CN113300386A - Frequency controller design method and system based on alternating direction multiplier method - Google Patents

Frequency controller design method and system based on alternating direction multiplier method Download PDF

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CN113300386A
CN113300386A CN202110564669.3A CN202110564669A CN113300386A CN 113300386 A CN113300386 A CN 113300386A CN 202110564669 A CN202110564669 A CN 202110564669A CN 113300386 A CN113300386 A CN 113300386A
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李玲芳
陈义宣
孙鹏
周俊东
王云辉
伞晨峻
许岩
司大军
游广增
陈姝敏
高杉雪
何烨
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Yunnan Power Grid Co Ltd
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Abstract

The application provides a frequency controller design method and a system based on an alternating direction multiplier method, which comprises the following steps: s10, establishing a load frequency control model according to the power system; s20, establishing an optimization model with the control performance and the sparsity of the gain matrix of the controller as parameters; and S30, processing the parameter control performance and the parameter controller gain matrix sparsity in the optimization model by using an alternating direction multiplier method. A distributed optimal Load Frequency Control (LFC) strategy mathematical model is constructed based on quadratic polynomial and matrix sparseness, and an Alternating Direction Multiplier Method (ADMM) is adopted for solving to design a load frequency controller with frequency deviation of 0 and excellent dynamic performance, so that the problems that the optimized controller has more parameters and a heuristic optimization algorithm can not necessarily obtain an optimal solution are solved.

Description

Frequency controller design method and system based on alternating direction multiplier method
Technical Field
The present invention relates to the field of automatic control technologies, and in particular, to a method and an apparatus for designing a frequency controller based on an alternating direction multiplier method.
Background
Load Frequency Control (LFC) is to adjust the frequency of the system to a rated value or to maintain the area link exchange power at a planned value. Frequency stability is an important indicator of power quality of a power system. Any sudden change in load may result in a deviation in the inter-system link exchange power and a fluctuation in the system frequency. Therefore, to ensure power quality, a Load Frequency Control (LFC) system is required, which aims to maintain the system frequency at a nominal value and minimize unplanned link exchange power between control areas as much as possible.
In order to improve the performance of load frequency control, some advanced control methods are adopted in the prior art to design a load frequency controller. Some adopt robust control strategy to restrain system frequency deviation caused by load change, some adopt adaptive control strategy to promote system control performance when system operating point changes, and some adopt optimal control strategy to restrain system frequency deviation and tie line power deviation. In addition, model predictive control, active disturbance rejection control, sliding mode control, and event driven control are also used to design the load frequency controller to improve control performance.
However, when the methods are applied to the design of the load frequency controller of the actual multi-region power system, parameter setting is difficult. The controller parameter setting of the robust control strategy based on the linear matrix inequality is relatively easy, but the method generally needs to carry out reduced-order preprocessing on a system model, so that the loss of the dynamic characteristic of a part of the system can be caused. Some design load frequency controllers by heuristic optimization algorithm, including setting controller parameters by particle swarm optimization algorithm and determining parameters of fractional order controller by grey wolf optimization algorithm. However, it cannot be theoretically ensured that the heuristic optimization algorithms can obtain the optimal solution of the controller parameters, and particularly for the actual multi-region power system, the heuristic optimization algorithms may not necessarily obtain the optimal solution because more controller parameters need to be optimized.
Disclosure of Invention
The application provides a frequency controller design method and a frequency controller design system based on an alternating direction multiplier method, a distributed optimal Load Frequency Control (LFC) strategy mathematical model is constructed based on quadratic polynomial and matrix sparseness, and an Alternating Direction Multiplier Method (ADMM) is adopted to solve to design a load frequency controller with frequency deviation of 0 and excellent dynamic performance, so that the problems that the number of optimized controller parameters is large and the optimal solution cannot be necessarily obtained by a heuristic optimization algorithm are solved.
In one aspect, the present application provides a method for designing a frequency controller based on an alternating direction multiplier method, including:
s10, establishing a load frequency control model according to the power system;
s20, establishing a parameter optimization model for controlling the performance and the sparsity of the gain matrix of the controller;
and S30, processing the parameter control performance and the parameter controller gain matrix sparsity in the optimization model by using an alternating direction multiplier method.
Preferably, the method for establishing the load frequency control model according to the power system comprises the following steps:
model of ith zone in interconnected power system:
Figure RE-GDA0003146178780000021
Figure RE-GDA0003146178780000022
Figure RE-GDA0003146178780000023
Figure RE-GDA0003146178780000024
n represents the number of zones included in the interconnected power system under study,
Figure RE-GDA0003146178780000025
representing a load disturbance at time t, Δ fi(t) represents the frequency deviation at time t,
Figure RE-GDA0003146178780000026
An active power output adjustment amount at time t,
Figure RE-GDA0003146178780000027
Representing the governor valve position adjustment, delta, at time ti(t) represents the rotor angular deviation at time t,
Figure RE-GDA0003146178780000028
a time constant representing the speed regulator,
Figure RE-GDA0003146178780000029
Representing the time constant of the turbine and
Figure RE-GDA00031461787800000210
which represents the time constant of the power system,
Figure RE-GDA00031461787800000211
representing the gain, R, of the power systemiA speed regulation coefficient representing the power system; ksijRepresenting the gain of the connection between zone i and zone j, K if there is no power exchange between these two zonessijIs 0;
rewriting (1) to (4) into a matrix form:
Figure RE-GDA00031461787800000212
Figure RE-GDA00031461787800000213
Figure RE-GDA00031461787800000214
Figure RE-GDA00031461787800000215
in the formula, Xi(t) represents the state vector of region i at time t, Xj(t) represents the state vector, U, of region j at time ti(t) represents the input vector of the controller at time t.
Preferably, the method for establishing the parameter optimization model for controlling the performance and the sparsity of the gain matrix of the controller comprises the following steps:
the load frequency control of the interconnected power system of the n regions is expressed as:
Figure RE-GDA0003146178780000031
U＝-KX (6)
in the formula: x ═ X1,X2,…,Xn]；U＝[U1,U2,…,Un]；D＝[ΔPd1,ΔPd2,…,ΔPdn]；
Figure RE-GDA0003146178780000032
K represents a controller gain matrix;
according to the matrix, the proposed load frequency controller design method can be expressed as:
min J(K)+γg(K) (7)
wherein J (X) represents a frequency deviation index, and H is the system2Norm of
Figure RE-GDA0003146178780000033
P is Gramian considerable matrix; g (x) represents a sparsification index of the controller structure, and L is adopted1Norm is expressed as
Figure RE-GDA0003146178780000034
KijRepresenting the ith row and jth column element, W, of the matrix KijRepresents a non-negative weight and when KijW is not equal to 0ij＝1/|KijI, when Kij0 and 0< ε<Time 1W ij1/| epsilon |; γ is a scalar and is a positive number;
subject to(A-B2K)TP+P(A-B2K)
＝-(Q-KTRK) (8)
the equation constraint described by the equation (8) as the system stability condition can be obtained through the theoretical analysis of the dynamic system stability.
Preferably, the method for processing the parameter control performance and the sparsity of the gain matrix of the parameter controller in the optimization model by using the alternating direction multiplier method comprises the following steps:
according to the formula
Figure RE-GDA0003146178780000035
Wherein K represents a variable for controlling performance J (K) and a variable for controlling communication complexity g (G);
according to the formula
Figure RE-GDA0003146178780000036
In the formula, Λ represents a Lagrange multiplier; ρ represents a positive scalar.
Alternately solving the frequency deviation index J (x) and the G optimization controller structure index G (x) of the K optimization system according to an alternate direction multiplier method, wherein the alternate solving comprises the following steps:
initialization K0,G0,Λ0(ii) a According to
Figure RE-GDA0003146178780000041
Ask for Kk+1(ii) a According to
Figure RE-GDA0003146178780000042
Calculating Gk+1(ii) a According to Λk+1＝Λk+ρ(Kk+1-Gk+1) Calculating Λk+1(ii) a Judge Kk+1-Gk+1Less than or equal to epsilon and Kk+1-KkIf not, solving K againk+1(ii) a If yes, K is obtained.
In another aspect, the present application provides a frequency controller design system based on an alternating direction multiplier method, including:
the power model module is used for establishing a load frequency control model according to the power system;
the parameter model module is used for establishing a parameter optimization model for controlling the performance and the sparsity of the gain matrix of the controller;
and the parameter optimizing module is used for processing the parameter control performance and the parameter controller gain matrix sparsity in the optimization model by using an alternating direction multiplier method.
Preferably, the power model module includes:
model of ith zone in interconnected power system:
Figure RE-GDA0003146178780000043
Figure RE-GDA0003146178780000044
Figure RE-GDA0003146178780000045
Figure RE-GDA0003146178780000046
n represents the number of zones included in the interconnected power system under study,
Figure RE-GDA0003146178780000047
representing a load disturbance at time t, Δ fi(t) represents the frequency deviation at time t,
Figure RE-GDA0003146178780000048
An active power output adjustment amount at time t,
Figure RE-GDA0003146178780000049
Representing the governor valve position adjustment, delta, at time ti(t) represents the rotor angular deviation at time t,
Figure RE-GDA00031461787800000410
a time constant representing the speed regulator,
Figure RE-GDA00031461787800000411
Indicating steamTime constant of turbine and
Figure RE-GDA00031461787800000412
which represents the time constant of the power system,
Figure RE-GDA00031461787800000413
representing the gain, R, of the power systemiA speed regulation coefficient representing the power system; ksijRepresenting the gain of the connection between zone i and zone j, K if there is no power exchange between these two zonessijIs 0;
rewriting (1) to (4) into a matrix form:
Figure RE-GDA00031461787800000414
Figure RE-GDA00031461787800000415
Figure RE-GDA0003146178780000051
Figure RE-GDA0003146178780000052
in the formula, Xi(t) represents the state vector of region i at time t, Xj(t) represents the state vector, U, of region j at time ti(t) represents the input vector of the controller at time t.
Preferably, the parameter model module includes:
the load frequency control of the interconnected power system of the n regions is expressed as:
Figure RE-GDA0003146178780000053
U＝-KX (6)
in the formula: x ═ X1,X2,…,Xn]；U＝[U1,U2,…,Un]；D＝[ΔPd1,ΔPd2,…,ΔPdn]；
Figure RE-GDA0003146178780000054
K represents a controller gain matrix;
according to the matrix, the proposed load frequency controller design method can be expressed as:
min J(K)+γg(K) (7)
wherein J (X) represents a frequency deviation index, and H is the system2Norm of
Figure RE-GDA0003146178780000055
P is Gramian considerable matrix; g (x) represents a sparsification index of the controller structure, and L is adopted1Norm is expressed as
Figure RE-GDA0003146178780000056
KijRepresenting the ith row and jth column element, W, of the matrix KijRepresents a non-negative weight and when KijW is not equal to 0ij＝1/|KijI, when Kij0 and 0< ε<Time 1W ij1/| epsilon |; γ is a scalar and is a positive number;
subject to(A-B2K)TP+P(A-B2K)
＝-(Q-KTRK) (8)
the equation constraint described by the equation (8) as the system stability condition can be obtained through the theoretical analysis of the dynamic system stability.
Preferably, the parameter optimization module includes:
according to the formula
Figure RE-GDA0003146178780000061
Wherein K represents a variable for controlling performance J (K) and a variable for controlling communication complexity g (G);
according to the formula
Lp(K,G,Λ)＝J(K)+γg(G)+trace(ΛT(K-G)) +(ρ/2)||K-G||2 (10)
In the formula, Λ represents a Lagrange multiplier; ρ represents a positive scalar.
Alternately solving the frequency deviation index J (x) and the G optimization controller structure index G (x) of the K optimization system according to an alternate direction multiplier method, wherein the alternate solving comprises the following steps:
initialization K0,G0,Λ0(ii) a According to
Figure RE-GDA0003146178780000062
Ask for Kk+1(ii) a According to
Figure RE-GDA0003146178780000063
Calculating Gk+1(ii) a According to Λk+1＝Λk+ρ(Kk+1-Gk+1) Calculating Λk+1(ii) a Judge Kk+1-Gk+1Less than or equal to epsilon and Kk+1-KkIf not, solving K againk+1(ii) a If yes, K is obtained.
The application provides a frequency controller design method and system based on an alternating direction multiplier method.
Drawings
FIG. 1 is a flowchart illustrating a method for designing a frequency controller based on an alternative direction multiplier method according to an embodiment;
FIG. 2 is a diagram illustrating a model analysis of an ith area in an interconnected power system according to an embodiment;
FIG. 3 is a flow chart of an ADMM-based distributed optimization algorithm according to an embodiment;
fig. 4 is a block diagram of a frequency controller design system based on an alternative direction multiplier method according to an embodiment.
Detailed Description
The application provides a frequency controller design method and a frequency controller design system based on an alternating direction multiplier method, a distributed optimal Load Frequency Control (LFC) strategy mathematical model is constructed based on quadratic polynomial and matrix sparseness, and an Alternating Direction Multiplier Method (ADMM) is adopted to solve to design a load frequency controller with frequency deviation of 0 and excellent dynamic performance, so that more optimized controller parameters are solved, and an optimal solution cannot necessarily be obtained by a heuristic optimization algorithm.
The present application relates to a method for designing a frequency controller based on an alternating direction multiplier method, as shown in fig. 1,
s10, establishing a load frequency control model according to the power system;
s20, establishing a parameter optimization model for controlling the performance and the sparsity of the gain matrix of the controller;
and S30, processing the parameter control performance and the parameter controller gain matrix sparsity in the optimization model by using an alternating direction multiplier method.
In an optimization model constructed by an optimal FLC strategy, an objective function comprises two terms which respectively represent control performance and controller gain matrix sparsity, so that double objectives of zero frequency deviation and optimal system dynamic performance are achieved, the response speed of a system is improved, and meanwhile, oscillation and instability of system frequency caused by deterioration of system dynamic behavior are reduced. The frequency control performance equivalent to that of a centralized control strategy can be obtained, and the communication complexity is low; then, an Alternating Direction Multiplier Method (ADMM) is adopted to solve the optimization problem, the optimization target can be decomposed into two sub-optimization problems which can be solved in an analytic mode by utilizing the characteristics of the ADMM, and further the parameter setting efficiency is improved, and the method is suitable for an actual multi-region power system.
Specifically, in an embodiment of the present application, an implementation process includes the following detailed steps:
and S10, establishing a load frequency control model according to the power system. Each region in the regional interconnected power system is provided with a dispatching control center, and the system frequency and the exchange power on the inter-region tie lines are monitored. Consider, in building each load frequency model: at present, most of turbonators and hydraulic generators are provided with speed regulating devices, and the generators can respond to the frequency change of a system; the load frequency control aims at small disturbance, and two conditions of a linear model can be approximately adopted. Fig. 2 shows a block diagram of a load frequency control system of an ith zone in a zone interconnected power system constructed in the present application.
Figure RE-GDA0003146178780000071
Figure RE-GDA0003146178780000072
Figure RE-GDA0003146178780000073
Figure RE-GDA0003146178780000074
In the formula: n represents the number of zones included in the interconnected power system under study;
Figure RE-GDA0003146178780000075
representing a load disturbance at time t; Δ fi(t)、
Figure RE-GDA0003146178780000076
And deltai(t) respectively representing frequency deviation, active power output adjustment quantity, speed regulator valve position adjustment quantity and rotor angle deviation at the moment t;
Figure RE-GDA0003146178780000077
and
Figure RE-GDA0003146178780000078
respectively representing the time constants of the speed regulator, the steam turbine and the power system;
Figure RE-GDA0003146178780000079
and RiRespectively representing the gain and speed regulation coefficients of the power system; ksijRepresenting the gain of the connection between zone i and zone j, K if there is no power exchange between these two zonessijIs 0.
For the purpose of explanation of the subsequent design method, the differential equation sets (1) to (4) for describing the model are rewritten into a matrix form:
Figure RE-GDA00031461787800000710
in the formula:
Figure RE-GDA0003146178780000081
Figure RE-GDA0003146178780000082
Figure RE-GDA0003146178780000083
in the formula: xi(t) and Xj(t) represents the state vectors of region i and region j, respectively, at time t; ui (t) represents the input vector of the controller at time t.
And S20, establishing a parameter optimization model for controlling the performance and the sparsity of the gain matrix of the controller. Based on the load frequency control model, the present application proposes a design method of a distributed optimal load frequency controller based on an alternating direction multiplier (ADMM).
According to equation (5), the load frequency control problem of the interconnected power system comprising n zones can be described as:
Figure RE-GDA0003146178780000084
U＝-KX (6)
in the formula: x ═ X1,X2,…,Xn]；U＝[U1,U2,…,Un]；D＝[ΔPd1,ΔPd2,…,ΔPdn]；
Figure RE-GDA0003146178780000085
Where K represents the controller gain matrix.
The design method of the optimal load frequency controller has two objective functions: the method comprises the following steps of firstly, performing secondary optimal control performance, namely a frequency deviation index of a load disturbance passing through a load frequency controller in an area; second, controller gain matrix sparsity.
The load frequency controller design method proposed in the present application can be described by the following optimization problem:
min J(K)+γg(K) (7)
wherein J (X) represents a frequency deviation index, and H is the system2Norm of
Figure RE-GDA0003146178780000086
P is Gramian considerable matrix; g (x) represents a sparsification index of the controller structure, and L is adopted1Norm is expressed as
Figure RE-GDA0003146178780000087
KijRepresenting the ith row and jth column element, W, of the matrix KijRepresents a non-negative weight and when KijW is not equal to 0ij＝1/|KijI, when Kij0 and 0< ε<Time 1W ij1/| epsilon |; γ is a scalar and is a positive number.
For the optimization problem of objective function minimization, larger γ means smaller g (x), i.e. sparser matrix K. By adding the controller sparsification index g (x) into the target function, the elements of the controller gain matrix K can be made to be zero as much as possible on the premise of ensuring the optimal control performance, so that the number of signals needing to be fed back is reduced.
subject to(A-B2K)TP+P(A-B2K)
＝-(Q-KTRK) (8)
The equation constraint described by the equation (8) as the system stability condition can be obtained through the theoretical analysis of the dynamic system stability.
And S30, processing the parameter control performance and the parameter controller gain matrix sparsity in the optimization model by using an alternating direction multiplier method. The optimization model containing the control performance index J and the communication complexity index g described in the formulas (7) and (8) can be effectively solved by adopting an ADMM algorithm. The ADMM algorithm decomposes the optimization problem required to be solved into two sub-optimization problems, and then alternately and iteratively solves the two sub-optimization problems to finally obtain the solution of the original optimization problem.
In the present application, the strategy for implementing distributed optimal load frequency control by using ADMM is described as the following optimization problem:
Figure RE-GDA0003146178780000091
to facilitate the application of the ADMM algorithm, the variables in the control performance j (K) and the communication complexity G (G) are represented by K and G in equation (9), respectively. The variables K and G are equal according to the algebraic constraint K-G ═ 0. As can be seen from equation (9), the optimization model described by equations (7) and (8) can be decomposed into two sub-problems 1) the frequency deviation index J (x) for the K optimization system; 2) the controller structure index G (x) is optimized for G. According to the method framework of the ADMM, the two sub-problems are solved alternately, and finally, the distributed optimal load frequency control strategy can be obtained. The process of solving the optimization problem described in equation (9) using the ADMM algorithm is shown in fig. 3.
Alternately solving the frequency deviation index J (x) and the G optimization controller structure index G (x) of the K optimization system according to an alternate direction multiplier method, wherein the alternate solving comprises the following steps:
initialization K0,G0,Λ0(ii) a According to
Figure RE-GDA0003146178780000092
Ask for Kk+1(ii) a According to
Figure RE-GDA0003146178780000093
Calculating Gk+1(ii) a According to Λk+1＝Λk+ρ(Kk+1-Gk+1) Calculating Λk+1(ii) a Judge Kk+1-Gk+1Less than or equal to epsilon and Kk+1-KkIf not, solving K againk+1(ii) a If yes, K is obtained.
Lp is calculated as:
Lp(K,G,Λ)＝J(K)+γg(G)+trace(ΛT(K-G)) +(ρ/2)||K-G||2 (10)
in the formula, Λ represents a Lagrange multiplier; ρ represents a positive scalar.
The design of the application utilizes the characteristics of ADMM to decompose an optimization target into two sub-optimization problems which can be solved in an analytic mode, so that the parameter setting efficiency is improved, and the method is suitable for an actual multi-region power system. The frequency control is carried out through the optimal LFC strategy, so that the frequency deviation is zero and the dynamic performance of the system is optimal. The calculation efficiency of the parameter setting of the controller is improved while the frequency control performance of the system is optimized. The frequency control performance equivalent to that of a centralized control strategy can be obtained, and the communication complexity is low.
In another aspect, referring to fig. 4, the present application provides a frequency controller design system based on an alternating direction multiplier method, including:
the power model module is used for establishing a load frequency control model according to the power system;
the parameter model module is used for establishing a parameter optimization model for controlling the performance and the sparsity of the gain matrix of the controller;
and the parameter optimizing module is used for processing the parameter control performance and the parameter controller gain matrix sparsity in the optimization model by using an alternating direction multiplier method.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (8)

1. A frequency controller design method based on an alternating direction multiplier method comprises the following steps:
s10, establishing a load frequency control model according to the power system;
s20, establishing an optimization model with the control performance and the sparsity of the gain matrix of the controller as parameters;
and S30, processing the parameter control performance and the parameter controller gain matrix sparsity in the optimization model by using an alternating direction multiplier method.
2. The method for designing a frequency controller based on the alternating direction multiplier method according to claim 1, wherein the method for establishing the load frequency control model according to the power system comprises the following steps:
model of ith zone in interconnected power system:
Figure RE-FDA0003146178770000011
Figure RE-FDA0003146178770000012
Figure RE-FDA0003146178770000013
Figure RE-FDA0003146178770000014
wherein N represents the number of zones included in the interconnected power system under study,
Figure RE-FDA0003146178770000015
representing a load disturbance at time t, Δ fi(t) represents the frequency deviation at time t,
Figure RE-FDA0003146178770000016
An active power output adjustment amount at time t,
Figure RE-FDA0003146178770000017
Representing the governor valve position adjustment, delta, at time ti(t) represents the rotor angular deviation at time t,
Figure RE-FDA0003146178770000018
a time constant representing the speed regulator,
Figure RE-FDA0003146178770000019
Representing the time constant of the turbine and
Figure RE-FDA00031461787700000110
which represents the time constant of the power system,
Figure RE-FDA00031461787700000111
representing the gain, R, of the power systemiA speed regulation coefficient representing the power system; ksijIndicating the gain of the connection between region i and region j if there is no work between the two regionsRate exchange rule KsijIs 0;
rewriting (1) to (4) into a matrix form:
Figure RE-FDA00031461787700000112
Figure RE-FDA00031461787700000113
Figure RE-FDA00031461787700000114
Figure RE-FDA0003146178770000021
in the formula, Xi(t) represents the state vector of region i at time t, Xj(t) represents the state vector, U, of region j at time ti(t) represents the input vector of the controller at time t.
3. The method according to claim 2, wherein the method for establishing the parameter optimization model based on the sparsity of the control performance and the controller gain matrix comprises:
the load frequency control of the interconnected power system of the n regions is expressed as:
Figure RE-FDA0003146178770000022
U＝-KX (6)
in the formula: x ═ X1,X2,…,Xn]；U＝[U1,U2,…,Un]；D＝[ΔPd1,ΔPd2,…,ΔPdn]；
Figure RE-FDA0003146178770000023
K represents a controller gain matrix;
according to the matrix, the proposed load frequency controller design method can be expressed as:
min J(K)+γg(K) (7)
wherein J (X) represents a frequency deviation index, and H is the system2Norm of
Figure RE-FDA0003146178770000024
P is Gramian considerable matrix; g (x) represents a sparsification index of the controller structure, and L is adopted1Norm is expressed as
Figure RE-FDA0003146178770000025
KijRepresenting the ith row and jth column element, W, of the matrix KijRepresents a non-negative weight and when KijW is not equal to 0ij＝1/|KijI, when Kij0 and 0<ε<Time 1Wij1/| epsilon |; γ is a scalar and is a positive number;
subject to(A-B2K)TP+P(A-B2K)
＝-(Q-KTRK) (8)
the equation constraint described by the equation (8) as the system stability condition can be obtained through the theoretical analysis of the dynamic system stability.
4. The method as claimed in claim 3, wherein the method for processing the parameter control performance and the sparsity of the gain matrix of the parameter controller in the optimization model by using the alternative direction multiplier method comprises:
according to the formula
Figure RE-FDA0003146178770000031
Wherein K represents a variable for controlling performance J (K) and a variable for controlling communication complexity g (G);
according to the formula
Figure RE-FDA0003146178770000032
In the formula, Λ represents a Lagrange multiplier; ρ represents a positive scalar;
alternately solving the frequency deviation index J (x) and the G optimization controller structure index G (x) of the K optimization system according to an alternate direction multiplier method, wherein the alternate solving comprises the following steps:
initialization K0,G0,Λ0(ii) a According to
Figure RE-FDA0003146178770000033
Ask for Kk+1(ii) a According to
Figure RE-FDA0003146178770000034
Calculating Gk+1(ii) a According to Λk+1＝Λk+ρ(Kk+1-Gk+1) Calculating Λk+1(ii) a Judge Kk+1-Gk+1Less than or equal to epsilon and Kk+1-KkIf not, solving K againk +1(ii) a If yes, K is obtained.
5. A system for designing a frequency controller based on an alternating direction multiplier method, comprising:
the power model module is used for establishing a load frequency control model according to the power system;
the parameter model module is used for establishing a parameter optimization model for controlling the performance and the sparsity of the gain matrix of the controller;
and the parameter optimizing module is used for processing the parameter control performance and the parameter controller gain matrix sparsity in the optimization model by using an alternating direction multiplier method.
6. The system according to claim 5, wherein the power model module comprises:
model of ith zone in interconnected power system:
Figure RE-FDA0003146178770000035
Figure RE-FDA0003146178770000036
Figure RE-FDA0003146178770000037
Figure RE-FDA0003146178770000038
n represents the number of zones included in the interconnected power system under study,
Figure RE-FDA0003146178770000039
representing a load disturbance at time t, Δ fi(t) represents the frequency deviation at time t,
Figure RE-FDA00031461787700000310
An active power output adjustment amount at time t,
Figure RE-FDA00031461787700000311
Representing the governor valve position adjustment, delta, at time ti(t) represents the rotor angular deviation at time t,
Figure RE-FDA00031461787700000312
a time constant representing the speed regulator,
Figure RE-FDA00031461787700000313
Representing the time constant of the turbine and
Figure RE-FDA00031461787700000314
which represents the time constant of the power system,
Figure RE-FDA00031461787700000315
representing the gain, R, of the power systemiA speed regulation coefficient representing the power system; ksijRepresenting the gain of the connection between zone i and zone j, K if there is no power exchange between these two zonessijIs 0;
rewriting (1) to (4) into a matrix form:
Figure RE-FDA0003146178770000041
Figure RE-FDA0003146178770000042
Figure RE-FDA0003146178770000043
Figure RE-FDA0003146178770000044
in the formula, Xi(t) represents the state vector of region i at time t, Xj(t) represents the state vector, U, of region j at time ti(t) represents the input vector of the controller at time t.
7. The system according to claim 6, wherein the parametric model module comprises:
the load frequency control of the interconnected power system of the n regions is expressed as:
Figure RE-FDA0003146178770000045
U＝-KX (6)
in the formula: x ═ X1,X2,…,Xn]；U＝[U1,U2,…,Un]；D＝[ΔPd1,ΔPd2,…,ΔPdn]；
Figure RE-FDA0003146178770000046
K represents a controller gain matrix;
according to the matrix, the proposed load frequency controller design method can be expressed as:
min J(K)+γg(K) (7)
wherein J (X) represents a frequency deviation index, and H is the system2Norm of
Figure RE-FDA0003146178770000047
P is Gramian considerable matrix; g (x) represents a sparsification index of the controller structure, and L is adopted1Norm is expressed as
Figure RE-FDA0003146178770000051
KijRepresenting the ith row and jth column element, W, of the matrix KijRepresents a non-negative weight and when KijW is not equal to 0ij＝1/|KijI, when Kij0 and 0<ε<Time 1Wij1/| epsilon |; γ is a scalar and is a positive number;
subject to(A-B2K)TP+P(A-B2K)
＝-(Q-KTRK) (8)
the equation constraint described by the equation (8) as the system stability condition can be obtained through the theoretical analysis of the dynamic system stability.
8. The system of claim 7, wherein the parameter optimization module comprises:
according to the formula
Figure RE-FDA0003146178770000052
Wherein K represents a variable for controlling performance J (K) and a variable for controlling communication complexity g (G);
according to the formula
Lp(K,G,Λ)＝J(K)+γg(G)+trace(ΛT(K-G))+(ρ/2)||K-G||2 (10)
In the formula, Λ represents a Lagrange multiplier; ρ represents a positive scalar;
alternately solving the frequency deviation index J (x) and the G optimization controller structure index G (x) of the K optimization system according to an alternate direction multiplier method, wherein the alternate solving comprises the following steps:
initialization K0,G0,Λ0(ii) a According to
Figure RE-FDA0003146178770000053
Ask for Kk+1(ii) a According to
Figure RE-FDA0003146178770000054
Calculating Gk+1(ii) a According to Λk+1＝Λk+ρ(Kk+1-Gk+1) Calculating Λk+1(ii) a Judge Kk+1-Gk+1Less than or equal to epsilon and Kk+1-KkIf not, solving K againk +1(ii) a If yes, K is obtained.
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