CN113162063B - Design method of multi-direct-current coordination controller for inhibiting ultralow frequency oscillation - Google Patents

Design method of multi-direct-current coordination controller for inhibiting ultralow frequency oscillation Download PDF

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CN113162063B
CN113162063B CN202110149535.5A CN202110149535A CN113162063B CN 113162063 B CN113162063 B CN 113162063B CN 202110149535 A CN202110149535 A CN 202110149535A CN 113162063 B CN113162063 B CN 113162063B
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direct current
coordinated controller
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CN113162063A (en
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伍文城
王晓茹
曾雪松
李文帆
李天鸷
陈谦
李彬
邹朋
杨帆
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Southwest Jiaotong University
Southwest Electric Power Design Institute Co Ltd of China Power Engineering Consulting Group
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/48—Controlling the sharing of the in-phase component
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/50—Controlling the sharing of the out-of-phase component
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin

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Abstract

The invention provides a design method of a multi-direct current coordination controller for inhibiting ultralow frequency oscillation, which comprises the steps of firstly establishing a state space model of an open-loop system, then randomly generating a series of controllers to be selected, obtaining a closed-loop system matrix and a characteristic value thereof, screening a stable closed-loop system matrix through the characteristic value, obtaining the minimum damping ratio of all the modes of the stable closed-loop system matrix, and finding out the maximum minimum damping ratio of the stable closed-loop system matrix through comparison. In order to optimize the performance of the controller, a differential evolution algorithm is applied to generate a new generation of controller to be tested, and the maximization of the minimum damping ratio of a closed-loop system is realized through loop iteration, so that the damping of all oscillation modes including an ultra-low frequency mode is improved. The invention can realize the design of a centralized type, a distributed type based on a lead-lag compensator structure and other three types of multi-direct-current coordinated controllers in one set of algorithm, and is convenient for comparing the performance of the coordinated controllers with various structures.

Description

Design method of multi-direct-current coordination controller for inhibiting ultralow frequency oscillation
Technical Field
The invention relates to the technical field of power systems, in particular to a design method of a multi-direct-current coordination controller for inhibiting ultralow frequency oscillation.
Background
In order to cope with climate change, the proportion of clean energy represented by hydropower in an electric power system is higher and higher, but when the proportion of the hydropower reaches a certain scale, the system also has an ultralow frequency oscillation phenomenon with the frequency lower than 0.1 Hz. According to reports, ultralow frequency oscillation often occurs in small power grids mainly comprising hydropower or isolated power grids, such as domestic power grids in the zang region, Yuguang and Jinsu direct current island systems; or an ultra-low frequency phenomenon occurs in the debugging process of an asynchronous networking system which is interconnected through direct current, such as 2016 (2016) asynchronous networking of a Yunnan power grid and a southern main grid, and 2018 asynchronous networking of southwest and China.
According to the current research, the system generates ultra-low frequency oscillation, mainly because the speed regulator parameters of the hydroelectric generating set in a power grid are unreasonable and the water hammer effect causes the phase difference between the power regulation of the water turbine and the waveform of the system frequency oscillation to be close to 90 degrees, and the water turbine has nearly half of the oscillation period to be in a reverse regulation state, namely the output of the water turbine is increased when the system frequency is increased, so that the system frequency oscillation is intensified. The over-small proportional constant, the over-large integral constant, or the over-large time constant of the water hammer effect of the speed regulator are not good for the stability of the system. Based on the above knowledge, the literature on the current research on ultra-low frequency oscillation suppression measures mainly focuses on how to optimize the parameters of the speed regulator of the hydroelectric generating set or the stabilizer of the power system. In an actual system, the damping characteristic and the adjusting performance of the speed regulating system are limited by the hydraulic system, the fixed parameters of the water turbine and the primary frequency modulation capability of the system, so that the problem of the frequency stability of the system cannot be solved ideally by optimizing the parameters of the speed regulating system. According to the research on the southwest power grid, the damping of the ultralow frequency oscillation mode is only improved to 2%, that is, the parameters of 138 unit speed regulators in the power grid need to be optimized, which is a huge workload.
With the progress of research, it is gradually recognized that the imbalance between the generator power and the system load power is a direct cause of the frequency oscillation of the high-water-electricity-ratio system. After the asynchronous interconnection of the system, the load power depends on the direct current transmission power and the local load, when the local load or the direct current system transmission power changes, disturbance to the system frequency is generated, and if the water-electricity ratio of the system is high, ultralow frequency oscillation is also induced. Therefore, aiming at the ultra-low frequency oscillation phenomenon occurring in the direct current asynchronous interconnection power grid, the damping is improved by utilizing the additional control function of the direct current, and the method is also a potential scheme concerned by engineering technicians.
The structure of the multi-loop direct current coordination control system has two modes, one mode is centralized, a central controller is arranged in the system and used for acquiring a plurality of wide area signals from the system and sending power modulation commands to each loop of direct current, and the power modulation commands are shown in fig. 1; the other is distributed type, in which a central controller is not installed in the system, but a separate controller is installed in each loop of dc power, and the dc power transmitted by the loop is modulated according to the input signal received by the controller, as shown in fig. 2. Based on the difference of feedback signals, the control system can be divided into two categories of state feedback and output feedback.
The existing multi-direct current coordination controller has the following problems in a longitudinal view: (1) whether centralized coordination control or distributed coordination control is adopted, the given controller structure is greatly different from the actually adopted proportional-integral or lead-lag controller structure, and is difficult to be adopted by engineering technicians; (2) most of the systems are based on state feedback, but the actual system states are not all observable, and the popularization and application in the actual system are difficult. From the existing results, a state feedback-based multi-direct current coordinated control system has a mature design method. However, partial state variables of the power system, such as quadrature axis transient potentials, are not easy to measure, so that it is difficult to realize full state quantity feedback of the unit, and the method realized based on the state variables is susceptible to model accuracy in practical application. Local output feedback quantities which are usually and conveniently obtained by an alternating current-direct current system comprise a power angle, a rotating speed, an excitation voltage, electromagnetic power, terminal voltage and current of a generator and the like, and the popularization of PMU enables output feedback control based on a remote input signal to be relatively easily realized, so that a design method based on output feedback has higher practical value in a power system. The multi-direct current control co-modulator is a multi-input multi-output MIMO problem, damping ratio constraint is added, a controller design problem based on output feedback is represented as a bilinear matrix inequality problem, the problem is NP-difficult, the controller is difficult to solve, and although methods such as road following, projective transformation, homotopic transformation and the like can convert the controller into a linear matrix inequality which is easy to solve. According to the application experience of the inventor, the method is generally only suitable for systems with lower orders, such as a system with more than ten orders, and whether the solution can be successfully solved has certain uncertainty. In engineering practice, the control effects of multiple controller structural types need to be compared in the controller design stage, so a unified coordinated controller design method is expected to achieve the following goals: (1) the controller is based on the output feedback type for implementation; (2) the design method can conveniently compare the performance of the coordinated controller with a centralized structure and a distributed structure, and comprises the adoption of a common controller structure based on the lead-lag shown in figure 3 in the sub-controllers in the distributed structure; (3) the design method can specify the order of the controller so as to avoid the problem of performance degradation caused by the order reduction of the controller; (4) the design method can be applied to relatively large-scale systems. From the prior literature reports, a design method of a multi-DC coordinated controller capable of simultaneously realizing 4 targets is not reported. The bottleneck for achieving the above goal is the difficulty of solving the output feedback controller, because when the matrix inequality method is used for solving, the product form of the unknown system matrix and the unknown controller matrix exists, so that the system matrix is a bilinear matrix inequality, which is very difficult to solve, but if the controller matrix is generated randomly, and then the inequality converted into the LMI at this time is checked, the solution thought is greatly simplified.
Disclosure of Invention
The invention aims to provide a design method of a multi-direct-current coordination controller for inhibiting ultralow frequency oscillation, which aims to solve the problem of ultralow frequency oscillation of a high-water-power specific gravity system.
The invention provides a design method of a multi-direct current coordination controller for inhibiting ultralow frequency oscillation, which comprises the following steps:
step 1: inputting power system model state space model parameters A, B, C, D; dimension n of input and output signals u 、n y (ii) a Setting the order of the multiple DC coordinated controllers to be solved and the number n of DC loops d (ii) a The structure types of the multi-DC coordinated controller to be solved comprise a centralized type, a distributed type or a distributed type based on a lead-lag compensator structure; initializing differential evolution parameters including a scaling factor F, a cross probability constant CR and a population size N p (ii) a Maximum number of iterations g max (ii) a An iteration error limit epsilon, and setting the initial iteration time g to be 1;
step 2: calculating the number n of decision variables according to the structure type of the multi-DC coordinated controller to be solved v And randomly generating a random number including N p Multiple direct current coordinated controller initial population matrix to be solved for each controller
Figure GDA0003756905810000031
The ith row vector of the initial population matrix represents the ith controller individual K i ；
And step 3: selecting a corresponding method according to the structure type of the multi-DC coordinated controller to be solved to enable N to be obtained p Individual controller K i Converting the parameters into matrix parameters of a state space equation of the controller to be solved, and generating a corresponding closed-loop system matrix A ci ；
And 4, step 4: calculating each closed loop system matrix A ci And judging a closed-loop system matrix A according to the characteristic value ci Whether or not to stabilize, for stabilizing closed loop system matrix A ci Entering the step 5; if N is present p If the closed loop system matrix corresponding to each controller is unstable, returning to the step 2;
and 5: computing the closed-loop System matrix A ci The damping ratio of each mode is calculated to obtain the controller unit K i Corresponding minimum damping ratio ρ min_i As the controller unit K i An adaptation value of;
step 6: repeating the steps 4-5Until the adaptive value calculation of all the controllers of the current generation is completed, the optimal solution of the minimum damping ratio of the current generation is obtained through comparison operation
Figure GDA0003756905810000039
And the optimal solution
Figure GDA0003756905810000032
Corresponding controller individual
Figure GDA0003756905810000033
And 7: for N in this generation p The controller individuals carry out cross, variation and selection operations to generate a new generation of controller individuals
Figure GDA0003756905810000034
Let g be g + 1;
and 8: if g is less than or equal to g max Or
Figure GDA0003756905810000035
Returning to the step 3; otherwise, go to step 9;
and step 9: outputting an optimal solution of minimum damping ratio
Figure GDA0003756905810000036
And the optimal solution
Figure GDA0003756905810000037
Corresponding controller individual
Figure GDA0003756905810000038
Further, the order determining method for the multiple dc coordinated controllers to be solved in step 1 is as follows:
(1) When the structure type of the multi-direct current coordination controller to be solved is the centralized multi-direct current coordination controller, the order of the input multi-direct current coordination controller to be solved is represented as n k ；
(2) When the structure type of the multi-DC coordination controller to be solved is distributed multi-DCWhen the controllers are coordinated, the order of the input multiple direct current coordinated controller to be solved is represented as n d n k ；
(3) When the structure type of the multi-DC coordinated controller to be solved is a distributed multi-DC coordinated controller based on a lead-lag compensator structure, the order of the input multi-DC coordinated controller to be solved is represented as 4n d 。
Further, in step 2, a decision variable number n is calculated according to the structure type of the multiple direct current coordinated controllers to be solved v The method comprises the following steps:
(1) when the structure type of the multi-DC coordinated controller to be solved is the centralized multi-DC coordinated controller, the decision variable number n is calculated v Is expressed as:
Figure GDA0003756905810000041
(2) when the structure type of the multi-DC coordinated controller to be solved is a distributed multi-DC coordinated controller, calculating the number n of decision variables v Is expressed as:
Figure GDA0003756905810000042
(3) when the structure type of the multi-DC coordinated controller to be solved is a distributed multi-DC coordinated controller based on a lead-lag compensator structure, calculating the number n of decision variables v Is expressed as: n is v ＝7n d 。
Further, in step 3, the following method is selected to establish the state space equation of the multiple direct current coordination controller to be solved:
(1) when the structure type of the multi-direct current coordination controller to be solved is a centralized multi-direct current coordination controller, the state space matrix representation form of the centralized multi-direct current coordination controller is as follows:
Figure GDA0003756905810000043
in the formula (I), the compound is shown in the specification,
Figure GDA0003756905810000044
(2) when the structure type of the multiple dc coordinated controller to be solved is a distributed multiple dc coordinated controller, the state space matrix representation form of the distributed multiple dc coordinated controller is as follows:
Figure GDA0003756905810000051
in the formula (I), the compound is shown in the specification,
Figure GDA0003756905810000052
D kl ∈R；l＝1,2,…,n d ；
(3) when the structural type of the multi-DC coordinated controller to be solved is a distributed multi-DC coordinated controller based on a lead-lag compensator structure, a transfer function of the sub-controller of the I return DC is set as follows:
Figure GDA0003756905810000053
in the formula, T lm For measuring the time constant of the link, T * Is the time constant of each link, K gain_ Is the amplification factor, s is the differential operator in Laplace transform;
converting the transfer function of the l return direct current sub-controller into a state space equation to be expressed as:
Figure GDA0003756905810000054
the matrix parameters of each system in the l-th loop direct current state space equation can be obtained by the following formula:
Figure GDA0003756905810000055
Figure GDA0003756905810000061
C kl ＝[0 0 0 K gain_l ]；
D kl ＝0；
then the state space matrix of the distributed multi-dc coordinated controller based on the lead-lag compensator structure is represented as:
Figure GDA0003756905810000064
Figure GDA0003756905810000065
Figure GDA0003756905810000066
Figure GDA0003756905810000067
Further, in step 3, in order to obtain the matrix parameters of the multi-dc coordinated control state space equation, n is randomly generated v One-dimensional vector K of individual elements v Expressed as:
K v ＝{(k 1 ,k 2 ,...,k nv )|k imin ≤k i ≤k imax }；
obtaining a one-dimensional vector K v And then, generating system matrix parameters { A ] of a corresponding state space matrix according to the structure type of the multi-DC coordinated controller to be solved by the following method k ,B k ,C k ,D k }：
(1) When the structure type of the multi-DC coordinated controller to be solved is the centralized multi-DC coordinated controller, the number n of the decision variables v ＝(n k +n u )×(n k +n y ) One-dimensional vector K v The system matrix parameter { A is obtained by transforming as follows k ,B k ,C k ,D k }：
Figure GDA0003756905810000062
Figure GDA0003756905810000063
Figure GDA0003756905810000071
Figure GDA0003756905810000072
(2) When the structure type of the multi-DC coordinated controller to be solved is a distributed multi-DC coordinated controller, the number of the decision variables n v ＝n d (n k +1) 2 To this (n) k +1) 2 Through the same transformation method of each parameter as that of the centralized multi-direct-current coordination controller in the step (1), each matrix parameter of the sub-controller state space equation of the I return direct current can be obtained as { A } kl ,B kl ,C kl ,D kl When the matrix parameters of all the sub-controllers are obtained, the system matrix parameters { A ] of the distributed multi-DC coordination controller k ,B k ,C k ,D k The following:
Figure GDA0003756905810000073
(3) when the structure type of the multi-DC coordinated controller to be solved is a distributed multi-DC coordinated controller based on a lead-lag compensator structure, the number of the decision variables n is decided v ＝7n d For the 7 parameters, the system matrix parameter of the I-th return DC sub-controller is obtained by the same transformation method as the centralized multi-DC coordinated controller in (1) and is { A kl ,B kl ,C kl ,D kl Represents as follows:
Figure GDA0003756905810000081
after obtaining the system matrix parameters of each DC controller, the system matrix parameters { A ] of the distributed multi-DC coordinated controller based on the lead-lag compensator structure k ,B k ,C k ,D k The method comprises the following steps:
Figure GDA0003756905810000082
further, in step 3, N is generated by the following method p Individual controller K i Corresponding closed-loop system matrix:
Figure GDA0003756905810000083
further, in step 7, the mutation operation is:
Figure GDA0003756905810000084
in the formula (I), the compound is shown in the specification,
Figure GDA0003756905810000085
representing the candidate controller individuals of the next iteration, r1, r2, r3 e {1,2, …, N P Are integers different from each other, and r1, r2, r3 are different from the current target vector index i, so the population size N P ≥4；
Figure GDA0003756905810000086
Figure GDA0003756905810000087
To randomly select three different controllers from a population of controllers of a current generationA body; f is a scaling factor and has a value range of [0,2 ]]。
Further, the method of the interleaving operation in step 7 is:
Figure GDA0003756905810000091
wherein rand (). epsilon [0,1]Are uniformly distributed random numbers; j represents the jth variable; CR is a cross probability constant; the value range is [0,1 ]]The size is predetermined; randn (n) v )∈[1,2,…,n v ]Indexed for randomly selected dimension variables.
Further, the method of selecting operation in step 7 is:
Figure GDA0003756905810000092
in the formula, Obj () represents an adaptation value.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
1. The invention can realize the design of a centralized type multi-direct current coordination controller, a distributed type multi-direct current coordination controller based on a lead-lag compensator structure and the like in one set of algorithm, and is convenient for comparing the performance of the coordination controllers with various structures.
2. The invention is based on a 'generation-inspection' method, a controller is randomly generated firstly, and then whether the damping ratio meets the requirement is inspected, so that the difficulty of solving the non-linear matrix inequality is avoided, and the optimized controller can be obtained through a differential evolution algorithm.
3. In the design of the multi-direct-current coordination controller, a centralized controller and a distributed controller with specified orders can be directly solved, so that the problem of performance degradation caused by order reduction of the controllers is avoided;
4. the invention randomly generates the controllers firstly, then checks whether the closed-loop system matrixes are stable one by one, and obtains the performance index of the closed-loop system only for the stable closed-loop system matrixes, thereby avoiding a large amount of invalid operations, improving the calculation efficiency and being suitable for the design of the multi-direct-current coordination controller of a large-scale system.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention, and therefore should not be considered as limiting the scope, and it is obvious for those skilled in the art that other related drawings can be obtained according to these drawings without inventive efforts.
Fig. 1 is a schematic structural diagram of a centralized multi-dc coordination controller according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a distributed multi-DC coordinated controller according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a multi-DC-based coordinated controller based on a lead-lag compensator structure according to an embodiment of the present invention;
FIG. 4 is a schematic view of an LMI area;
FIG. 5 is a flow chart of a design method according to an embodiment of the present invention;
FIG. 6a is a graph of exemplary time domain simulation results without a controller.
Fig. 6b, fig. 6c, and fig. 6d are graphs of time domain simulation results of three types of multi-dc coordinated controllers applying centralized type, distributed type, lead-lag type, and the like, respectively:
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, 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 some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The design idea of the invention is as follows:
the equation of motion of the rotor for an equivalent system can be expressed as:
Figure GDA0003756905810000101
in the formula, T J For equivalent system rotor moment of inertia, Δ T M To mechanical torque, Δ T E Is electromagnetic torque, delta omega is angular velocity variation, D is damping coefficient, delta T dc The torque variation is added to the direct current.
Let the transfer function of the prime mover regulation system be G GOV (s), the mechanical torque variation can be decomposed into:
Figure GDA0003756905810000102
in the formula, delta is the power angle variation,
Figure GDA0003756905810000103
the phase corresponding to the transfer function of the system is adjusted for the prime mover.
Defining damping torque variation
Figure GDA0003756905810000111
Synchronous torque variation
Figure GDA0003756905810000112
Figure GDA0003756905810000113
Damping coefficient of prime mover regulating system
Figure GDA0003756905810000114
Then there are:
Figure GDA0003756905810000115
let the additional DC modulation rate be Δ P DC ＝G DC (s) Δ ω, emulating the prime mover modulation system Δ T M Equivalent method, also written as DC additional torque DeltaT Sdc Synchronous with DC by Delta T Ddc And (c) the sum, i.e.:
ΔT dc ＝ΔT Sdc +ΔT Ddc ＝ΔT Sdc +D dc Δω (4)
after the dc additional torque is measured, equation (3) can be rewritten as:
Figure GDA0003756905810000116
when the specific gravity of water and electricity in the system is larger, (D) GOV + D) is negative or weak damping. Reasonably designed high-voltage direct-current additional control law G DC (s) making
Figure GDA00037569058100001117
Thereby offsetting the negative damping or weak damping influence of the hydroelectric generating set in the system on the system. Therefore, the essential problem of suppressing the ultralow frequency oscillation by using the high voltage direct current is to find a reasonable additional control law G DC (s) to maximize the minimum damping ratio of the system.
The AC-DC hybrid system state space model is assumed to be described as:
Figure GDA0003756905810000117
in the above formula, the first and second carbon atoms are,
Figure GDA0003756905810000118
in the form of a state vector, the state vector,
Figure GDA0003756905810000119
in order to input the vector, the vector is input,
Figure GDA00037569058100001110
in order to output the vector, the vector is,
Figure GDA00037569058100001111
in the form of a matrix of states,
Figure GDA00037569058100001112
is an input matrix.
Set high voltage DC additional control law G DC The state space equation of(s) is expressed as:
Figure GDA00037569058100001113
order to
Figure GDA00037569058100001114
The equation (7) is substituted for the equation (6) to obtain a closed-loop system state space equation:
Figure GDA00037569058100001115
wherein:
Figure GDA00037569058100001116
therefore, the problem of finding the additional control law for suppressing the high-voltage direct current with ultralow oscillation is converted into finding a proper matrix { A } k ,B k ,C k ,D k Make the closed-loop system matrix A c The minimum damping ratio of all modes including the ultra-low frequency oscillation mode meets the requirement, and is generally specified to be 5% in engineering practice.
If a constant xi is given, -, cos θ > 0, if a symmetric positive definite matrix P, -, P exists T > 0, such that the following holds:
Figure GDA0003756905810000121
A c configuring LMI area as shown in figure 4 for the characteristic value of the closed-loop system matrix, namely the closed-loop system matrix A c The minimum damping ratio is greater than cos θ.
The optimal output feedback controller of the system can be designed by solving the following optimization problem:
Figure GDA0003756905810000122
where ρ is a matrix A of the closed-loop system c Damping ratio of each mode, ρ set For a given damping ratio, P is the matrix A of the closed-loop system c And a symmetrical positive definite matrix with the same dimension.
Application of equation (11) to solve for optimal output feedback controller due to cos θ PA c 、sinθPA c The product term of one unknown number and two unknown matrixes is a nonlinear matrix inequality and cannot be solved by a linear matrix method. If the controller G is randomly generated dc ＝{A k ,B k ,C k ,D k }, then closed-loop system matrix A c As is known, by using a half-and-half search method, cos θ is gradually increased, and the nonlinear matrix inequality in equation (11) is converted into a linear matrix inequality, so that the solution can be performed by using tools such as Yalmip. However, considering that the solving complexity of the linear matrix inequality is high, the efficiency is low, and the method is particularly suitable for a system with a high order, if the matrix characteristic value of the closed-loop system is directly solved, whether the system is stable or not and whether the damping ratio meets the requirement or not are judged according to the characteristic value, and the calculation efficiency can be greatly improved. Because the existing numerical calculation tool matlab can solve all the eigenvalues of the matrix with the scale of 5000 x 5000 on a common notebook computer, the method can be applied to the design of controllers of higher-order subsystems. That is, equation (11) can be simplified as:
Figure GDA0003756905810000123
to sum up, the controller design method of the present invention can be summarized as follows: first, randomGenerate a series of controllers G dc ＝{A k ,B k ,C k ,D k Seeking a closed-loop system matrix A c And its eigenvalue, a closed-loop system matrix A whose real part of all eigenvalues is less than 0 c Determining as stable system, and determining matrix A of each stable closed-loop system c The minimum damping ratio in all the modes can be obtained, and the closed-loop system matrix A with the minimum damping ratio in all the modes meeting the constraint condition can be found out through comparison c . In order to optimize the performance of the controller, a differential evolution algorithm is applied to generate a new generation of controller to be tested, and the optimized controller is obtained through loop iteration.
Therefore, as shown in fig. 5, the present embodiment proposes a method for designing a multi-dc coordinated controller for suppressing ultra-low frequency oscillation, which includes the following steps:
step 1: inputting power system model state space model parameters A, B, C, D; dimension n of input and output signals u 、n y (ii) a Setting the order of the multiple DC coordinated controllers to be solved and the number n of DC loops d (ii) a Setting structural types of a multi-direct-current coordination controller to be solved, wherein the structural types comprise a centralized type, a distributed type or a distributed type based on a lead-lag compensator structure; initializing differential evolution parameters, including a scaling factor C F Cross probability C R Population size N p (ii) a Maximum number of iterations g max (ii) a An iteration error limit epsilon, and setting the initial iteration time g to be 1;
In this embodiment, the order of the multiple dc coordinated controller to be solved in step 1 is as follows:
(1) when the structure type of the multi-direct current coordination controller to be solved is the centralized multi-direct current coordination controller, the order of the input multi-direct current coordination controller to be solved is represented as n k ；
(2) When the structure type of the multi-direct current coordination controller to be solved is a distributed multi-direct current coordination controller, the order of the input multi-direct current coordination controller to be solved is represented as n d n k ；
(3) When the structure type of the multi-DC coordinated controller to be solved is a distributed multi-DC coordinated controller based on a lead-lag compensator structure, the input is ready to be solvedSolving the order of the multi-DC coordinated controller to be 4n d 。
Step 2: calculating the number n of decision variables according to the structure type of the multi-DC coordinated controller to be solved v And randomly generating a random number including N p Multiple direct current coordinated controller initial population matrix to be solved for each controller
Figure GDA0003756905810000131
The ith row vector of the initial population represents the ith controller individual K i ；
In step 2, the number n of decision variables is calculated according to the structure type of the multi-DC coordinated controller to be solved v The method comprises the following steps:
(1) when the structure type of the multi-DC coordinated controller to be solved is a centralized multi-DC coordinated controller, the number n of decision variables is calculated v Is expressed as:
Figure GDA0003756905810000132
(2) when the structure type of the multi-DC coordinated controller to be solved is a distributed multi-DC coordinated controller, calculating the number n of decision variables v Is expressed as:
Figure GDA0003756905810000141
(3) when the structure type of the multi-DC coordinated controller to be solved is a distributed multi-DC coordinated controller based on a lead-lag compensator structure, calculating the number n of decision variables v Is expressed as:
n v ＝7n d (15)
therefore, the order of the multi-DC coordinated controller to be solved and the number of the calculated decision variables are shown in Table 1.
Table 1:
Figure GDA0003756905810000142
in this embodiment, a random one-dimensional vector K v Has a value range of [ k ] imin ,k imax ]An inclusion N can be randomly generated using the following rule p The initial population of the multiple direct current coordinated controllers to be solved of each controller individual is as follows:
Figure GDA0003756905810000143
in the formula (I), the compound is shown in the specification,
Figure GDA0003756905810000144
a j-dimension component representing the ith individual of the g-th generation controller; n is a radical of o The number of the population, namely the number of the controllers to be tested in the current generation; the function rand () generates a value belonging to [0,1 ]]Random number of intervals. Can be used in the subsequent
Figure GDA0003756905810000145
Representing the ith controller entity for the g-th iteration.
And step 3: selecting a corresponding method according to the structure type of the multi-DC coordinated controller to be solved to convert the multi-DC coordinated controller to be solved into a state space matrix, and converting the state space matrix into a state space matrix according to N p Individual controller K i Generating a corresponding closed-loop system matrix A by the corresponding system matrix parameters ci ；
In this embodiment, in step 3, the following method is selected to establish the state space matrix of the multiple dc coordinated controllers to be solved:
(1) when the structure type of the multi-direct current coordination controller to be solved is a centralized multi-direct current coordination controller, the state space matrix representation form of the centralized multi-direct current coordination controller is as follows:
Figure GDA0003756905810000151
in the formula (I), the compound is shown in the specification,
Figure GDA0003756905810000152
such as n k N being full-order control, e.g. n k If < n, the price is reduced;
(2) when the structure type of the multiple dc coordinated controller to be solved is a distributed multiple dc coordinated controller, the state space matrix representation form of the distributed multiple dc coordinated controller is as follows:
Figure GDA0003756905810000153
in the formula (I), the compound is shown in the specification,
Figure GDA0003756905810000154
D kl ∈R；l＝1,2,…,n d ；
(3) when the structural type of the multi-DC coordinated controller to be solved is a distributed multi-DC coordinated controller based on a lead-lag compensator structure, a transfer function of the sub-controller of the I return DC is set as follows:
Figure GDA0003756905810000155
in the formula, T lm For measuring the time constant of the link, T * (i.e. T) l1 、T l2 、T l3 、T l4 、T l5 Etc.) as the time constant of each link, K gain_l For magnification, s is the differential operator in the laplace transform.
Converting the transfer function of the l return direct current sub-controller into a state space equation to be expressed as:
Figure GDA0003756905810000161
the system matrix parameters in the l-th feedback direct current state space equation are obtained by the following formula (20):
Figure GDA0003756905810000162
Then the state space matrix of the distributed multi-dc coordinated controller based on the lead-lag compensator structure is represented as:
Figure GDA0003756905810000163
the multi-DC coordinated controller to be solved is given by Table 1 k ,B k ,C k ,D k And (3) as the differential evolution algorithm can only optimize one-dimensional vectors, firstly randomly generating n-containing multi-direct-current coordination controllers which are converted into state space matrixes and are to be solved in step 3 v One-dimensional vector K of individual elements v Expressed as:
Figure GDA0003756905810000164
obtaining a one-dimensional vector K v And then, generating system matrix parameters { A ] of a corresponding state space matrix according to the structure type of the multi-DC coordinated controller to be solved by the following method k ,B k ,C k ,D k }：
(1) When the structure type of the multi-DC coordinated controller to be solved is the centralized multi-DC coordinated controller, the number n of the decision variables v ＝(n k +n u )×(n k +n y ) One-dimensional vector K v The system matrix parameter { A is obtained by transforming as follows k ,B k ,C k ,D k }：
Figure GDA0003756905810000171
Figure GDA0003756905810000172
Figure GDA0003756905810000173
Figure GDA0003756905810000174
(2) When the structure type of the multi-DC coordinated controller to be solved is a distributed multi-DC coordinated controller, the number of the decision variables n v ＝n d (n k +1) 2 To this (n) k +1) 2 The system matrix parameter of the first return DC controller can be obtained as { A } through the same conversion method as the centralized multi-DC coordinated controller in (1) kl ,B kl ,C kl ,D kl Obtaining the system matrix parameters { A ] of the distributed multi-DC coordination controller by the following method after obtaining the system matrix parameters of all the sub-controllers k ,B k ,C k ,D k }：
Figure GDA0003756905810000175
(3) When the structure type of the multi-DC coordinated controller to be solved is a distributed multi-DC coordinated controller based on a lead-lag compensator structure, the number of the decision variables n is decided v ＝7n d For the 7 parameters, the system matrix parameter of the I-th return DC sub-controller is obtained by the same transformation method as the centralized multi-DC coordinated controller in (1) and is { A kl ,B kl ,C kl ,D kl Represents as follows:
Figure GDA0003756905810000181
after obtaining the system matrix parameters of each DC controller, the system matrix parameters { A } of the distributed multi-DC coordinated controller based on the lead-lag compensator structure k ,B k ,C k ,D k The method comprises the following steps:
Figure GDA0003756905810000182
the state space matrix and the system matrix parameters of the multi-DC coordinated controller to be solved are obtained, a closed-loop system matrix can be generated through an equation (9), and for N, the closed-loop system matrix is obtained p Individual controller K i Inputting each corresponding system matrix parameter into formula 9 to generate a corresponding closed-loop system matrix A ci Expressed as follows:
Figure GDA0003756905810000183
and 4, step 4: calculating each closed loop system matrix A ci And judging a closed-loop system matrix A according to the characteristic value ci Whether or not to stabilize, for stabilizing closed loop system matrix A ci Entering the step 5; if N is present p If the closed loop system matrix corresponding to each controller is unstable, returning to the step 2; the method for calculating the matrix eigenvalue is the prior art, and is not repeated herein, but as described above, whether the closed-loop system matrix is stable or not can be determined by determining whether the real part of the eigenvalue is less than 0 (i.e., whether the rightmost eigenvalue of the closed-loop system matrix is located on the left half plane), and determining the closed-loop system matrix with the real part of the eigenvalue less than 0 as a stable system; in the step 4, the matrix A of the closed-loop system is judged through the eigenvalue ci Whether or not to stabilize, for stabilized A ci And then the damping ratio of each mode is obtained, so that the calculation amount can be reduced to a large extent.
And 5: computing the closed-loop System matrix A ci The corresponding damping ratio is obtained to obtain the controller individual K i Corresponding minimum damping ratio ρ min_i As the controller unit K i An adaptation value of; computing the closed-loop System matrix A ci The method of damping ratio of each mode is prior art and will not be described herein.
Step 6: repeating the steps 4-5 until the calculation of the adaptive values of all the controller individuals in the current generation is completed, and obtaining the optimal solution of the minimum damping ratio in the current generation through comparison operation
Figure GDA0003756905810000191
And the optimal solution
Figure GDA0003756905810000192
Corresponding controller individual
Figure GDA0003756905810000193
And 7: for N in this generation p The controller individuals carry out the operations of crossing, mutation and selection to generate a new generation of controller individuals
Figure GDA0003756905810000194
Let g be g + 1;
(1) mutation operation
The variation operation is to select three different controller individuals from the controller individuals of the current generation to carry out differential operation to generate a new generation of target controller individuals. The target controller for performing mutation operation on the current generation is set as
Figure GDA0003756905810000195
(i.e., the individual controller for the g-th iteration), three different individuals were randomly selected from the population of controllers of this generation
Figure GDA0003756905810000196
Generating candidate of new-generation controller based on following operations
Figure GDA0003756905810000197
Figure GDA0003756905810000198
Wherein r1, r2, r3 ∈ {1,2, …, N ∈ {1,2, … ∈ P Are integers different from each other, and r1, r2, r3 are different from the current target vector index i, so the population size N P Not less than 4; f is a scaling factor and has a value range of [0,2 ]]To control the degree of scaling of the difference vector.
(2) Crossover operation
The interleaving operation is from the present generationRandomly selecting two different individuals in a controller population
Figure GDA0003756905810000199
Application controller individual
Figure GDA00037569058100001910
(l is index of subscript different from i) of the target controller
Figure GDA00037569058100001911
Corresponding component, thereby generating a new generation of candidate individuals
Figure GDA00037569058100001912
To ensure the controller individuals
Figure GDA00037569058100001913
By first making a random selection
Figure GDA00037569058100001914
At least one bit is composed of
Figure GDA00037569058100001915
Contributions, and for other components, determined by a cross-probability factor CR
Figure GDA00037569058100001916
Wherein the component is from
Figure GDA00037569058100001917
Or also
Figure GDA00037569058100001918
The method of the cross operation comprises the following steps:
Figure GDA00037569058100001919
wherein rand (). epsilon [0,1]Is a uniformly distributed random number, j represents the jth variable, and CR is a cross-over profileRate constant of [0,1 ]]The size is predetermined; randn (n) v )∈[1,2,…,n v ]Indexed for randomly selected dimension variables.
(3) Selection operation
The selection operation determines whether the variant and cross-generation controller entity can enter the new-generation controller cluster. Test individuals generated after mutation and cross operation
Figure GDA0003756905810000201
And
Figure GDA0003756905810000202
compete only when
Figure GDA0003756905810000203
Adapted value of and
Figure GDA0003756905810000204
equal or better, is selected as a new generation of individuals
Figure GDA0003756905810000205
Otherwise, it will directly
Figure GDA0003756905810000206
As a child. The method for selecting the operation comprises the following steps:
Figure GDA0003756905810000207
in the formula, Obj () represents an adaptation value.
And 8: if g is less than or equal to g max Or
Figure GDA0003756905810000208
Returning to the step 3; otherwise, go to step 9;
and step 9: outputting an optimal solution of minimum damping ratio
Figure GDA0003756905810000209
And with the mostOptimal solution
Figure GDA00037569058100002010
Corresponding controller individual
Figure GDA00037569058100002011
Examples of the invention
The CIGRE Nordic 32 bus test system adopted in the test has 19 sets in total, 2 loops of direct current are adopted, wherein 1 loop is LCC direct current, the other 1 loop is VSC direct current, the set parameters in the bus test system are adjusted to enable the bus test system to have an ultralow frequency oscillation mode, and a 12-order discrete state space model of the system as shown in formula (35) is obtained through identification:
Figure GDA00037569058100002012
the state space model is a 4-input 4-output 12-order model, and the system matrix parameters A, B, C, D are shown as equation (36).
The model input model has LCC DC current command I (t), VSC DC active command P (t), VSC sending end reactive command Qr (t), and receiving end reactive command Qi (t), i.e. u (t) ([ I (t) P (t)) Q r (t) Q i (t)] T The output of the model is the rotation speed (per unit) of 4 sets in the network, i.e. y (t) ([ S) ] G1 S G2 S G3 S G4 ] T 。
Figure GDA0003756905810000211
By applying eigenvalue analysis to the system matrix A, 3 modes with damping ratios lower than 5% can be found in the system, including ultralow-frequency oscillation at 0.0628Hz, the damping ratio is only 3.39%, and low-frequency oscillation modes at 0.5721Hz and 0.9715Hz, the damping ratios are only 2.15% and 3.42%, respectively.
In order to test the performance of the controller designed by the design method, three types of controllers are respectively designed according to the method:
(1) the structure of the centralized multi-direct current coordination controller is shown in fig. 3, and the order of the controller is 3 orders;
(2) the distributed multi-DC coordinated controller has a structure as shown in FIG. 4, wherein the order of each controller is 3;
(3) the distributed multi-dc coordinated controller based on the lead-lag compensator structure is shown in fig. 5.
After the three types of multi-direct-current coordinated controllers are applied to the CIGRE Nordic 32 bus test system, the main oscillation modes of the matrix of the closed-loop system are shown in Table 2. And the time domain simulation is carried out on the closed loop system, the system output without the controller is shown in figure 6a, and the system output when three multi-direct current coordinated controllers such as a centralized controller, a distributed controller, an advance-lag controller and the like are applied is respectively shown in figures 6b to 6 d.
Table 2:
Figure GDA0003756905810000212
Figure GDA0003756905810000221
as can be seen from table 2 and fig. 6a to 6d, the minimum damping ratio of the closed-loop system matrix is also above 5% after the multi-dc coordinated controller is applied, and both meet the design requirements.
In addition, it should be noted that if a homotopic transformation algorithm is adopted based on the obtained centralized multi-dc coordinated controller, a convergence solution cannot be obtained after multiple iterations, and thus a distributed multi-dc coordinated controller cannot be obtained. This shows that the performance of the controller optimization algorithm in the design method of the invention is superior to that of the homotopic transformation algorithm.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (6)

1. A design method of a multi-direct current coordination controller for inhibiting ultralow frequency oscillation is characterized by comprising the following steps:
step 1: input power system model state space model parameters A, B, C, D; dimension n of input and output signals u 、n y (ii) a Setting the order of the multiple DC coordinated controllers to be solved and the number n of DC loops d (ii) a Setting structural types of a multi-direct-current coordination controller to be solved, wherein the structural types comprise a centralized type, a distributed type or a distributed type based on a lead-lag compensator structure; initializing differential evolution parameters including a scaling factor F, a cross probability constant CR and a population size N p (ii) a Maximum number of iterations g max (ii) a An iteration error limit epsilon, and setting the initial iteration time g to be 1;
step 2: calculating the number n of decision variables according to the structure type of the multi-DC coordinated controller to be solved v And randomly generating a random number including N p Multiple direct current coordinated controller initial population matrix to be solved for each controller
Figure FDA0003756905800000011
The ith row vector of the initial population matrix represents the ith controller individual K i ；
And step 3: selecting a corresponding method according to the structure type of the multi-DC coordinated controller to be solved to convert the multi-DC coordinated controller to be solved into a state space matrix, and according to the state space matrix N p Individual controller K i Generating a corresponding closed-loop system matrix A by the corresponding system matrix parameters ci ；
And 4, step 4: calculating each closed loop system matrix A ci And judging a closed-loop system matrix A according to the characteristic value ci Whether or not to stabilize, for stabilizing closed loop system matrix A ci Entering the step 5; if N is present p If the closed loop system matrix corresponding to each controller is unstable, returning to the step 2;
and 5: computing the closed-loop System matrix A ci The damping ratio of each mode is calculated to obtain the controller unit K i Corresponding minimum damping ratio ρ min_i As the controller unit K i An adaptation value of;
step 6: repeating the steps 4-5 until the calculation of the adaptive values of all the controller individuals in the current generation is completed, and obtaining the optimal solution of the minimum damping ratio in the current generation through comparison operation
Figure FDA0003756905800000012
And the optimal solution
Figure FDA0003756905800000013
Corresponding controller individual
Figure FDA0003756905800000014
And 7: for N in this generation p The controller individuals carry out the operations of crossing, mutation and selection to generate a new generation of controller individuals
Figure FDA0003756905800000015
Let g be g + 1;
and 8: if g is less than or equal to g max Or
Figure FDA0003756905800000016
Returning to the step 3; otherwise, go to step 9;
and step 9: outputting an optimal solution of minimum damping ratio
Figure FDA0003756905800000017
And the optimal solution
Figure FDA0003756905800000018
Corresponding controller individual
Figure FDA0003756905800000019
In step 1, the order of the multi-DC coordinated controller to be solved is as follows:
(1) when the structure type of the multi-DC coordinated controller to be solved is centralized multi-DC coordinated controlWhen the controller is manufactured, the order of the input multiple direct current coordinated controller to be solved is expressed as n k ；
(2) When the structure type of the multi-direct current coordination controller to be solved is a distributed multi-direct current coordination controller, the order of the input multi-direct current coordination controller to be solved is represented as n d n k ；
(3) When the structure type of the multi-DC coordinated controller to be solved is a distributed multi-DC coordinated controller based on a lead-lag compensator structure, the order of the input multi-DC coordinated controller to be solved is represented as 4n d ；
In step 2, the number n of decision variables is calculated according to the structural type of the multi-DC coordinated controller to be solved v The method comprises the following steps:
(1) when the structure type of the multi-DC coordinated controller to be solved is the centralized multi-DC coordinated controller, the decision variable number n is calculated v Is expressed as:
Figure FDA0003756905800000021
(2) when the structure type of the multi-DC coordinated controller to be solved is a distributed multi-DC coordinated controller, calculating the number n of decision variables v Is expressed as:
Figure FDA0003756905800000022
(3) when the structure type of the multi-DC coordinated controller to be solved is a distributed multi-DC coordinated controller based on a lead-lag compensator structure, calculating the number n of decision variables v Is expressed as: n is v ＝7n d ；
And 3, establishing the state space matrix of the multi-DC coordination controller to be solved by selecting the following method:
(1) when the structure type of the multi-DC coordinated controller to be solved is a centralized multi-DC coordinated controller, the state space matrix representation form of the centralized multi-DC coordinated controller is as follows:
Figure FDA0003756905800000023
in the formula (I), the compound is shown in the specification,
Figure FDA0003756905800000024
(2) when the structure type of the multi-dc coordinated controller to be solved is a distributed multi-dc coordinated controller, the state space matrix representation form of the distributed multi-dc coordinated controller is as follows:
Figure FDA0003756905800000031
in the formula (I), the compound is shown in the specification,
Figure FDA0003756905800000032
D kl ∈R；l＝1,2,…,n d ；
(3) when the structural type of the multi-DC coordinated controller to be solved is a distributed multi-DC coordinated controller based on a lead-lag compensator structure, a transfer function of the sub-controller of the I return DC is set as follows:
Figure FDA0003756905800000033
in the formula, T lm For measuring the time constant of the link, T * Is the time constant of each link, K gain_l Is a magnification factor; s is a differential operator in the Laplace transform;
converting the transfer function of the l return direct current sub-controller into a state space equation to be expressed as:
Figure FDA0003756905800000034
The matrix parameters of each system in the l-th loop direct current state space equation can be obtained by the following formula:
Figure FDA0003756905800000035
Figure FDA0003756905800000041
C kl ＝[0 0 0 K gain_l ]；
D kl ＝0；
then the state space matrix of the distributed multi-dc coordinated controller based on the lead-lag compensator structure is represented as:
Figure FDA0003756905800000042
Figure FDA0003756905800000043
Figure FDA0003756905800000044
Figure FDA0003756905800000045
2. the design method of multiple dc coordinated controllers for suppressing the ultra-low frequency oscillation according to claim 1, wherein in step 3, the multiple dc coordinated controllers to be solved converted into the state space matrix are randomly generated to include n v One-dimensional vector K of elements v Expressed as:
Figure FDA0003756905800000047
obtaining a one-dimensional vector K v And then, generating system matrix parameters { A ] of a corresponding state space matrix according to the structure type of the multi-DC coordinated controller to be solved by the following method k ，B k ，C k ，D k }：
(1) When the structure type of the multi-DC coordinated controller to be solved is the centralized multi-DC coordinated controller, the number n of the decision variables v ＝(n k +n u )×(n k +n y ) One-dimensional vector K v The system matrix parameter { A is obtained by transforming as follows k ，B k ，C k ，D k }：
Figure FDA0003756905800000046
Figure FDA0003756905800000051
Figure FDA0003756905800000052
Figure FDA0003756905800000053
(2) When the structure type of the multi-DC coordinated controller to be solved is a distributed multi-DC coordinated controller, the number of the decision variables n v ＝n d (n k +1) 2 To this (n) k +1) 2 Through the same transformation method of each parameter as that of the centralized multi-direct-current coordination controller in the step (1), each matrix parameter of the sub-controller state space equation of the I return direct current can be obtained as { A } kl ，B kl ，C kl ，D kl When the matrix parameters of all the sub-controllers are obtained, the system of the distributed multi-direct-current coordination controllerMatrix parameter { A } k ，B k ，C k ，D k The method comprises the following steps:
Figure FDA0003756905800000054
(3) when the structure type of the multi-DC coordinated controller to be solved is a distributed multi-DC coordinated controller based on a lead-lag compensator structure, the number of the decision variables n is decided v ＝7n d And for the 7 parameters, obtaining the system matrix parameter of the l-th return direct current sub-controller by the same conversion method as the centralized multi-direct current coordinated controller in (1) as { A } kl ，B kl ，C kl ，D kl Denotes as follows:
Figure FDA0003756905800000061
after obtaining the system matrix parameters of each DC controller, the system matrix parameters { A } of the distributed multi-DC coordinated controller based on the lead-lag compensator structure k ，B k ，C k ，D k The method comprises the following steps:
Figure FDA0003756905800000062
3. the design method of multiple DC coordinated controllers for suppressing ultra-low frequency oscillation according to claim 1, wherein the following method is adopted to generate N in step 3 p A controller unit K i Corresponding closed-loop system matrix:
Figure FDA0003756905800000063
4. the design method of multiple dc coordinated controllers for suppressing ultra-low frequency oscillation as claimed in claim 1, wherein said mutation operation in step 7 is:
Figure FDA0003756905800000064
in the formula (I), the compound is shown in the specification,
Figure FDA0003756905800000065
the controller individuals to be selected, r1, r2, r 3E {1, 2, …, N, representing the next iteration P H, are integers different from each other, and r1, r2, r3 are different from the current target vector index i, so the population size N P ≥4；
Figure FDA0003756905800000066
Figure FDA0003756905800000067
Randomly selecting three different controller individuals from the controller cluster of the current generation; f is a scaling factor and has a value range of [0, 2 ]]。
5. The design method of multiple dc coordinated controllers for suppressing ultra-low frequency oscillation according to claim 4, wherein the method of interleaving operation in step 7 is:
Figure FDA0003756905800000071
wherein rand (). epsilon [0, 1]Are uniformly distributed random numbers; j represents the jth variable; CR is a cross probability constant; the value range is [0, 1 ]]The size is predetermined; randn (n) v )∈[1，2，…，n v ]Indexed for randomly selected dimension variables.
6. The design method of the multi-dc coordinated controller for suppressing the ultra-low frequency oscillation according to claim 5, wherein the method of selecting operation is:
Figure FDA0003756905800000072
in the formula, Obj () represents an adaptation value.
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