples are possible.

In examples, a difference value or value may be determined at specific time intervals. For example, a first difference value may be determined with respect to changes between the first time and the second time, and a second difference value may be determined with respect to the second time and a third time, later than the second time. This may be repeated at regular intervals, such as event minute or few minutes or tens of minutes. This may allow for dynamic changes in the operational state of the grid (e.g. changes in the topology of the grid) to be monitored over time.

This may allow a grid operator to be informed of a change in operational state as an when it occurs, which may allow for a rapid response to the change.

In some examples, the particular change in operational state of the grid may be determined using a trained machine learning model. For example, referring to Figure 10, there is illustrated a trained machine learning model 1004. For example, the trained machine learning model may be a trained neural network, such as a deep neural network, although other examples are possible. The trained machine learning model 1004 may have been trained to map input data 1002 representing one or more difference values onto one 1006 of a plurality of changes in operational states of the electric power grid 200. For example, the input data 1002 may be a column vector formed from each of the difference values of a matrix of difference values, for example as per the matrix shown in Figure 9. In examples, the trained machine learning model 1004 may classify the input data 1002 to a particular one of any number of possible changes in operational states that the trained machine learning model 1004 has been trained to classify into. For example, there may be two changes in operational states (e.g. from 'normal' to 'abnormal' and from 'abnormal' to 'normal), or there may be a more complex distribution of changes in operational states (e.g. there may be a change in operational state associated with each of the electrical connections between zones in the grid 400 of Figure 4 becoming non-operational). Accordingly, in examples, an input of a matrix of determined difference values (e.g. as per Figure 9) into the trained machine learning model 1004 may result in an output change in operational state indicating that a particular one of the connections (e.g. transmission line) of the grid 400 of Figure 4 has become non-operational.

In examples, the method may comprise training the machine learning model 1004 to provide the trained machine learning model 1004. For example, training the machine learning model 1004 may comprise providing training data sets (not shown).

For example, there may be many, for example tens or hundreds or thousands of training data sets. Each training data set may comprise one or more said difference values and a corresponding ground truth change in operational state of the electric power grid. For a given set, the ground truth change in operational state represents a change in operational state that is known to have occurred between the times associated with a respective difference values. Training the machine learning model may then comprise adjusting one or more parameters of the machine learning model (such as weights of neurons of a neural network) to minimize a difference between, for each training data set, the ground truth change in operational state and the change in operational state onto which the one or more difference values is mapped by the machine learning model 1004. Accordingly, once the machine learning model 1004 is trained, inputting data 1002 representing one or more difference values into the trained machine learning model 1004 will result in the trained machine learning model 1004 outputting the particular one 1006 of the plurality of changes in operational states to which those determined one or more difference values corresponds.

Accordingly, in examples, the method may comprise inputting data 1002 representing the determined difference values into the trained machine learning model 1004, thereby to identify the particular change in operational state 1006 of the electric power grid based on the determined difference values. For example, identifying the particular change in operational state 1006 may comprise obtaining the output 1006 of the machine learning model 1004 that is output on the basis of the input of the determined difference value or values into the trained machine learning model 1002.

Using the trained machine learning model 1004 may allow for a flexible way to determine a change in operational state of the grid, which need not rely on a hard-coded algorithm. For example, through its training, the machine learning model 1004 may be able to classify the determined one or more difference values into a particular change in operational state based on subtle patterns or nuances in those values which it has learned, and which might otherwise be missed or difficult to account for in a hard-coded classification algorithm.

In some of the above examples, the particular power change was provided by at least one power unit 219 having a particular grid location (i.e. Z24). However, in some examples, there may be a plurality of such power units 219 each having a different location m. In some examples, the method may comprise performing steps 102 to 106 of Figure 1 for a particular power change by at least one first power unit of the plurality of power units, to determine one value of the electric power flow characteristic corresponding to the at least one first power unit. The method may then comprise performing steps 102 to 106 of Figure 1 for a particular power change by at least one second power unit of the plurality of power units, to determine another value of the electric power flow characteristic corresponding to the at least one second power unit. These two values of the electric power flow characteristic can be used to determine yet another value of the electric power flow characteristic (e.g. these two values can be averaged to provide more reliable value), or these two values can be used to determine a value of a further electric power flow characteristic (e.g. grid inertia determined through simultaneous equations).

For example, equation (18) may be re-written to include the superscript in denoting the particular location of a power unit performing the particular change: 407,1M) = foff It (ZmO 1 o o p(s)clsdr ni B --BI"(Z,,,d)) H (19).

By determining (pri(t) for each of a plurality of different power unit locations in, but keeping i and/ the same, a set of simultaneous equations may be established via which Hi and/or H, can be determined.

As another example, an operational state (or change in operational state) of the grid may be determined based on such multiple values of the electric power flow characteristic associated with respective multiple different power change grid locations. For example, performing the power change at different grid locations may allow for different sensitivity in the determined electric power flow characteristic with respect to different grid locations. For example, a power change by a power unit located at zone Z1 may provide particular sensitivity in the determination of the voltage phase angle difference between zones in the lower half of the grid in the sense of Figure 4, and a power change by a power unit located at zone Z32 may provide particular sensitivity in the determination of the voltage phase angle difference between zones in the lower half of the grid in the sense of Figure 4. In examples, the voltage phase angle difference values from both may be combined (e.g. concatenated) in order to provide an input (e.g. for the trained machine learning model 704 or the trained machine learning model 1004) in order to determine an operational state of the grid (or change in operational state of the grid) with greater overall sensitivity to different areas of the grid 400. Other examples are possible.

Although in some of the above examples grid topology is given as an example of an operational state of the grid, in other examples, other operational states may be determined, such as a particular distribution of inertia in the grid. For example, as above in equation (18), the amplitude of you(t) is proportional to the difference between the inertia at the first grid location i and the inertia at the second grid location 1. As such, in cases where the impedances are known or assumed not to change (that is, for a given constant grid topology), the one or more values of the electric power flow characteristic may be compared to one or more values representative of a particular relative distribution of inertia in the grid (for the given topology), or to a plurality of sets of one or more values each set being representative of a respective different relative distribution of inertia in the grid. Accordingly, a current operational state of the grid (that is, a current relative distribution of inertia in the grid) can be determined. In a similar way, changes in an operational state of the grid (that is, changes in relative distribution of inertia in the grid) can be determined based on one or more of the difference values. As another example, as described above in some examples the electric power flow characteristic may itself be inertia (e.g. as calculated from equation (19) e.g. using simultaneous equations). In this case, the one or more values of the electric power flow characteristic may be used directly to identify a current operational state of the grid, such as a current distribution of inertia, or changes in operational state of the grid, such as changes in the distribution of inertia in the grid. Other examples are possible.

In some of the above examples, a value of an electric power flow characteristic is determined based on a power change by a power unit 219 (or based on multiple repetitions or cycles of the power change by the power unit 219). However, it will be appreciated that this need not necessarily be the case, and that in other examples, a value of an electric power flow characteristic may be determined based on one or more power changes by one or more power units. For example, there may be a plurality of power changes (e.g. by one or more power units located in a particular region of the grid) occurring in a particular first time window. Each individual power change may be correlated with a respective at least one value of the first parameter at a first grid location and at least one value of the first parameter at a second grid location. For each individual power change, the difference between the at least one value of the first parameter at the first grid location and at least one value of the first parameter at the second grid location may be determined. The power changes (for example the amplitudes of the power changes) may be averaged to determine an average power change in the first time window, and the respective differences (for example the amplitude of the differences) in values of the first parameter may be averaged to determine an average difference between the at least one value of the first parameter at the first grid location and at least one value of the first parameter at the second grid location in the first time window. The average difference may be divided by the average power change to determine e.g. a voltage phase angle difference per unit power change.

For example, a plurality of power changes, each having a step function waveform u(i), may be indicated in a plurality of sets of event data. The plurality of power changes may each have occurred in a first time window. For example, there may be Ni power changes in total in the first time window, the nth power change having a magnitude of C. The average power change P(t) of the power changes indicated in the sets of event data in the first time window T may be given by: P(t) = N, Lin (20) where u(t) = t > 0 (21) 0, t 0 The average sign compensated voltage phase angle difference response Wid(t) to the power change may be given by: Wid(t) = N 71-ENL1 sgn(C")coid(r" + t) (22) where the factor you (r" + t) indicates the determined voltage phase angle difference (py beginning at the time TT, of the nth power change. The sign compensation is to take into account that the absolute value IC" I of the power change is used in equation (20), and hence voltage phase angle differences cpi J that correspond to negative power changes should be accordingly sign compensated before averaging. The duration of t in equation (22) may be limited, for example, it may be limited to be no longer than the duration of the shortest of the n power changes. A value indicative of the voltage phase angle difference for a particular (e.g. unit) power change may be determined by dividing the magnitude of (t) by the magnitude of P(t).

It is noted that averaging over multiple cycles or repetitions of a particular sinusoidal power change would be a special case of the above example described with reference to equations (20) and (21), where in that case u(t) would be sin(t) for 0<t<cl and 0 otherwise (where d is the period of the sinusoidal waveform); (.; would be constant over all 11; r" would be the time at the start of the nth sinusoidal cycle; and t in equation (22) would be limited to d (the period of the sinusoidal waveform). Here again, a value indicative of the voltage phase angle difference for a particular (e.g. unit) power change may be determined by dividing the amplitude of 'Po (t) by the amplitude of P(t).

In any case, the voltage phase angle difference per unit power change is an example of an electric power flow characteristic. As above its value may be indicative of a current topology or operational state of the grid. The value of the voltage phase angle difference per unit power change determined for a first time window may be compared to the value of the voltage phase angle difference per unit power change determined for a second, later, time window in order to determine a change in topology or operational state of the grid, as discussed above. Determining the voltage phase angle difference per unit power change may allow that the same power change or changes need not be used in each time window in order to determine changes in grid topology or operational state of the grid between the time windows.

In some of the above examples the first parameter is indicative of a voltage phase angle of AC electricity flowing in the grid. However, it will be appreciated that this need not necessarily be the case and that other first parameters may be used, as long as a change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit causes a change in value of a first parameter of electric power flow in the electric power grid.

For example, in some examples, the first parameter may be indicative of a magnitude of the voltage of electricity flowing in the electric power grid. For example, in this case, the grid may be a DC grid. A change in power provided/consumed from the grid by a power unit 219 will cause a change in the magnitude of the voltage at each grid location (relative to ground). This is because P = V/Z, where P is power, V is voltage, and Z is impedance (which in a DC grid is the same as resistance R). Accordingly, a particular power change at a particular grid location will cause a respective change in voltage magnitude at another grid location.

Further, the amount by which the voltage magnitude will change at the another grid location is dependent on the impedance (resistance) between the location of the particular power change and the another grid location. Accordingly, similar techniques to those described above for voltage phase amplitude can be applied to voltage magnitude. For example, similarly to as for the voltage phase angle, in the example of the first parameter being indicative of a voltage magnitude, the difference between the at least one value of the first parameter first location and the at least one value of the first parameter at the second grid location may be indicative of an amplitude of a difference between voltage magnitude at the first grid location and voltage magnitude at the second grid location. Since the amount by which the voltage in each location will change is indicative of the impedance (resistance) between the location of the power change and each locations, the difference is indicative of a difference between a first impedance between the at least one power unit and the first grid location and a second impedance between the at least one power unit and the second grid location. This difference is itself an example of a value of the electric power flow characteristic. In examples, similarly to as above, values of other electric power flow characteristics may be derived from this difference. Other examples are possible.

Referring to Figure 11, there is illustrated a system 1100 according to an example. In this example, the system 1100 comprises the computing system 205, a plurality of the measurement devices 220A, 220B, and a plurality of the power units 219A, 219B. In this example, the measurement devices 220A, 220B and the power units 219A, 219B are in communication with the computing system 205 over a computer network 1101, such as the Internet. The measurement devices 220A, 220B may be located at different grid locations in an electric power grid (not shown in Figure 11). Each measurement device 220A, 220B may be according to any one of the example measurement devices 220 described above with reference to Figures 1 to 10. The power units 219A, 219B may be located at the same or different grid locations in the electric power grid. Each power unit 219A, 219B may be according to any one of the example measurement devices 220 described above with reference to Figures 1 to 10. In this example, a first power unit 219A is configured to receive a control signal over the network 1101 from the computing system 205 to perform a particular power change. A second power unit 219B comprises a data generating device 218 and is configured to generate change data on a particular power change performed by the power unit 219B and transmit this change data to the computing device 205. The computing device 205 may be according to any of the examples described above with reference to Figures 1 to 10. In this example, the computing system 205 comprises a first database 1102, a second database 1104, a processing system 1106 and an output device 1108. For example, the first database 1102 may store time series of values of the first parameter measured at different grid locations. The second database 1104 may store data on one or more particular power changes that have been performed in the grid. For example, for each power change, the second database 1104 may store time series of power values for particular power changes at particular grid locations. As another example, the data in the second database 1104 may comprise one or more of a time of the change, a waveform of the change, a magnitude or amplitude of the change, and a location of the change The processing system 1106 may obtain data from the first database 1102 and the second database 1104 and perform processing on these data For example, the processing system 1106 may correlate a particular power change with at least one value of the first parameter at a first grid location and at least one value of the first parameter at a second grid location, for example according to any of the examples described above with reference to Figures 1 to 10. The processing system 1106 may determine a difference between the at least one value of the first parameter at the first grid location and the at least one value of the first parameter at the second grid location, and determine, based on this difference, a value of an electric power flow characteristic, for example according to any of the examples described above with reference to Figures 1 to 10. The processing system 1108 may output data indicative of the results of the processing (such as data indicative of one or more determined values of an electric power flow characteristic, one or more determined difference values, one or more determined operational states of the electric power grid and/or one or more determined changes in operational states of the electric power grid, for example as per any of the examples described above with reference to Figure 1 to 10) to the output device 1108. In some examples, the output device 1108 may be a storage or memory, for example such that the computing system 205 or another device (not shown) can access the data indicative of the results of the processing. In some examples, the output device may comprise a display screen, such as a computer monitor, configured to display the data indicative of the results of the processing. For example, this may indicate to a grid operator an operational state of the electric power grid, which may allow the grid operator to take any action as necessary to maintain the grid in a desired operating state. As another example, this data may be provided to traders, such as electricity market traders, such as energy market traders and/or capacity market traders.

Referring to Figure 12, there is illustrated an apparatus 1200 according to an example. The apparatus 1200 may be configured to perform the method according to any one of the examples described above with reference to Figures 1 to 11. The apparatus 1200 may provide the computing system 205 according to any of the examples described above with reference to Figures 1 to 11. In this example, the apparatus 1200 comprises an input interface 1206, a processor 1202, a memory 1204, and an output interface 1208. The memory 1204 may store a computer program comprising instructions which, when executed by the computing system 205 (e.g. specifically the processor 1202 of the apparatus 1200), cause the computing system to perform the method according to any one of the examples described above with reference to Figures 1 to 11. The input interface 1206 may be configured to receive input data and pass this data to the processor 1202 for processing. For example, this input data may comprise data indicative of values of the first parameter and particular power changes. The output interface 1208 may be configured to receive output data from the processor 1202 and provide this for e.g. storage or display. For example, this output data may comprise one or more of determined electric power flow characteristics, determined difference values, determined operational states of the grid, and determined changes in operational states of the grid. Other examples are possible.

In some examples, the particular power change described above may be a change in active power consumed from the grid 200 by a power unit 219 or provided to the grid 200 by a power unit 2019. Alternatively, or additionally, in some examples, the power change described above may be a change in reactive power consumed from the grid 200 by a power unit 219 or provided to the grid 200 by a power unit 219.

In some of the above examples, the data generating devices 218 send the sets of change data to the computing system 205. However, it will be appreciated that this need not necessarily be the case and that in other examples, the data generating devices 218 may send the sets of change data to one or more other computing systems (not shown) for storage. In these examples, the computing system 205 may obtain the sets of event data from the one or more other computing systems (not shown). Other examples are possible.

In some of the above examples, each grid location corresponds to a respective different zone Z1 to Z33. However, it will be appreciated that this need not necessarily be the case, and that in other examples, each grid location may correspond to a cluster or group of zones Z1 to Z33. For example, each grid location may represent an area or region of the grid 200 comprising a plurality of sublocations (e.g. Z1 to Z3). In these examples, the values of the first parameter (e.g. phase angle) measured at different sublocations may be pre-processed in the space-time domain before the difference between locations is determined. For example, the space-time processing may comprise clustering sublocations into a cluster or group (e.g. Z1 to Z3), and averaging over the values of the first parameter measured at each sublocation in the cluster or group. For example, sublocations may be clustered or grouped according geographic and/or grid location. For example, sublocations that are in the same or similar geographic and/or grid location may be clustered or grouped together.

As an example, the first grid location may correspond to a first area or region of the grid comprising a first plurality of sublocations (e.g. Z1 to Z3) in the grid 200, and/or the second grid location may correspond to a second area or region of the grid comprising a second plurality of sublocations (e.g. Z31 to Z33) in the grid 200. In such examples, determining the at least one value of the first parameter at a particular grid location may comprise: for each of the plurality of sublocations of the particular grid location, correlating the particular power change with at least one value of the first parameter at the sublocation, thereby to obtain a plurality of sets of at least one value of the first parameter, each set corresponding to a respective sublocation; averaging over the plurality of sets of at least one value of the first parameter; and determining the at least one value of the first parameter at a particular grid location based on the average of the plurality of sets of at least one value of the first parameter.

For example, for a particular grid location (e.g. labelled ZG l', not shown) formed of the group of sublocations Z1 to Z3, the at least one value of the first parameter (e.g. phase angle yozal) may be given by the sum of the at least one value of the first parameter for each of the sublocations Z1 to Z3, divided by the number of sublocations (e.g. yozei = V:;; vi). It will he appreciated that, in examples, either one or each of the first grid location and the second grid location may correspond to I) a respective single location or point in the grid at which the at least one value of the first parameter is measured, or 2) a respective plurality (e.g. a group or cluster) of sublocations or points in the grid at each of which at least one value of the first parameter is measured.

The above examples are to be understood as illustrative examples of the invention. It is to be understood that any feature described in relation to any one example may be used alone, or in combination with other features described, and may also be used in combination with one or more features of any other of the examples, or any combination of any other of the examples. Furthermore, equivalents and modifications not described above may also be employed without departing from the scope of the invention, which is defined in the accompanying claims.

Claims

CLAIMS1. A computer-implemented method of determining a value of an electric power flow characteristic of an electric power grid, the grid comprising at least one power unit configured to consume electric power from and/or provide electric power to the electric power grid, a change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit causing a change in value of a first parameter of electric power flow in the electric power grid, the method comprising: a) correlating a particular change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit with at least one value of the first parameter at a first grid location and at least one value of the first parameter at a second grid location; b) determining a difference between the at least one value of the first parameter at the first grid location and the at least one value of the first parameter at the second grid location; and c) determining, based on the determined difference, a value of the electric power flow characteristic of the electric power grid.
2. The method according to claim 1, wherein the value of the electric power flow characteristic is indicative of a difference between a first impedance between the at least one power unit and the first grid location and a second impedance between the at least one power unit and the second grid location.
3. The method according to claim 1 or claim 2, wherein the first parameter is indicative of a phase of AC electricity flowing in the electric power grid.
4. The method according to claim 3, wherein determining the value of the electric power flow characteristic is further based on one or both of a value of grid inertia at the first grid location and a value of grid inertia at the second grid location.
5. The method according to claim 3, wherein the value of the electric power flow characteristics is indicative of at least one of: grid inertia at the first grid location; grid inertia at the second grid location; a proportion of the particular change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit experienced at the first grid location; and a proportion of the particular change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit experienced at the second grid location.
6. The method according to any one of claim 1 to claim 5, wherein there are a plurality of second grid locations, and wherein the method comprises performing steps a) to c) for each one of the plurality of second grid locations.
7. The method according to claim 6, wherein there are a plurality of first grid locations, and wherein the method comprises performing steps a) to c) for each combination of first and second grid locations.
8. The method according to any one of claim 1 to claim 7, wherein the method comprises identifying, based on the determined value or values of the electric power flow characteristic, a particular operational state of the electric power grid.
9. The method according to claim 8, wherein the method comprises: inputting data representing the determined value or values of the electric power flow characteristic into a trained machine learning model, the trained machine learning model having been trained to map input data representing one or more values of the electric power flow characteristic onto one of a plurality of operational states of the electric power grid, thereby to identify the particular operational state of the electric power grid based on the determined value or values of the electric power flow characteristic.
10. The method according to claim 9, wherein the method comprises training the machine learning model to provide the trained machine learning model, wherein training the machine learning model comprises: providing training data sets, each training data set comprising one or more values of the electric power flow characteristic and a corresponding ground truth operational state of the electric power grid; and adjusting one or more parameters of the machine learning model to minimize a difference between, for each training data set, the ground truth operational state of the electric power grid and the operational state of the electric power grid onto which the one or more values of the electric power flow characteristic is mapped by the machine learning model.
11. The method according to any one of claim 1 to claim 10, wherein the method comprises: d) performing steps a) to c) to determine a first value of the electric power flow characteristic corresponding to a first time; e) performing steps a) to c) to determine a second value of the electric power flow characteristic corresponding to a second time, later than the first time; f) determining a difference value representing a difference between the first value of the electric power flow characteristic and the second value of the electric power flow characteristic.
12. The method according to claim 11, wherein there are a plurality of second grid locations, and wherein the method comprises performing steps d) to f) for each one of the plurality of second grid locations.
13 The method according to claim 12, wherein there are a plurality of first grid locations, and wherein the method comprises performing steps d) to f) for each combination of first and second grid locations, thereby to determine a difference value for each combination.
14. The method according to claim any one of claim 11 to claim 13, wherein the method comprises identifying, based on the determined difference value or values, a particular change in operational state of the electric power grid.
15. The method according to claim 14, wherein the method comprises: inputting data representing the difference value or values into a trained machine learning model, the trained machine learning model having been trained to map input data representing one or more such difference values onto a particular one of a plurality of changes in operational state of the electric power grid, thereby to identify the particular change in operational state of the electric power grid based on the determined difference value or difference values.
16. The method according to claim 15, wherein the method comprises training the machine learning model to provide the trained machine learning model, wherein training the machine learning model comprises: providing training data sets, each training data set comprising one or more said difference values and a corresponding ground truth change in operational state of the electric power grid; and adjusting one or more parameters of the machine learning model to minimize a difference between, for each training data set, the ground truth operational state of the electric power grid and the change in operational state of the electric power grid onto which the one or more difference values is mapped by the machine learning model.
17. The method according to any one of claims 8 to 10 or claims 14 to 16, wherein a particular operational state represents a particular topology of electrical connections between grid locations in the electric power grid.
18. The method according to any one of claim 1 to claim 17, wherein the first parameter is indicative of a voltage phase angle of AC electricity flowing in the electric power grid.
19. The method according to claim 18, wherein the difference is indicative of an amplitude of a difference between the voltage phase angle at the first grid location and the voltage phase angle at the second grid location.
20. The method according to any one of claim 1 to claim 17, wherein the first parameter is indicative of a magnitude of voltage of the electricity flowing in the electric power grid.
21. The method according to claim 20, wherein the difference is indicative of an amplitude of a difference between voltage magnitude at the first grid location and voltage magnitude at the second grid location.
22. The method according to any one of claim 1 to claim 21, wherein the method comprises: determining the at least one value of the first parameter at the first grid location and/or the at least one value of the first parameter at the second grid location.
23. The method according to claim 22, wherein determining the at least one value of the first parameter at a particular grid location comprises: correlating each one of a plurality of sets of at least one first value of the first parameter at the particular grid location with a respective change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit; averaging the plurality of sets of at least one first value; and determining the at least one value of the first parameter at the particular grid location based on the average of the plurality of sets of at least one first value.
24. The method according to claim 22 or claim 23, wherein the first grid location comprises a first plurality of sublocations in the grid and/or the second grid location comprises a second plurality of sublocations in the grid, and wherein determining the at least one value of the first parameter at a particular grid location comprises: for each of the plurality of sublocations of the particular grid location, correlating the particular change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit with at least one value of the first parameter at the sublocation, thereby to obtain a plurality of sets of at least one value of the first parameter, each set corresponding to a respective sublocation; averaging the plurality of sets of at least one value of the first parameter; and determining the at least one value of the first parameter at the particular grid location based on the average of the plurality of sets of at least one value of the first parameter.
25. The method according to any one of claim 22 to 24 when dependant on claim 18 or claim 19, wherein determining the at least one value of the voltage phase angle at a particular grid location comprises accumulating changes in measured voltage phase angle measured at the particular grid location.
26. The method according to any one of claim 1 to claim 25, wherein the method comprises: causing the at least one power unit to perform the particular change in consumption of electric power from or provision of electric power to the electric power grid.
27. The method according to any one of claim 1 to claim 25, wherein the method comprises: obtaining change data generated by at least one data generating device respectively associated with the at least one power unit, the change data being indicative of the particular change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit; and based on the obtained change data, correlating the particular change in consumption of electric power from or provision of electric power to the electric power grid by the at least one power unit with the at least one value of the first parameter at the first grid location and the at least one value of the first parameter at a second grid location.
28. The method according to any one of claim 1 to claim 27, wherein the grid comprises a plurality of power units, each power unit being configured to consume electric power from and/or provide electric power to the electric power grid, a change in consumption of electric power from or provision of electric power to the electric power grid by each power unit causing a respective change in value of the first parameter, each power unit having a different grid location, wherein the method comprises: performing steps a) to c) for a particular change in consumption of electric power from or provision of electric power to the electric power grid by at least one first power unit of the plurality of power units, to determine a third value of the electric power flow characteristic corresponding to the at least one first power unit; performing steps a) to c) for a particular change in consumption of electric power from or provision of electric power to the electric power grid by at least one second power unit of the plurality of power units, to determine a fourth value of the electric power flow characteristic corresponding to the at least one second power unit; and determining a fifth value of the electric power flow characteristic, or a value of a further electric power flow characteristic of the electric power grid, based on the third value and the fourth value.
29. Apparatus configured to perform the method according to any one of claims 1 to 28.
30. A system comprising the apparatus according to claim 29 and a plurality of measurement devices, each measurement device configured to measure a value of the first parameter at a respective different grid location.
31. A computer program comprising instructions which, when executed by a computing system, cause the computing system to perform the method of any one of claims 1 to 28.