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CN113300386B - 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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CN113300386B
CN113300386B CN202110564669.3A CN202110564669A CN113300386B CN 113300386 B CN113300386 B CN 113300386B CN 202110564669 A CN202110564669 A CN 202110564669A CN 113300386 B CN113300386 B CN 113300386B
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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 to solve 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 zones 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. The method comprises the following steps of adopting a robust control strategy to restrain system frequency deviation caused by load change, adopting an adaptive control strategy to improve system control performance when a system operating point changes, and adopting an optimal control strategy to restrain the system frequency deviation and call wire 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 actual multi-zone power system load frequency controller, 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 usually needs to carry out reduction preprocessing on a system model, so that the loss of partial dynamic characteristics of the system can be caused. Some load frequency controllers are designed by adopting a heuristic optimization algorithm, including setting controller parameters by adopting a particle swarm optimization algorithm and determining parameters of a fractional order controller by adopting a grey wolf optimization algorithm. However, it is theoretically not guaranteed that the heuristic optimization algorithms can obtain the optimal solution of the controller parameters, and particularly for an actual multi-region power system, the number of the controller parameters to be optimized is large, and the heuristic optimization algorithms cannot necessarily obtain the optimal solution.
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 sparsification, 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 optimized controller has more parameters and a heuristic optimization algorithm can not necessarily solve the optimal solution 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 includes:
model of ith zone in interconnected power system:
Figure GDA0003146178780000021
Figure GDA0003146178780000022
Figure GDA0003146178780000023
Figure GDA0003146178780000024
n represents the number of zones included in the interconnected power system under study,
Figure GDA0003146178780000025
representing a load disturbance at time t, Δ fi(t) shows a frequency deviation at time t,
Figure GDA0003146178780000026
An active power output adjustment amount at time t,
Figure GDA0003146178780000027
Governor valve position adjustment, Δ δ, at time ti(t) represents the rotor angular deviation at time t,
Figure GDA0003146178780000028
showing the time constant of the governor,
Figure GDA0003146178780000029
Representing time constants of steam turbine and
Figure GDA00031461787800000210
which represents the time constant of the power system,
Figure GDA00031461787800000211
representing the gain, R, of the power systemiA speed regulation coefficient representing the power system; k issijRepresenting 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) - (4) into a matrix form:
Figure GDA00031461787800000212
Figure GDA00031461787800000213
Figure GDA00031461787800000214
Figure 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 based on the control performance and the sparsity of the controller gain matrix comprises the following steps:
the load frequency control of the interconnected power systems of the n regions is expressed as:
Figure GDA0003146178780000031
U＝-KX (6)
in the formula: x ═ X1,X2,…,Xn]；U＝[U1,U2,…,Un]；D＝[ΔPd1,ΔPd2,…,ΔPdn]；
Figure GDA0003146178780000032
K represents a controller gain matrix;
according to the matrix, the proposed load frequency controller design method can be expressed as follows:
min J(K)+γg(K) (7)
wherein J (X) represents a frequency deviation index, and H is the number of the system2Norm of
Figure GDA0003146178780000033
P is a Gramian observable matrix; g (X) represents a sparseness index of the controller structure, and L is adopted1Norm is expressed as
Figure GDA0003146178780000034
KijDenotes 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/|KijWhen 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 equation (8) as the system stability condition can be obtained by the theoretical analysis of the dynamic system stability.
Preferably, the method for processing the parameter control performance and the parameter controller gain matrix sparsity in the optimization model by using the alternating direction multiplier method comprises the following steps:
according to the formula
Figure 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 GDA0003146178780000036
In the formula, Λ represents a Lagrange multiplier; ρ represents a positive scalar.
Alternately solving a frequency deviation index J (x) of the K optimization system and a G optimization controller structure index G (x) according to an alternate direction multiplier method, wherein the alternate solving comprises the following steps:
initialization K0,G0,Λ0(ii) a According to
Figure GDA0003146178780000041
Ask for Kk+1(ii) a According to
Figure GDA0003146178780000042
Calculating Gk+1(ii) a According to Λk+1＝Λk+ρ(Kk+1-Gk+1) Calculating Λk+1(ii) a Judge K | |k+1-Gk+1| | < 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 GDA0003146178780000043
Figure GDA0003146178780000044
Figure GDA0003146178780000045
Figure GDA0003146178780000046
n denotes the number of zones included in the interconnected power system under study,
Figure GDA0003146178780000047
representing a load disturbance at time t, Δ fi(t) represents the frequency deviation at time t,
Figure GDA0003146178780000048
An active power output adjustment amount at time t,
Figure GDA0003146178780000049
Representing the governor valve position adjustment, delta, at time ti(t) represents the rotor angular deviation at time t,
Figure GDA00031461787800000410
showing the time constant of the governor,
Figure GDA00031461787800000411
Representing time constants of steam turbine and
Figure GDA00031461787800000412
which represents the time constant of the power system,
Figure GDA00031461787800000413
representing the gain, R, of the power systemiA speed regulation coefficient representing the power system; k issijDenotes 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 GDA00031461787800000414
Figure GDA00031461787800000415
Figure GDA0003146178780000051
Figure 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 GDA0003146178780000053
U＝-KX (6)
in the formula: x ═ X1,X2,…,Xn]；U＝[U1,U2,…,Un]；D＝[ΔPd1,ΔPd2,…,ΔPdn]；
Figure 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 number of the system2Norm of
Figure GDA0003146178780000055
P is a Gramian observable matrix; g (X) represents a sparseness index of the controller structure, and L is adopted1Norm is expressed as
Figure GDA0003146178780000056
KijDenotes the ith row and jth column element, W, of the matrix KijRepresenting non-negative weightsAnd 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 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 GDA0003146178780000062
Ask for Kk+1(ii) a According to
Figure GDA0003146178780000063
Calculating Gk+1(ii) a According to Λk+1＝Λk+ρ(Kk+1-Gk+1) Calculating Λk+1(ii) a Judge K | |k+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 zone 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 with control performance and controller gain matrix sparsity;
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 hydro-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 GDA0003146178780000071
Figure GDA0003146178780000072
Figure GDA0003146178780000073
Figure GDA0003146178780000074
In the formula: n represents the number of zones included in the interconnected power system under study;
Figure GDA0003146178780000075
representing a load disturbance at time t; Δ fi(t)、
Figure GDA0003146178780000076
And Δ δi(t) respectively representing frequency deviation, active power output adjustment quantity, governor valve position adjustment quantity and rotor angle deviation at the moment t;
Figure GDA0003146178780000077
and
Figure GDA0003146178780000078
respectively representing the time constants of the speed regulator, the steam turbine and the power system;
Figure GDA0003146178780000079
and RiRespectively representing the gain and speed regulation coefficients of the power system; k issijDenotes 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 convenience of explanation of the subsequent design method, the differential equations (1) to (4) for describing the model are rewritten into a matrix form:
Figure GDA00031461787800000710
in the formula:
Figure GDA0003146178780000081
Figure GDA0003146178780000082
Figure 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 including n zones can be described as:
Figure GDA0003146178780000084
U＝-KX (6)
in the formula: x ═ X1,X2,…,Xn]；U＝[U1,U2,…,Un]；D＝[ΔPd1,ΔPd2,…,ΔPdn]；
Figure 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 that firstly, the quadratic optimal control performance is the frequency deviation index of load disturbance passing through a load frequency controller in one area; second, the sparsity of the gain matrix of the controller.
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 number of the system2Norm of
Figure GDA0003146178780000086
P is Gramian considerable matrix; g (X) represents a sparseness index of the controller structure, and L is adopted1Norm is expressed as
Figure GDA0003146178780000087
KijDenotes 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/|KijWhen 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 equation (8) as the system stability condition can be obtained by 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 comprising 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 optimization problem required to be solved is decomposed into two sub-optimization problems by the ADMM algorithm, the two sub-optimization problems are alternately and iteratively solved, and finally the solution of the original optimization problem is obtained.
In the present application, the strategy for implementing distributed optimal load frequency control by using ADMM is described as the following optimization problem:
Figure GDA0003146178780000091
to facilitate the application of the ADMM algorithm, K and G are used in equation (9) to represent the variables in control performance j (K) and communication complexity G (G), respectively. According to the algebraic constraint K-G-0, the variables K and G are equal. 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 GDA0003146178780000092
Ask for Kk+1(ii) a According to
Figure 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.
All possible combinations of the technical features of the above embodiments may not be described for the sake of brevity, but should be considered as within the scope of the present disclosure 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 various changes and modifications can be made by those skilled in the art without departing from the spirit of the invention, and these changes and modifications are all within the scope of the invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (4)

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;
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 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 FDA0003586399660000011
Figure FDA0003586399660000012
Figure FDA0003586399660000013
Figure FDA0003586399660000014
wherein N represents the number of zones included in the interconnected power system under study,
Figure FDA0003586399660000015
representing a load disturbance at time t, Δ fi(t) represents the frequency deviation at time t,
Figure FDA0003586399660000016
An active power output adjustment amount at time t,
Figure FDA0003586399660000017
Governor valve position adjustment, Δ δ, at time ti(t) represents the rotor angular deviation at time t,
Figure FDA0003586399660000018
a time constant representing the speed regulator,
Figure FDA0003586399660000019
Representing the time constant of the turbine and
Figure FDA00035863996600000110
which represents the time constant of the power system,
Figure FDA00035863996600000111
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 FDA00035863996600000112
Figure FDA00035863996600000113
Figure FDA00035863996600000114
Figure FDA0003586399660000021
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;
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 FDA0003586399660000022
U＝-KX (6)
in the formula: x ═ X1,X2,…,Xn]；U＝[U1,U2,…,Un]；D＝[ΔPd1,ΔPd2,…,ΔPdn]；
Figure FDA0003586399660000023
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: (×) Indicating the frequency deviation index, using the system H2Norm trace (B)1 TPB1) (ii) a P is Gramian considerable matrix; g (b)×) Expressing the sparseness index of the controller structure, using L1Norm is expressed as
Figure FDA0003586399660000024
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 equation (8) as the system stability condition can be obtained by the theoretical analysis of the dynamic system stability.
2. The method for designing the frequency controller based on the alternating direction multiplier method as claimed in claim 1, 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 alternating direction multiplier method comprises:
according to the formula
Figure FDA0003586399660000025
Wherein K and G both represent controller gain matrices;
according to the formula
Figure FDA0003586399660000031
In the formula, Λ represents a Lagrange multiplier; ρ represents a positive scalar;
frequency deviation index J (J) of K optimization system according to alternative direction multiplier method×) And G optimizing a controller structure index G: (×) And (3) alternately solving, including:
initialization K0,G0,Λ0(ii) a According to
Figure FDA0003586399660000032
Ask for Kk+1(ii) a According to
Figure FDA0003586399660000033
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, then K is calculated againk +1(ii) a If yes, K is obtained.
3. 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;
the optimization parameter 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 power model module comprises:
model of ith zone in interconnected power system:
Figure FDA0003586399660000034
Figure FDA0003586399660000035
Figure FDA0003586399660000036
Figure FDA0003586399660000037
n denotes the number of zones included in the interconnected power system under study,
Figure FDA0003586399660000038
representing a load disturbance at time t, Δ fi(t) shows a frequency deviation at time t,
Figure FDA0003586399660000039
An active power output adjustment amount at time t,
Figure FDA00035863996600000310
Governor valve position adjustment, Δ δ, at time ti(t) represents the rotor angular deviation at time t,
Figure FDA00035863996600000311
a time constant representing the speed regulator,
Figure FDA00035863996600000312
Representing the time constant of the turbine and
Figure FDA00035863996600000313
which represents the time constant of the power system,
Figure FDA00035863996600000314
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 FDA00035863996600000315
Figure FDA0003586399660000041
Figure FDA0003586399660000042
Figure FDA0003586399660000043
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;
the parametric model module includes:
the load frequency control of the interconnected power systems of the n regions is expressed as:
Figure FDA0003586399660000044
U＝-KX (6)
in the formula: x ═ X1,X2,…,Xn]；U＝[U1,U2,…,Un]；D＝[ΔPd1,ΔPd2,…,ΔPdn]；
Figure FDA0003586399660000045
K represents a controller gain matrix;
according to the matrix, the proposed load frequency controller design method can be expressed as follows:
min J(K)+γg(K) (7)
wherein J: (×) Indicating the frequency deviation index, using H of the system2Norm of
Figure FDA0003586399660000046
P is a Gramian observable matrix; g (b)×) Expressing the sparseness index of the controller structure, using L1Norm is expressed as
Figure FDA0003586399660000047
KijDenotes 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 system of claim 3, wherein the parameter optimization module comprises:
according to the formula
Figure FDA0003586399660000051
Wherein K and G both represent controller gain matrices;
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;
frequency deviation index J (J) of K optimization system according to alternative direction multiplier method×) And G optimizing the controller structure index G: (×) And (3) alternately solving, comprising:
initialization K0,G0,Λ0(ii) a According to
Figure FDA0003586399660000052
Ask for Kk+1(ii) a According to
Figure FDA0003586399660000053
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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