CN102420559A - Generator wide-area damping control method based on system identification and genetic algorithm - Google Patents

Abstract

The invention relates to a generator wide area damping control method based on system identification and genetic algorithm, and belongs to the technical field of power system stability analysis. Firstly, a power system simulation model is established, a small-amplitude random disturbance time sequence signal is injected into a generator excitation end of a generator wide-area damping controller, a controlled system model identification module identifies an open-loop controlled system model between the generator excitation end and a wide-area feedback input time sequence signal, a continuous controlled system model is input into a controller parameter solving module by using a genetic algorithm, and parameters of the generator wide-area damping controller are calculated. The feedback signal of the generator wide-area damping controller obtained by the method has good observability on the interval low-frequency oscillation mode. The method can obviously improve the damping ratio of the interval low-frequency oscillation mode and ensure the safe and stable operation of the system. The structure of the generator wide-area damping controller adopted by the invention is the same as that of the traditional PSS, and the generator wide-area damping controller is simple and easy for engineering practice.

Description

Generator wide-area damping control method based on system identification and genetic algorithm

Technical Field

The invention relates to a generator wide area damping control method based on system identification and genetic algorithm, and belongs to the technical field of power system stability analysis.

Background

With interconnection of regional power grids and continuous expansion of the scale of a power system, the problem of low-frequency oscillation in the interval is increasingly prominent, and the safe and stable operation of the power system is seriously threatened.

The conventional method for suppressing low frequency oscillation is to apply an additional damping controller (hereinafter referred to as PSS) to the excitation side of the generator. However, since the PSS uses the local signal as the feedback input signal, the observability of the interval oscillation mode in the signal is poor, and coordination among a plurality of local controllers is difficult, the problem of interval low-frequency oscillation is still not solved effectively in a system with a large number of PSS.

A Wide Area Measurement System (WAMS) can acquire a far-end electric signal in real time by using a synchronous phasor Measurement unit, and provides a new selection scheme for a feedback signal of a generator Wide Area damping controller. The technology for suppressing the interval low-frequency oscillation by using the wide-area signal measured by the wide-area measurement system as the PSS feedback signal is called generator wide-area damping control. The generator wide-area damping controller well solves the problem of observability of the PSS signal, and therefore the generator wide-area damping controller has great potential for restraining low-frequency oscillation of a power system.

The traditional local damping controller design is usually carried out based on a single-machine infinite system, and the phase compensation of the controller is designed through a damping torque theory. In the generator wide-area damping control, the generator wide-area damping controller mounting point and the whole system are connected into a whole by acquiring wide-area feedback signals, and the assumption of a single-machine infinite system is not applicable any more.

Disclosure of Invention

The invention aims to provide a generator wide-area damping control method based on system identification and genetic algorithm, which is used for inhibiting interval low-frequency oscillation of a power system, improving the dynamic stability of the operation of the power system, obviously improving the damping ratio of a low-frequency oscillation mode after a controlled system is put into a generator wide-area damping controller, and ensuring the safe and stable operation of the system.

The invention provides a generator wide area damping control method based on system identification and genetic algorithm, which comprises the following steps:

(1) establishing a power system simulation model, wherein the model comprises equipment in a power system and power system operation parameters, the equipment comprises a generator, a regulator, a transformer, a bus, an alternating current line, a direct current line, a reactive power compensator and a parallel capacitor reactor, and the power system operation parameters comprise power flow and load of the power system; a controlled system model identification module is arranged and used for identifying an open-loop system model controlled by a generator wide-area damping controller; setting a module for solving parameters of the generator wide area damping controller by using a genetic algorithm, wherein the module is used for solving parameters of each link of the generator wide area damping controller; arranging a generator wide-area damping controller module for realizing the generator wide-area damping control;

(2) a generator excitation end of a generator wide-area damping controller is installed in a power system, and a small-amplitude random disturbance timing sequence signal { u } is injected_t}，u_tFor the value of small amplitude random disturbance signal at time T, T is 1, 2 … T_total，T_totalIn order to simulate the total steps, the wide-area feedback input time sequence signal { y) of the generator wide-area damping controller is collected under the condition that the generator wide-area damping controller operates in an open loop mode_tWide-area feedback input timing signal y_tThe number of data is N, T_totalWill signal { u_tAnd { y }_tInputting the data into the model identification module of the controlled system;

(3) the controlled system model identification module identifies an open-loop controlled system model between a generator excitation end provided with a generator wide-area damping controller and a wide-area feedback input time sequence signal, and the specific process comprises the following steps:

(3-1) calculating the wide-area feedback input timing signal { y) according to the following equation_tThe smoothed zero-mean timing signal y_tcp0}：

<math> <mrow> <msub> <mi>y</mi> <mrow> <mi>tcp</mi> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>y</mi> <mi>t</mi> </msub> <mo>-</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>y</mi> <mi>t</mi> </msub> <mo>;</mo> </mrow> </math>

(3-2) setting the model structure of the open-loop controlled system to be U (theta), wherein the parameter vector

Obtaining a controlled system model set for the parameters of the model structure U (theta)

U^*＝{U(θ)|θ∈D_μ}

Where D is the dimension of the parameter θ, D_μA subset of the d-dimensional real number set;

(3-3) smoothing the zero mean value timing signal { y) of step (3-1)_tcp0And the small-amplitude randomly disturbed input signal u_tSubstituting the predicted value into a prediction function, predicting a predicted value at the moment t of injecting a small-amplitude random disturbance timing sequence signal:

<math> <mrow> <mi>U</mi> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>:</mo> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>|</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>u</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> </mrow> </math>

wherein g (y)_t-1，u_t-1θ) is a predictor function;

(3-4) calculating the true value y of the wide-area feedback time sequence signal of the power system at the time t of injecting the small-amplitude random disturbance time sequence signal_tSum and t time predicted value

Error e (t, θ) between:

<math> <mrow> <mi>&epsiv;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>y</mi> <mi>t</mi> </msub> <mo>-</mo> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>|</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>

(3-5) setting a forecast error criterion function of the power system as follows:

J₁(θ)＝Tr[ΛD(θ)]

wherein Λ is a weighted positive definite matrix, <math> <mrow> <mi>D</mi> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>&epsiv;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <msup> <mi>&epsiv;</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>

(3-6) minimizing the prediction error criterion function:

<math> <mrow> <msub> <mover> <mi>&theta;</mi> <mo>^</mo> </mover> <mi>N</mi> </msub> <mo>=</mo> <mi>arg</mi> <mi>min</mi> <msub> <mi>J</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> </mrow> </math>

wherein

Is a function of the prediction error criterion J₁(θ) obtaining a minimum value of the model parameter value; model (model)

Is a controlled system model set U^*The system model is used for enabling the prediction error criterion function to obtain a minimum value.

(3-7) repeating the steps (3-2) to (3-6) M times to obtain M controlled system models

Model set U of_I，

<math> <mrow> <msub> <mi>U</mi> <mi>I</mi> </msub> <mo>=</mo> <mo>{</mo> <mi>U</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&theta;</mi> <mo>^</mo> </mover> <msub> <mi>N</mi> <mi>i</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>|</mo> <mi>i</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>M</mi> <mo>}</mo> </mrow> </math>

Wherein i is 1, 2 …, and M is the total number of times steps (3-2) to (3-6) are repeated;

(3-8) setting the true value y of the wide-area feedback input time sequence signal of the power system at the time t of injecting the small-amplitude random disturbance time sequence signal_tPredicted value at time t

The degree of fit between them is:

<math> <mrow> <mi>fit</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&theta;</mi> <mo>^</mo> </mover> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mn>100</mn> <mo>&times;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msqrt> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>&epsiv;</mi> <msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <msub> <mover> <mi>&theta;</mi> <mo>^</mo> </mover> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>/</mo> <msqrt> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <msub> <mi>y</mi> <mrow> <mi>tcp</mi> <mn>0</mn> </mrow> </msub> <mn>2</mn> </msup> </msqrt> </mrow> </mrow> </math>

obtaining a controlled system model set U according to the fitting degree calculation formula_IThe fitness value of each model in the system is selected as the system model with the highest fitness valueAn open-loop system model between the excitation end of the generator and the wide-area feedback time sequence signal is obtained;

(3-9) converting the open-loop controlled system model between the generator excitation end provided with the generator wide-area damping controller and the wide-area feedback input time sequence signal from a discrete form G (z) to a continuous form G(s) by adopting a zero-order holding conversion method;

(4) inputting the continuous controlled system model obtained in the step (3-9) into the parameter module for solving the controller by the genetic algorithm, and calculating the parameters of the wide area damping controller of the generator, wherein the specific process is as follows:

(4-1) the filtering of the generator wide-area damping controller in the power system adopts band-pass filtering, the band-pass filtering adopts a band-pass filter, and the transfer function expression of the band-pass filter is as follows:

<math> <mrow> <msub> <mi>H</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mfrac> <mn>1</mn> <mi>Q</mi> </mfrac> <msub> <mi>&omega;</mi> <mn>0</mn> </msub> <mo>&CenterDot;</mo> <mi>s</mi> </mrow> <mrow> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>+</mo> <mfrac> <mn>1</mn> <mi>Q</mi> </mfrac> <msub> <mi>&omega;</mi> <mn>0</mn> </msub> <mi>s</mi> <mo>+</mo> <msup> <msub> <mi>&omega;</mi> <mn>0</mn> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>,</mo> </mrow> </math>

where Q is the quality factor of the band pass filter,

Δ ω is the pass band width of the band pass filter, ω₀Is the center frequency, omega, of the band-pass filter₀The value is the low-frequency oscillation frequency of the controlled power system interval;

(4-2) calculating to obtain the phase shift parameter and the gain parameter of the generator wide area damping controller according to the continuous controlled system model obtained in the step (3-9), wherein the specific process is as follows:

(4-2-1) setting the phase shift of the generator wide-area damping controller to adopt three lead-lag links, wherein the gain is a proportionality coefficient, and the expression of the transfer function of the phase shift and the gain is as follows:

<math> <mrow> <msub> <mi>H</mi> <mi>&theta;</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>K</mi> <mo>&times;</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mn>1</mn> </msub> <mi>s</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mn>2</mn> </msub> <mi>s</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>3</mn> </msup> </mrow> </math>

wherein,

transfer function for lead-lag links, T₁To advance the time constant, T₂Is the lag time constant, K is the gain of the controller;

(4-2-2) setting the control targets of the generator wide area damping controller as follows: make the open loop continuously controlled system and the wide area resistor of the generatorThe damping ratio of all oscillation modes of a closed loop system consisting of the damping controller is improved to xi₀；

(4-2-3) according to the control target, establishing an objective function of the parameter module for solving the controller by using the genetic algorithm, and obtaining the objective function of the parameter module for solving the controller by using the genetic algorithm as follows:

<math> <mrow> <mi>min</mi> <mrow> <mo>(</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> (i＝1，2，…，n)

<math> <mrow> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>0.15</mn> <mo>-</mo> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> </mtd> <mtd> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> <mo>&lt;</mo> <msub> <mi>&xi;</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> <mo>&GreaterEqual;</mo> <msub> <mi>&xi;</mi> <mn>0</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math>

wherein: n represents the number of oscillation modes, xi, of the closed loop system_iRepresents the damping ratio of the ith oscillation mode;

(4-4) setting 0 < T₁＜1，0＜T₂< 1 and 0 < K < 10 as constraints of the objective function;

(4-5) setting calculation parameters of the genetic algorithm: the number of the populations is 200, the value range of the initial population is 0-1, the number of excellent individuals copied to the next generation is 20, the filial generation individuals are selected by adopting a championship method, the crossing proportion of the newly generated filial generation individuals is 0.8, and the variation adopts a self-adaptive mode;

(4-6) setting a DC blocking time constant of the generator wide area damping controller: t is_w4, the output upper limit value of the generator wide-area damping controller is +0.1, the output lower limit value is-0.1, and the optimal solution of the target function of the controller parameter module solved by the genetic algorithm, namely the lead time constant T of the generator wide-area damping controller is solved according to the calculation parameters of the genetic algorithm and the constraint conditions of the target function₁Hysteresis time constant T₂And an optimal value of the gain K of the controller.

The invention provides a generator wide area damping control method based on system identification and genetic algorithm, which has the advantages that:

1. the feedback signal of the generator wide-area damping controller obtained by the method is a real-time wide-area signal measured by a wide-area measurement system, and the wide-area signal has good observability on an interval low-frequency oscillation mode.

2. By adopting the control method, the damping ratio of the inter-low-frequency oscillation mode in the power system can be obviously improved after the controlled system is put into the generator wide-area damping controller, and the safe and stable operation of the power system is ensured.

3. The structure of the generator wide-area damping controller adopted by the invention is the same as that of the traditional PSS, and the generator wide-area damping controller is simple and easy for engineering practice.

Drawings

FIG. 1 is a block flow diagram of the method of the present invention.

FIG. 2 is a flow chart of generator wide area damping control in the method of the present invention.

FIG. 3 is a block diagram of a closed loop system consisting of an open loop continuous controlled system and a generator wide area damping controller according to an embodiment of the method of the present invention.

FIG. 4 is a schematic diagram of a small amplitude random disturbance signal at the excitation end of a generator according to an embodiment of the method of the present invention.

FIG. 5 is a schematic diagram of the wide-area feedback input timing signal when the generator wide-area damping controller operates in an open loop according to an embodiment of the method of the present invention.

Fig. 6 is a diagram illustrating an effect of a change of an active power curve of a tie line before and after a wide-area damping controller of a generator is turned on when a three-phase instantaneous short-circuit fault occurs in the tie line in an interval of a power system in an embodiment of a method of the present invention.

Detailed Description

The invention provides a generator wide area damping control method based on system identification and genetic algorithm, a flow chart of which is shown in figure 1, and the specific process is as follows:

(1) establishing a power system simulation model, wherein the model comprises equipment in a power system and power system operation parameters, the equipment comprises a generator, a regulator, a transformer, a bus, an alternating current line, a direct current line, a reactive power compensator and a parallel capacitor reactor, and the power system operation parameters comprise power flow and load of the power system; a controlled system model identification module is arranged and used for identifying an open-loop system model controlled by a generator wide-area damping controller; setting a module for solving parameters of the generator wide area damping controller by using a genetic algorithm, wherein the module is used for solving parameters of each link of the generator wide area damping controller; and arranging a generator wide-area damping controller module for realizing the generator wide-area damping control.

(2) A generator excitation end of a generator wide-area damping controller is installed in a power system, and a small-amplitude random disturbance timing sequence signal { u } is injected_t}，u_tFor the value of small amplitude random disturbance signal at time T, T is 1, 2 … T_total，T_totalIn order to simulate the total steps, the wide-area feedback input time sequence signal { y) of the generator wide-area damping controller is collected under the condition that the generator wide-area damping controller operates in an open loop mode_tWide-area feedback input timing signal y_tThe number of data is N, T_totalWill signal { u_tAnd { y }_tInputting the data into the model identification module of the controlled system;

if the interval low-frequency oscillation mode of the system is to be identified, the small-amplitude fluctuation excitation signal should be distributed uniformly in the frequency range smaller than 2Hz, and the system is disturbed equally. Therefore, a small random disturbance signal injected into the excitation end of the generator in the simulation power system is generated by small Gaussian white noise through a second-order low-pass filter with the cut-off frequency of 2 Hz.

The wide area feedback input time sequence signal collected by the invention is an interval bus frequency difference signal.

(3) The controlled system model identification module identifies an open-loop controlled system model between a generator excitation end provided with a generator wide-area damping controller and a wide-area feedback input time sequence signal, and the specific process comprises the following steps:

(3-1) calculating the wide-area feedback input timing signal { y) according to the following equation_tThe smoothed zero-mean timing signal y_tcp0}：

<math> <mrow> <msub> <mi>y</mi> <mrow> <mi>tcp</mi> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>y</mi> <mi>t</mi> </msub> <mo>-</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>y</mi> <mi>t</mi> </msub> <mo>;</mo> </mrow> </math>

(3-2) setting the model structure of the open-loop controlled system to be U (theta), wherein the parameter vector

Obtaining a controlled system model set for the parameters of the model structure U (theta)

U^*＝{U(θ)|θ∈D_μ}

Where D is the dimension of the parameter θ, D_μA subset of the d-dimensional real number set;

the model structure usually selected is BJ model, OE model, ARX model, state space model, etc.

(3-3) smoothing the zero mean value timing signal { y) of step (3-1)_tcp0And the small-amplitude randomly disturbed input signal u_tSubstituting the predicted value into a prediction function, predicting a predicted value at the moment t of injecting a small-amplitude random disturbance timing sequence signal:

<math> <mrow> <mi>U</mi> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>:</mo> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>|</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>u</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> </mrow> </math>

wherein g (y)_t-1，u_t-1θ) is a predictor function;

(3-4) calculating the true value y of the wide-area feedback time sequence signal of the power system at the time t of injecting the small-amplitude random disturbance time sequence signal_tSum and t time predicted value

Error e (t, θ) between:

<math> <mrow> <mi>&epsiv;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>y</mi> <mi>t</mi> </msub> <mo>-</mo> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>|</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>

(3-5) setting a forecast error criterion function of the power system as follows:

J₁(θ)＝Tr[ΛD(θ)]

wherein Λ is a weighted positive definite matrix, <math> <mrow> <mi>D</mi> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>&epsiv;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <msup> <mi>&epsiv;</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>

(3-6) minimizing the prediction error criterion function:

<math> <mrow> <msub> <mover> <mi>&theta;</mi> <mo>^</mo> </mover> <mi>N</mi> </msub> <mo>=</mo> <mi>arg</mi> <mi>min</mi> <msub> <mi>J</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> </mrow> </math>

wherein

Is a function of the prediction error criterion J₁(θ) obtaining a minimum value of the model parameter value; model (model)

Is a controlled system model set U^*The system model is used for enabling the prediction error criterion function to obtain a minimum value.

The smaller the value of the prediction error criterion function is, the closer the prediction value is to the true value, and the closer the model parameter value is to the true model is.

(3-7) repeating the steps (3-2) to (3-6) M times to obtain M controlled system models

Model set U of_I，

<math> <mrow> <msub> <mi>U</mi> <mi>I</mi> </msub> <mo>=</mo> <mo>{</mo> <mi>U</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&theta;</mi> <mo>^</mo> </mover> <msub> <mi>N</mi> <mi>i</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>|</mo> <mi>i</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>M</mi> <mo>}</mo> </mrow> </math>

Where i is 1, 2 …, and M is the total number of times steps (3-2) to (3-6) are repeated.

(3-8) setting the true value y of the wide-area feedback input time sequence signal of the power system at the time t of injecting the small-amplitude random disturbance time sequence signal_tPredicted value at time t

The degree of fit between them is:

<math> <mrow> <mi>fit</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&theta;</mi> <mo>^</mo> </mover> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mn>100</mn> <mo>&times;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msqrt> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>&epsiv;</mi> <msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <msub> <mover> <mi>&theta;</mi> <mo>^</mo> </mover> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>/</mo> <msqrt> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <msub> <mi>y</mi> <mrow> <mi>tcp</mi> <mn>0</mn> </mrow> </msub> <mn>2</mn> </msup> </msqrt> </mrow> </mrow> </math>

obtaining a controlled system model set U according to the fitting degree calculation formula_ISelecting a system model with the highest fitting degree value as an open-loop system model between a generator excitation end and a wide-area feedback time sequence signal according to the fitting degree value of each model; the higher the fitness value, the better the model can describe the controlled system.

(3-9) converting the open-loop controlled system model between the generator excitation end provided with the generator wide-area damping controller and the wide-area feedback input time sequence signal from a discrete form G (z) to a continuous form G(s) by adopting a zero-order holding conversion method;

(4) inputting the continuous controlled system model obtained in the step (3-9) into the module for solving the controller parameter by using the genetic algorithm, and calculating the parameter of the generator wide area damping controller, wherein the structure diagram of the wide area damping controller is shown in fig. 2, and the specific process is as follows:

(4-1) the filtering of the generator wide-area damping controller in the power system adopts band-pass filtering, the band-pass filtering adopts a band-pass filter, and the transfer function expression of the band-pass filter is as follows:

<math> <mrow> <msub> <mi>H</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mfrac> <mn>1</mn> <mi>Q</mi> </mfrac> <msub> <mi>&omega;</mi> <mn>0</mn> </msub> <mo>&CenterDot;</mo> <mi>s</mi> </mrow> <mrow> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>+</mo> <mfrac> <mn>1</mn> <mi>Q</mi> </mfrac> <msub> <mi>&omega;</mi> <mn>0</mn> </msub> <mi>s</mi> <mo>+</mo> <msup> <msub> <mi>&omega;</mi> <mn>0</mn> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>,</mo> </mrow> </math>

where Q is the quality factor of the band pass filter,

Δ ω is the pass band width of the band pass filter, ω₀Is the center frequency of the band-pass filter; omega₀The value is the low-frequency oscillation frequency of the controlled system interval.

(4-2) calculating to obtain the phase shift parameter and the gain parameter of the generator wide area damping controller according to the continuous controlled system model obtained in the step (3-9), wherein the specific process is as follows:

(4-2-1) setting the phase shift of the generator wide-area damping controller to adopt three lead-lag links, wherein the gain is a proportionality coefficient, and the expression of the transfer function of the phase shift and the gain is as follows:

<math> <mrow> <msub> <mi>H</mi> <mi>&theta;</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>K</mi> <mo>&times;</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mn>1</mn> </msub> <mi>s</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mn>2</mn> </msub> <mi>s</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>3</mn> </msup> </mrow> </math>

wherein,transfer function for lead-lag links, T₁To advance the time constant, T₂K is the gain of the controller for the lag time constant.

(4-2-2) setting the control targets of the generator wide area damping controller as follows: the damping ratio of all oscillation modes of a closed loop system consisting of the open loop continuous controlled system and the generator wide area damping controller is improved to xi₀；

(4-2-3) according to the control target, establishing an objective function of the parameter module for solving the controller by using the genetic algorithm, and obtaining the objective function of the parameter module for solving the controller by using the genetic algorithm as follows:

<math> <mrow> <mi>min</mi> <mrow> <mo>(</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> (i＝1，2，…，n)

<math> <mrow> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>0.15</mn> <mo>-</mo> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> </mtd> <mtd> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> <mo>&lt;</mo> <msub> <mi>&xi;</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> <mo>&GreaterEqual;</mo> <msub> <mi>&xi;</mi> <mn>0</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math>

wherein: n represents the number of oscillation modes, xi, of the closed loop system_iRepresenting the i-th oscillation mode damping ratio.

(4-4) given 0 < T₁＜1，0＜T₂< 1 and 0 < K < 10 as constraints of the objective function.

(4-5) setting calculation parameters of the genetic algorithm: the population number is 200, the value range of the initial population is 0-1, the number of excellent individuals copied to the next generation is 20, the filial generation individuals are selected by adopting a championship method, the crossing proportion of the newly generated filial generation individuals is 0.8, and the variation adopts a self-adaptive mode.

(4-6) setting a DC blocking time constant of the generator wide area damping controller: t is_w4, the output upper limit value of the generator wide-area damping controller is +0.1, the output lower limit value is-0.1, and the optimal solution of the target function of the controller parameter module solved by the genetic algorithm, namely the lead time constant T of the generator wide-area damping controller is solved according to the calculation parameters of the genetic algorithm and the constraint conditions of the target function₁Hysteresis time constant T₂And an optimal value of the gain K of the controller.

The method comprises a simulation power system module, a controlled system model identification module and a controller parameter calculation module by using a genetic algorithm. The basic analysis process is that a small-amplitude random disturbance signal is injected into a generator excitation end provided with a generator wide-area damping controller in a simulation power system, a wide-area feedback input signal of the generator wide-area damping controller under an open-loop condition is collected, the small-amplitude disturbance signal and the wide-area feedback input signal are input into a controlled system model identification module as analysis objects, an open-loop system model between the generator excitation end provided with the generator wide-area damping controller and a wide-area feedback input sequential signal is obtained through identification, and generator wide-area damping controller parameters are optimized through a genetic algorithm solving controller parameter module according to a control target.

FIG. 2 shows a generator wide-area damping controller structure adopted by the method of the invention. Wherein H_θ(s) is the phase-shift and gain-link transfer function structure, H_fAnd(s) is a band-pass filtering link transfer function structure. K is the gain, T₁、T₂Respectively a lead time constant and a lag time constant of the phase shifting link. Omega₀And Q are the passband center frequency and the quality factor of the bandpass filter respectively.

The method combines system identification and genetic algorithm, and optimally designs parameters of a phase shift link and a gain link in the generator wide-area damping controller, so that the damping ratio of a controlled power system meets the requirement after the generator wide-area damping controller is put into use.

The following is one embodiment of the method of the present invention:

the generator wide-area damping control is implemented at the excitation end of the generator, and the purpose is to suppress interval low-frequency oscillation existing in different areas in a power grid. The wide-area feedback signal is selected from a bus frequency difference signal of two places. The designed generator wide area damping controller adopts a traditional generator PSS structure, as shown in figure 2. When a generator wide-area damping controller is not added, a three-phase instantaneous short-circuit fault is applied to a tie line in a power grid system interval, an active power curve of the tie line is measured, and a prony analysis shows that the frequency of an interval low-frequency oscillation mode is about 0.60Hz, and the damping ratio is 3.1%. The aim of the wide-area damping control of the generator is to improve the damping ratio of the low-frequency oscillation mode of the system to more than 15%.

Step 1: and injecting a small-amplitude random disturbance signal into the simulation power system, and collecting a bus frequency difference signal of two places as an open-loop wide-area feedback input signal of the generator wide-area damping controller.

The small random disturbance signal injected into the excitation end of the generator is obtained by Gaussian white noise through a low-pass filter with the cut-off frequency of 2 Hz. FIG. 4 is a schematic diagram of a small random disturbance signal injected into the excitation end of the generator. And collecting bus frequency difference signals of two places in the power system as open-loop wide-area feedback input signals of the generator wide-area damping controller. Fig. 5 shows the bus frequency difference signal between two locations.

Step 2: and identifying an open-loop system model between the generator excitation end and the bus frequency difference signals of the two places.

Firstly, mean value removing processing is carried out on the two-place bus frequency difference signals, and the processed two-place bus frequency difference signals and small-amplitude random disturbance signals are input into a controlled system model identification module. And aiming at a plurality of different model structures, a plurality of controlled system models are identified by using a controlled system model identification module, the fitting degree of each controlled system model is calculated, and the model with the maximum fitting degree value is selected as the controlled system model. Converting the model from a discrete form to a continuous form to obtain a continuous transfer function expression of a controlled system:

$G\left(s\right)=\frac{0.01035{\mathrm{<figure-callout\; id="4"\; label="s"\; filenames="HDA0000104445070000021.png,HDA0000104445070000022.png"\; state="\{\{state\}\}">s</figure-callout>}}^4+0.07688s^3-0.8249s^2-5.179s-6.262}{{\mathrm{<figure-callout\; id="4"\; label="s"\; filenames="HDA0000104445070000021.png,HDA0000104445070000022.png"\; state="\{\{state\}\}">s</figure-callout>}}^4+5.075s^3+67.08{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000104445070000021.png,HDA0000104445070000022.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+84.39s+736}$

and step 3: and optimizing parameters of each link of the generator wide area damping controller by adopting a genetic algorithm based on the controlled system model obtained by identification.

And extracting the cloud and precious oscillation mode component in the cloud and precious frequency difference feedback signal by using a band-pass filter. The quality factor Q of the band-pass filter is set to 1.5, the center frequency omega₀Set to the yunrong low frequency oscillation mode frequency of 0.58 Hz. According to the band-pass filter transfer function expression:

<math> <mrow> <msub> <mi>H</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mfrac> <mn>1</mn> <mi>Q</mi> </mfrac> <msub> <mi>&omega;</mi> <mn>0</mn> </msub> <mo>&CenterDot;</mo> <mi>s</mi> </mrow> <mrow> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>+</mo> <mfrac> <mn>1</mn> <mi>Q</mi> </mfrac> <msub> <mi>&omega;</mi> <mn>0</mn> </msub> <mi>s</mi> <mo>+</mo> <msup> <msub> <mi>&omega;</mi> <mn>0</mn> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>,</mo> </mrow> </math>

the available controller bandpass filter transfer function is:

$H_p\left(s\right)=\frac{2.43s}{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000104445070000021.png,HDA0000104445070000022.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2.43s+13.28}$

and (3) forming a closed-loop control system by using the identified transfer function G(s) of the controlled system and the transfer function H(s) of the generator wide-area damping controller, as shown in fig. 3.

The parameter to be solved by the generator wide-area damping controller is a lead time constant T₁Hysteresis time constant T₂And a gain K, calculating the optimal solution of the parameters meeting the generator wide-area damping control target by using a genetic algorithm

According to the aim of the wide-area damping control of the generator, the damping ratio of the low-frequency oscillation mode of the system is improved to 15%, and a genetic algorithm objective function is given:

<math> <mrow> <mi>min</mi> <mrow> <mo>(</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> (i＝1，2，…，n)

<math> <mrow> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>0.15</mn> <mo>-</mo> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> </mtd> <mtd> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> <mo>&lt;</mo> <mn>15</mn> <mo>%</mo> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> <mo>&GreaterEqual;</mo> <mn>15</mn> <mo>%</mo> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

giving the lead time constant T of the parameter to be optimized₁Hysteresis time constant T₂And the value range of the gain: 0 < T₁＜1，0＜T₂< 1 and 0 < K < 10 as constraints of the objective function.

Setting calculation parameters of a genetic algorithm: the population number is 200, the value range of the initial population is 0-1, the number of excellent individuals copied to the next generation is 20, the filial generation individuals are selected by adopting a championship method, the crossing proportion of the newly generated filial generation individuals is 0.8, and the variation adopts a self-adaptive mode.

Setting a DC blocking time constant of the generator wide area damping controller: t is_w4, the output upper limit value of the generator wide-area damping controller is +0.1, the output lower limit value is-0.1, and the optimal solution of the target function of the controller parameter module solved by the genetic algorithm, namely the lead time constant T of the generator wide-area damping controller is solved according to the calculation parameters of the genetic algorithm and the constraint conditions of the target function₁0.020, lag time constant T₂0.019 and the gain K of the controller-5.91.

And 4, step 4: the designed generator wide-area damping controller is put into a power grid system, the effect of the amplitude limiting link on the output of the controller is considered, and the gain of the controller is adjusted, so that the energy output of the controller is in a proper range.

The genetic algorithm optimizes the controller gain to-5.91, but under the gain, the controller output seriously exceeds the amplitude limit, and the controller gain is adjusted to-3.

The adjusted generator wide-area damping controller is put into a power grid system, a three-phase instantaneous short-circuit fault is applied to an interval tie line, a comparison graph of active power curve changes of the tie line before and after the generator wide-area damping controller is put into the interval tie line is shown in fig. 6, and the system damping ratio can be improved from 3.2% to 22.2% through prony analysis.

Claims (1)

1. A generator wide area damping control method based on system identification and genetic algorithm is characterized by comprising the following steps:

(1) establishing a power system simulation model, wherein the model comprises equipment in a power system and power system operation parameters, the equipment comprises a generator, a regulator, a transformer, a bus, an alternating current line, a direct current line, a reactive power compensator and a parallel capacitor reactor, and the power system operation parameters comprise power flow and load of the power system; a controlled system model identification module is arranged and used for identifying an open-loop system model controlled by a generator wide-area damping controller; setting a module for solving parameters of the generator wide area damping controller by using a genetic algorithm, wherein the module is used for solving parameters of each link of the generator wide area damping controller; arranging a generator wide-area damping controller module for realizing the generator wide-area damping control;

(2) a generator excitation end of a generator wide-area damping controller is installed in a power system, and a small-amplitude random disturbance timing sequence signal { u } is injected_t}，u_tFor the value of small amplitude random disturbance signal at time T, T is 1, 2 … T_total，T_totalIn order to simulate the total steps, the wide-area feedback input time sequence signal { y) of the generator wide-area damping controller is collected under the condition that the generator wide-area damping controller operates in an open loop mode_tWide-area feedback input timing signal y_tThe number of data is N, T_totalWill signal { u_tAnd { y }_tInputting the data into the model identification module of the controlled system;

(3) the controlled system model identification module identifies an open-loop controlled system model between a generator excitation end provided with a generator wide-area damping controller and a wide-area feedback input time sequence signal, and the specific process comprises the following steps:

(3-1) calculating the wide-area feedback input timing signal { y) according to the following equation_tThe smoothed zero-mean timing signal y_tcp0}：

<math> <mrow> <msub> <mi>y</mi> <mrow> <mi>tcp</mi> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>y</mi> <mi>t</mi> </msub> <mo>-</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>y</mi> <mi>t</mi> </msub> <mo>;</mo> </mrow> </math>

(3-2) setting the model structure of the open-loop controlled system to be U (theta), wherein the parameter vector

Obtaining a controlled system model set for the parameters of the model structure U (theta)

U^*＝{U(θ)|θ∈D_μ}

Where D is the dimension of the parameter θ, D_μA subset of the d-dimensional real number set;

(3-3) smoothing the zero mean value timing signal { y) of step (3-1)_tcp0And the small-amplitude randomly disturbed input signal u_tSubstituting the predicted value into a prediction function, predicting a predicted value at the moment t of injecting a small-amplitude random disturbance timing sequence signal:

<math> <mrow> <mi>U</mi> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>:</mo> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>|</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>u</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> </mrow> </math>

wherein g (y)_t-1，u_t-1θ) is a predictor function;

(3-4) calculating the true value y of the wide-area feedback time sequence signal of the power system at the time t of injecting the small-amplitude random disturbance time sequence signal_tSum and t time predicted value

Error e (t, θ) between:

<math> <mrow> <mi>&epsiv;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>y</mi> <mi>t</mi> </msub> <mo>-</mo> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>|</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>

(3-5) setting a forecast error criterion function of the power system as follows:

J₁(θ)＝Tr[ΛD(θ)]

wherein Λ is a weighted positive definite matrix, <math> <mrow> <mi>D</mi> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>&epsiv;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <msup> <mi>&epsiv;</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>

(3-6) minimizing the prediction error criterion function:

<math> <mrow> <msub> <mover> <mi>&theta;</mi> <mo>^</mo> </mover> <mi>N</mi> </msub> <mo>=</mo> <mi>arg</mi> <mi>min</mi> <msub> <mi>J</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> </mrow> </math>

whereinIs a function of the prediction error criterion J₁(θ) obtaining a minimum value of the model parameter value; model (model)

Is a controlled system model set U^*The system model is used for enabling the prediction error criterion function to obtain a minimum value.

(3-7) repeating the steps (3-2) to (3-6) M times to obtain M controlled system models

Model set U of_I，

<math> <mrow> <msub> <mi>U</mi> <mi>I</mi> </msub> <mo>=</mo> <mo>{</mo> <mi>U</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&theta;</mi> <mo>^</mo> </mover> <msub> <mi>N</mi> <mi>i</mi> </msub> </msub> <mo>)</mo> </mrow> <mo>|</mo> <mi>i</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>M</mi> <mo>}</mo> </mrow> </math>

Wherein i is 1, 2 …, and M is the total number of times steps (3-2) to (3-6) are repeated;

(3-8) setting the true value y of the wide-area feedback input time sequence signal of the power system at the time t of injecting the small-amplitude random disturbance time sequence signal_tPredicted value at time t

The degree of fit between them is:

<math> <mrow> <mi>fit</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&theta;</mi> <mo>^</mo> </mover> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mn>100</mn> <mo>&times;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msqrt> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>&epsiv;</mi> <msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <msub> <mover> <mi>&theta;</mi> <mo>^</mo> </mover> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>/</mo> <msqrt> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <msub> <mi>y</mi> <mrow> <mi>tcp</mi> <mn>0</mn> </mrow> </msub> <mn>2</mn> </msup> </msqrt> </mrow> </mrow> </math>

obtaining a controlled system model set U according to the fitting degree calculation formula_ISelecting a system model with the highest fitting degree value as an open-loop system model between a generator excitation end and a wide-area feedback time sequence signal according to the fitting degree value of each model;

(3-9) converting the open-loop controlled system model between the generator excitation end provided with the generator wide-area damping controller and the wide-area feedback input time sequence signal from a discrete form G (z) to a continuous form G(s) by adopting a zero-order holding conversion method;

(4) inputting the continuous controlled system model obtained in the step (3-9) into the parameter module for solving the controller by the genetic algorithm, and calculating the parameters of the wide area damping controller of the generator, wherein the specific process is as follows:

(4-1) the filtering of the generator wide-area damping controller in the power system adopts band-pass filtering, the band-pass filtering adopts a band-pass filter, and the transfer function expression of the band-pass filter is as follows:

<math> <mrow> <msub> <mi>H</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mfrac> <mn>1</mn> <mi>Q</mi> </mfrac> <msub> <mi>&omega;</mi> <mn>0</mn> </msub> <mo>&CenterDot;</mo> <mi>s</mi> </mrow> <mrow> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>+</mo> <mfrac> <mn>1</mn> <mi>Q</mi> </mfrac> <msub> <mi>&omega;</mi> <mn>0</mn> </msub> <mi>s</mi> <mo>+</mo> <msup> <msub> <mi>&omega;</mi> <mn>0</mn> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>,</mo> </mrow> </math>

where Q is the quality factor of the band pass filter,

Δ ω is the pass band width of the band pass filter, ω₀Is the center frequency, omega, of the band-pass filter₀The value is the low-frequency oscillation frequency of the controlled power system interval;

(4-2) calculating to obtain the phase shift parameter and the gain parameter of the generator wide area damping controller according to the continuous controlled system model obtained in the step (3-9), wherein the specific process is as follows:

(4-2-1) setting the phase shift of the generator wide-area damping controller to adopt three lead-lag links, wherein the gain is a proportionality coefficient, and the expression of the transfer function of the phase shift and the gain is as follows:

<math> <mrow> <msub> <mi>H</mi> <mi>&theta;</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>K</mi> <mo>&times;</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mn>1</mn> </msub> <mi>s</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mn>2</mn> </msub> <mi>s</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>3</mn> </msup> </mrow> </math>

wherein,transfer function for lead-lag links, T₁To advance the time constant, T₂Is the lag time constant, K is the gain of the controller;

(4-2-2) setting the control targets of the generator wide area damping controller as follows: the damping ratio of all oscillation modes of a closed loop system consisting of the open loop continuous controlled system and the generator wide area damping controller is improved to xi₀；

(4-2-3) according to the control target, establishing an objective function of the parameter module for solving the controller by using the genetic algorithm, and obtaining the objective function of the parameter module for solving the controller by using the genetic algorithm as follows:

<math> <mrow> <mi>min</mi> <mrow> <mo>(</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> (i＝1，2，…，n)

<math> <mrow> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>0.15</mn> <mo>-</mo> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> </mtd> <mtd> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> <mo>&lt;</mo> <msub> <mi>&xi;</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>&xi;</mi> <mi>i</mi> </msub> <mo>&GreaterEqual;</mo> <msub> <mi>&xi;</mi> <mn>0</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math>

wherein: n represents the number of oscillation modes, xi, of the closed loop system_iRepresents the damping ratio of the ith oscillation mode;

(4-4) setting 0 < T₁＜1，0＜T₂< 1 and 0 < K < 10 as constraints of the objective function;

(4-5) setting calculation parameters of the genetic algorithm: the number of the populations is 200, the value range of the initial population is 0-1, the number of excellent individuals copied to the next generation is 20, the filial generation individuals are selected by adopting a championship method, the crossing proportion of the newly generated filial generation individuals is 0.8, and the variation adopts a self-adaptive mode;

(4-6) setting a DC blocking time constant of the generator wide area damping controller: t is_w4, the output upper limit value of the generator wide-area damping controller is +0.1, the output lower limit value is-0.1, and the optimal solution of the target function of the controller parameter module solved by the genetic algorithm, namely the lead time constant T of the generator wide-area damping controller is solved according to the calculation parameters of the genetic algorithm and the constraint conditions of the target function₁Hysteresis time constant T₂And an optimal value of the gain K of the controller.

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