CN105116218B - Power circuit current harmonics detection method based on input Observer Theory - Google Patents

Abstract

A power line current harmonic detection method based on input observer theory relates to power line signal processing. A power line current harmonic detection method based on input observer theory that can accurately analyze the magnitude of the harmonic component in the current signal is provided. Sampling the current and grid voltage signals from the power line to obtain the current signal sequence; passing the sampled current signal through an integral link to obtain the integral of the current signal, and using each frequency component as a new state quantity to establish an augmented state Space equation; the grid voltage signal obtained by sampling is passed through the AC zero-crossing detection circuit to detect the zero-crossing point of the grid voltage signal; the frequency of the measured signal is obtained by detecting the rising edge jump, and the phase accumulation error is cleared at the same time; through the design A Romberg observer, and prove the effectiveness of the observer, observe the size of each frequency component.

Description

Current Harmonic Detection Method of Power Line Based on Input Observer Theory

technical field

The invention relates to power line signal processing, in particular to a current harmonic detection method.

Background technique

With the extensive use of power electronic devices, the problem of current harmonics in the power grid has attracted widespread attention. When the harmonic components in the power grid exceed the limit standard, it will seriously affect the safety, reliability, stability and economy of the power system and electrical equipment operation, and also pollute the surrounding electrical environment.

Harmonic detection is an important part of harmonic problems, and it is also the starting point and main basis for analyzing and controlling harmonic problems. On the one hand, harmonic detection can identify whether the harmonic levels of the actual power system and harmonic source users meet the specified standards, and it is also an important basis for evaluating power quality. Harmonic detection can also be used for the debugging of harmonic source equipment and other electrical equipment, and the measurement of the commissioning process, so as to ensure the safe and economical operation of the power system and equipment after the equipment is put into operation. On the other hand, harmonic detection is the basis of power quality compensation, which can provide basis for real-time compensation, equipment (active power filter (APF), etc.) compensation, etc. Therefore, the rapid and accurate detection of harmonic components in power systems is of great significance to the control of power quality and the suppression and compensation of harmonics.

Along with the whole process of power system development, harmonic detection has experienced the development process of frequency domain, time domain, neural network, and adaptive parameter identification, and has formed a variety of detection methods. Frequency-domain harmonic detection methods mainly include: FFT detection method based on Fourier analysis and detection method based on wavelet transform. Time-domain harmonic detection methods mainly include: generalized reactive current separation method based on Fryze time-domain analysis and instantaneous reactive power theoretical detection method. Other methods include neural network-based harmonic detection methods and adaptive parameter identification methods.

Chinese patent CN103547328A discloses a harmonic detection method and a related device. Among them, a harmonic detection method includes: sampling the electrical signal from the power line to obtain an electrical signal sequence of N points; performing N-point real fast Fourier transform RFFT operations on the electrical signal sequence of N points to obtain the first complex number sequence; Harmonic extraction processing is performed on the first complex number sequence to obtain a second complex number sequence; virtual and real combination processing is performed on the second complex number sequence to obtain a third complex number sequence; RFFT operation is performed on the third complex number sequence to obtain a fourth complex number sequence; the fourth complex number sequence is obtained. Combine virtual and real to get N-point harmonic sequence.

Contents of the invention

The purpose of the present invention is to provide a power line current harmonic detection method based on input observer theory that can accurately analyze the magnitude of the harmonic component in the current signal.

The present invention comprises the steps:

1) Sampling the current and grid voltage signals from the power line to obtain the current signal sequence;

2) Pass the sampled current signal through an integral link to obtain the integral of the current signal, and use each frequency component as a new state quantity to establish an augmented state space equation; the sampled grid voltage signal is passed through the AC process The zero detection circuit detects the zero-crossing point of the grid voltage signal; by detecting the rising edge transition, the frequency of the measured signal is obtained by solving, and the accumulated phase error is cleared at the same time;

3) By designing a Romberg observer and proving the effectiveness of the observer, observe the magnitude of each frequency component.

In step 2), the specific implementation method is as follows:

Assuming that im ( _t ) is the periodic current signal to be measured, since im ( _t ) can be regarded as composed of the sum of DC, fundamental and harmonic components, it can be expressed as a Fourier series as follows :

Among them, angular frequency ω=2πf, f=50Hz, a ₀ is a DC component, a _i cos(iωt)+b _i sin(iωt) is a sinusoidal signal with a frequency of iω(i=1,2...n) , a _i , b _i are the parameters of the i-th component, the amplitude A _i and the initial phase of the i-th component for:

If the values of the parameters {a ₀ ,a ₁ b ₁ ,...a _i b _i ...a _n b _n } are observed, the amplitude and phase of each frequency component can be calculated, that is, the current Detection of DC magnitude, fundamental and harmonics of signal i _m (t). Taking i _m (t) as the input quantity, a dynamic system is constructed through an integral link, and the first-order state space equation of the system is described as follows:

in, output is y;

In the case of steady-state work, the harmonic coefficient {a ₀ a ₁ b ₁ …a _n b _n } changes slowly, in order to observe the values of the coefficients a _i and b _i of each frequency component, each frequency component is used as a new state quantity,

Then the original state space equation is extended to the form of the augmented matrix as follows:

in,

The model is a linear time-varying system.

For linear time-varying systems, a time-varying Romberg observer is designed to realize online observation of parameters {a ₀ a ₁ b ₁ …a _n b _n }.

In step 3), the specific method of the size of each frequency component of the observation is as follows:

To design a time-varying Romberg observer, first, construct an identical model whose state estimate can be directly measured, the model is the state observer, on this basis, through the output error to correct the estimated model of the state, so that the estimated value of the state tends to the true state of the system,

Wherein, the weighting matrix L(wt) of the error signal is a matrix of (2n+2)×1,

L(wt)＝[l ₀ l _a0 l _a1 cos(ωt) l _b1 sin(ωt)…l _an cos(nωt) l _bn sin(nωt)] ^T

Among them, l ₀ l _a0 l _a1 ... l _an l _bn are constants whose values determine the convergence speed of each state component of the observer.

define error signal Then the dynamic system of the error is:

If it is proved that when t→∞, the state quantity will converge to x, that is, is close to 0, it can be proved that the Lomberg observer can observe the harmonic component of i _m (t), which also proves that the harmonic detection method proposed by the present invention is effective.

Proposition 1 (Designing Lyapunov Functions): Definition D＝{1 1/l _a0 1/l _a1 1/l _b1 …1/l _bn } is a diagonal matrix, take l ₀ >0, l _ai >0, l _bi >0 (i=1,2…n ), then V is a Lyapunov function.

Proof 1: Since D is a positive definite diagonal matrix, then

where V is continuously differentiable and satisfies:

(1) V(0)=0, and for all

(2) In R ²⁽ⁿ⁺¹⁾ ,

Therefore, V is a Lyapunov function, Proposition 1 is proved.

Proposition 2 (convergence analysis of Romberg observer): state quantity of Romberg observer converges to the state quantity x.

Proof 2: Since the error system is a time-varying system, the validity of the observer is proved by the Russell invariant set principle as follows:

define set It can be seen that it is a consistent positive invariant set of the error system.

definition is the largest invariant set in the set S(R).

According to Russell's invariant set principle, when t→∞, every point starting from S(R) converges to E, that is, for any Both meet:

At the same time, for Satisfy:

Since the set {1 cos(ωt) sin(ωt)...cos(nωt) sin(nωt)} is linearly independent, the solution to the above equation exists and is unique,

the largest invariant set is a single-element set whose element is the origin, and Proposition 2 is proved.

It should be noted that the Russell invariant set principle provides a proof of the stability of the error system, but does not give an analysis of the convergence rate. Refer to the definition of Lyapunov function It can be seen that the values of l ₀ , _{la ai} , l _bi (i=1,2...n) directly affect the convergence speed of the Romberg observer. The shortest convergence time of the Lomberg observer of the present invention to observe the nth harmonic is (2n+1)Ts. When Ts is very small, reasonable selection of l ₀ , _lai , _lbi may obtain better real-time observation effect .

In order to accurately analyze the magnitude of the harmonic components in the signal, the present invention proposes a new current harmonic detection method——a harmonic detection method based on input observer technology, which is also suitable for current harmonic detection in power lines .

It should be noted that the Romberg observer described here is not an instrument, but a Romberg observer belonging to the field of modern control.

Description of drawings

Fig. 1 is a principle diagram of voltage signal zero-crossing detection in the present invention.

Fig. 2 is a closed-loop model diagram of observer state estimation in the present invention.

FIG. 3 is an example diagram of the present invention specifically applied in a three-phase uncontrolled rectification circuit.

Fig. 4 is a flow chart of the steps of the harmonic detection method provided by the present invention.

Fig. 5 is a schematic diagram of iterative calculation of phase θ(k) in the algorithm of the present invention.

Fig. 6 is an error analysis diagram of the simulated current and the observed current according to the present invention.

FIG. 7 is a waveform diagram of the measured current signal with white noise added in the present invention.

Fig. 8 is a current waveform diagram of the fundamental wave detected by the present invention.

Fig. 9 is a current waveform diagram of the fifth harmonic detected by the present invention.

Fig. 10 is a current waveform diagram of the 7th harmonic detected by the present invention.

Fig. 11 is a current waveform diagram of total harmonics detected by the present invention.

Detailed ways

The invention provides a new harmonic detection method, which can accurately analyze the magnitude of the harmonic of the current signal in the power line.

Embodiments of the present invention include the following steps:

1) Sampling the current and grid voltage signals from the power line to obtain the current signal sequence;

2) Pass the sampled current signal through an integral link to obtain the integral of the current signal, and use each frequency component as a new state quantity to establish an augmented state space equation; the sampled grid voltage signal is passed through the AC process The zero detection circuit detects the zero-crossing point of the grid voltage signal; by detecting the rising edge jump, the frequency of the measured signal is obtained by solving, and the accumulated phase error is cleared at the same time;

3) By designing a Romberg observer and proving the effectiveness of the observer, observe the magnitude of each frequency component.

In step 2), the sampled measured current signal will be sent to the integration link, and the sampled grid voltage signal will pass through the AC zero-crossing detection circuit to detect the zero-crossing point of the grid voltage signal, as shown in Figure 1. By detecting the rising edge transition, the frequency of the measured signal is obtained by solving, and the accumulated phase error is cleared at the same time.

The specific implementation method is as follows:

Assuming that im ( _t ) is the periodic current signal to be measured, since im ( _t ) can be regarded as composed of the sum of DC, fundamental and harmonic components, it can be expressed as a Fourier series as follows :

Among them, angular frequency ω=2πf, f=50Hz, a ₀ is a DC component, a _i cos(iωt)+b _i sin(iωt) is a sinusoidal signal with a frequency of iω(i=1,2...n) , a _i , b _i are the parameters of the i-th component, the amplitude A _i and the initial phase of the i-th component for:

If the values of the parameters {a ₀ ,a ₁ b ₁ ,...a _i b _i ...a _n b _n } are observed, the amplitude and phase of each frequency component can be calculated, that is, the current Detection of DC magnitude, fundamental and harmonics of signal i _m (t). Taking i _m (t) as the input quantity, a dynamic system is constructed through an integral link, and the first-order state space equation of the system is described as follows:

in, The output is y.

In the case of steady-state operation, the harmonic coefficient {a ₀ a ₁ b ₁ … a _n b _n } changes slowly. In order to observe the values of the coefficients a _i and b _i of each frequency component, each frequency component is used as a new state quantity:

Then the original state space equation is extended to the form of the augmented matrix as follows:

in,

The model is a linear time-varying system. Next, the present invention designs a time-varying Romberg observer for this system to realize online observation of parameters {a ₀ a ₁ b ₁ ... a _n b _n }.

In step (3), the embodiment of the present invention's observation harmonic is as follows:

A time-varying Romberg observer is designed, and the closed-loop state estimation model of the observer is shown in Figure 2. First, construct an identical model with state estimates It can be measured directly, and this man-made system is the state observer. On this basis, by outputting the error to correct the estimated model of the state, so that the estimated value of the state tends to the real state of the system.

Wherein, the weighting matrix L(wt) of the error signal is a matrix of (2n+2)×1,

L(wt)＝[l ₀ l _a0 l _a1 cos(ωt) l _b1 sin(ωt)…l _an cos(nωt) l _bn sin(nωt)] ^T

Among them, l ₀ l _a0 l _a1 ... l _an l _bn are constants whose values determine the convergence speed of each state component of the observer.

define error signal Then the dynamic system of the error is

If it is proved that when t→∞, the state quantity will converge to x, that is, is close to 0, it can be proved that the observer can observe the harmonic component of i _m (t), which proves that the harmonic detection method proposed by the present invention is effective.

Proposition 1 (Designing Lyapunov Functions): Definition D＝{1 1/l _a0 1/l _a1 1/l _b1 …1/l _bn } is a diagonal matrix, take l ₀ >0, l _ai >0, l _bi >0 (i=1,2…n ), then V is a Lyapunov function.

Proof 1: Since D is a positive definite diagonal matrix, then

where V is continuously differentiable and satisfies

(1) V(0)=0, and for all

(2) In R ²⁽ⁿ⁺¹⁾ ,

Therefore, V is a Lyapunov function, Proposition 1 is proved.

Proposition 2 (Observer Convergence Analysis): The State Quantity of the Observer converges to the state quantity x.

Proof 2: Since the error system is a time-varying system, the effectiveness of the observer is proved by the Russell invariant set principle as follows,

define set It can be seen that it is a consistent positive invariant set of the error system.

definition is the largest invariant set in the set S(R).

According to Russell's invariant set principle, when t→∞, every point starting from S(R) converges to E, that is, for any Satisfied

At the same time, for Satisfy

Since the set {1 cos(ωt) sin(ωt)...cos(nωt) sin(nωt)} is linearly independent, the solution to the above equation exists and is unique,

the largest invariant set is a single-element set whose element is the origin, and Proposition 2 is proved.

It should be noted that the Russell invariant set principle provides a proof of the stability of the error system, but does not give an analysis of the convergence rate. Refer to the definition of Lyapunov function It can be seen that the values of l ₀ , _{la ai} , l _bi (i=1,2...n) directly affect the convergence speed of the observer. The shortest convergence time of the observer observing the nth harmonic of the present invention is (2n+1)Ts. When Ts is very small, reasonable selection of l ₀ , _lai , _lbi may obtain better real-time observation effect.

Fig. 3 is the flow chart of the steps of the harmonic detection method provided by the present invention, comprising the following steps:

(1) Acquire current and voltage signals 100 .

The current signal and the voltage signal are sampled separately.

The current signal is then sent to the integration link, see step (2).

The collected voltage signal is converted into a square wave, and the rising edge transition is detected by software. Since the frequency of the current in the power grid is changing, in order to ensure that the frequency information in the algorithm is consistent with the frequency of the measured current, it is necessary to perform the following iterative calculation on the phase θ(k), as shown in Figure 4. Wherein, T0, T1, T2, T3, etc. are four consecutive calculation cycles.

T1: θ(k+1)=w _T0 Ts+θ(k)

T2: θ(k+1)=w _T1 Ts+θ(k)

T3: θ(k+1)=w _T2 Ts+θ(k)

...

First of all, since the frequency changes slowly, the angular frequency calculated at the end of the last power frequency cycle can be used for this cycle (for example, the angular frequency w _T0 calculated at the end of the T0 cycle is used for the T1 cycle), and the phase is accumulated so that The frequency inside the algorithm is approximately equal to the frequency of the signal under test. However, since the existence of errors is unavoidable, the accumulation of errors will be caused during the phase accumulation process. In order to avoid this situation, at each rising edge detected, θ is cleared to eliminate the accumulated errors, that is, in The phase error is cleared at the end of each power frequency cycle.

(2) Pass the current signal through the integration link to establish the augmented state equation 101 .

The current signal i _m (t) is used as the input quantity, and the dynamic system is constructed through an integral link,

where the output is y.

Taking the harmonic coefficient {a ₀ a ₁ b ₁ …a _n b _n } of each frequency component as a new state quantity, construct an augmented state matrix,

in

(3) Build an observer to observe the size 102 of each frequency component.

Initialize each state quantity, at k=0 time, the state quantity Set the parameters l ₀ , l _ai , l _bi , and the calculation period is Ts.

From the observer equation we know:

At time k, x ₁ (k) is obtained after integrating the collected current signal, and the continuous observer is written in a discrete form, and the estimated value of each state at time k+1 is:

(4) Error calculation 103 .

Calculation error When the relative error approaches 1%, it can generally be considered that the error has converged, and the state estimate has tended to the real state of the system, and the parameter Therefore, the frequency components at time k can be calculated, and the amplitude and phase of the fundamental wave and each harmonic can be calculated further. If the relative error does not meet the requirements, the observer enters the next iteration.

In order to make the purpose, features and advantages of the present invention more obvious and understandable, the new method of harmonic detection proposed in the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments. The embodiments are only some embodiments of the present invention, not all embodiments.

The harmonic detection method of the present invention can be applied to all power lines. Since the three-phase uncontrolled rectifier circuit has typical nonlinear load characteristics, the present invention is described by taking the detection of the three-phase uncontrolled rectifier circuit as an example.

Next, the programmable three-phase voltage source is used to simulate the three-phase grid voltage, and by analyzing the harmonic detection effect of the three-phase uncontrolled rectification AC side current signal, the harmonic analysis of the present invention is explained more clearly. For the circuit structure, see Fig. 5 It is an example diagram of the application of the harmonic detection method proposed by the present invention in a three-phase uncontrolled rectification circuit, and the circuit parameters are shown in Table 1.

Table 1 Three-phase uncontrolled rectification circuit parameters

Fig. 6 is an error analysis of the simulated current and the observed current, where the error current is the difference between the simulated current and the observed current. It can be seen that after a brief oscillation, the observed current can quickly track the simulated current. The variation range of the error current is within ±0.1A.

Parameters of each frequency harmonic component Able to converge within one cycle of the observed current.

noise pair parameter There is no influence on the convergence, and it can be stabilized within one power frequency cycle. When the load changes suddenly at 0.15s, can quickly converge to new values.

The observer-based harmonic detection method of the present invention overcomes the limitation that instantaneous reactive power and other detection methods can only measure total harmonic current, and can detect harmonic components of each specified frequency at the same time, as shown in Figures 7-11. Because the simulation uses a three-phase symmetrical circuit, the current harmonics do not contain even-order items, and the value of the 3-fold harmonic is also very small. The picture shows the measured current signal with white noise added, and Figures 8 to 11 show the detected fundamental, 5th, 7th and total harmonic current signals respectively. When the load changes suddenly in 0.15s, the detected currents of each frequency can also transition to a new state smoothly.

Table 2 compares the results of the harmonic detection method proposed by the present invention with the FFT algorithm. The amplitude (peak) of each frequency harmonic component calculated by the FFT algorithm is listed in Table 2. At the same time, the amplitude of each harmonic obtained after observation and calculation It is also recorded in Table 2, and the analysis of each harmonic error is shown in the relative error (Relative error) in Table 2. It can be seen from Table 2 that, compared with the harmonic components obtained by the FFT algorithm, the relative error of this method is less than 0.3%, indicating that the observer algorithm can accurately detect the fundamental and harmonic components in the current. in, is the average value after stabilization.

Table 2 Observer method harmonic analysis of the present invention and Fourier analysis method contrast

The invention proposes a current harmonic detection method based on the input observer theory. This method makes the measured current go through an integral link to form a state quantity, and uses the fundamental wave and each harmonic component as a new state quantity, and designs an observer to observe it, and uses Lyapunov's theorem and Russell's different The variation set principle analyzes the convergence and stability of the observer. Compared with other harmonic detection methods, this method can detect single-circuit current, and can be used to detect harmonics in single-phase, three-phase three-wire system or three-phase four-wire system; it can measure fundamental wave and harmonic components of each frequency; It can quickly and accurately detect harmonics; when the load current changes suddenly, the method has a fast convergence speed and has good dynamic tracking performance; it has good anti-interference performance to noise.

Claims (2)

1. based on the power line current harmonic detection method of input observer theory, it is characterized in that comprising the steps: 1) Sampling the current and grid voltage signals from the power line to obtain the current signal sequence; 2) Pass the sampled current signal through an integral link to obtain the integral of the current signal, and use each frequency component as a new state quantity to establish an augmented state space equation; the sampled grid voltage signal is passed through the AC process The zero detection circuit detects the zero-crossing point of the grid voltage signal; by detecting the rising edge transition, the frequency of the measured signal is obtained by solving, and the accumulated phase error is cleared at the same time; The specific implementation method is as follows: Assuming that im ( _t ) is the periodic current signal to be measured, since im ( _t ) is considered to be composed of the sum of DC, fundamental and harmonic components, it can be expressed as a Fourier series as follows: Among them, angular frequency ω=2πf, f=50Hz, a ₀ is a DC component, a _i cos(iωt)+b _i sin(iωt) is a sinusoidal signal with angular frequency iω, where i=1,2...n , a _i , b _i are the parameters of the i-th component, the amplitude A _i and the initial phase of the i-th component for: If the values of the parameters {a ₀ ,a ₁ b ₁ ,...a _i b _i ...a _n b _n } are observed, then the amplitude and phase of each frequency component are calculated, that is, the current signal i The detection of DC flow, fundamental wave and harmonic of _m (t); taking i _m (t) as an input quantity, a dynamic system is constructed through an integral link, and the first-order state space equation of the system is described as follows: in, output is y; In the case of steady-state work, the harmonic coefficient {a ₀ a ₁ b ₁ …a _n b _n } changes slowly, in order to observe the values of the coefficients a _i and b _i of each frequency component, each frequency component is used as a new state quantity, Then the original state space equation is extended to the form of the augmented matrix as follows: in, For linear time-varying systems, a time-varying Romberg observer is designed to realize online observation of parameters {a ₀ a ₁ b ₁ …a _n b _n }; 3) By designing a Romberg observer and proving the effectiveness of the observer, observe the magnitude of each frequency component. 2. as claimed in claim 1 based on the power line current harmonic detection method of input observer theory, it is characterized in that in step 3) in, the concrete method of each frequency component size of described observation is as follows: To design a time-varying Romberg observer, first, construct an identical model whose state estimate is directly measured, the model is the state observer, on this basis, through the output error to correct the estimated model of the state, so that the estimated value of the state tends to the true state of the system, Among them, the weighting matrix L(ωt) of the error signal is a matrix of (2n+2)×1, L(ωt)＝[l ₀ l _a0 l _a1 cos(ωt)l _b1 sin(ωt)…l _an cos(nωt)l _bn sin(nωt)] ^T Among them, l ₀ l _a0 l _a1 ...l _an l _bn are constants, whose values determine the convergence speed of each state component of the observer; define error signal Then the dynamic system of the error is: If it is proved that when t→∞, the state quantity will converge to x, that is, is close to 0, it can be proved that the Lomberg observer can observe the harmonic component of i _m (t), which means that the proposed harmonic detection method is effective.