CN102420559B - 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. First, a power system simulation model is established, and a small random disturbance timing signal is injected into the generator excitation terminal of the generator wide-area damping controller. The controlled system model identification module identifies the opening and closing between the generator excitation terminal and the wide-area feedback input timing The continuous controlled system model is input to the module of solving the controller parameters with the genetic algorithm to calculate the parameters of the generator wide-area damping controller. The feedback signal of the wide-area damping controller of the generator obtained by the method of the invention has good observability for the interval low-frequency oscillation mode. The method can significantly improve the damping ratio of the interval low-frequency oscillation mode, thereby ensuring the safe and stable operation of the system. The structure of the generator wide-area damping controller adopted in the present invention is the same as that of the traditional PSS, which 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 technique

With the interconnection of regional power grids and the continuous expansion of the scale of the power system, the problem of interval low-frequency oscillation has become increasingly prominent, which seriously threatens the safe and stable operation of the power system.

The traditional way to suppress low-frequency oscillation is to apply an additional damping controller (Power Stability Stabilizer, hereinafter referred to as PSS) on the excitation side of the generator. However, because PSS uses local signals as feedback input signals, the observability of the interval oscillation mode in the signal is poor, and the coordination among multiple local controllers is also difficult. Therefore, in a large number of PSS installed systems, the interval low-frequency oscillation problem still exists. cannot be effectively resolved.

The Wide Area Measurement System (Wide Area Measurement System, hereinafter referred to as WAMS) uses the synchrophasor measurement unit to collect remote electrical signals in real time, providing a new selection scheme for the feedback signal of the generator wide area damping controller. This technology of using the wide-area signal measured by the wide-area measurement system as the PSS feedback signal to suppress the interval low-frequency oscillation is called generator wide-area damping control. The generator wide-area damping controller solves the problem of PSS signal observability very well, so it has great potential for suppressing low-frequency oscillation of power system.

The traditional local damping controller design is often based on a single-machine infinite system, and the phase compensation of the controller is designed through the damping torque theory. In the generator wide-area damping control, the installation point of the generator wide-area damping controller is connected with the entire system as a whole by collecting wide-area feedback signals, and the assumption of a single-machine infinite system is no longer applicable.

Contents of the invention

The purpose of the present invention is to propose a generator wide-area damping control method based on system identification and genetic algorithm, which is used to suppress the interval low-frequency oscillation of the power system, improve the dynamic stability of the power system operation, and make the controlled system power generation After the wide-area damping controller is installed, the damping ratio of the low-frequency oscillation mode is significantly improved to ensure the safe and stable operation of the system.

The generator wide-area damping control method based on system identification and genetic algorithm proposed by the present invention includes the following steps:

(1) Establish a power system simulation model, which includes the equipment in the power system and the operating parameters of the power system. The equipment is generators, regulators, transformers, busbars, AC lines, DC lines, reactive power compensators and shunt capacitor reactors , the operating parameters of the power system are the power flow and load of the power system; set up a controlled system model identification module to identify the open-loop system model controlled by the generator wide-area damping controller; set up a genetic algorithm to solve the generator wide-area damping The controller parameter module is used to obtain the parameters of each link of the generator wide-area damping controller; a generator wide-area damping controller module is set to realize the generator wide-area damping control;

(2) Install the generator excitation terminal of the generator wide-area damping controller in the power system, inject a small random disturbance timing signal {u _t }, u _t is the value of the small random disturbance signal at time t, t=1,2 …T _total , T _total is the total number of simulation steps. In the open-loop operation of the generator wide-area damping controller, the wide-area feedback input timing signal {y _t } of the generator wide-area damping controller is collected, and the wide-area feedback input The number of data of the time series signal {y _t } is N, N=T _total , input the signals {u _t } and {y _t } into the above-mentioned model identification module of the controlled system;

(3) The controlled system model identification module identifies the open-loop controlled system model between the generator excitation terminal installed with the generator wide-area damping controller and the wide-area feedback input timing signal. The specific process includes the following steps:

(3-1) Calculate the stationary zero-mean time-series signal {y _tcp0 } of the above wide-area feedback input time-series signal {y _t } as follows:

${\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="0"\; label="y\; tcp"\; filenames="HDA0000104445070000021.png,HDA0000104445070000022.png"\; state="\{\{state\}\}">y</figure-callout></span><figure-callout\; id="0"\; label="y\; tcp"\; filenames="HDA0000104445070000021.png,HDA0000104445070000022.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; ;</span>$

(3-2) Set the model structure of the above open-loop controlled system as U(θ), where the parameter vector is the parameter of the model structure U(θ), and the model set of the controlled system is obtained

U ^* ＝{U(θ)|θ∈D _μ }

where d is the dimension of the parameter θ, and D _μ is a subset of the d-dimensional real number set;

(3-3) Substitute the stationary zero-mean time-series signal {y _tcp0 } of step (3-1) and the above-mentioned small random disturbance input signal {u _t } into the prediction function, and predict the forecast value injected into the small random disturbance time-series signal at time t :

$\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; :</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>$

Where g(y _t-1 , u _t-1 , θ) is the forecast function;

之间的误差ε(t，θ)：(3-4) Calculate the real value y t of the power system wide-area feedback time-series signal injected with a small random disturbance time-series signal at time _t and the predicted value at time t

The error between ε(t, θ):

$\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

(3-5) Set the forecast error criterion function of the power system as:

J ₁ (θ)=Tr[ΛD(θ)]

Among them, Λ is a weighted positive definite matrix, $\mathrm{D.}\left(\mathrm{\&theta;}\right)=\frac{1}{N}\underset{t=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&epsiv;}(t,\mathrm{\&theta;}){\mathrm{\&epsiv;}}^T(t,\mathrm{\&theta;});$

(3-6) Minimize the above forecast error criterion function:

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; min</span>}{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>$

是使预报误差准则函数J₁(θ)取得最小值的模型参数值；模型

为被控系统模型集合U^*中使得预报误差准则函数取得极小值的系统模型。in

is the model parameter value that makes the forecast error criterion function J ₁ (θ) obtain the minimum value; the model

It is the system model that makes the prediction error criterion function obtain the minimum value in the controlled system model set U ^* .

的模型集合U_I，(3-7) Repeat steps (3-2) to (3-6) M times to obtain M controlled system models

model set U _I ,

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; \}</span>$

Wherein i=1, 2..., M, M is the total number of times of repeating step (3-2)～step (3-6);

之间的拟合度为：(3-8) Set the real value y t of the power system wide-area feedback input timing signal injected into the small random disturbance timing signal at time _t and the predicted value at time t

The fit between is:

$\mathrm{<span\; class="notranslate">\; fit</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 100</span>}<span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; /</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="0"\; label="y\; tcp"\; filenames="HDA0000104445070000021.png,HDA0000104445070000022.png"\; state="\{\{state\}\}">y</figure-callout></span><figure-callout\; id="0"\; label="y\; tcp"\; filenames="HDA0000104445070000021.png,HDA0000104445070000022.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

According to the above calculation formula of fitting degree, the fitting degree value of each model in the controlled system model set U _I is obtained, and the system model with the highest fitting degree value is selected as the switch between the excitation terminal of the generator and the wide-area feedback timing signal ring system model;

(3-9) Using the zero-order hold transformation method, the open-loop controlled system model between the generator excitation terminal installed with the generator wide-area damping controller and the wide-area feedback input sequence signal is transformed into a discrete form G(z) Convert to continuous form G(s);

(4) Input the continuous controlled system model obtained in the above steps (3-9) into the above-mentioned module of solving the controller parameters with the genetic algorithm, and calculate the parameters of the generator wide-area damping controller. The specific process is as follows:

(4-1) It is assumed that the filter of the generator wide-area damping controller in the power system adopts a band-pass filter, and the band-pass filter adopts a band-pass filter. The transfer function expression of the band-pass filter is:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}{{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="s"\; filenames="HDA0000104445070000021.png,HDA0000104445070000022.png"\; state="\{\{state\}\}">s</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span>$

Δω为带通滤波器的通带宽度，ω₀为带通滤波器的中心频率，ω₀取值为被控电力系统区间低频振荡频率；where Q is the quality factor of the bandpass filter,

Δω is the passband width of the band-pass filter, ω ₀ is the center frequency of the band-pass filter, and ω ₀ is the interval low-frequency oscillation frequency of the controlled power system;

(4-2) According to the continuous controlled system model in the above step (3-9), the phase-shift parameters and gain parameters of the generator wide-area damping controller are calculated, and the specific process is as follows:

(4-2-1) Set the phase shift of the wide-area damping controller of the generator to adopt three lead-lag links, and the gain is a proportional coefficient. The transfer function expression of the phase shift and gain is:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&times;</span>{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="HDA0000104445070000021.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="1"\; label="s"\; filenames="HDA0000104445070000021.png"\; state="\{\{state\}\}">s</figure-callout></span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="T"\; filenames="HDA0000104445070000021.png,HDA0000104445070000022.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}$

为超前滞后环节的传递函数，T₁为超前时间常数，T₂为滞后时间常数，K为控制器的增益；in,

is the transfer function of the lead-lag link, T ₁ is the lead time constant, T ₂ is the lag time constant, and K is the gain of the controller;

(4-2-2) Set the control target of the generator wide-area damping controller as follows: to increase the damping ratio of all oscillation modes of the closed-loop system composed of the open-loop continuous controlled system and the generator wide-area damping controller to ξ ₀ ;

(4-2-3) According to the above-mentioned control objectives, establish the objective function of solving the controller parameter module with the genetic algorithm, and obtain the objective function of solving the controller parameter module with the genetic algorithm as:

$\min \left(\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}g\left({\mathrm{\&xi;}}_i\right)\right),$ (i=1,2,...,n)

$\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 0.15</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& {\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}\right.<span\; class="notranslate">\; ,</span>$

Among them: n represents the number of oscillation modes of the above closed-loop system, _ξi represents the damping ratio of the i-th oscillation mode;

(4-4) Set 0<T ₁ <1, 0<T ₂ <1 and 0<K<10 as the constraints of the above objective function;

(4-5) Set the calculation parameters of the genetic algorithm: the number of populations is 200, the value range of the initial population is 0 to 1, the number of good individuals copied to the next generation is 20, and the offspring individuals are selected by the championship method. The proportion of crossover in the newly generated offspring individuals is 0.8, and the mutation adopts an adaptive method;

(4-6) Set the DC blocking time constant of the generator wide-area damping controller: T _w = 4, the output upper limit of the generator wide-area damping controller is +0.1, and the output lower limit is -0.1, according to The above-mentioned genetic algorithm calculates parameters and objective function constraints, and obtains the optimal solution of the objective function of the controller parameter module by using genetic algorithm, that is, the lead time constant T ₁ , lag time constant T ₂ and The optimal value of the gain K of the controller.

The generator wide-area damping control method based on system identification and genetic algorithm proposed by the present invention has the following advantages:

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

2. By adopting the control method of the present invention, after the controlled system is put into the generator wide-area damping controller, the damping ratio of the low-frequency oscillation mode in the middle interval of the power system is significantly improved, ensuring safe and stable operation of the power system.

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

Description of drawings

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

Fig. 2 is a flowchart of generator wide-area damping control in the method of the present invention.

Fig. 3 is a block diagram of a closed-loop system composed of an open-loop continuous controlled system and a generator wide-area damping controller in 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 the generator in an embodiment of the method of the present invention.

Fig. 5 is a schematic diagram of wide-area feedback input timing signals when the generator wide-area damping controller is in open-loop operation in an embodiment of the method of the present invention.

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

Detailed ways

The generator wide-area damping control method based on system identification and genetic algorithm proposed by the present invention has a flow chart as shown in Figure 1, and the specific process is as follows:

(1) Establish a power system simulation model, which includes the equipment in the power system and the operating parameters of the power system. The equipment is generators, regulators, transformers, busbars, AC lines, DC lines, reactive power compensators and shunt capacitor reactors , the operating parameters of the power system are the power flow and load of the power system; set up a controlled system model identification module to identify the open-loop system model controlled by the generator wide-area damping controller; set up a genetic algorithm to solve the generator wide-area damping The controller parameter module is used to obtain the parameters of each link of the generator wide-area damping controller; a generator wide-area damping controller module is set to realize the generator wide-area damping control.

(2) Install the generator excitation terminal of the generator wide-area damping controller in the power system, inject a small random disturbance timing signal {u _t }, u _t is the value of the small random disturbance signal at time t, t=1,2 …T _total , T _total is the total number of simulation steps. In the open-loop operation of the generator wide-area damping controller, the wide-area feedback input timing signal {y _t } of the generator wide-area damping controller is collected, and the wide-area feedback input The number of data of the time series signal {y _t } is N, N=T _total , input the signals {u _t } and {y _t } into the above-mentioned model identification module of the controlled system;

To identify the interval low-frequency oscillation mode of the system, the small-amplitude fluctuation excitation signal should have uniform energy distribution within the frequency range of less than 2 Hz, and equally disturb the system. Therefore, the small-amplitude random disturbance signal injected into the excitation terminal of the generator in the simulated power system is generated by a small-amplitude Gaussian white noise through a second-order low-pass filter with a cutoff frequency of 2 Hz.

The wide-area feedback input timing signal collected by the present invention is an interval bus frequency difference signal.

(3) The controlled system model identification module identifies the open-loop controlled system model between the generator excitation terminal installed with the generator wide-area damping controller and the wide-area feedback input timing signal. The specific process includes the following steps:

(3-1) Calculate the stationary zero-mean time-series signal {y _tcp0 } of the above wide-area feedback input time-series signal {y _t } as follows:

${\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="0"\; label="y\; tcp"\; filenames="HDA0000104445070000021.png,HDA0000104445070000022.png"\; state="\{\{state\}\}">y</figure-callout></span><figure-callout\; id="0"\; label="y\; tcp"\; filenames="HDA0000104445070000021.png,HDA0000104445070000022.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; ;</span>$

为该模型结构U(θ)的参数，得到被控系统模型集合(3-2) Set the model structure of the above open-loop controlled system as U(θ), where the parameter vector

is the parameter of the model structure U(θ), and the model set of the controlled system is obtained

U ^* ＝{U(θ)|θ∈D _μ }

where d is the dimension of the parameter θ, and D _μ is a subset of the d-dimensional real number set;

The model structures usually selected include BJ model, OE model, ARX model and state space model.

(3-3) Substitute the stationary zero-mean time-series signal {y _tcp0 } of step (3-1) and the above-mentioned small random disturbance input signal {u _t } into the prediction function, and predict the forecast value injected into the small random disturbance time-series signal at time t :

$\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; :</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>$

Where g(y _t-1 , u _t-1 , θ) is the forecast function;

(3-4) Calculate the real value y t of the power system wide-area feedback time-series signal injected with a small random disturbance time-series signal at time _t and the predicted value at time t The error between ε(t, θ):

$\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

(3-5) Set the forecast error criterion function of the power system as:

J ₁ (θ)=Tr[ΛD(θ)]

Among them, Λ is a weighted positive definite matrix, $\mathrm{D.}\left(\mathrm{\&theta;}\right)=\frac{1}{N}\underset{t=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&epsiv;}(t,\mathrm{\&theta;}){\mathrm{\&epsiv;}}^T(t,\mathrm{\&theta;});$

(3-6) Minimize the above forecast error criterion function:

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; min</span>}{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>$

是使预报误差准则函数J₁(θ)取得最小值的模型参数值；模型为被控系统模型集合U^*中使得预报误差准则函数取得极小值的系统模型。in

is the model parameter value that makes the forecast error criterion function J ₁ (θ) obtain the minimum value; the model It is the system model that makes the prediction error criterion function obtain the minimum value in the controlled system model set U ^* .

The smaller the value of the forecast error criterion function, the closer the forecast value is to the real value, and the closer the model parameter values are to the real model.

的模型集合U_I，(3-7) Repeat steps (3-2) to (3-6) M times to obtain M controlled system models

model set U _I ,

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; \}</span>$

Wherein i=1, 2..., M, M is the total number of times of repeating step (3-2) to step (3-6).

之间的拟合度为：(3-8) Set the real value y t of the power system wide-area feedback input timing signal injected into the small random disturbance timing signal at time _t and the predicted value at time t

The fit between is:

$\mathrm{<span\; class="notranslate">\; fit</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 100</span>}<span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; /</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; tcp</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

According to the above calculation formula of fitting degree, the fitting degree value of each model in the controlled system model set U _I is obtained, and the system model with the highest fitting degree value is selected as the switch between the excitation terminal of the generator and the wide-area feedback timing signal Ring system model; the higher the fit value, the better the model can describe the controlled system.

(3-9) Using the zero-order hold transformation method, the open-loop controlled system model between the generator excitation terminal installed with the generator wide-area damping controller and the wide-area feedback input sequence signal is transformed into a discrete form G(z) Convert to continuous form G(s);

(4) The continuous controlled system model that above-mentioned step (3-9) obtains is input to above-mentioned module of solving controller parameter with genetic algorithm, calculates the parameter of generator wide-area damping controller, the structure of described wide-area damping controller As shown in Figure 2, the specific process is as follows:

(4-1) It is assumed that the filter of the generator wide-area damping controller in the power system adopts a band-pass filter, and the band-pass filter adopts a band-pass filter. The transfer function expression of the band-pass filter is:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}{{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="s"\; filenames="HDA0000104445070000021.png,HDA0000104445070000022.png"\; state="\{\{state\}\}">s</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span>$

where Q is the quality factor of the bandpass filter, Δω is the passband width of the band-pass filter, ω ₀ is the center frequency of the band-pass filter; ω ₀ is the interval low-frequency oscillation frequency of the controlled system.

(4-2) According to the continuous controlled system model in the above step (3-9), the phase-shift parameters and gain parameters of the generator wide-area damping controller are calculated, and the specific process is as follows:

(4-2-1) Set the phase shift of the wide-area damping controller of the generator to adopt three lead-lag links, and the gain is a proportional coefficient. The transfer function expression of the phase shift and gain is:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&times;</span>{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="HDA0000104445070000021.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="1"\; label="s"\; filenames="HDA0000104445070000021.png"\; state="\{\{state\}\}">s</figure-callout></span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="T"\; filenames="HDA0000104445070000021.png,HDA0000104445070000022.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}$

为超前滞后环节的传递函数，T₁为超前时间常数，T₂为滞后时间常数，K为控制器的增益。in,

For the transfer function of the lead-lag link, T ₁ is the lead time constant, T ₂ is the lag time constant, and K is the gain of the controller.

(4-2-2) Set the control target of the generator wide-area damping controller as follows: to increase the damping ratio of all oscillation modes of the closed-loop system composed of the open-loop continuous controlled system and the generator wide-area damping controller to ξ ₀ ;

(4-2-3) According to the above-mentioned control objectives, establish the objective function of solving the controller parameter module with the genetic algorithm, and obtain the objective function of solving the controller parameter module with the genetic algorithm as:

$\min \left(\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}g\left({\mathrm{\&xi;}}_i\right)\right),$ (i=1,2,...,n)

$\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 0.15</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& {\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}\right.<span\; class="notranslate">\; ,</span>$

Where: n represents the number of oscillation modes of the above closed-loop system, and ξ _i represents the damping ratio of the i-th oscillation mode.

(4-4) 0<T ₁ <1, 0<T ₂ <1, and 0<K<10 are given as constraint conditions of the above-mentioned objective function.

(4-5) Set the calculation parameters of the genetic algorithm: the number of populations is 200, the value range of the initial population is 0 to 1, the number of good individuals copied to the next generation is 20, and the offspring individuals are selected by the championship method. The proportion of crossover in the newly generated offspring individuals is 0.8, and the mutation adopts an adaptive method.

(4-6) Set the DC blocking time constant of the generator wide-area damping controller: T _w = 4, the output upper limit of the generator wide-area damping controller is +0.1, and the output lower limit is -0.1, according to The above-mentioned genetic algorithm calculates parameters and objective function constraints, and obtains the optimal solution of the objective function of the controller parameter module by using genetic algorithm, that is, the lead time constant T ₁ , lag time constant T ₂ and The optimal value of the gain K of the controller.

The method of the invention includes a simulation power system module, a controlled system model identification module and a genetic algorithm calculation module for controller parameters. The basic analysis process is to inject a small random disturbance signal into the generator excitation terminal where the generator wide-area damping controller is installed in the simulated power system, collect the wide-area feedback input signal of the generator wide-area damping controller in the open-loop situation, and convert The above-mentioned small disturbance signal and wide-area feedback input signal are input into the model identification module of the controlled system as analysis objects, and the open-loop system model between the excitation terminal of the generator installed with the generator wide-area damping controller and the wide-area feedback input timing signal is obtained through identification , according to the control objective, the parameters of the generator wide-area damping controller are optimized by using the genetic algorithm to solve the controller parameter module.

Fig. 2 shows the structure of the generator wide-area damping controller adopted by the method of the present invention. Among them, H _θ (s) is the transfer function structure of the phase-shifting and gain link, and H _f (s) is the transfer function structure of the band-pass filter link. K is the gain, T ₁ and T ₂ are the lead time constant and lag time constant of the phase shifting link respectively. ω ₀ , Q are the passband center frequency and quality factor of the bandpass filter, respectively.

The method of the invention combines system identification and genetic algorithm to optimize the design of the parameters of the phase shifting link and the gain link in the generator wide-area damping controller, so that after the generator wide-area damping controller is put into operation, the damping ratio of the controlled power system fulfil requirements.

Below is an embodiment of the inventive method:

The wide-area damping control of the generator is implemented at the excitation end of the generator to suppress the interval low-frequency oscillation existing in different regions of the power grid. The wide-area feedback signal is the bus frequency difference signal of the two places. The designed generator wide-area damping controller adopts the traditional generator PSS structure, as shown in Figure 2. When the generator wide-area damping controller is not installed, a three-phase instantaneous short-circuit fault is imposed on the tie line of the power grid system, and the active power curve of the tie line is measured. According to the prony analysis, the frequency of the interval low-frequency oscillation mode is about 0.60Hz, and the damping The ratio is 3.1%. The goal of generator wide-area damping control is to increase the damping ratio of the system's low-frequency oscillation mode to more than 15%.

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

The small-amplitude random disturbance signal injected into the excitation terminal of the generator is obtained by passing Gaussian white noise through a low-pass filter with a cutoff frequency of 2 Hz. Fig. 4 is a schematic diagram of a small random disturbance signal injected into the excitation terminal of the generator. The frequency difference signal of the bus in the two places in the power system is collected as the open-loop wide-area feedback input signal of the generator wide-area damping controller. Figure 5 shows the bus frequency difference signals of the two places.

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

Firstly, the frequency difference signal of the buses in the two places is removed from the mean value, and the processed frequency difference signal and the small-amplitude random disturbance signal are input into the model identification module of the controlled system. For multiple different model structures, use the controlled system model identification module to identify multiple controlled system models, calculate the fitting degree of each controlled system model, and select the model with the largest fitting value as the controlled system model. Transform the above model from discrete form to continuous form to obtain the continuous transfer function expression of the controlled system:

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

Step 3: Based on the controlled system model obtained by identification, the parameters of each link of the generator wide-area damping controller are optimized by genetic algorithm.

The Yunnan-Guizhou oscillation mode component in the Yunnan-Guizhou frequency difference feedback signal is extracted by using a band-pass filter. The quality factor Q of the band-pass filter is set to 1.5, and the center frequency ω ₀ is set to the frequency of the Yunnan-Guizhou low-frequency oscillation mode of 0.58Hz. According to the bandpass filter transfer function expression:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}}{{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="s"\; filenames="HDA0000104445070000021.png,HDA0000104445070000022.png"\; state="\{\{state\}\}">s</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span>$

The transfer function of the controller bandpass filter can be obtained as:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2.43</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}{{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="s"\; filenames="HDA0000104445070000021.png,HDA0000104445070000022.png"\; state="\{\{state\}\}">s</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2.43</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 13.28</span>}}$

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

The parameters that need to be solved for the generator wide-area damping controller are lead time constant T ₁ , lag time constant T ₂ and gain K, and the genetic algorithm is used to calculate the optimal solution for the above parameters to meet the goal of generator wide-area damping control

According to the goal of the generator wide-area damping control is to increase the damping ratio of the low-frequency oscillation mode of the system to 15%, the objective function of the genetic algorithm is given as:

$\min \left(\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}g\left({\mathrm{\&xi;}}_i\right)\right),$ (i=1,2,...,n)

$\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 0.15</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& {\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; \%</span>\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; \%</span>\end{array}\right.$

Given the value ranges of the lead time constant T ₁ , lag time constant T ₂ and gain of the parameters to be optimized: 0<T ₁ <1, 0<T ₂ <1 and 0<K<10, take them as the constraints of the objective function condition.

Set the calculation parameters of the genetic algorithm: the number of 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 offspring individuals are selected by the championship method, and the newly generated offspring The proportion of crossover among individuals is 0.8, and the variation adopts an adaptive method.

Set the DC blocking time constant of the generator wide-area damping controller: T _w = 4, the output upper limit of the generator wide-area damping controller is +0.1, the output lower limit is -0.1, and the parameters are calculated according to the above genetic algorithm and the objective function constraint conditions, obtain the optimal solution of the objective function of the controller parameter module by genetic algorithm, that is, the leading time constant T ₁ =0.020, the lagging time constant T ₂ =0.019 and the control of the generator wide-area damping controller The gain of the device K=-5.91.

Step 4: Put the designed generator wide-area damping controller into the power grid system, and adjust the controller gain to make the energy output of the controller within a suitable range considering the controller output is affected by the limiting link.

The controller gain optimized by the genetic algorithm is K=-5.91, but the controller output seriously exceeds the limit under this gain, and the controller gain is adjusted to K=-3.

Put the adjusted generator wide-area damping controller into the power grid system, apply a three-phase instantaneous short-circuit fault to the section tie line, and compare the change of the active power curve of the tie line before and after using the generator wide-area damping controller is shown in Figure 6 , the system damping ratio can be increased 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}：

$y_{\mathrm{tcp}0}=y_t-\frac{1}{N}\underset{t=1}{\overset{N}{\mathrm{\&Sigma;}}}{y}_t;$

(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 random disturbance timing 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:

$U\left(\mathrm{\&theta;}\right):\hat{y}\left(t\right|\mathrm{\&theta;})=g(y_{t-1},u_{t-1},\mathrm{\&theta;})$

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:

$\mathrm{\&epsiv;}(t,\mathrm{\&theta;})=y_t-\hat{y}\left(t\right|\mathrm{\&theta;});$

(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, $D\left(\mathrm{\&theta;}\right)=\frac{1}{N}\underset{t=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&epsiv;}(t,\mathrm{\&theta;}){\mathrm{\&epsiv;}}^T(t,\mathrm{\&theta;});$

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

${\widehat{\mathrm{\&theta;}}}_N=\arg \min J_1\left(\mathrm{\&theta;}\right)$

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^*A system model for minimizing the prediction error criterion function;

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

Model set U of_I，

$U_I=\left\{U\left({\widehat{\mathrm{\&theta;}}}_{N_i}\right)\right|i=\mathrm{1,2},....,M\}$

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:

$\mathrm{fit}\left({\widehat{\mathrm{\&theta;}}}_N\right)=100\&times;(1-\sqrt{\frac{1}{N}\underset{t=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&epsiv;}{(t,{\widehat{\mathrm{\&theta;}}}_N)}^2}/\sqrt{\frac{1}{N}\underset{t=1}{\overset{N}{\mathrm{\&Sigma;}}}{y_{\mathrm{tcp}0}}^2}$

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:

$H_p\left(s\right)=\frac{\frac{1}{Q}{\mathrm{\&omega;}}_0\&CenterDot;s}{s^2+\frac{1}{Q}{\mathrm{\&omega;}}_{0}s+{{\mathrm{\&omega;}}_0}^2},$

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:

$H_{\mathrm{\&theta;}}\left(s\right)=K\&times;{\left(\frac{1+T_{1}s}{1+T_{2}s}\right)}^3$

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:

$\min \left(\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}g\left({\mathrm{\&xi;}}_i\right)\right),(i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n)$

$g\left({\mathrm{\&xi;}}_i\right)=\left\{\begin{array}{cc}0.15-{\mathrm{\&xi;}}_i& {\mathrm{\&xi;}}_i<{\mathrm{\&xi;}}_0\\ 0& {\mathrm{\&xi;}}_i\&GreaterEqual;{\mathrm{\&xi;}}_0\end{array}\right.,$

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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