CN106292295A - The method that superconducting energy storage based on Implicit Generalized PREDICTIVE CONTROL suppression Electromechanical Disturbance is propagated - Google Patents

Abstract

The invention discloses a method based on implicit generalized predictive control for superconducting energy storage to suppress the propagation of electromechanical disturbance. S1: through Laplace transformation, a complex frequency domain model of electromechanical disturbance propagation in the power system is established, and the propagation of disturbance in the power system is theoretically analyzed law; S2: install a superconducting energy storage device on the busbar of the power system, use the generalized predictive control principle to control the input and output active power of the superconducting magnetic energy storage device, and suppress the propagation of the electromechanical disturbance; S3: use simulation software Verify the effectiveness of active controllers in suppressing the propagation of electromechanical disturbances in power systems. The invention quickly and accurately tracks the change of the generator rotor angular velocity incremental difference under different disturbances, realizes the suppression of electromechanical disturbances, and can stabilize the rapid system. The method is simple, fast in response, high in control accuracy, and Advantages such as overshooting.

Description

Method of Suppressing Electromechanical Disturbance Propagation with Superconducting Energy Storage Based on Implicit Generalized Predictive Control

technical field

The invention relates to a method for suppressing electromechanical disturbance propagation by superconducting energy storage based on implicit generalized predictive control.

Background technique

The rapid growth of power demand has made my country's power grid more complex and large, and the dynamic characteristics of the power system have become more complex. The impact of power system disturbance propagation on the stability of the power grid has become even greater, making the possibility of large-scale power grid accidents caused by disturbances It is greatly increased, which eventually makes it difficult to suppress the propagation of power system disturbances. The power system is subject to various disturbances all the time, which makes the mechanical power of the generator unbalanced with the output electromagnetic power, and the rotor speed of the generator changes, so that it no longer operates at a synchronous speed. As a result, the generator enters a dynamic process, and the propagation of the disturbance in the system shows that the system frequency presents a spatiotemporal distribution characteristic in time and space. According to the law of disturbance propagation in the system, by installing energy storage devices on the bus and taking appropriate control measures, the propagation of disturbances in the system can be effectively controlled, the frequency distribution characteristics of the system can be improved, and the stability of the system can be improved.

Relevant studies have shown that the dynamic change of generator speed caused by electromechanical disturbance in the system propagates in the form of waves and presents the characteristics of time and space distribution. Continuum Modeling regards the power system with a large spatial distribution span as a spatially continuous distributed generator, transmission line and load as a whole, and the generator rotor moment of inertia, damping and line impedance are represented by a continuously distributed density function , and introduce it into the generator rocking equation, get the second-order partial differential equation about time and space, and use the relevant theory of wave mechanics to study the fluctuation law of the disturbance in the system, thus revealing the propagation mechanism of the disturbance in the system, as Studying the electromechanical dynamic characteristics of power systems provides a new perspective.

The superconducting magnetic energy storage device can quickly and independently control active and reactive power in four quadrants. Its performance depends on the control method adopted. Only by adopting an effective control method can the SMES quickly and accurately suppress the propagation of electromechanical disturbances. The voltage and current double closed-loop PI control is the most extensive and practical control method, which controls the input current and output voltage separately, the output of the voltage outer loop is used as the current command, and the current inner loop controls the input current to quickly track the current command. However, due to the nonlinear characteristics of the converter, the stability and system performance of the PI controller are sensitive to parameter changes and external disturbances, and the robustness is poor. The SMES nonlinear PID controller is designed without depending on the mathematical model of the controlled system. It has the characteristics of simple structure, easy implementation and strong adaptability, but its parameter design needs further research. The fuzzy logic control SMES is used to improve the system characteristics. The simulation results prove the effectiveness of the control method in improving the stability of the power grid. However, it is difficult to implement in engineering because of the complex algorithms involved. In order to solve the above problems, this paper adopts generalized predictive control to realize the effective control of SMES.

Generalized Predictive Control (GPC, Generalized Predictive Control), as a main optimal control strategy, uses control strategies such as multi-step prediction, rolling optimization and feedback correction to control the control object, which can effectively overcome the inaccurate model, Non-linear, time-varying effects, while also coping with excessive parameter changes.

Contents of the invention

The purpose of the present invention is to provide a method based on implicit generalized predictive control of superconducting energy storage to suppress the propagation of electromechanical disturbance, which can realize the suppression of electromechanical disturbance, and can quickly stabilize the system, with fast response speed and high control precision .

In order to solve the above-mentioned technical problems, the present invention provides a method for suppressing the propagation of electromechanical disturbance based on implicit generalized predictive control of superconducting energy storage, the method comprising the following steps:

S1: Establish a complex frequency domain model of electromechanical disturbance propagation in the power system through Laplace transform, and theoretically analyze the propagation law of disturbance in the power system;

S2: Install a superconducting energy storage device on the busbar of the power system, obtain the object of random interference according to the propagation law, and use an active controller to control the input and output active work of the superconducting magnetic energy storage device according to the principle of generalized predictive control power, achieving suppression of the electromechanical disturbance propagation.

Further, the method also includes:

S3: Use simulation software to verify the suppression effect of the active controller on the propagation of electromechanical disturbances in the power system.

Further, the step S2 includes the following steps:

S21: A superconducting energy storage device is installed on the busbar of the power system. According to the propagation law of the disturbance in the power system, the controlled autoregressive integral sliding average model is used as the prediction model to describe the object of random disturbance, and the least squares with forgetting factor is used to describe the object of random disturbance. The multiplication identification method obtains the optimal control quantity of the prediction model;

S22: Using the rotor angular velocity increment in the power system as the input of the prediction model to control the active power of the measurement model, the active power of the prediction model is output to the power system through the superconducting energy storage device, so as to suppress the propagation of electromechanical disturbance.

Further, the constraints satisfied by the optimal control amount are:

Δu(k) _min ≤Δu(k)≤Δu(k) _max

In the formula, Δu(k) is the optimal control quantity of the prediction model, Δu(k) _min is the lower limit of the control quantity, and Δu(k) _max is the upper limit of the control quantity.

The beneficial effects of the present invention are as follows: the present invention quickly and accurately tracks the change of the angular velocity incremental difference of the generator rotor under different disturbances, and adopts a generalized predictive control superconducting energy storage device to realize the suppression of electromechanical disturbances and stabilize the rapid system , the method has the advantages of simplicity, quick response, high control precision, and no overshoot. Moreover, the present application obtains the optimal control quantity of the prediction model by adopting the least square identification method with forgetting factor, which effectively avoids the inaccurate and cumbersome problem of parametric modeling caused by the nonlinearity of the superconducting energy storage device.

Description of drawings

Figure 1 is a schematic diagram of a uniform chain power system;

Fig. 2 is the schematic diagram of the kth section of the uniform chain system;

Fig. 3 is the schematic diagram of SMES under generalized predictive control;

Fig. 4 is the curve diagram of 60 generator chain system disturbance signals;

Fig. 5 is a graph of the angular velocity incremental difference of the generator rotor under the action of disturbance 1;

Fig. 6 is a graph of the angular velocity incremental difference of the rotor of the first generator under the action of disturbances 1, 2 and 3;

Figure 6-1 is a graph showing the angular velocity incremental difference of the rotor of the first generator under the action of disturbance 4;

Figure 7 is a schematic diagram of the parallel SMES on the third bus;

Fig. 8 is the characteristic curve diagram of tracking given value;

Fig. 9 is a controller input curve diagram;

Fig. 10 is a graph of the rotor angular velocity incremental difference under the action of disturbance 1;

Fig. 11 is a graph of the rotor phase angle incremental difference under disturbance 1;

Fig. 12 is a graph of the output active power P of the SMES.

detailed description

The specific embodiments of the present invention are described below so that those skilled in the art can understand the present invention, but it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes Within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are included in the protection list.

A method based on implicit generalized predictive control for superconducting energy storage to suppress the propagation of electromechanical disturbances, the method comprising the following steps:

S1: Through Laplace transform, the complex frequency domain model of electromechanical disturbance propagation in the power system is established, and the law of disturbance propagation in the power system is theoretically analyzed. The specific method is as follows:

Figure 1 is a chain discrete power system model, in which R is the resistance of the transmission line, X is the reactance of the transmission line, M is the angular momentum of the generator, and D is the damping of the rotor of the generator.

According to the actual operation of the power system, this paper makes the following settings for the system model shown in Figure 1: (1) The per-unit value of all bus voltages is 1.0; (2) The transmission line parameters are the same and R/X<<1, that is Neglect the line resistance; (3) The mechanical power of the generator is constant; (4) The voltage phase angle difference δ between adjacent buses is small, satisfying sinδ≈δ, cosδ≈1; (5) D/M<<1.

Figure 2 shows the relationship between the transmission power P _k of the kth line and the phase angles θ _k and θ _k+1 of the kth and k+1 bus voltages:

${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula, U _k and U _k+1 respectively represent the bus voltage of the kth bus and the k+1th bus, and B is the susceptance between the kth bus and the k+1th bus, and the simplified formula (1) is

${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&ap;</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&ap;</span>\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

The relationship between the power increment Δp _k of the k-th line and the voltage phase angle increment Δθ _k of the generator node where the k-th bus is located is:

Δp _k (t)≈BΔθ _k (t) (3)

Since the internal impedance of the generator is ignored, the rotor angle of the generator is equal to the phase angle of the connected bus voltage, so the generator speed increment is

${\mathrm{<span\; class="notranslate">\; \&Delta;\&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}\frac{{\mathrm{<span\; class="notranslate">\; d\&Delta;\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; f</span>}}\frac{{\mathrm{<span\; class="notranslate">\; d\&Delta;\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

The swing equation of the generator on the kth bus is:

$\mathrm{<span\; class="notranslate">\; m</span>}\frac{{\mathrm{<span\; class="notranslate">\; d\&Delta;\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; dt</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; D.</span>}\frac{{\mathrm{<span\; class="notranslate">\; d\&Delta;\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Delta;p</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

By doing Laplace transform on formula (5), we can get

s ² Δθ _k (s)＝M ^-1 [-DsΔθ _k (s)-B(2Δθ _k (s)-Δθ _k+1 (s)-Δθ _k-1 (s))] (6)

S2: Install a superconducting energy storage device on the busbar of the power system. The propagation law of the disturbance in the power system uses the controlled autoregressive integral sliding average model as the prediction model to describe the object of random disturbance, and is identified by the least square method with forgetting factor The method obtains the optimal control quantity of the predictive model; the schematic diagram of the output active power of the generalized predictive control superconducting energy storage device (SMES) is shown in Figure 3, and the rotor angular velocity increment in the power system is used as the input control of the predictive model The active power of the model is measured, and the active power of the predicted model is output to the power system through the superconducting energy storage device, so as to suppress the propagation of electromechanical disturbance.

The damping power of a stand-alone infinite system with SMES is composed of the system's own damping power and the damping power introduced by SMES. By controlling the equivalent parameters of SMES, D _SMES can be effectively controlled. When positive damping is introduced into SMES, the total damping of the system can be improved and the propagation of electromechanical disturbance can be effectively suppressed. The parameter settings for selecting SMES are as follows: 400MJ/300MVA SMES system, rated line voltage 20kV, rated frequency 60Hz, superconducting magnet inductance value 2H, superconducting magnet rated current 20kA, the AC side impedance and inductance of the SMES converter are respectively 0.007pu and 0.22pu, the minimum and maximum current allowed during the operation of the superconducting magnet are 2kA and 20kA, the rated voltage of the DC side capacitor is 40kV, the DC side equivalent capacitance is 375μF, and the maximum change rate of the current reference input is 200p.u ./s.

The invention adopts the implicit algorithm as the correction algorithm of the generalized predictive control method, avoids a large number of intermediate calculations for solving the Diophantine equation on-line, and improves the reaction speed.

Generalized predictive control uses a controlled autoregressive integral moving average model to describe objects subject to random disturbances:

A(z ^-1 )y(k)=B(z ^-1 )u(k-1)+C(z ^-1 )ξ(k)/Δ (7)

In the formula, y(k), u(k), ξ((k) are the output of the system, the input of the system and the discrete white noise with an average value of 0. A(z ^-1 ), B(z ^-1 ) and C( z ^-1 ) are the polynomials of z ^-1 of order n _a , n _b and n _c respectively, Δ=1-z ^-1 , z ^-1 is the backward shift operator, for example z ^-1 y(k)=y( k- ¹ ).If the time delay of the system is greater than zero, the coefficients b ₀ , b ₁ , If it is set to 0, it means the corresponding time lag of the control object. In order to simplify the calculation process, C(z ^-1 ) is usually set to 1.

The optimization performance index at time k adopts the objective function

$\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

In the formula, n is the predicted length, m is the control length, the expected output value is w(k+j)=α ^j y(k)+(1-α ^j )y _r , y _r is the set value, y(k) is the current output of the system, and α is the smoothness coefficient.

The optimal output prediction value is

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

In the formula, Y is the predicted output sequence, ΔU is the control increment sequence; ΔU=[Δu(k),Δu(k+1),…,Δu(k+n-1)] ^T , f=[f(k +1),f(k+2),…,f(k+n)] ^T .

Let W=[w(k+1),w(k+2),…,w(k+n)] ^T , use the optimal predicted value instead of Y, the formula (10) is the optimal control law of GPC

ΔU＝(G ^T G+λI) ^-1 G ^T (Wf) (10)

In the formula, the softening coefficient λ and the set value vector W are known, and the matrix G and the open-loop prediction vector f are unknown. The implicit self-correction method directly identifies G and f through the prediction equation according to the input and output data.

According to formula (9), n parallel predictors can be obtained as

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ...</span>\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

It can be seen from formula (11) that all elements in G are in the last equation, so G can be obtained by identifying the last equation of formula (11). From formula (11) can get

y(k+n)＝g _n-1 Δu(k)+...+g ₀ Δu(k+n-1)+f(k+n)+E _n ξ(k+n) (12)

Let X(k)=[Δu(k),Δu(k+1),…,Δu(k+n-1),1], θ(k)=[g _n-1 ,g _n-2 ,… ,g ₀ ,f(k+n)] ^T ,

Then formula (12) can be simplified as

y(k+n)=X(k)θ(k)+E _n ξ(k+n) (13)

The output predicted value is

y((k+n)|k)=X(k)θ(k) (14)

At time k, X(kn) is known, E _n ξ(k+n) is white noise with an average value of zero, and the parameter vector θ(k) is estimated by ordinary least squares method. However, usually E _n ξ(k+n) is not white noise, so the control strategy is combined with parameter estimation, that is, the estimated value predicted by the auxiliary output Instead of outputting the predicted value y(k|(kn)), consider The only difference from the actual value y(k) is white noise ε(k). Let y(k|(kn)) represent the predicted value of n-step output at kn time, Represents the estimated value of n-step auxiliary output prediction at kn time, that is, by

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

inferred

$\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$

Estimate the parameter vector θ(k) using the least squares method:

$\left\{\begin{array}{c}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; f</span>}\\ \mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\\ \mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

In the formula, λ ₁ is the forgetting factor, 0<λ ₁ <1,

The matrix G can be obtained from formula (17):

n-step estimate at time k for

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 19</span>}<span\; class="notranslate">\; )</span>$

The prediction vector f at the next moment is

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\left(\begin{array}{c}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ \mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>\end{array}\right)<span\; class="notranslate">\; =</span>\left(\begin{array}{c}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\\ \stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ \stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\end{array}\right)<span\; class="notranslate">\; +</span>\left(\begin{array}{c}\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right)\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 20</span>}<span\; class="notranslate">\; )</span>$

Obtaining G and f, according to formula (10), the optimal control quantity at the current moment can be obtained as

u(k)=u(k-1)+g ^T (Wf) (21)

In the formula, g ^T is the first row of the matrix (G ^T G+λI) ^-1 G ^T .

One of the greatest advantages of the generalized predictive control algorithm is because the system's processing constraints are enabled by predictive optimization governed by constraint satisfaction. Therefore, in this application, the constraint condition that the optimal control quantity satisfies is

Δu(k) _min ≤Δu(k)≤Δu(k) _max

In the formula, Δu(k) is the optimal control quantity of the prediction model, Δu(k) _min is the lower limit of the control quantity, and Δu(k) _max is the upper limit of the control quantity.

S3: Use simulation software (MATLAB/Simulink) to verify the suppression effect of the active controller on the propagation of electromechanical disturbances in the power system, specifically:

The simulation model adopted by the present invention is a uniform discrete chain system with n=60 as shown in FIG. 1 . Its standard parameters are as follows: (1) ignore the transmission line resistance between adjacent generators R = 0, reactance X = 2p.u.; (2) angular momentum of the generator rotor M = 20p.u., rotor damping D =0.01pu, ignoring the internal impedance of the generator; (3) The impedance Z ₀ from the initial disturbance point to point B =0. Simulation time T = 10s.

1. Carry out simulation analysis on the disturbance propagation characteristics of discrete chain power system. Assuming the initial disturbance is shown in Figure 4, disturbance 1 is a pulse disturbance (the disturbance occurs at 0.5 time with an amplitude of 1 p.u., and the disturbance disappears at 1.2s), which simulates an instantaneous short-circuit fault. The fault occurred on the bus 1 and the load transmission line. A short circuit occurred at 0.5s and the load was cut off by the relay protection. At 1.2s, the reclosing was successful and the fault disappeared. Disturbance 2 simulates the input mechanical power change of wind turbines caused by gusts; disturbance 3 is a step signal, which is equivalent to an increase in load operation; disturbance 4 is the introduction of random wind disturbances, simulating the input mechanical power changes of wind turbines caused by random winds .

When the disturbance 1 occurs at the bus 1, the incremental difference of the rotor angular velocity of each generator is shown in the figure. It can be seen from Figure 5 that after the disturbance occurs, the angular velocity increment difference of the generator rotor closest to the disturbance is the largest, and the disturbance propagates in the form of waves in the system.

From Figure 6 and Figure 6-1, it can be found that under the action of disturbance 1, disturbance 2, and disturbance 3, when the disturbance stops, the angular velocity incremental difference of the generator rotor becomes smaller and smaller, tends to be flat, and is infinitely close to 0. Under the action of disturbance 4 Gaussian white noise, the angular velocity incremental difference of the generator rotor fluctuates violently, and the fluctuation cannot be weakened under the damping effect of the system itself, which has a huge impact on the system.

2. Carry out simulation analysis on SMES based on generalized predictive control. Simulation parameter settings: Tc _p =0.026, K _v =10, T _vm =0.02, ΔP _max =0.95, ΔP _min =-0.5. Suppose the system model is

y(k)-0.92623y(k-1)=0.03773u(k-1)+ξ(k)/Δ (23)

The simulation parameters are taken as: p=n=15, m=2, λ=0.04, λ ₁ =1, α=0.9. Initial values of RLS parameters: g _n-1 = 1, f(k+n) = 1, P0 = 10 ⁵ I, and the rest are 0. ξ(k) ∈ [-0.2, 0.2] uniformly distributed white noise. When the tracking reference value is a square wave, the characteristic curve of tracking a given value is shown in Figure 8. The controller input waveform is shown in Figure 9.

3. Disturbance control simulation

Disturbance 1 occurs at busbar 1, and SMES is installed at busbar 3 (as shown in Figure 8). The variation of the rotor angular velocity incremental difference of the first generator is shown in Fig. 10. Observing Figure 10, it can be seen that the use of PI control has a certain inhibitory effect on the disturbance propagation. At time t=2.6s, the incremental difference of the rotor angular velocity approaches 0, and the system stabilizes again. Under the wide-area predictive control, the disturbance propagation is obviously suppressed and the system is rapidly stabilized, and the incremental difference of the rotor angular velocity approaches 0 at time t=1.65s. Without SMES, the maximum incremental difference of rotor angular velocity is 11×10 ^-4 pu at t=1.0695s, and the minimum incremental difference of rotor angular velocity is -5.38×10 ^-4 pu when t=1.29s; under PI control, t= At 1.053s, the maximum value of rotor angular velocity incremental difference is 9.19×10 ^-4 pu, and at t=1.26s, the minimum value of rotor angular velocity incremental difference is -5.1×10 ^-4 pu; under generalized predictive control, the rotor angular velocity at t=1.04s The maximum incremental difference is 9×10 ^-4 pu, and the minimum rotor angular velocity incremental difference is -2.3×10 ^{- 4} pu at t=1.28s; the comparison shows that the reduction percentage of the minimum rotor angular velocity incremental difference under GPC control is 57%, and the rotor angular velocity incremental difference deviates from the stable value, the control effect is obviously better than that without SMES and PI control.

Disturbance 1 occurs at bus 1, and SMES is installed at bus 3. The phase angle incremental difference change of the first generator is shown in Fig. 11. It can be seen from Figure 11 that: when SMES is not added, the maximum value of phase angle increment is 0.2rad at t=2.5s; the maximum value of phase angle increment difference at t=1.2s under PI control is 0.0548rad; under generalized predictive control, t= The maximum difference of the phase angle increment at 1.187s is 0.028rad; the comparison shows that under GPC control, the system re-stabilization time is reduced by 52.6%, and the phase angle increment difference is reduced by 85.9%. GPC control can quickly and effectively suppress Propagation of electromechanical disturbances.

Disturbance 1 occurs at bus 1, and SMES is installed at bus 3. The output active power of SMES is shown in Figure 12. It can be seen from Fig. 12 that the output active power of SMES under PI control is small, and its maximum output power is 0.4009 p.u., which cannot effectively track the power change in the system; the output power of SMES under wide-area predictive control is stable, and its maximum power is 0.95 p.u. p.u., track power changes in time, and effectively suppress the propagation of electromechanical disturbances.

To sum up, the present invention establishes a mathematical model of electromechanical disturbance propagation in a complex power system by using Laplace transform through basic assumptions and discrete modeling, and analyzes its propagation law. The system and SMES are simulated by MATLAB, and the following conclusions are drawn: By quickly and accurately tracking the change of the angular velocity incremental difference of the generator rotor under different disturbances, the generalized predictive control of the superconducting energy storage device is used to suppress the electromechanical disturbance, and The system can be quickly stabilized. This method has the advantages of simplicity, fast response, high control precision, and no overshoot.

Claims (4)

1. the method that superconducting energy storage based on an Implicit Generalized PREDICTIVE CONTROL suppression Electromechanical Disturbance is propagated, it is characterised in that bag Include following steps:

S1: converted by Laplace, is set up the complex frequency domain model that power system Electromechanical Disturbance is propagated, draws in power system and disturb Dynamic propagation law；

S2: install superconducting magnetic energy storage additional on the bus of described power system, draws random disturbances according to described propagation law Object, utilizes active controller to control the input and output active power of superconducting magnetic energy storage according to generalized predictive control principle, Realize suppressing described Electromechanical Disturbance to propagate.

The side that superconducting energy storage based on Implicit Generalized PREDICTIVE CONTROL the most according to claim 1 suppression Electromechanical Disturbance is propagated Method, it is characterised in that the method also includes:

S3: utilize the inhibition that Electromechanical Disturbance in power system is propagated by simulation software checking active controller.

The side that superconducting energy storage based on Implicit Generalized PREDICTIVE CONTROL the most according to claim 1 suppression Electromechanical Disturbance is propagated Method, it is characterised in that described step S2 comprises the following steps:

S21: install superconducting magnetic energy storage additional on the bus of described power system, uses controlled autoregressive according to described propagation law Integration moving average model describes the object of random disturbances as forecast model, by the least squares identification of band forgetting factor Method obtains the optimum control amount of described forecast model；

S22: use rotor velocity increment in described power system having as the input control forecasting model of forecast model Merit power, it was predicted that the active power of model exports in power system by superconducting magnetic energy storage, it is achieved suppression Electromechanical Disturbance passes Broadcast.

The side that superconducting energy storage based on Implicit Generalized PREDICTIVE CONTROL the most according to claim 3 suppression Electromechanical Disturbance is propagated Method, it is characterised in that in described step S21, the constraints that described optimum control amount meets is:

Δu(k)_min≤Δu(k)≤Δu(k)_max

In formula, Δ u (k) is the optimum control amount of forecast model, Δ u (k)_minFor the lower limit of controlled quentity controlled variable, Δ u (k)_maxFor controlling The higher limit of amount.