Robust control method, device and medium for distributed power generation system in active distribution network

Abstract

This invention discloses a robust control method, device, and medium for distributed generation systems in an active distribution network. The method includes: establishing a discrete-time model of the distributed generation system in an active distribution network, considering the system model jump caused by changes in equivalent load, sensor and actuator distortion and offset due to faults, and external disturbances; constructing a Lyapunov function to obtain sufficient conditions for the stochastic stability and robust controller existence of the distributed generation system in the active distribution network; and finally, calculating the controller gain matrix K corresponding to ensure system stability by continuously reducing the disturbance suppression rate γ in the stability conditions. i When the disturbance suppression rate γ is minimized and the system is stable, the optimal controller gain matrix K is obtained. i * This invention can improve the robustness of the control system to disturbances, thereby ensuring the safe and stable operation of distributed generation systems in active distribution networks.

Description

Robust control methods, equipment and media for distributed generation systems in active distribution networks Technical Field

[0001] This invention relates to distributed generation systems and robust control theory in active distribution networks, specifically to a robust control method, equipment, and medium for distributed generation systems in active distribution networks. Background Technology

[0002] In recent years, with social progress and technological development, distributed generation systems in active distribution networks have gradually become an indispensable part of people's production and daily life. This inevitably leads to an increase in the consumption of distributed generation in active distribution networks. Under these circumstances, if the load is not properly handled, it can easily lead to the deterioration and instability of distributed generation systems in active distribution networks, and even large-scale power outages. Therefore, a thorough understanding of the random fluctuations in the load of distributed generation systems in active distribution networks is of great significance for the safe and stable operation of distributed generation systems in active distribution networks and for people's production and daily life.

[0003] In reality, on the one hand, sudden environmental changes, component aging, and external interference can cause changes in the equivalent load of the infinite bus, leading to corresponding changes in system parameters. On the other hand, under network attacks or interference, communication between the sensor and controller channels and between the controller and actuator channels may fail, resulting in a decrease in system reliability and security. Furthermore, due to the complexity and variability of actual operating conditions, simply analyzing the stability performance of distributed generation systems in active distribution networks is insufficient to meet actual engineering design requirements. If a distributed generation system in an active distribution network is disturbed and deviates from its stable state during actual operation, and cannot promptly return to its original stable state, it will affect the quality of transmitted power, leading to unstable supply voltage and frequency, which will affect the safety of electrical equipment. If it cannot return to a stable state for an extended period, it may even paralyze the entire distributed generation system in the active distribution network. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a robust control method, device, and medium for distributed generation systems in active distribution networks. The aim is to solve problems such as system jumps, sensor and actuator failures, and external disturbances in distributed generation systems within active distribution networks, thereby enabling the distributed generation systems in active distribution networks to have better robustness and ensuring their safe and stable operation.

[0005] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0006] The present invention provides a stable and robust control method for distributed generation systems in active distribution networks, characterized by the following steps:

[0007] Step 1: Linearize and discretize the distributed generation system in the active distribution network to establish a model of the distributed generation system in the active distribution network;

[0008] Step 2: Construct an output mode-dependent feedback controller;

[0009] Step 3: Establish a closed-loop system model for distributed generation in an active distribution network;

[0010] Step 4: Construct the Lyapunov function for the distributed generation closed-loop system model in the active distribution network at time k;

[0011] Step 5: Based on Lyapunov stability theory and linear matrix inequality analysis, obtain sufficient conditions for the stochastic stability of the distributed generation system model in the active distribution network and the existence of a robust controller when a fault occurs in the channel between the sensor and the actuator.

[0012] Step 6: Determine whether the sufficient condition is true. If it is true, it indicates that a symmetric positive definite matrix X exists. i and Y i When a fault occurs in the channel between the sensor and the actuator, the distributed generation closed-loop system model in the active distribution network at time k is stochastically stable and meets the robust performance index. The gain matrix of the controller is K. i =Y i X i -1 If the distributed generation closed-loop system model in the active distribution network at time k is unstable and does not meet the robust performance index when the sensor and actuator fail, there is no controller gain matrix, and the process is stopped.

[0013] Step 7: Continuously reduce the disturbance suppression rate γ and return to step 6 for execution until the process stops, then execute step 8;

[0014] Step 8: Select the minimum disturbance rejection rate γ that ensures system stability and meets robust performance requirements. * The corresponding controller gain matrix is ​​used as the optimal controller gain matrix K. i * Thus, when a failure occurs in the channel between the sensor and the actuator, the optimal controller gain matrix K is utilized. i * Stable and robust control is implemented for the distributed generation system in the active distribution network at time k.

[0015] The robust control method for distributed generation systems in active distribution networks described in this invention is also characterized in that, in step 1, a model of the distributed generation system in an active distribution network is established using equation (1):

[0016]

[0017] In equation (1), x(k) is the state vector containing the frequency and voltage information of the distributed generation system in the active distribution network at time k; z(k) is the control output containing the frequency and voltage information of the distributed generation system in the active distribution network at time k; u(k) represents the control input containing the frequency and voltage information of the distributed generation system in the active distribution network at time k; w(k) represents the disturbance of the frequency and voltage information of the distributed generation system in the active distribution network at time k; r(k) represents the Markov state variable that causes the distributed generation system in the active distribution network to jump due to the change of equivalent load during operation at time k, and the Markov state variable r(k) takes values ​​in the finite set Λ={1,2,…,i,…,N}, i∈Λ, N is a positive integer; A(r(k)), B1(r(k)), B2(r(k)), C(r(k)), D(r(k)) represent the system state equation matrix of the distributed generation system in the active distribution network under five equivalent loads, respectively.

[0018] In step 2, the output mode-dependent feedback controller is constructed using equation (2):

[0019] u(k)=Π2(r(k))K(r(k))Π1(r(k))x(kd k (2)

[0020] Equation (2), K(r(k)) is the controller gain matrix related to the Markov state variable r(k), Π1(r(k))=diag{α1(r(k)),…,α l (r(k)), …, α n (r(k))} represents a diagonal matrix representing the degree of channel failure occurrence between n controllers and actuators related to the Markov state variable r(k), α l (r(k))∈[0,1] represents the degree of channel failure between the l-th controller and actuator associated with the Markov state variable r(k), when α l (r(k)) = 0 indicates that no fault has occurred, when α l (r(k))∈(0,1) represents a partial fault, when α l (r(k))=1 indicates a complete fault; l∈[1,n]; Π2(r(k))=diag{β1(r(k)),…,β s (r(k)), …, β m (r(k))} represents a diagonal matrix representing the degree of channel failure between m sensors and the controller, related to the Markov state variable r(k), β s(r(k))∈[0,1] represents the degree of channel failure between the s-th sensor and the controller associated with the Markov state variable r(k), when β s (r(k)) = 0 indicates that no fault has occurred, when β s (r(k))∈(0,1) represents a partial fault, when β s (r(k)) = 1 indicates a complete fault; s ∈ [1, m]; d k Let d be the transmission delay of data at time k in the communication network. k ∈[0, d M ], d M This represents the maximum transmission delay.

[0021] In step 3, let the five system state equation matrices when r(k) = i be denoted as: A i =A(r(k)), B 1i =B1(r(k), B 2i =B2(r(k), C i =C(r(k)), D i =D(r(k)); Let the feedback controller when r(k) = i be denoted as: K i =K(r(k)); Let r(k) = i, the diagonal matrix representing the degree of channel fault occurrence between n controllers and actuators is denoted as: Π 1i =Π1(r(k)); Let r(k) = i, the diagonal matrix representing the degree of channel fault occurrence between m sensors and the controller is denoted as Π1(r(k)); 2i =Π2(r(k)); Let r(k) = i, and denote the degree of channel failure between the l-th controller and the actuator as α. li =α l (r(k)); Let β denote the degree of channel failure between the s-th sensor and the controller when r(k) = i. si =β s (r(k)), thus using equation (3) to establish a closed-loop system model of distributed generation in the active distribution network:

[0022]

[0023] definition It is Π 1i The expected matrix, and has ε{·} represents expectation. Let be a diagonal matrix, and we have:

[0024]

[0025]

[0026] definition It is Π 2i The expected matrix, and has Let be a diagonal matrix, and we have:

[0027]

[0028]

[0029] Define matrix matrix And by rewriting equation (3), we get equation (8):

[0030]

[0031] In equation (8), A i (l,s) is a matrix containing unknown variables, and we have:

[0032]

[0033] In equation (9), O n It is an n-dimensional zero matrix;

[0034] In equation (8), Let be a matrix containing system state information, delay information, and external disturbances at time k, and we have:

[0035]

[0036] In equation (10), x(kd) k ) is kd k The state variables of the distributed generation system in the active distribution network at all times; x(kd M ) is kd M The state vector of the distributed generation system in the active distribution network at all times;

[0037]

[0038] In step 4, the Lyapunov function is constructed using equation (12):

[0039] V(k)=V1(k)+V2(k)+V3(k) (12)

[0040] In equation (12), V(k) is the Lyapunov function constructed for the distributed generation closed-loop system in the active distribution network at time k, used to test the rate of change with respect to sampling time k, and thus determine the stability of the distributed generation system in the active distribution network. It consists of three parts: V1(k), V2(k), and V3(k), and has the following:

[0041] V1(k)=x T (k)P i x(k) (13)

[0042] In equation (13), P i Let r(k) be the symmetric positive definite matrix corresponding to the Markov state variable r(k) = i; T denotes the transpose.

[0043]

[0044] In equation (14), Q is a symmetric positive definite matrix;

[0045]

[0046] In equation (15), y(j) = x(j+1) - x(j) represents the difference between the state vector x(j+1) at time j+1 and the state vector x(j) at time j; R is a symmetric positive definite matrix.

[0047] In step 5, the sufficient condition is obtained using equations (16) and (17):

[0048]

[0049] In equation (16), * indicates that the upper right triangular elements of the matrix are symmetrical with the lower left triangular elements, and O 4n×8n It is a 4n×8n dimensional zero matrix, O 4n×n It is a 4n×n dimensional zero matrix. For 4n×n 2 Zero-dimensional matrix, O 2n×8n It is a 2n×8n dimensional zero matrix. For 2n×n 2 Zero-dimensional matrix, O 2n×n It is a 2n×n dimensional zero matrix, O 8n×n It is an 8n×n dimensional zero matrix. For 8n×n 2 Zero-dimensional matrix For n×n 2 Zero-dimensional matrix For n 2 ×n 2 Zero-dimensional matrix For n2 ×n-dimensional zero matrix Let be a linear matrix containing unknown variables, and we have:

[0050]

[0051] In equation (18), X i and These are the three symmetric positive definite matrices corresponding to the Markov state variable r(k) = i, -γ 2 I n Let I be a linear matrix containing unknown variables, where γ is the perturbation suppression ratio; n It is an n-dimensional identity matrix; O n It is an n-dimensional zero matrix;

[0052] In equation (16), Let be a linear matrix containing unknown variables, and we have:

[0053]

[0054] In equation (19), α is an unknown scalar, and Y i Let r(k) be the symmetric positive definite matrix corresponding to the Markov state variable r(k) = i.

[0055] In equation (16), Let be a linear matrix containing unknown variables, and we have:

[0056]

[0057] In equation (16), Let be a linear matrix containing unknown variables, and we have:

[0058]

[0059] In equation (16), Let be a linear matrix containing unknown variables, and we have:

[0060]

[0061] In equation (22), For the system transition, under different transition probabilities, the matrix X... i The corresponding change is a symmetric positive definite matrix, and π ij (k) represents the state transition probability from the Markov state variable r(k) = i at time k to the Markov state variable r(k+1) = j at time k+1, and πij (k)=Pr{r(k+1)=j|r(k=i};τ is an unknown scalar;

[0062] In equation (16), Let be a linear matrix containing unknown variables, and we have:

[0063]

[0064] In equation (16), Let be a linear matrix containing unknown variables, and we have:

[0065]

[0066] In equation (16), Let be a linear matrix containing unknown variables, and we have:

[0067]

[0068] In equation (25), Let be the l-th linear matrix containing unknown variables, and we have:

[0069]

[0070] In equation (26), O (l-1)m×1 It is a (l-1)m×1 dimensional zero matrix, O (n-1)m×1 It is an (n-1)m×1 dimensional zero matrix, O (n-l)m×1 It is an (nl)m×1 dimensional zero matrix. Let be a linear matrix containing unknown variables, and we have:

[0071]

[0072] In equation (27), v ls Let be a scalar containing unknown variables, and we have:

[0073]

[0074] In equation (28), It is α li Expectations It is β si Expectations;

[0075] In equation (16), Let be a linear matrix containing unknown variables, and we have:

[0076]

[0077] In equation (16), Let be a linear matrix containing unknown variables, and we have:

[0078]

[0079] The present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing any of the robust control methods, and the processor is configured to execute the program stored in the memory.

[0080] The present invention provides a computer-readable storage medium on which a computer program is stored, wherein the computer program, when executed by a processor, performs any of the steps of the robust control method.

[0081] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0082] 1. This invention focuses on distributed generation systems in active distribution networks, researching stability and robust control strategies for such systems. Considering the impact of system parameter fluctuations, sensor and actuator failures, and external disturbances, a discrete-time closed-loop model of the distributed generation system in an active distribution network is established, and a robust controller is designed. This provides solutions for system stability and robust control, enabling the distributed generation system in the active distribution network to remain stable and exhibit good robust performance under the aforementioned conditions.

[0083] 2. This invention establishes a linear matrix inequality that includes coupling terms resulting from the multiplication of sensor and actuator fault matrices and unknown variables. Based on a decoupling strategy, the coupling terms are analyzed and processed to obtain sufficient conditions for the stability of distributed generation systems in active distribution networks. This enables the distributed generation systems in active distribution networks to operate stably when sensors and actuators fail, thereby reducing conservatism.

[0084] 3. This invention obtains the optimal controller gain matrix K by optimizing the minimum disturbance rejection rate γ. i * This enables distributed generation systems in active distribution networks to have better anti-interference performance, thereby enhancing the robustness of the system and allowing for reasonable control of the output of distributed generation systems in active distribution networks. This ensures the safe and stable operation of distributed generation systems in active distribution networks and is of great significance for the further development of distributed generation systems in active distribution networks. Attached Figure Description

[0085] Figure 1 is a schematic diagram of a distributed generation system in an active distribution network;

[0086] Figure 2 is the system state response diagram under disturbance.

[0087] Figure 3 is a flowchart of the stochastic stability and robust controller solution for a distributed generation system in an active distribution network when sensor and actuator failures occur. Detailed Implementation

[0088] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0089] Referring to Figure 3, a stochastic stability robust control method for a distributed generation system in an active distribution network when sensor and actuator failures occur includes the following steps:

[0090] Step 1: Establish a distributed generation system model in an active distribution network:

[0091] Referring to Figure 1, considering the system parameter jumps and external disturbances in the distributed generation system of the active distribution network, its discrete-time model is as follows:

[0092]

[0093] In equation (1), x(k) is the state vector containing the frequency and voltage information of the distributed generation system in the active distribution network at time k; z(k) is the control output containing the frequency and voltage information of the distributed generation system in the active distribution network at time k; u(k) represents the control input containing the frequency and voltage information of the distributed generation system in the active distribution network at time k; w(k) represents the disturbance of the frequency and voltage information of the distributed generation system in the active distribution network at time k; r(k) represents the Markov state variable that causes the distributed generation system in the active distribution network to jump due to the change of equivalent load during operation at time k, and the Markov state variable r(k) takes values ​​in the finite set Λ={1,2,…,i,…,N}, i∈Λ, N is a positive integer; A(r(k)), B1(r(k)), B2(r(k)), C(r(k)), D(r(k)) represent the system state equation matrix of the distributed generation system in the active distribution network under five equivalent loads, respectively.

[0094] Step 2: Construct an output mode-dependent feedback controller using equation (2):

[0095] u(k)=Π2(r(k))K(r(k))Π1(r(k))x(kd k (2)

[0096] Equation (2), K(r(k)) is the controller gain matrix related to the Markov state variable r(k), Π1(r(k))=diag{α1(r(k)),…,αl (r(k)), …, α n (r(k))} represents a diagonal matrix representing the degree of channel failure occurrence between n controllers and actuators related to the Markov state variable r(k), α l (r(k))∈[0,1] represents the degree of channel failure between the l-th controller and actuator associated with the Markov state variable r(k), when α l (r(k)) = 0 indicates that no fault has occurred, when α l (r(k))∈(0,1) represents a partial fault, when α l (r(k))=1 indicates a complete fault; l∈[1,n]; Π2(r(k))=diag{β1(r(k)),…,β s (r(k)), …, β m (r(k))} represents a diagonal matrix representing the degree of channel failure between m sensors and the controller, related to the Markov state variable r(k), β s (r(k))∈[0,1] represents the degree of channel failure between the s-th sensor and the controller associated with the Markov state variable r(k), when β s (r(k)) = 0 indicates that no fault has occurred, when β s (r(k))∈(0,1) represents a partial fault, when β s (r(k)) = 1 indicates a complete fault; s ∈ [1, m]; d k Let d be the transmission delay of data at time k in the communication network. k ∈[0, d M ], d M This represents the maximum transmission delay.

[0097] Step 3: Let the state equation matrices of the five systems when r(k) = i be denoted as: A i =A(r(k)), B 1i =B1(r(k), B 2i =B2(r(k), C i =C(r(k)), D i =D(r(k)); Let the feedback controller when r(k) = i be denoted as: K i =K(r(k)); Let r(k) = i, the diagonal matrix representing the degree of channel fault occurrence between n controllers and actuators is denoted as: Π 1i =Π1(r(k)); Let r(k) = i, the diagonal matrix representing the degree of channel fault occurrence between m sensors and the controller is denoted as Π1(r(k)); 2i =Π2(r(k)); Let r(k) = i, and denote the degree of channel failure between the l-th controller and the actuator as α.li =α l (r(k)); Let β denote the degree of channel failure between the s-th sensor and the controller when r(k) = i. si =β s (r(k)), thus using equation (3) to establish a closed-loop system model of distributed generation in the active distribution network:

[0098]

[0099] definition It is Π 1i The expected matrix, and has ε{·} represents expectation. Let be a diagonal matrix, and we have:

[0100]

[0101]

[0102] definition It is Π 2i The expected matrix, and has Let be a diagonal matrix, and we have:

[0103]

[0104]

[0105] Define matrix matrix And by rewriting equation (3), we get equation (8):

[0106]

[0107] In equation (8), A i (l,s) is a matrix containing unknown variables, and we have:

[0108] A i (l, s) = [A i B 1i Π 2i K i Π 1i O n B 2i (9)

[0109] In equation (9), O n It is an n-dimensional zero matrix;

[0110] In equation (8), Let be a matrix containing system state information, delay information, and external disturbances at time k, and we have:

[0111]

[0112] In equation (10), x(kd) k ) is kd k The state variables of the distributed generation system in the active distribution network at all times; x(kd M ) is kd M The state vector of the distributed generation system in the active distribution network at all times;

[0113]

[0114] Step 4: Construct the Lyapunov function for the distributed generation closed-loop system model in the active distribution network at time k using equation (12):

[0115] V(k)=V1(k)+V2(k)+V3(k) (12)

[0116] In equation (12), V(k) is the Lyapunov function constructed for the distributed generation closed-loop system in the active distribution network at time k, used to test the rate of change with respect to sampling time k, and thus determine the stability of the distributed generation system in the active distribution network. It consists of three parts: V1(k), V2(k), and V3(k), and has the following:

[0117] V1(k)=x T (k)P i x(k) (13)

[0118] In equation (13), P i Let r(k) be the symmetric positive definite matrix corresponding to the Markov state variable r(k) = i; T denotes the transpose.

[0119]

[0120] In equation (14), Q is a symmetric positive definite matrix;

[0121]

[0122] In equation (15), y(j) = x(j+1) - x(j) represents the difference between the state vector x(j+1) at time j+1 and the state vector x(j) at time j; R is a symmetric positive definite matrix.

[0123] Step 5: Based on the Lyapunov function constructed in Step 4, according to the Lyapunov stability theory and the linear matrix inequality analysis method, first determine the stochastic stability of the distributed generation system in the active distribution network when the sensors and actuators fail, and obtain the sufficient conditions for the stochastic stability of the distributed generation system in the active distribution network.

[0124] Step 5.1: Differentiate the Lyapunov function V(k) to obtain ΔV(k), and we have:

[0125] ε{ΔV(k)}=ε{ΔV1(k)+ΔV2(k)+ΔV3(k)} (16)

[0126] In equation (16), ΔV(k) consists of three parts: ΔV1(k), ΔV2(k), and ΔV3(k), ε{·} represents the expectation, and we have:

[0127]

[0128] In equation (17), This indicates that when the system jumps, the matrix P changes under different transition probabilities. i The corresponding changes in the symmetric positive definite matrix and β ls Let be a matrix containing unknown variables, and we have:

[0129]

[0130] In equation (18), v ls Let be a matrix containing unknown variables, and we have:

[0131]

[0132] In equation (19), It is α li Expectations It is β si Expectations;

[0133] ε{ΔV2(k)}=ε{x T (k)Qx(k)-x T (kd M )Qx(kd M )} (20)

[0134]

[0135] In equation (21), * indicates that the elements in the upper right triangle of the matrix are symmetric to the elements in the lower left triangle, Υ is a matrix containing unknown variables, and we have:

[0136]

[0137] In equation (22), Let be a matrix containing unknown variables, and we have:

[0138]

[0139] In equation (21), η(k) is a matrix containing system state information and delay information, and we have:

[0140] η(k)=[x T (k)x T (kd k )x T (kd M )] T (twenty four)

[0141] Substitute equations (17), (18), and (19) into equation (16), and add and subtract z from both sides of equation (16). T (k)z(k)-γ 2 w T If (k)w(k), then:

[0142]

[0143] In equation (25), Ψ(l,s) is a matrix containing unknown variables, and we have:

[0144]

[0145] In equation (26), Ξ 11 Let be a matrix containing unknown variables, and we have:

[0146]

[0147] In equation (27), -γ 2 I n Let I be a linear matrix containing unknown variables, where γ is the perturbation suppression ratio; n It is an n-dimensional identity matrix;

[0148] According to Schur's lemma, if:

[0149]

[0150] In equation (28), Ξ 12Let be a matrix containing unknown variables, and we have:

[0151]

[0152] In equation (27), Ξ 13 Let be a matrix containing unknown variables, and we have:

[0153]

[0154] In equation (30), Σ is a matrix containing unknown variables, and we have:

[0155]

[0156] In equation (31), χ l Let be the l-th matrix containing unknown variables, and we have:

[0157]

[0158] In equation (28), Ξ 22 Let be a matrix containing unknown variables, and we have:

[0159]

[0160] In equation (28), O 2n×2mn It is a zero matrix containing 2n×2mn dimensions;

[0161] In equation (28), Ξ 33 Let be a matrix containing unknown variables, and we have:

[0162]

[0163] According to Lyapunov stability theory, when the external perturbation w(k) ≠ 0, for a given positive integer d... M If there exists a symmetric positive definite matrix P i If R>0, Q>0 makes equation (28) true, then the closed-loop power generation system shown in equation (3) has a robust disturbance suppression rate γ and executes step 5.2; otherwise, step 5.2 cannot be executed.

[0164] Step 5.2: Solve for the robust controller:

[0165] If we perform an equivalent transformation on Ξ in (28), then we have:

[0166]

[0167] In equation (35), Ξ 120 Let be a matrix containing unknown variables, and we have:

[0168] Ξ 120 =P i Ξ 12 (36)

[0169] In equation (35), Ξ 220 Let be a matrix containing unknown variables, and we have:

[0170] Ξ 220 =P i Ξ 220 P i (37)

[0171] In equation (35), Ξ 130 Let be a matrix containing unknown variables, and we have:

[0172] Ξ 130 =P i Ξ 13 (38)

[0173] In equation (35), Ξ 330 Let be a matrix containing unknown variables, and we have:

[0174] Ξ 330 =P i Ξ 330 P i (39)

[0175] Define X i P i =I,X i Let matrix Y be an unknown variable matrix. i =K i X i ;

[0176] use and αI n Alternative And using Theorem 2x T y≤x T Zx+y T Z -1 y and the Schul complement lemma, where x and y are n×1 dimensional vectors and Z is an n-dimensional positive definite matrix, equation (35) can be rewritten as:

[0177]

[0178] In equation (40), Ξ 121 Let be a matrix containing unknown variables, and we have:

[0179]

[0180] In equation (41), Let be a matrix containing unknown variables, and we have:

[0181]

[0182] In equation (42), α is an unknown scalar;

[0183] In equation (41), Let be a matrix containing unknown variables, and we have:

[0184]

[0185] In equation (40), Ξ 16 Let be a linear matrix containing unknown variables, and we have:

[0186]

[0187] In equation (40), Ξ 17 Let be a linear matrix containing unknown variables, and we have:

[0188]

[0189] In equation (40), Ξ 24 Let be a linear matrix containing unknown variables, and we have:

[0190]

[0191] In equation (40), Ξ 35 Let be a linear matrix containing unknown variables, and we have:

[0192] Ξ 35 =[Γ1... Γ l ... Γ n (47)

[0193] In equation (47), Γ l Let be the l-th linear matrix containing unknown variables, and we have:

[0194]

[0195] In equation (48), O (l-1)m× 1 is a (l-1)m×1 dimensional zero matrix, O (n-1)m×1 It is an (n-1)m×1 dimensional zero matrix, O(n-l)m×1 It is an (nl)m×1 dimensional zero matrix. Let be a linear matrix containing unknown variables, and we have:

[0196]

[0197] In equation (40), Ξ 55 Let be a linear matrix containing unknown variables, and we have:

[0198]

[0199] In equation (40), Ξ 66 Let be a linear matrix containing unknown variables, and we have:

[0200]

[0201] Define matrix

[0202] Furthermore, due to:

[0203]

[0204]

[0205] In equation (52), τ represents an unknown variable;

[0206] Combining equation (52), equation (53) is multiplied before and after equation (40):

[0207]

[0208] We can obtain:

[0209]

[0210] In equation (54), * indicates that the upper right triangular elements of the matrix are symmetrical with the lower left triangular elements, and O 4n×8n It is a 4n×8n dimensional zero matrix, O 4n×n It is a 4n×n dimensional zero matrix. For 4n×n 2 Zero-dimensional matrix, O 2n×8n It is a 2n×8n dimensional zero matrix. For 2n×n 2 Zero-dimensional matrix, O 2n×nIt is a 2n×n dimensional zero matrix, O 8n×n It is an 8n×n dimensional zero matrix. For 8n×n 2 Zero-dimensional matrix For n×n 2 Zero-dimensional matrix For n 2 ×n 2 Zero-dimensional matrix For n 2 ×n-dimensional zero matrix Let be a linear matrix containing unknown variables, and we have:

[0211]

[0212] In equation (55), These are two symmetric positive definite matrices corresponding to the Markov state variable r(k) = i;

[0213] In equation (54), Let be a linear matrix containing unknown variables, and we have:

[0214]

[0215] In equation (56), For the system transition, under different transition probabilities, the matrix X... i The corresponding change is a symmetric positive definite matrix, and π ij (k) represents the state transition probability from the Markov state variable r(k) = i at time k to the Markov state variable r(k+1) = j at time k+1, and π ij (k)=Pr{r(k+1)=j|r(k)=i};

[0216] In equation (54), Let be a linear matrix containing unknown variables, and we have:

[0217]

[0218] Step 6: According to Lyapunov stability theory, for a given positive integer d... M If there exists a symmetric positive definite matrix P i >0, R>0, Q>0 And matrix Y i X iIf equation (43) holds, it means that when a fault occurs in the channel between the sensor and the actuator, the distributed generation system in the active distribution network at time k is stochastically stable and satisfies the robust performance index, and the controller gain matrix is ​​K. i =Y i X i -1 If the distributed generation system model in the active distribution network at time k is not stochastically stable and does not meet the robust performance index when the sensor and actuator fail, there is no controller gain matrix, and the calculation is stopped.

[0219] Step 7: Continuously reduce the disturbance suppression rate γ and return to step 6 for execution until the process stops, then execute step 8;

[0220] Step 8: Select the minimum disturbance rejection rate γ that ensures system stability and meets robust performance requirements. * The corresponding controller gain matrix is ​​used as the optimal controller gain matrix K. i * Thus, when a failure occurs in the channel between the sensor and the actuator, the optimal controller gain matrix K is utilized. i * Stable and robust control is implemented for the distributed generation system in the active distribution network at time k.

[0221] Example:

[0222] The stochastic stability robust control method for distributed generation systems in active distribution networks proposed in this invention ensures that the system remains stochastically stable and possesses a certain degree of anti-interference capability even under external disturbances. The specific implementation method is as follows:

[0223] Step 1: The controlled object is a distributed generation system in a closed-loop active distribution network, and its state-space model is given by formula (3). The system parameters are:

[0224]

[0225]

[0226]

[0227] C1=[0 0.2 -0.1], C2=[0 0.3 -0.1], D1=D2=0.4, d M =4.

[0228] The Markov chain state transition probability matrix is:

[0229]

[0230] Let the number of channels from the controller to the actuator be n=3, and the diagonal matrix Π 11 =Π 12 =diag{0.8,0.1,0.2}, the number of sensor-to-controller channels is m=1, and the diagonal matrix Π 21 =Π 22 =0.2.

[0231] Step 2: When there is an external disturbance in the system, let's assume the external disturbance is:

[0232]

[0233] And assume the initial state is x0 = [-10.80.3] T The controller gain matrix can be obtained as follows:

[0234] K1=[-4.69963.7700.582]; K2=[0.6873-0.39602.553];

[0235] Under the action of the aforementioned controller, the state trajectory of the controlled system is shown in Figure 2. It can be seen that under the action of a non-zero external disturbance, for a given positive real number γ, the closed-loop system 3 is stochastically stable under the action of controller 2 and satisfies the set robust performance index, which is γ = 1.2.

[0236] Step 4: Continuously decrease the disturbance rejection ratio γ. When γ = 1.001, the optimal controller gain matrix is ​​obtained.

[0237] K1 * = [-4.07354.48061.2237]; K2 * = [0.8311 - 0.35062.1180];

[0238] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any way. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention shall fall within the scope of the invention.

Claims

1. A robust control method for a distributed generation system in an active distribution network, characterized in that, The process includes the following steps: Step 1: Linearize and discretize the distributed generation system in the active distribution network to establish a model of the distributed generation system in the active distribution network; Step 2: Construct a feedback controller with output mode correlation; Step 3: Establish a closed-loop system model of the distributed generation system in the active distribution network; Step 4: Construct the Lyapunov function of the closed-loop system model of the distributed generation system in the active distribution network at time k; Step 5: Based on Lyapunov stability theory and linear matrix inequality analysis, obtain sufficient conditions for the stochastic stability of the distributed generation system model in the active distribution network and the existence of a robust controller when a fault occurs in the channel between the sensor and the actuator; Step 6: Determine whether the sufficient conditions are met. If they are met, it indicates the existence of a symmetric positive definite matrix X. i and Y i When a fault occurs in the channel between the sensor and the actuator, the distributed generation closed-loop system model in the active distribution network at time k is stochastically stable and meets the robust performance index. The gain matrix of the controller is K. i =Y i X i -1 If the system remains stable and meets the robust performance index, proceed to step 7; otherwise, it indicates that the distributed generation closed-loop system model in the active distribution network at time k is unstable and does not meet the robust performance index when the sensor and actuator fail, there is no controller gain matrix, and the process stops; Step 7: Continuously decrease the disturbance suppression rate γ and return to step 6 until the process stops, then proceed to step 8; Step 8: Select the minimum disturbance suppression rate γ that keeps the system stable and meets the robust performance index. * The corresponding controller gain matrix is ​​used as the optimal controller gain matrix K. i * Thus, when a failure occurs in the channel between the sensor and the actuator, the optimal controller gain matrix K is utilized. i * Stable and robust control is implemented for the distributed generation system in the active distribution network at time k.

2. The robust control method for distributed generation systems in an active distribution network according to claim 1, characterized in that, In step 1, the distributed generation system model in the active distribution network is established using equation (1): (1) In equation (1), x(k) is the state vector containing the frequency and voltage information of the distributed generation system in the active distribution network at time k; x(k+1) is the state vector containing the frequency and voltage information of the distributed generation system in the active distribution network at time k+1; z(k) is the control output containing the frequency and voltage information of the distributed generation system in the active distribution network at time k; u(k) represents the control input containing the frequency and voltage information of the distributed generation system in the active distribution network at time k; w(k) represents the frequency and voltage information received by the distributed generation system in the active distribution network at time k. The disturbance amount of information; r(k) represents the Markov state variable that causes the distributed generation system in the active distribution network to jump due to the change of equivalent load when the distributed generation system is running at time k. The Markov state variable r(k) takes values ​​in the finite set Λ={1,2,…,i,…,N}, where i∈Λ and N is a positive integer; A(r(k)), B1(r(k)), B2(r(k)), C(r(k)), and D(r(k)) represent the system state equation matrices of the distributed generation system in the active distribution network under five equivalent loads.

3. The robust control method for distributed generation systems in an active distribution network according to claim 2, characterized in that, In step 2, the output mode-dependent feedback controller is constructed using equation (2): u(k) = Π2(r(k))K(r(k))Π1(r(k))x(kd) k (2) Equation (2), K(r(k)) is the controller gain matrix related to the Markov state variable r(k), Π1(r(k))=diag{α1(r(k)),…, , …, α n (r(k))} represents a diagonal matrix representing the degree of channel failure occurrence between n controllers and actuators related to the Markov state variable r(k), α l (r(k))∈[0,1] represents the degree of channel failure between the l-th controller and actuator associated with the Markov state variable r(k), when α l (r(k))=0 indicates that no fault has occurred, when α l (r(k))∈(0,1) represents a partial fault, when α l (r(k))=1 indicates a complete fault; l∈[1,n];Π2(r(k))=diag{β1(r(k)),…,β s (r(k)), …, β m (r(k))} represents a diagonal matrix representing the degree of channel failure between m sensors and the controller, related to the Markov state variable r(k), β s (r(k))∈[0,1] represents the degree of channel failure between the s-th sensor and the controller associated with the Markov state variable r(k), when β s (r(k))=0 indicates that no fault has occurred, when β s (r(k))∈(0,1) represents a partial fault, when β s (r(k)) = 1 indicates a complete fault; s∈[1,m]; d k Let d be the transmission delay of data at time k in the communication network. k ∈[0, d M ], d M For the maximum transmission delay, x(kd) k ) is kd k A state vector that contains frequency and voltage information of the distributed generation system in the active distribution network at all times.

4. The robust control method for distributed generation systems in an active distribution network according to claim 3, characterized in that, In step 3, let the five system state equation matrices when r(k)=i be denoted as: A i =A(r(k)), B 1i =B1(r(k), B 2i =B2(r(k), C i =C(r(k)), D i =D(r(k)); Let the feedback controller when r(k)=i be denoted as: K i =K(r(k)); Let r(k) = i, the diagonal matrix representing the degree of channel fault occurrence between the n controllers and actuators is denoted as: Π 1i =Π1(r(k)); Let r(k) = i, then the diagonal matrix representing the degree of channel fault occurrence between the m sensors and the controller is denoted as Π1(r(k)). 2i =Π2(r(k)); Let r(k) = i, and denote the degree of channel failure between the l-th controller and the actuator as . When r(k) = i, the degree of channel failure between the s-th sensor and the controller is denoted as β. si =β s (r(k)), thus using equation (3) to establish a closed-loop system model of distributed generation in the active distribution network: (3) Definition It is Π 1i The expected matrix, and has ε{•} represents expectation. Let be a diagonal matrix, and we have: (4) (5) Definition It is Π 2i The expected matrix, and has ， Let be a diagonal matrix, and we have: (6) (7) Define matrix ,matrix And by rewriting equation (3), we get equation (8): In equation (8), Let be a matrix containing unknown variables, and we have: In equation (9), It is an n-dimensional zero matrix; in equation (8), Let be a matrix containing system state information, delay information, and external disturbances at time k, and we have: In equation (10), for The state variables of the distributed generation system in the active distribution network at all times; for The state vector of the distributed generation system in the active distribution network at all times; (11)。 5. The robust control method for distributed generation systems in an active distribution network according to claim 4, characterized in that, In step 4, the Lyapunov function is constructed using equation (12): In equation (12), Let V1(k), V2(k), and V3(k) be the Lyapunov function constructed for the distributed generation closed-loop system in the active distribution network at time k. This function is used to test the rate of change with respect to sampling time k, thereby determining the stability of the distributed generation system in the active distribution network. It consists of three parts: V1(k), V2(k), and V3(k), and has the following properties: In equation (13), P i Let r(k) = i be the symmetric positive definite matrix corresponding to the Markov state variable r(k); T denotes the transpose. In equation (14), Q is a symmetric positive definite matrix; In equation (15), This represents the state vector of the system at time j+1. The difference between the state vector x(j) at time j and the state vector x(j) at time j; R is a symmetric positive definite matrix.

6. The robust control method for distributed generation systems in an active distribution network according to claim 5, characterized in that, In step 5, the sufficient condition is obtained using equations (16) and (17): (16) In equation (16) of equation (17), This represents a linear matrix containing unknown variables. * indicates that the elements in the upper right triangle are symmetric to the elements in the lower left triangle. O 4n×8n It is a 4n×8n dimensional zero matrix, O 4n×n It is a 4n×n dimensional zero matrix. For 4n×n 2 Zero-dimensional matrix, O 2n×8n It is a 2n×8n dimensional zero matrix. For 2n×n 2 Zero-dimensional matrix, O 2n×n It is a 2n×n dimensional zero matrix, O 8n×n It is an 8n×n dimensional zero matrix. For 8n×n 2 Zero-dimensional matrix For n×n 2 Zero-dimensional matrix For n 2 ×n 2 Zero-dimensional matrix For n 2 ×n-dimensional zero matrix It is an n×n dimensional zero matrix. for The first row and first column of the matrix contains the unknown variables, and we have: In equation (18), and ， These are the three symmetric positive definite matrices corresponding to the Markov state variable r(k) = i. Let I be a linear matrix containing unknown variables, where γ is the perturbation suppression ratio; n It is an n-dimensional identity matrix; O n It is an n-dimensional zero matrix; in equation (16), for The first row and second column of the matrix contains a linear matrix with unknown variables, and we have: In equation (19), Y is an unknown scalar. i Let r(k) be the symmetric positive definite matrix corresponding to the Markov state variable r(k) = i; in equation (16), for The first row and sixth column of the matrix contains a linear matrix with unknown variables, and the following is true: In equation (16) of equation (20), for The first row and seventh column of the matrix contains a linear matrix with unknown variables, and the following is true: In equation (16) of equation (21), for The second row and second column of the matrix contains a linear matrix with unknown variables, and we have: In equation (22), For the system transition, under different transition probabilities, the matrix X... i The corresponding change is a symmetric positive definite matrix, and ， Represents the Markov state variables at time k. Markov state variables transitioning to time k+1 The state transition probability, and π ij (k)=Pr{r(k+1)=j|r(k)=i};τ is an unknown scalar;In equation (16), for The linear matrix in the second row and fourth column contains the unknown variables, and has the following: In equation (16) of equation (23), for The linear matrix in the 3rd row and 3rd column contains the unknown variables, and we have: In equation (16) of equation (24), for The linear matrix in row 3, column 5 contains the unknown variables, and we have: In equation (25), Let be the l-th linear matrix containing unknown variables, and we have: In equation (26), O (l-1)m×1 It is a (l-1)m×1 dimensional zero matrix, O (n-1)m×1 It is an (n-1)m×1 dimensional zero matrix, O (n-l)m×1 It is an (nl)m×1 dimensional zero matrix. Let be a linear matrix containing unknown variables, and we have: In equation (27), Let be a scalar containing unknown variables, and we have: In equation (28), yes Expectations yes The expectation; in equation (16), for The linear matrix in row 5 and column 5 contains the unknown variables, and has the following: In equation (16) of equation (29), for The linear matrix in row 6 and column 6 contains the unknown variables, and we have: (30)。 7. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing the robust control method of any one of claims 1-6, the processor being configured to execute the program stored in the memory.

8. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program is executed by the processor to perform the steps of the robust control method according to any one of claims 1-6.

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