A distributed multi-objective optimization control method for flexible DC systems

Abstract

The present invention discloses a distributed multi-objective optimization control method for a flexible DC system, which belongs to the field of flexible DC system control technology. The goals of voltage regulation and power sharing can be achieved simultaneously by only using the information of adjacent VSCs; a dynamic model of a flexible DC system is established based on linear power flow, and the model has a low dimension and is universal for flexible DC systems with different topological structures; the proposed distributed controller is designed based on a new observer and is derived through linear quadratic optimal theory. Reasonable selection of the observer can ensure the stability of the controller and improve the convergence speed of the distributed control strategy. The proposed distributed optimal controller is superior to the existing distributed controller and exhibits strong robustness under communication failures, topological changes and delays.

Description

Technical Field

[0001] The present invention belongs to the technical field of flexible direct current system control, and in particular relates to a distributed multi-objective optimization control method for a flexible direct current system. Background Art

[0002] Driven by the need to improve efficiency, enhance reliability and reduce environmental impact, more and more photovoltaics (PV) are integrated into the power grid through power inverters. In addition, many DC charging piles are connected to the distribution network to meet the charging needs of electric vehicles (EVs). In this case, the power loss caused by the power conversion of PV and EV in the AC distribution network cannot be ignored. The DC distribution network (DCDN) based on voltage source converter (VSC) is an effective way to accommodate more PV and EV penetration with higher efficiency and flexibility. In addition, DCDN does not face problems such as reactive power compensation, frequency stability and synchronization. Due to the advantages of efficiency, flexibility and reliability, DCDN occupies an important position in the future smart grid architecture.

[0003] In the DC distribution network DCDN, the uncertainty of a high proportion of photovoltaics will cause frequent fluctuations in node voltage and power flow. How to solve the problem of frequent power fluctuations in DCDN has always been a research focus. VSC can achieve fast and accurate power flow regulation in DCDN and is the most important control device in DCDN. According to the communication conditions and control cycle, the control structure of VSC mainly includes primary control and secondary control. The former mainly includes voltage level control, power level control and droop control. For the primary control of VSC, only local voltage and power information is available. Therefore, when the photovoltaic power generation power changes randomly at different nodes, it is difficult to achieve reasonable power flow distribution and voltage level relying solely on VSC primary control.

[0004] Secondary control is studied to achieve reasonable power flow distribution of the entire system. According to communication conditions, secondary control can be divided into centralized control and distributed control. Secondary control requires a centralized control center to periodically collect global information, perform system-wide optimization, and send commands to each control device. Although centralized control methods can use global information to achieve fast and effective control, the high requirements for network communication limit the application of centralized control in some cases.

[0005] Compared with centralized control, distributed control eliminates the control center and only requires information from neighboring devices. Due to its advantages such as low communication burden and high reliability, distributed control has become an attractive control method for widely dispersed controllable devices in medium and low voltage distribution networks. The consensus algorithm is used in the distributed control of DC microgrids to achieve the goals of load balancing, minimizing generation costs and voltage regulation.

[0006] Traditional consistency-based distributed control methods for microgrids focus on the final state of the microgrid and ignore the convergence performance. In order to improve the convergence performance of distributed control, distributed optimal controllers are proposed for AC microgrids and AC grids. The work currently conducted by researchers is very inspiring in the distributed control of microgrids, but there are still certain limitations in the application of DCDN. Compared with microgrids, DCDNs are larger in scale and have more variable network topologies, so a general dynamic model of DCDN is necessary. In addition, DCDNs are usually powered by multiple VSCs. The strong coupling between VSC power injection and VSC bus voltage in DCDN makes it difficult to distribute VSC power and restore the nominal voltage of all buses at the same time. DCDN control is a complex multi-objective control problem. Research on more universal multi-terminal DCDNs is still lacking. Summary of the invention

[0007] In view of the above problems existing in the prior art, the present invention proposes a distributed multi-objective optimization control method for a flexible DC system, which has a reasonable design, solves the shortcomings of the prior art and has good effects.

[0008] A distributed multi-objective optimization control method for a flexible DC system comprises the following steps:

[0009] S1. Construct a dynamic model of a multi-terminal flexible DC system based on a linear power flow model;

[0010] S2, introduce a new observer to design a distributed optimal controller using only the information of neighboring VSCs;

[0011] S3. Optimize the observer gain.

[0012] Furthermore, in S1, constructing a dynamic model of a multi-terminal flexible DC system specifically includes:

[0013] The multi-terminal flexible DC system consists of multiple voltage source converters (VSCs) connected to different renewable energy stations and AC grids. The node voltage change caused by Described as:

[0014] (1);

[0015] Where: is the Jacobian matrix, is the voltage sensitivity matrix;

[0016] When VSC operates reference power regulation, The voltage dynamic model of the VSC at each bus node is:

[0017] (2);

[0018] Where: For the The voltage of the VSC at the bus node, For the The reference power change of the VSC at each bus node, For the The VSC voltage at the bus node is The voltage sensitivity coefficient of the VSC reference power at the bus node, is the number of busbar nodes;

[0019] The change in line transmission power caused by the change in VSC reference power for:

[0020] (3);

[0021] Where: and Respectively represent busbar node and The voltage change of each bus node is: ,and ;

[0022] Combining formula (1), formula (3) is further expressed as:

[0023] (4);

[0024] Where: For the The VSC voltage at the bus node is Voltage sensitivity coefficient of the VSC reference power at each bus node;

[0025] No. The change in the VSC transmission power at each bus node It is expressed as:

[0026] (5);

[0027] Where: For the The transmission power of the VSC at the bus node is The sensitivity coefficient of the operating reference power of the VSC at each bus node;

[0028] Considering the regulation of VSC reference power, a dynamic model of VSC power is established:

[0029] (6);

[0030] in, Indicates The transmission power of the VSC at each bus node;

[0031] Therefore, the dynamic model of VSC load rate is:

[0032] (7);

[0033] in, For the The load rate of the VSC at the bus node, For the The maximum capacity of the VSC at each bus node;

[0034] Furthermore, in S2, designing a distributed optimal controller specifically includes:

[0035] The dynamic model of the flexible DC system is written in distributed form:

[0036] (8);

[0037] (9);

[0038] Where: are the variables of the discrete state equation, for The coefficient matrix of For the The VSC distributed controller input at each bus is , For the Measurement information of VSC at each bus node; for No. List, for The coefficient matrix of ; For the matrix No. OK, is the association matrix determined by the communication links;

[0039] An observer-based distributed controller is designed to The control matrix of the controller of the VSC at the bus node is for:

[0040] (10);

[0041] Where: is the feedback gain No. OK, is the output of the observer;

[0042] According to the optimal control law, the feedback gain Given by:

[0043] (11);

[0044] Where: The control input matrix The weight matrix of is a constant positive definite matrix, By solving the Riccati equation, we can calculate:

[0045] (12);

[0046] In the formula, is the state vector The weight matrix of

[0047] For The VSC at the bus node, the observer Designed for:

[0048] (13);

[0049] In the formula, is the observer gain.

[0050] Furthermore, in S3, in order to determine the observer gain in equation (13): , define the matrix for:

[0051] (14);

[0052] In order for the observer is stable, and a nonlinear optimization method is used to find the appropriate observer gain so that the matrix For Schur, nonlinear optimization methods include but are not limited to sequential quadratic programming algorithms and genetic algorithms;

[0053] According to equations (8), (10) and (11), the closed-loop system is reduced to:

[0054] (15);

[0055] in, For the Observer error at each bus node;

[0056] For the system (15), define the matrix for:

[0057] (16);

[0058] in, ;

[0059] From system (15), we have:

[0060] (17);

[0061] Where: yes The spectral radius of is the observer error matrix;

[0062] In order to improve the stability and convergence speed of the closed-loop system, the observer gain is obtained by offline optimization, with the goal of minimizing The modulus of the eigenvalues ​​is The modulus of the eigenvalues ​​is , the goal of observer gain optimization is:

[0063] (18).

[0064] Beneficial technical effects brought by the present invention:

[0065] The present invention proposes a distributed multi-objective optimization control method for multi-terminal flexible DC systems, which can simultaneously achieve the goals of voltage regulation and power sharing by only using the information of adjacent VSCs; a dynamic model of the flexible DC system is established based on linear power flow, which has a low dimension and is universal for flexible DC systems with different topological structures; the proposed distributed controller is designed based on a new observer and is derived through linear quadratic optimal theory. Reasonable selection of the observer can ensure the stability of the controller and improve the convergence speed of the distributed control strategy. Simulation and comparison results show that the proposed distributed optimal controller is superior to the existing distributed controller and shows strong robustness under communication failures, topology changes and delays. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 It is a schematic diagram of a typical multi-terminal flexible DC system in the present invention.

[0067] Figure 2 It is the communication framework in the distributed control of the present invention.

[0068] Figure 3 This is a curve diagram of the deviation parameters under the control method proposed in the present invention.

[0069] Figure 4 This is a VSC voltage curve diagram under the control method proposed in the present invention.

[0070] Figure 5 This is a VSC load rate curve diagram under the control method proposed in the present invention.

[0071] Figure 6 The reference power comparison diagram of VSC operation under different control modes.

[0072] Figure 7 This is the deviation parameter curve diagram under the traditional distributed control method.

[0073] Figure 8 This is the VSC voltage curve diagram using the traditional distributed control method.

[0074] Fig. 9 This is a VSC load rate curve using the traditional distributed control method.

[0075] Fig.10 The voltage recovery process diagram under different time delays;

[0076] Among them, (a) is the voltage recovery process diagram under 100ms delay, (b) is the voltage recovery process diagram under 150ms delay, and (c) is the voltage recovery process diagram under 200ms delay.

[0077] Fig.11 It is the VSC load rate diagram under different time delays;

[0078] Among them, (a) is the VSC load rate diagram under 100ms delay, (b) is the VSC load rate diagram under 150ms delay, and (c) is the VSC load rate diagram under 200ms delay. DETAILED DESCRIPTION

[0079] The specific implementation of the present invention is further described below in conjunction with specific embodiments:

[0080] A distributed multi-objective optimization control method for a flexible DC system comprises the following steps:

[0081] S1. Construct a dynamic model of DC distribution network based on linear power flow model;

[0082] The multi-terminal flexible DC system consists of multiple VSCs connecting different renewable energy stations and AC power grids to improve the flexibility and reliability of system operation. Figure 1 It is a typical multi-terminal flexible DC system, in which converter stations 1~4 are connected to the external AC power grid and use droop control to achieve power distribution, and converter stations 5~6 are connected to the new energy base and use fixed power control.

[0083] In DC systems, Active injection power at the bus node for:

[0084] (1);

[0085] Where: For the busbar node to the The line admittance of a bus node, and Respectively busbar node and The voltage of the bus node, is the number of bus nodes in the DC system.

[0086] For VSC nodes, power injection for:

[0087] (2);

[0088] Where: and Respectively The reference voltage and reference power of the VSC at each bus node, For the The droop coefficient of the VSC at each bus node is: For the The reference power of the VSC at the bus node. For a VSC using voltage level control, the droop coefficient is infinite; for a VSC using power level control, the droop coefficient is 0.

[0089] According to (1) and (2), we can get:

[0090] (3);

[0091] For lines connected to VSC , No. busbar node to the The transmission power of each bus node for:

[0092] (4);

[0093] According to formula (4), The VSC power at a bus node can also be expressed as:

[0094] (5);

[0095] Where: Indicates The set of all buses connected to a bus.

[0096] In the DC system, the random change of renewable energy output will cause the voltage to deviate from the rated value. At the same time, due to the influence of line resistance, droop control cannot accurately achieve power balancing in the converter station. The control objectives of the multi-terminal flexible DC system include voltage regulation and power balancing of VSC.

[0097] There are multiple bus nodes in the flexible DC system, and it is impossible to keep the voltage of each bus at the rated value. The goal of voltage regulation in the flexible DC system is to minimize the variance of the voltage of all droop-controlled VSC bus nodes from the rated value:

[0098] (6);

[0099] Where: Indicates the rated voltage, The number of VSCs for droop control.

[0100] VSC load balancing control: Voltage regulation will cause the power of VSC to change. Maintaining VSC load balancing can avoid VSC overload and improve the safety of DCDN.

[0101] The VSC load rate is defined as:

[0102] (7);

[0103] Where: For the The load rate of the VSC at the bus node, For the The capacity of the VSC at the bus node.

[0104] The minimum difference of VSC load rate is used as the objective function of VSC load balancing control:

[0105] (8);

[0106] In order to design a feedback controller based on linear quadratic optimal control theory, it is first necessary to establish a discrete time model of the flexible DC system. In a flexible DC system, the response speed of the secondary control is much slower than that of the primary control. Therefore, the influence of the primary control transient process can be ignored in the secondary control. The present invention uses the linear power flow sensitivity of the flexible DC system to construct a dynamic model to reduce the complexity of the model.

[0107] Secondary control is performed by adjusting the VSC operating reference power. According to formula (3), the VSC reference power change The node voltage change caused by It can be described as:

[0108] (9);

[0109] Where: is the Jacobian matrix, is the voltage sensitivity matrix.

[0110] When VSC operates reference power regulation, The voltage dynamic model of the VSC at each bus node is:

[0111] (10);

[0112] Where: For the The voltage of the VSC at the bus node, For the The reference power change of the VSC at each bus node, For the The VSC voltage at the bus node is The voltage sensitivity coefficient of the VSC reference power at the bus node, is the number of busbar nodes.

[0113] According to formula (4), the line transmission power change caused by the VSC reference power change is for:

[0114] (11);

[0115] Where: and Respectively represent busbar node and The voltage change of each bus node is: ,and .

[0116] Combined with formula (6), formula (8) can be further expressed as:

[0117] (12);

[0118] Where: For the The VSC voltage at the bus node is The voltage sensitivity coefficient of the VSC reference power at the bus node.

[0119] No. The change in the VSC transmission power at each bus node It is expressed as:

[0120] (13);

[0121] Where: For the The transmission power of the VSC at the bus node is The sensitivity coefficient of the operating reference power of the VSC at the bus node.

[0122] Considering the regulation of VSC reference power, a dynamic model of VSC power is established:

[0123] (14);

[0124] in, Indicates The transmission power of the VSC at each bus node;

[0125] Therefore, the dynamic model of VSC load rate is:

[0126] (15);

[0127] in, For the The load rate of the VSC at the bus node, For the The maximum capacity of the VSC at the bus node.

[0128] S2, introduce a new observer to design a distributed optimal controller using only the information of neighboring VSCs;

[0129] Distributed communication between VSCs in a flexible DC system Figure 2 As shown, the VSC can obtain the voltage and load rate information of the adjacent VSC through point-to-point communication.

[0130] In equations (6) and (8), the control of the flexible DC system is a multi-objective minimization problem. For multi-objective minimization problems, it is often difficult to effectively define global consistency variables using traditional consistency control algorithms.

[0131] In order to achieve voltage regulation and power balance between VSCs in a distributed communication system, The VSC of the bus node introduces the state deviation parameter :

[0132] (16);

[0133] Where: Set Contains the The VSC of the bus node and the VSC connected to it for communication.

[0134] For example, Figure 2 VSC1,x1 in is expressed as:

[0135] (17);

[0136] According to the dynamic model of voltage and VSC load factor, the deviation parameter The dynamic model is:

[0137] (18);

[0138] In addition, the following global cost function is defined:

[0139] (19);

[0140] Where: is the weight coefficient of control cost;

[0141] For all VSCs, the concise form is:

[0142] (20);

[0143] Where: , , , It is given by formula (18).

[0144] The voltage regulation and power sharing problem between VSCs in the flexible DC system is transformed into the stability problem of the deviation system (20). For the VSC at the i-th bus node, when the deviation parameter When it reaches 0, voltage regulation and VSC load balancing between adjacent VSCs are achieved.

[0145] The dynamic model of the flexible DC system is written in distributed form:

[0146] (twenty one);

[0147] (twenty two);

[0148] Where: are the variables of the discrete state equation, for The coefficient matrix of For the The VSC distributed controller input at each bus is , For the Measurement information of VSC at each bus node; for No. List, for The coefficient matrix of ; For the matrix No. OK, is the association matrix determined by the communication links;

[0149] An observer-based distributed controller is designed to The control matrix of the controller of the VSC at the bus node is for:

[0150] (twenty three);

[0151] Where: is the feedback gain No. OK, is the output of the observer;

[0152] According to the optimal control law, the feedback gain Given by:

[0153] (twenty four);

[0154] Where: The control input matrix The weight matrix of is a constant positive definite matrix, By solving the Riccati equation, we can calculate:

[0155] (25);

[0156] In the formula, is the state vector The weight matrix of

[0157] For The VSC at the bus node, the observer Designed for:

[0158] (26);

[0159] In the formula, for No. List.

[0160] S3, optimizing the observer gain;

[0161] In order to determine the observer gain in equation (13): , define the matrix for:

[0162] (27);

[0163] Theorem 1: For the system (21) under the distributed controller (23), if there exists a gain matrix So that the matrix is Schur's, then the observer (26) is stable.

[0164] Proof: For the The observer error of the VSC at the bus node is:

[0165] (28);

[0166] According to (21), (23) and (24), the closed-loop system is reduced to:

[0167] (29);

[0168] Combining formula (29), we can get The observer error dynamics of the VSC at each bus node is:

[0169] (30);

[0170] The dynamic characteristics of all observer errors are given as follows:

[0171] (31);

[0172] If there is a gain matrix , so that the matrix For Schur, then:

[0173] (32);

[0174] That is, under the action of controller (23), the observer is stable.

[0175] In addition, it can be seen from (29) and (31) that:

[0176] (33);

[0177] Where: ;

[0178] Using the Matrix and The stability of the closed-loop system (29) is obtained to be stable. In addition, the deviation system (20) is stable, and the goals of voltage regulation and power sharing between VSCs can be achieved.

[0179] So in order to make the observer is stable, and a nonlinear optimization method is used to find a suitable observer gain so that the matrix M is Schur. The nonlinear optimization method includes but is not limited to sequential quadratic programming algorithm and genetic algorithm;

[0180] The observer gain has a crucial influence on the stability and convergence speed of the closed-loop system (29). For the system (29), the matrix is ​​defined as for:

[0181] (34);

[0182] From system (29), we have:

[0183] (35);

[0184] Where: yes The spectral radius of is the observer error matrix. In order to improve the stability and convergence speed of the closed-loop system, the observer gain is obtained through offline optimization, and the goal is to minimize The modulus of the eigenvalues ​​of The modulus of the eigenvalues ​​is , the goal of observer gain optimization is:

[0185] (36);

[0186] In order to verify the effectiveness of the proposed control algorithm, the present invention builds a simulation platform based on PSCAD / EMTDC. Figure 1 The six-terminal DC system shown.

[0187] The rated voltage of the DC system is ±10kV. Converter stations 1~4 adopt droop control and are connected to the external AC power grid. Their rated capacity is 10MW, the droop coefficient is 0.25kV / MW, and the initial value of the operating reference power is 5MW. Converter stations 5~6 adopt fixed power control and are connected to the new energy base. The output power is 12MW and 14MW respectively. The DC system parameters are shown in Table 1.

[0188] Table 1 DC system parameter table;

[0189] ;

[0190] 1. Analysis of control strategies;

[0191] The control effect of the proposed distributed control method is analyzed. The controller starts working at 2s and the control interval is 100ms. During the control process, the deviation parameters of each VSC are as follows: Figure 3 As shown, the VSC voltage and VSC load rate are Figure 4 and Figure 5 As shown in the figure. At the initial moment, the maximum voltage deviation and the maximum VSC load rate deviation are 0.0374 pu and 0.0559 pu, respectively. Under the action of the designed controller, the VSC deviation parameter decreases after 2.0s and reaches 0 after 3.5s, requiring a total of 15 rounds of control. After the control is completed, the maximum voltage deviation drops to 0.0081 pu and the maximum VSC load rate deviation drops to 0.0098 pu. The simulation results show that the proposed control method improves the VSC load balance and voltage level.

[0192] 2. Algorithm comparison and analysis;

[0193] The centralized control method and the static optimization method are compared with the proposed distributed control method. According to equations (20) and (21), the centralized controller is designed using the classic LQR. The static optimization method uses the sequential quadratic programming method with the objective of equation (9).

[0194] The final solutions of VSC reference power under different methods are as follows: Figure 6 As shown. Table 2 shows the corresponding VSC voltage and VSC load rate. The target is calculated according to Equation (6) and Equation (8). The simulation results show that the proposed distributed control method can obtain the same results as the centralized control method. Compared with the static optimization method, the target value of the distributed control method is slightly larger than that of the static optimization method because the cost function in Equation (19) is not completely equivalent to Equation (6) and Equation (8). In application, the small difference between distributed control and static optimization can be ignored.

[0195] Table 2 VSC voltage and VSC load rate table;

[0196] ;

[0197] 3. Comparative analysis of algorithm convergence speed;

[0198] The convergence speed can be improved by deriving the distributed optimal controller by solving the Riccati equation. To verify this, the convergence speed is compared using the traditional distributed control method. The deviation parameters under the traditional distributed control method are as follows: Figure 7 The corresponding VSC voltage and VSC load rate are shown as Figure 8 and Fig. 9 As shown. According to the traditional distributed control method, the control process is completed in 7.0 seconds. From 2.0 seconds to 7.0 seconds, the traditional distributed control method requires 50 rounds of control. Compared with the traditional distributed control method, the control method proposed in the present invention only requires 15 rounds of control, which shows the advantage of fast convergence speed.

[0199] 4. Analysis of delay impact;

[0200] The control performance under 100ms, 150ms and 200ms delays is analyzed. The voltage recovery process under different delays is shown in Figure 2. Fig.10 The VSC load rate under different delays is shown in Fig.11 As shown. Under time delays of 100 ms, 150 ms, and 200 ms, the control process is completed in 3.5 s, 4.5 s, and 5.4 s, respectively. The final VSC voltage and VSC power under different time delays are the same. The results show that with the increase of time delay, the convergence speed of the control process will decrease, but the voltage regulation and power sharing goals between VSCs can also be achieved. The simulation results show that the proposed distributed controller is still effective in the presence of time delay.

[0201] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A distributed multi-objective optimization control method for a flexible DC system, characterized in that: The following steps are involved: S1. Construct a dynamic model of a multi-terminal flexible DC system based on a linear power flow model; S2, introduce a new observer to design a distributed optimal controller using only the information of neighboring VSCs; S3, optimizing the observer gain; In S1, constructing a dynamic model of a multi-terminal flexible DC system specifically includes: The multi-terminal flexible DC system consists of multiple voltage source converters VSC connected to different renewable energy stations and AC power grids. The node voltage change ΔV caused by the VSC reference power change ΔP is described as: ΔV=-J -1 ΔP=SΔP;(1) Where: J is the Jacobian matrix, S is the voltage sensitivity matrix; When the VSC operates with reference power adjustment, the voltage dynamic model of the VSC at the i-th bus node is: Where: V i is the voltage of the VSC at the i-th bus node, ΔP j,r is the reference power change of the VSC at the jth bus node, S i,j is the voltage sensitivity coefficient of the VSC voltage at the i-th bus node to the VSC reference power at the j-th bus node, and N is the number of bus nodes; Line transmission power change ΔP caused by VSC reference power change im for: Where: ΔV i and ΔV m Respectively represent the voltage changes of the i-th bus node and the m-th bus node, i, j, m∈[1,N], and i≠j≠m; Combining formula (1), formula (3) is further expressed as: Where: S m,j is the voltage sensitivity coefficient of the VSC voltage at the mth bus node to the VSC reference power at the jth bus node; The transmission power change of VSC at the i-th bus node ΔP i,V It is expressed as: Where: T i,j is the sensitivity coefficient of the transmission power of the VSC at the i-th bus node to the operating reference power of the VSC at the j-th bus node; Considering the regulation of VSC reference power, a dynamic model of VSC power is established: Among them, P i,V represents the transmission power of the VSC at the i-th bus node; Therefore, the dynamic model of VSC load rate is: Among them, L i is the load rate of the VSC at the i-th bus node, P i,max is the maximum capacity of the VSC at the i-th bus node; In S2, designing a distributed optimal controller specifically includes: The dynamic model of the flexible DC system is written in distributed form: y i (k)=C i x(k);(9) Where: x is the variable of the discrete state equation, A is the coefficient matrix of x, u i is the VSC distributed controller input at the i-th bus, i.e., ΔP i,V ,y i B is the measurement information of the VSC at the i-th bus node; i is the i-th column of B, B is the coefficient matrix of u, u T =[ΔP 1,V ΔP 2,V …ΔP N,V ]; C is the correlation matrix determined by the communication link, C i is the i-th row of matrix C; An observer-based distributed controller is designed. For the VSC at the i-th bus node, the control matrix of the controller is for: Where: K i is the i-th row of feedback gain K, is the output of the observer; According to the optimal control law, the feedback gain K is given by: K=-(R+B T PB) -1 B T PA;(11) Where: R is the weighted matrix of the control input matrix u, P is a constant positive definite matrix, and P is calculated by solving the Riccati equation: PA+A T P-PBR -1 BP+Q=0; (12) Where Q is the weight matrix of the state vector x; For the VSC at the ith bus node, the observer Designed for: Where, L i is the observer gain.

2. A distributed multi-objective optimization control method for a flexible DC system according to claim 1, characterized in that: In S3, in order to determine the observer gain L in equation (13): i , define the matrix M as: In order for the observer is stable, and a nonlinear optimization method is used to find a suitable observer gain so that the matrix M is Schur. The nonlinear optimization method includes but is not limited to sequential quadratic programming algorithm and genetic algorithm; According to equations (8), (10) and (11), the closed-loop system is reduced to: in, is the observer error at the i-th bus node; For the system (15), define the matrix W for: Where G = [-B1K1,-B2K2,…,-B N K N ]; From system (15), we have: Where: ρ(W) is the spectral radius of W, is the observer error matrix; In order to improve the stability and convergence speed of the closed-loop system, the observer gain is obtained through offline optimization. The goal is to minimize the modulus of the eigenvalue of W. The modulus of the eigenvalue of W is denoted as f. The goal of observer gain optimization is: minf = ρ(W) (18).

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