CN111478364B - Damping controller coordination parameter optimization method based on steepest descent method - Google Patents
Damping controller coordination parameter optimization method based on steepest descent method Download PDFInfo
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Abstract
The invention provides a damping controller coordination parameter optimization method based on a steepest descent method, which comprises the following steps: firstly, respectively constructing a wind power plant model, a photovoltaic power station model, a PSS model and a PODC model; secondly, analyzing the influence of the PSS and the PODC on the stability of the power system by establishing a dynamic model of the power system; then, respectively constructing a target function based on the characteristic value and a target function based on the damping ratio, and constructing a multi-target function; searching and optimizing the multi-objective function by using the SDA to obtain optimal parameters of the PSS and the PODC; and finally, verifying the optimized power system by using a characteristic value analysis and dynamic time domain simulation method to obtain optimal parameters of the PSS and the PODC, so that the small interference stability of the power system can be improved. The invention adopts the SDA to optimize the PSS and PODC coordination parameters, provides additional enough damping for the low-frequency oscillation existing in the power system, and improves the small interference stability of the system.
Description
Technical Field
The invention relates to the technical field of power systems, in particular to a damping controller coordination parameter optimization method based on a steepest descent method.
Background
In the face of the global increasingly serious environmental pollution problem and the energy shortage crisis, the development and utilization of renewable energy resources are receiving high attention from governments of various countries. The wind energy and the solar energy have stronger complementarity in time and region, and the wind energy and the solar energy are effectively combined and utilized, so that the defect of independent power generation in the energy utilization rate can be overcome, the reliability and the stability of power supply are improved, and the absorption capacity of a power grid to renewable energy sources is enhanced. However, as large-scale wind and photovoltaic energy sources are integrated into traditional power systems, the intermittent, random, and uncertainty increase of these renewable energy sources has a great impact on the safe and stable operation of the power system.
Low frequency oscillations typically occur in interconnected power systems with weak tie lines, and if the system is not sufficiently damped, the oscillations will persist, exacerbate and destabilize the system. Power System Stabilizers (PSS) may provide additional damping to the synchronous generator, effectively damping local oscillations. But is effective in suppressing the interval oscillation. A Unified Power Flow Controller (UPFC) can control transmission line power, change power flow distribution, and suppress power oscillations. The Power Oscillation Damping Controller (PODC) based on the UPFC has the advantages of flexible controllability and quick response when the PODC oscillates at low frequency in a damping area. Since adverse interactions between damping controllers can affect system stability, it is necessary to coordinate parameter optimization to improve their damping effect on low frequency oscillations of the power system.
Disclosure of Invention
Aiming at the defects in the background technology, the invention provides a method for optimizing the coordination parameters of the damping controller based on the steepest descent method, and the technical problem of damping low-frequency oscillation of a system after renewable energy is connected to the grid is solved.
The technical scheme of the invention is realized as follows:
a damping controller coordination parameter optimization method based on a steepest descent method comprises the following steps:
s1, connecting the power system stabilizer and the damping controller into a power system, and respectively constructing a wind power plant model, a photovoltaic power station model, a power system stabilizer model and a damping controller model;
s2, establishing a dynamic model of the power system, solving a characteristic value of the dynamic model of the power system, and solving a damping ratio of the dynamic model of the power system according to the characteristic value, wherein the characteristic value and the damping ratio are related to parameters of a stabilizer and a damping controller of the power system;
s3, respectively constructing an objective function based on the characteristic value and an objective function based on the damping ratio, and constructing a multi-objective function according to the objective function based on the characteristic value and the objective function based on the damping ratio;
s4, searching and optimizing the multi-objective function by using a steepest descent method to obtain optimal values of parameters of a power system stabilizer and a damping controller;
and S5, verifying the dynamic model of the power system by using a characteristic value analysis and dynamic time domain simulation method to obtain the optimal parameters of the power system stabilizer and the damping controller, so that the small interference stability of the power system can be improved.
The wind power plant model is as follows:
wherein, U ds Is the d-axis component of the stator voltage, U qs Is the q-axis component of the stator voltage, E d ' is the d-axis component of the transient potential, E q ' is the q-axis component of the transient potential, x s Is the stator synchronous reactance, x s ' is the stator transient reactance, i ds Is the d-axis component of the stator current, i qs Is the q-axis component of the stator current, R is the stator resistance, S is the rotor slip, ω is the synchronous speed, T' is the rotor time constant, U d ′ r Is the d-axis component of the rotor potential, U q ′ r Is the q-axis component of the rotor potential;
the photovoltaic power station model is as follows:
wherein n is 1 Is the number of parallel photovoltaic cells, n 2 Is the number of series-connected photovoltaic cells, I g Is the photo-generated current, I 1 Is the diode current, I is the photovoltaic cell output current, U is the open circuit voltage, R 1 Is the load resistance, q' is the electronic charge, k is the boltzmann constant, T is the absolute temperature, c is the battery ideality factor;
the power system stabilizer model is as follows:
wherein G(s) is the transfer function of PSS, s is the transfer factor, K PSS Is the gain, T, of the PSS 1 Is the time constant, T a1 、T a2 、T a3 And T a4 Are all the time constants of the PSS;
the damping controller model is as follows:
wherein g(s) is the transfer function of PODC, K PODC Is the gain, T, of PODC W1 Is the time constant, T b1 、T b2 、T b3 And T b4 Are all time constants for PODC.
The dynamic model of the power system is as follows:
where x is the vector of state variables, y is the vector of algebraic variables,
is a vector of system variables, f (-) is a differential equation, g (-) is an algebraic equation;
linearizing a dynamic model of the power system:
wherein the content of the first and second substances,
is the amount of change in the system variable,
is the gradient of the state variable of the differential equation,
is the gradient of the algebraic variable of the differential equation,
is the gradient of the state variable of an algebraic equation,
is the gradient of the algebraic variable of the algebraic equation,. DELTA.x is the variation of the state variable,. DELTA.y is the variation of the algebraic variable, A C Is a jacobian matrix.
The multi-objective function is:
Q(X)＝Q a +ψQ b (10)，
wherein Q (X) is a multi-objective function,
is an objective function based on the characteristic values,
is an objective function based on the damping ratio,. phi. 0 Is the maximum of the real part of the target eigenvalue, σ X Is the real part of the Xth eigenvalue, ζ 0 Is the minimum damping ratio, ζ, of the target characteristic value X Is the damping ratio of the xth characteristic value.
The constraint conditions of the multi-objective function are as follows:
σ 0 ≥σ X (13)，
ζ X ≥ζ 0 (14)，
wherein, K PSS Is the gain, T, of the PSS a1 And T a3 Are all the time constants, K, of the PSS PODC Is the gain, T, of PODC b1 And T b3 Are all time constants of PODC, K PSS-min Is the gain K of the PSS PSS Lower limit of (D), K PSS-max Is the gain K of the PSS PSS Upper limit of (1), T a1-min Is the time constant T a1 Lower limit of (D), T a1-max Is the time constant T a1 Upper limit of (1), T a3-min Is the time constant T a3 Lower limit of (D), T a3-max Is the time constant T a3 Upper limit of (1), K PODC-min Is the gain K of PODC PODC-min Lower limit of (D), K PODC-max Is the gain K of PODC PODC-min Upper limit of (1), T b1-min Time constant T b1 Lower limit of (D), T b1-max Time constant T b1 Upper limit of (1), T b3-min Time constant T b3 Lower limit of (D), T b3-max Time constant T b3 Upper limit of (1), σ 0 Is the maximum of the real part of the target eigenvalue, σ X Is the real part of the Xth eigenvalue, ζ 0 Is the minimum damping ratio, ζ, of the target characteristic value X Is the damping ratio of the xth characteristic value.
The method for searching and optimizing the multi-objective function by using the steepest descent method to obtain the optimal damping controller parameter comprises the following steps:
s41, setting the initial optimization parameter as X (1) The number of iterations i is 1, and a matrix H is set (i) Initial value of (H) (i) ＝[1]Maximum number of iterations is i max Wherein [1 ]]Representing an identity matrix;
s42, calculating the gradient of the multi-objective function Q (X)
S43, defining direction
In the direction S (i) Using a one-dimensional search method to obtain the optimal step size mu 2 (i) And satisfies the following conditions: Δ X (i) ＝μ 2 (i) S (i) And X (i+1) ＝X (i) +ΔX (i) Wherein X is (i+1) Is the i +1 th eigenvalue, X (i) Is the ith characteristic value, Δ X (i) Represents X (i) The amount of change in (c).
S44, optimizing the parameter X (i+1) Substituting into multi-objective function Q (X), if multi-objective function Q (X) has minimum value, then X (i+1) Ending the iteration for the optimal solution, otherwise, executing the step S45;
s45, calculating the multi-target function Q (X) in the parameter X (i+1) Gradient of (2)
Satisfies the following conditions:
wherein, Δ G (i) Represents the amount of change in the gradient of Q (X);
s46, updating matrix H (i+1) ：
S47, if i is equal to i +1<i max And returning to the step S43, otherwise, ending the iteration and outputting the parameter value of the last iteration.
The beneficial effect that this technical scheme can produce:
(1) the invention adopts the steepest descent method to optimize the coordination parameters of the damping controller, provides additional enough damping for the low-frequency oscillation existing in the power system and improves the small interference stability of the system;
(2) the method has strong searching capability, can effectively find the minimum value of the problem, and can improve the system stability after the wind energy and photovoltaic energy are connected to the grid.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a system diagram of an IEEE4 Motor 2 area including wind and photovoltaic power generation of the present invention;
FIG. 2 is a diagram of a wind power generation system of the present invention;
FIG. 3 is a diagram of a UPFC-based PODC model of the present invention;
FIG. 4 is a response curve diagram of the damping controller under the system fault test;
FIG. 5 is a graph of the expected eigenvalue and damping ratio distribution area of the present invention;
FIG. 6 is a schematic diagram of parameter coordination based on steepest descent algorithm according to the present invention;
FIG. 7 is a response curve for system fault testing before and after parameter optimization according to the present invention;
fig. 8 is a graph showing the response of the present invention before and after the optimization of parameters by varying the transmission power of the tie line.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive effort based on the embodiments of the present invention, are within the scope of the present invention.
FIG. 1 is a system diagram of an IEEE (institute of Electrical and Electronics Engineers)4 machine 2 area including wind power generation and photovoltaic power generation, and on the basis of FIG. 1, the embodiment of the invention provides a damping controller coordination parameter optimization method based on a steepest descent method, which comprises the following specific steps:
and S1, connecting the power system stabilizer and the damping controller into the power system, and respectively constructing a wind power plant model, a photovoltaic power station model, a power system stabilizer model and a damping controller model.
The wind power plant model is a 4-order model of the doubly-fed wind generator on a d-q axis:
wherein, U ds Is the d-axis component of the stator voltage, U qs Is the q-axis component of the stator voltage, E d ' is the d-axis component of the transient potential, E q ' is the q-axis component of the transient potential, x s Is the stator synchronous reactance, x s ' is the stator transient reactance, i ds Is the d-axis component of the stator current, i qs Is the q-axis component of the stator current, R is the stator resistance, S is the rotor slip, ω is the synchronous speed, T' is the rotor time constant, U d ′ r Is the d-axis component of the rotor potential, U q ′ r Is the q-axis component of the rotor potential. A wind power system based on a doubly-fed wind generator is shown in fig. 2.
The photovoltaic power station model is as follows:
wherein n is 1 Is the number of parallel photovoltaic cells, n 2 Is the number of series-connected photovoltaic cells, I g Is a photo-generated current, I 1 Is the diode current, I is the photovoltaic cell outputCurrent, U is open circuit voltage, R 1 Is the load resistance, q' is the electronic charge, k is the boltzmann constant, T is the absolute temperature, and c is the battery ideality factor.
The power system stabilizer model is as follows:
wherein G(s) is the transfer function of PSS, s is the transfer factor, K PSS Is the gain, T, of the PSS 1 Is the time constant, T a1 、T a2 、T a3 And T a4 Are all time constants of the PSS.
The damping controller model is as follows:
wherein g(s) is the transfer function of PODC, K PODC Is the gain, T, of PODC W1 Is the time constant, T b1 、T b2 、T b3 And T b4 Are all time constants for PODC. The PODC mainly includes links such as amplification, blocking, phase compensation, amplitude limiting, and the like, and a PODC model based on the UPFC is shown in fig. 3.
S2, establishing a dynamic model of the power system, solving a characteristic value of the dynamic model of the power system, and solving a damping ratio of the dynamic model of the power system according to the characteristic value, wherein the characteristic value and the damping ratio are related to parameters of a stabilizer and a damping controller of the power system;
the dynamic model of the power system is a differential-algebraic equation representing the dynamic characteristics of the power system:
where x is the vector of state variables, y is the vector of algebraic variables,
is a vector of system variables, f (-) is a differential equation, and g (-) is an algebraic equation.
Based on a linear system and the Lyapunov stability law, a characteristic value analysis method is the most suitable method for researching the small interference stability of the power system. Dynamic model of power system at stable operating point (x) 0 ,y 0 ) And (3) performing Taylor series expansion, wherein the linearized model is as follows:
wherein the content of the first and second substances,
is the amount of change in the system variable,
is the gradient of the state variable of the differential equation,
is the gradient of the algebraic variable of the differential equation,
is the gradient of the state variable of an algebraic equation,
is the gradient of the algebraic variable of the algebraic equation,. DELTA.x is the variation of the state variable,. DELTA.y is the variation of the algebraic variable, A C Is a jacobian matrix.
Suppose that
Is reversible, then equation (6) can be converted to:
where A is the state matrix of the power system. The complex eigenvalue of the state matrix a is λ ═ α ± j β, α is the real part of the complex eigenvalue, β is the imaginary part of the complex eigenvalue, the oscillation frequency is f ═ β/2 π, and the damping ratio ξ is defined as:
the key point of the small interference stability analysis is to solve the eigenvalue of the state matrix A. If all the real parts of the eigenvalues of the state matrix A are negative, the power system is stable under small interference; if at least one real part in all the characteristic values of the state matrix A is positive, the power system is unstable under small interference; if the real part of all eigenvalues of the state matrix a is negative but at least one real part is zero, the power system is critically stable under small disturbances.
After the characteristic value calculation is completed, obtaining a participation factor reflecting the relative contribution of the system state variable to the system mode by using the right characteristic vector w and the left characteristic vector v:
p ij ＝w ij v ji /(w T j v j ) (9)，
wherein p is ij Is the participation factor of the ith state variable to the jth characteristic value. For the eigenvalue λ i Satisfies Aw i ＝λ i w i N-dimensional column vector of w i Is λ i Satisfies v i A＝v i λ i N-dimensional row vector of v i Is λ i The left feature vector of (2).
To study the performance of the damping controller, the following cases were combined: case 1, no controller installed; case 2, install PSS only; case 3, install only UPFC-PODC; case 4, install PSS and UPFC-PODC. And using MATLAB/PSAT simulation software to perform stability test on the wind power-photovoltaic hybrid power system accessed by the damping controller. The results of the system eigenvalue analysis are shown in table 1.
TABLE 1 comparison of electromechanical oscillation modes of the system in different cases
From the results of table 1, it can be seen that when PSS or UPFC-PODC is installed in the power system, the variations in the characteristic values and damping ratios of the electromechanical oscillation modes of the power system are significant. When wind farms and photovoltaic power plants access the power system, the power system will introduce oscillation patterns related to both, which may exacerbate the oscillations of the power system. Comparing case 1 and case 2, it can be known that the installation of the PSS can obviously improve the damping ratio of the electromechanical mode, enhance the weak eigenvalue, improve the damping ratio related to the local oscillation to a greater extent, and suppress the local oscillation to a better effect. Comparing case 1 and case 3, it can be seen that the damping ratio of the power system with respect to the local oscillation mode is weakly enhanced after installation of the UPFC-PODC. However, it impairs the damping ratio associated with inter-region oscillation modes. In case 4, the damping ratio of the power system with respect to local and inter-area oscillation modes tends to increase after installation of the PSS and the UPFC-PODC. The power system has the best overall performance, and the effect of damping low-frequency oscillation is more effective.
To further analyze the performance of the damping controller in terms of small interference stability of the power system, a time domain simulation was performed using MATLAB/PSAT. Suppose that when the time is 1 second, three-phase short-circuit fault occurs in one of the double- circuit connecting lines 8 and 9, the fault clearing time is 0.05 second, and the connecting line recovers to operate after 1.05 seconds. The power angle response curve of the generator 1 in a short-circuit fault is shown in fig. 4.
As can be seen from fig. 4, after the damping controller is installed in the wind power-photovoltaic hybrid power system, when a short-circuit fault occurs in the power system, the damping controller has different degrees of suppression effects on power angle oscillation, so that the oscillation amplitude is reduced, the stabilization time is shortened, and the stability of the system is improved.
By analyzing the results of characteristic value calculation and time domain simulation, after the PSS and the UPFC-PODC are installed in the power system, the damping related to local and regional oscillation is improved to a certain extent, and the small interference stability of the power system is improved. However, in the initial stage of the low frequency oscillation, the performance is weaker than the suppression effect of the system in which only the PSS is mounted on the power angle oscillation. It can be known that there may be negative interactions between different damping controllers, which is not good for the small disturbance stability of the power system. Due to the basic control function inside the UPFC-PODC, the voltage control of its dc bus capacitor and PSS installed in the power system will have a negative impact, which will seriously affect both functions themselves and also may deteriorate the system stability. Measures must be taken to counteract the negative effects of damping controller parameters by coordinating and optimizing them on system stability.
S3, respectively constructing an objective function based on the characteristic value and an objective function based on the damping ratio based on the power system in the step S1, and constructing a multi-objective function according to the objective function based on the characteristic value and the objective function based on the damping ratio.
The multi-objective function is:
Q(X)＝Q a +ψQ b (10)，
wherein Q (X) is a multi-objective function;
is an objective function based on eigenvalues for improving weak eigenvalues of the system;
adjusting the damping ratio to an appropriate value based on an objective function of the damping ratio; psi is a weighting factor, is a constant selected from engineering practical experience, and is used for solving the stability problem of the multi-target power system, and the purpose is to ensure that Q is equal to a And Q b Keeping the same order of magnitude; sigma 0 Is the maximum of the real part of the target eigenvalue, σ X Is the real part of the Xth eigenvalue, ζ 0 Is the minimum damping ratio, ζ, of the target characteristic value X Is the damping ratio of the xth characteristic value.
And coordinating and optimizing damping controller parameters by minimizing a multi-objective function, wherein the constraint conditions of the multi-objective function are as follows:
σ 0 ≥σ X (13)，
ζ X ≥ζ 0 (14)，
wherein, K PSS Is the gain, T, of the PSS a1 And T a3 Are all the time constants, K, of the PSS PODC Is the gain, T, of PODC b1 And T b3 Are all time constants of PODC, K PSS-min Is the gain K of the PSS PSS Lower limit of (D), K PSS-max Is the gain K of the PSS PSS Upper limit of (1), T a1-min Is the time constant T a1 Lower limit of (D), T a1-max Is the time constant T a1 Upper limit of (1), T a3-min Is the time constant T a3 Lower limit of (D), T a3-max Is the time constant T a3 Upper limit of (1), K PODC-min Is the gain K of PODC PODC-min Lower limit of (D), K PODC-max Is the gain K of PODC PODC-min Upper limit of (1), T b1-min Time constant T b1 Lower limit of (D), T b1-max Time constant T b1 Upper limit of (1), T b3-min Time constant T b3 Lower limit of (D), T b3-max Time constant T b3 Upper limit of (1), σ 0 Is the maximum of the real part of the target eigenvalue, σ X Is the real part of the Xth eigenvalue, ζ 0 Is the minimum damping ratio, ζ, of the target characteristic value X Is the damping ratio of the xth characteristic value. When the objective function q (x) takes a minimum value, the distribution regions of the characteristic values and the damping ratio desired by the power system are as shown in fig. 5.
S4, searching and optimizing the multi-objective function by using a Steepest Descent method (SDA) to obtain the optimal values of the parameters of the power system stabilizer and the damping controller; as shown in fig. 6, the optimization method based on the steepest descent method is:
s41, setting the initial optimization parameter as X (1) The number of iterations i is 1, and a matrix H is set (i) Initial value of (H) (i) ＝[1]Maximum overlapGeneration number is i max Wherein [1 ]]Represents a unit matrix, H (i) Is a multi-objective function Q (X) at X (i) An approximate inverse of the second order sensitivity matrix at (a).
S42, calculating the gradient of the multi-objective function Q (X)
S43, defining direction
In the direction S (i) Using a one-dimensional search method to obtain the optimal step size mu 2 (i) And satisfies the following conditions: Δ X (i) ＝μ 2 (i) S (i) And X (i+1) ＝X (i) +ΔX (i) Wherein X is (i+1) Is the i +1 th eigenvalue, X (i) Is the ith characteristic value, Δ X (i) Represents X (i) The amount of change in (c);
s44, optimizing the parameter X (i+1) Substituting into multi-objective function Q (X), if multi-objective function Q (X) has minimum value, then X (i+1) Ending the iteration for the optimal solution, otherwise, executing the step S45;
s45, calculating the multi-objective function Q (X) in the optimization parameter X (i+1) Gradient of (2)
Satisfies the following conditions:
wherein, Δ G (i) Represents the amount of change in the Q (X) gradient;
s46, updating matrix H (i+1) ：
S47, iteration number i ═i +1, if i<i max And returning to the step S43, otherwise, ending the iteration and outputting the optimization parameters of the last iteration.
If the local optimal solution appears before the parameters meeting the requirements are obtained, the adjustment is carried out:
1) changing the initial values of the optimization parameters, and then repeating the steps S41-S47;
2) the damping controller parameters are adjusted from the locally optimal solution.
And S5, verifying the dynamic model of the power system by using the characteristic value analysis and the dynamic time domain simulation method to obtain the optimal parameters of the power system stabilizer and the damping controller, so that the small interference stability of the power system can be improved. FIG. 7 is a response curve diagram of the system fault test before and after the parameter optimization according to the present invention. In MATLAB/PSAT simulation software, characteristic value analysis and a dynamic time domain simulation method are utilized, and the improvement effect of the damping controller on the small interference stability of the system is compared before and after parameter optimization. As can be seen from fig. 7, after the parameter optimization is coordinated by the steepest descent method, when the system suffers from low-frequency oscillation, the oscillation amplitude of the power angle of the generator is significantly reduced, and the time for the system to recover to be stable is also shortened. The invention can provide enough additional damping for the low-frequency oscillation of the power system, improve the overall damping level of the system and effectively enhance the stability of the system. Fig. 8 is a response curve of the present invention before and after parameter optimization for varying link transmission power. The results of fig. 8 show that as the system tie-line power increases, the system suffers more intense oscillations, requiring a longer time to cancel the oscillations, before the damping controller parameters are optimized. After the parameters are coordinated and optimized by adopting the steepest descent method, the oscillation of the power angle of the generator can be obviously inhibited, and the stability can be quickly recovered. The effectiveness of the invention is further shown, the electromechanical oscillation generated by the system can be better damped, and the stability is better.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (6)
1. A damping controller coordination parameter optimization method based on a steepest descent method is characterized by comprising the following steps:
s1, accessing the power system stabilizer and the damping controller into a power system, and respectively constructing a wind power plant model, a photovoltaic power station model, a power system stabilizer PSS model and a damping controller PODC model;
s2, establishing a dynamic model of the power system, solving a characteristic value of the dynamic model of the power system, and solving a damping ratio of the dynamic model of the power system according to the characteristic value, wherein the characteristic value and the damping ratio are related to parameters of a stabilizer and a damping controller of the power system;
s3, respectively constructing an objective function based on the characteristic value and an objective function based on the damping ratio, and constructing a multi-objective function according to the objective function based on the characteristic value and the objective function based on the damping ratio;
s4, searching and optimizing the multi-objective function by using a steepest descent method to obtain optimal values of parameters of a power system stabilizer and a damping controller;
and S5, verifying the dynamic model of the power system by using a characteristic value analysis and dynamic time domain simulation method to obtain the optimal parameters of the power system stabilizer and the damping controller, so that the small interference stability of the power system can be improved.
2. The steepest descent method-based damping controller coordination parameter optimization method according to claim 1, wherein the wind farm model is:
wherein, U ds Is the d-axis component of the stator voltage, U qs Is the q-axis component, E ', of the stator voltage' d Is the d-axis component, E 'of the transient potential' q Is the q-axis component of the transient potential, x s Is stator synchronous reactance, x' s Is the stator transient reactance, i ds Is the d-axis component of the stator current, i qs Is the q-axis component of the stator current, R is the stator resistance, S is the rotor slip, ω is the synchronous speed, T 'is the rotor time constant, U' dr Is the d-axis component, U 'of the rotor potential' qr Is the q-axis component of the rotor potential;
the photovoltaic power station model is as follows:
wherein n is 1 Is the number of parallel photovoltaic cells, n 2 Is the number of series-connected photovoltaic cells, I g Is a photo-generated current, I 1 Is the diode current, I is the photovoltaic cell output current, U is the open circuit voltage, R 1 Is the load resistance, q' is the electronic charge, k is the boltzmann constant, T is the absolute temperature, c is the battery ideality factor;
the power system stabilizer model is as follows:
wherein G(s) is the transfer function of PSS, s is the transfer factor, K PSS Is the gain, T, of the PSS 1 Is the time constant, T, of the PSS a1 、T a2 、T a3 And T a4 Are all the time constants of the PSS;
the damping controller model is as follows:
wherein g(s) is the transfer function of PODC, K PODC Is the gain, T, of PODC W1 Is the time constant of PODC, T b1 、T b2 、T b3 And T b4 Are all time constants for PODC.
3. The steepest descent based damping controller coordination parameter optimization method of claim 1, wherein the dynamic model of the power system is:
where x is the vector of state variables, y is the vector of algebraic variables,
is the vector of the system variable, f (-) is the differential equation, g (-) is the algebraic equation;
linearizing a dynamic model of a power system:
wherein, the first and the second end of the pipe are connected with each other,
is the amount of change in the system variable,
is the gradient of the state variable of the differential equation,
is the gradient of the algebraic variable of the differential equation,
is the gradient of the state variable of an algebraic equation,
is the gradient of the algebraic variable of the algebraic equation,. DELTA.x is the variation of the state variable,. DELTA.y is the variation of the algebraic variable, A C Is a jacobian matrix.
4. The steepest descent method-based damping controller coordination parameter optimization method of claim 1, wherein the multi-objective function is:
Q(X)＝Q a +ψQ b (10)，
wherein Q (X) is a multi-objective function,
is an objective function based on the characteristic values,
is an objective function based on the damping ratio,. phi. 0 Is the maximum of the real part of the target eigenvalue, σ X Is the real part of the Xth eigenvalue, ζ 0 Is the minimum damping ratio, ζ, of the target characteristic value X Is the damping ratio of the xth characteristic value.
5. The method for optimizing the coordination parameter of the damping controller based on the steepest descent method according to claim 4, wherein the constraint conditions of the multi-objective function are as follows:
σ 0 ≥σ X (13)，
ζ X ≥ζ 0 (14)，
wherein, K PSS Is the gain, T, of the PSS a1 And T a3 Are all the time constants, K, of the PSS PODC Is the gain, T, of PODC b1 And T b3 Are all time constants of PODC, K PSS-min Is the gain K of the PSS PSS Lower limit of (D), K PSS-max Is the gain K of the PSS PSS Upper limit of (1), T a1-min Is a time constantNumber T a1 Lower limit of (D), T a1-max Is the time constant T a1 Upper limit of (1), T a3-min Is the time constant T a3 Lower limit of (D), T a3-max Is the time constant T a3 Upper limit of (1), K PODC-min Is the gain K of PODC PODC Lower limit of (D), K PODC-max Is the gain K of PODC PODC Upper limit of (1), T b1-min Time constant T b1 Lower limit of (D), T b1-max Time constant T b1 Upper limit of (1), T b3-min Time constant T b3 Lower limit of (D), T b3-max Time constant T b3 Upper limit of (1), σ 0 Is the maximum of the real part of the target eigenvalue, σ X Is the real part of the Xth eigenvalue, ζ 0 Is the minimum damping ratio, ζ, of the target characteristic value X Is the damping ratio of the xth characteristic value.
6. The damping controller coordination parameter optimization method based on the steepest descent method according to claim 1 or 5, wherein the method for searching and optimizing the multi-objective function by using the steepest descent method to obtain the optimal damping controller parameter comprises the following steps:
s41, setting the initial optimization parameter as X (1) The number of iterations i is 1, and a matrix H is set (i) Initial value of (H) (i) ＝[1]Maximum number of iterations is i max Wherein [1 ]]Representing an identity matrix;
s42, calculating the gradient of the multi-objective function Q (X)
S43, defining direction
In the direction S (i) Using a one-dimensional search method to obtain the optimal step size mu 2 (i) And satisfies the following conditions: Δ X (i) ＝μ 2 (i) S (i) And X (i+1) ＝X (i) +ΔX (i) Wherein X is (i+1) Is the i +1 th eigenvalue, X (i) Is the ith characteristic value, Δ X (i) Represents X (i) The amount of change in (c);
s44, optimizing the parameter X (i+1) Substituting into multi-objective function Q (X), if the multi-objective function Q (X) has minimum value, then X (i +1) Ending the iteration for the optimal solution, otherwise, executing the step S45;
s45, calculating the multi-target function Q (X) in the parameter X (i+1) Gradient of (2)
Satisfies the following conditions:
wherein, Δ G (i) Represents the amount of change in the Q (X) gradient;
s46, updating matrix H (i+1) ：
S47, if i is equal to i +1<i max And returning to the step S43, otherwise, ending the iteration and outputting the parameter value of the last iteration.
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