Event scheduling distributed estimation method of renewable micro-grid system under sensor network framework

Abstract

The invention discloses an event scheduling distributed estimation method of a renewable micro-grid system under a sensor network framework. The method comprises the following steps: 1, establishing a dynamic model of the renewable micro-grid system under the sensor network framework; 2, constructing a distributed estimator; 3, deriving one-step prediction of the ith sensor node at the kth moment; 4, calculating a one-step prediction error covariance upper bound of the ith sensor node at the kth moment; 5, deducing distributed estimator parameters of the ith sensor node at the (k + 1) th moment through the trace of the upper bound of the minimum estimation error covariance; 6, deducing state estimation of the ith sensor node at the (k + 1) th moment; and 7, solving the upper bound of the estimation error covariance of the ith sensor node at the (k + 1) th moment. According to the method, the problem that the existing state estimation method cannot process the state estimation of the renewable micro-grid system under the sensor network framework with inaccurate occurrence probability loss measurement and a dynamic event triggering mechanism at the same time is solved.

Description

Technical Field

[0001] The present invention relates to a distributed state estimation method, and more particularly to a distributed state estimation method for a renewable microgrid system with inaccurate occurrence probability of lost measurements under a sensor network framework based on event scheduling. Background Art

[0002] In recent years, renewable microgrids, as an efficient, environmentally friendly and highly autonomous form of power supply, have received extensive attention. Among them, sensor networks play a crucial role, responsible for real-time monitoring and data collection of various operating parameters in the microgrid, and are a key part of achieving precise control and optimized management of the microgrid. The design of state estimation algorithms based on sensor networks has become a hot issue attracting much attention. Compared with traditional centralized state estimation algorithms, distributed state estimation algorithms have the characteristics of high computational efficiency and low communication pressure. In distributed state estimation algorithms, sensor nodes are independent, which effectively avoids the problem of excessive state estimation errors caused by single-point failures. At present, most scholars have achieved some preliminary research results on the distributed state estimation problem based on traditional power systems, but the state estimation problem of renewable microgrids has not been fully studied. Therefore, it is of practical significance to study the distributed state estimation problem of renewable microgrids under the sensor network framework.

[0003] It should be noted that factors such as sensor failures and network congestion may lead to incomplete measurement data. In addition, there are various physical couplings between sensors, which also increase the possibility of incorrect observations and affect the overall estimation accuracy. Therefore, it is important to study the impact of lost measurements on distributed state estimation algorithms. In particular, lost measurements with inaccurate occurrence probabilities deserve further attention. To cope with limited network resources, event-triggered mechanisms have been applied to the state estimation problem of power systems, effectively improving the network situation. Compared with traditional static event-triggered mechanisms, dynamic event-triggered mechanisms can dynamically adjust the triggering conditions according to the real-time operating state of the system, while improving the system resource utilization rate, better ensuring the performance and reliability of the system. Therefore, dynamic event-triggered mechanisms can effectively cope with the impact brought by limited network resources and are of great significance for realizing the safe and stable operation of renewable microgrids.

[0004] Existing distributed state estimation methods are difficult to simultaneously handle the state estimation problem of renewable microgrids with inaccurate occurrence probability of lost measurements and limited network resources. In view of this situation, it is of practical significance to design a distributed state estimation method for a renewable microgrid system with inaccurate occurrence probability of lost measurements under a sensor network framework based on event scheduling. Summary of the Invention

[0005] To solve the problem of inaccurate occurrence probability loss measurement and limited network resources in the existing renewable microgrid state estimation, the present invention provides an event scheduling distributed estimation method for a renewable microgrid system under a sensor network framework.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] An event scheduling distributed estimation method for a renewable microgrid system under a sensor network framework, comprising the following steps:

[0008] Step 1: Establish a dynamic model of a renewable microgrid system under a sensor network framework based on event scheduling, and the specific steps are as follows:

[0009] Step 1.1: Establish a dynamic model of distributed generation units in a renewable microgrid:

[0010] Consider a renewable microgrid with a class of two distributed generation units, denoted as DGU r and DGU s , respectively. The two distributed generation units are connected by a three-phase line with non-zero impedance. Each distributed generation unit consists of a DC voltage source representing renewable energy, a voltage source converter, a series filter, and a step-up transformer. The step-up transformer connects the distributed generation unit to the remaining power grid through a common coupling point. Assume that the renewable microgrid operates under balanced conditions. For distributed generation units DGU r and DGU s , in the dq coordinate system rotating at ω 0 , the model is given by the following state equations:

[0011]

[0012] In the formula, j is the imaginary unit, used to represent the phasor relationship in the rotating coordinate system; and are the derivatives of (V r,dq , V s,dq ) and (V tr,dq , V ts,dq ) with respect to time, respectively, representing the rate of change of voltage with time; and are the derivatives of (I tr,dq , I ts,dq ) and (I rs,dq , I sr,dq ) with respect to time, respectively, representing the rate of change of current with time; (V r,dq , V s,dq ), (V tr,dq , V ts,dq ), (I tr,dq , I ts,dqand (I rs,dq , I sr,dq ) are respectively the dq components of the common coupling point voltage of DGU r and DGU s , the voltage across the voltage source converter, the series filter current, and the three-phase line current connecting two distributed generation units; (R tr , R ts ) and (L tr , L ts ) are respectively the resistance and inductance of the series filter in DGU r and DGU s ; (k r , k s ) is the transformer voltage ratio of DGU r and DGU s ; (R rs , L rs ) is the resistance and inductance on the three-phase line connecting DGU r and DGU s , satisfying R rs = R sr and L rs = L sr ; in the relevant area of each common coupling point, capacitors C tr and C ts are used to attenuate the influence of high-frequency harmonics of the load voltage;

[0013] Steps 1 and 2: Construct the state-space model of the renewable microgrid:

[0014]

[0015] In the formula, represents the derivative of x(t k ) with respect to time; x(t k ) is the state vector of the renewable microgrid at time t k ; u(t k ) is the known input vector at time t k ; A and B are matrices obtained from the state equations of the distributed generation units;

[0016] Steps 1 and 3: Construct the dynamic model of the renewable microgrid system under the sensor network framework:

[0017] Discretize the state-space model of the renewable microgrid with a state update period Δt to obtain the following dynamic model of the renewable microgrid system under the sensor network framework:

[0018] x k+1 = A d x k + B d uk +n k

[0019] y i,k = λ i,k C i,k x k +v i,k

[0020] wherein, x k+1 represents the state vector of the renewable microgrid system under the sensor network framework at the (k + 1)-th moment; A d and B d are the matrices obtained after discretization of matrices A and B respectively; x k represents the state vector of the renewable microgrid system under the sensor network framework at the k-th moment; u k represents the known input vector after discretization at the k-th moment; n k is the system noise sequence at the k-th moment with zero mean and covariance S k ; i represents the sensor node label, i = 1, 2,..., N, and N represents the number of sensor nodes; y i,k represents the measurement output of the i-th sensor node in the renewable microgrid system under the sensor network framework at the k-th moment; C i,k is the measurement matrix of the i-th sensor node in the renewable microgrid system under the sensor network framework at the k-th moment; v i,k is the measurement noise sequence of the i-th sensor node in the renewable microgrid system under the sensor network framework at the k-th moment; λ i,k is used to describe the missing measurement phenomenon with inaccurate occurrence probability of the i-th sensor node at the k-th moment;

[0021] Step 14. Introduce a dynamic event-triggering strategy:

[0022] For sensor node i:

[0023]

[0024] wherein, the superscript "T" represents taking the transpose of the matrix; is the transpose of ; represents the measurement output of the i-th sensor received by the estimator in the renewable microgrid system under the sensor network framework based on event scheduling at the k-th moment; s t is the event triggering moment; represents the measurement output of the i-th sensor in the renewable microgrid system under the sensor network framework based on event scheduling at the event triggering moment s t ; s t+1 is the next triggering moment after the triggering moment s t ; Θ(yi,k , π i,k ) represents the trigger function defined in the renewable microgrid system under the sensor network framework based on event scheduling; π i,k is the trigger threshold of the i-th sensor at time k in the renewable microgrid system under the sensor network framework based on event scheduling;

[0025] Step 2: Based on the measurements in Step 1, construct a distributed estimator:

[0026]

[0027] where, represents the one-step prediction of the i-th sensor node at the k-th moment; represents the state estimation of the i-th sensor node at the k-th moment; represents the state estimation of the i-th sensor node at the (k + 1)-th moment; ψ i represents the pre-given consensus parameter of the i-th sensor node; "Σ" is the summation symbol; is the set of adjacent nodes of the i-th sensor node; w ij represents the connection coefficient between the i-th sensor node and the j-th sensor node; K i,k+1 represents the distributed estimator parameter of the i-th sensor node at the (k + 1)-th moment; represents the one-step prediction of the j-th sensor node at the k-th moment; represents the measurement output of the i-th sensor received by the estimator at the (k + 1)-th moment in the renewable microgrid system under the sensor network framework based on event scheduling; C i,k+1 is the measurement matrix of the renewable microgrid system under the sensor network framework of the i-th sensor node at the (k + 1)-th moment; represents λ i,k+1 the nominal mathematical expectation of; λ i,k+1 is used to describe the phenomenon of missing measurements with inaccurate occurrence probability of the i-th sensor node at the (k + 1)-th moment;

[0028] Step 3: Based on deduce the one-step prediction of the i-th sensor node at the k-th moment

[0029] Step 4: By solving the matrix difference equation, calculate the upper bound X of the one-step prediction error covariance of the i-th sensor node at the k-th moment i,k+1|k :

[0030]

[0031] where, represents the transpose of A d ; Xi,k|k denotes the upper bound of the estimation error covariance of the \(i\)-th sensor node at the \(k\)-th moment; \(S\) k is the system noise \(n\) k at the covariance matrix at the \(k\)-th moment;

[0032] Step Five: According to the \(X\) obtained in Step Four i,k+1|k , derive the distributed estimator parameter \(K\) of the \(i\)-th sensor node at the \((k + 1)\)-th moment by minimizing the trace of the upper bound of the estimation error covariance i,k+1 :

[0033]

[0034] where,

[0035]

[0036] In the formula, denotes the square of; denotes \(\varepsilon\) i,k+1 the square of; \(\mu\) 1 , \(\mu\) 2 , \(\mu\) 3 , \(\mu\) 4 , \(\mu\) 5 , \(\mu\) 6 , \(\mu\) 7 , \(\mu\) 8 , \(\mu\) 9 are known scaling parameters; are respectively the reciprocals of \(\mu\) 2 , \(\mu\) 3 , \(\mu\) 4 , \(\mu\) 5 , \(\mu\) 6 , \(\mu\) 7 , \(\mu\) 9 ; is the transpose of \(C\) i,k+1 ; is the inverse of \(\varPhi\) i,k+1 ; is the transpose of; denotes the minimum value between 0.25 and both;

[0037] Step Six: According to the \(K\) obtained in Step Five i,k+1 , derive the state estimation of the \(i\)-th sensor node at the \((k + 1)\)-th moment

[0038] Step Seven: According to the \(K\) obtained in Step Five i,k+1 , solve for the upper bound \(X\) of the estimation error covariance of the \(i\)-th sensor node at the \((k + 1)\)-th moment i,k+1|k+1 :

[0039]

[0040] Among them,

[0041]

[0042] In the formula, and are the reciprocals of μ 1 and μ 8 respectively; is 's transpose; is the transpose of K i,k+1 ; is the transpose of Λ i,k+1|k ; R i,k+1 is the covariance matrix of the measurement noise v i,k+1 of the i-th sensor node at the (k + 1)-th moment in the renewable microgrid system under the sensor network framework; Let k = k + 1, and return to step two.

[0043] Compared with the prior art, the present invention has the following advantages:

[0044] 1. The present invention simultaneously considers the influence of inaccurate occurrence probability of lost measurements and the dynamic event-triggering mechanism on the performance of the state estimation algorithm, and obtains the minimum upper bound of the estimation error covariance based on the Riccati difference equation.

[0045] 2. The present invention uses a recursive method to estimate the state of the renewable microgrid system under the sensor network framework based on event scheduling. This method has the advantages of being easy to solve and suitable for online implementation. At the same time, for such state estimation problems, they can be divided into centralized state estimation and distributed state estimation. It should be noted that in centralized state estimation, the measurement outputs of all sensor nodes need to be expressed in a compact form. Therefore, for a sensor network with a large number of nodes, it requires a high computational cost. However, the distributed state estimation method used in the present invention has a lower computational burden.

[0046] 3. The present invention solves the problem that the existing state estimation methods cannot simultaneously handle the state estimation problem of the renewable microgrid system under the sensor network framework with inaccurate occurrence probability of lost measurements and the dynamic event-triggering mechanism, thereby improving the accuracy of the state estimation algorithm performance for such problems. It can be seen from the simulation diagram that as the nominal mathematical expectation of the lost measurements increases, the average mean square error of the state estimation decreases. Let ε 1,k = 0. When the nominal mathematical expectation of the lost measurements changes from 0.80 to 0.85, the average mean square error of sensor node 1 decreases by about 10%; when ε 1,k = 0, the nominal mathematical expectation of the lost measurements When changing from 0.85 to 0.90, the average mean square error of sensor node 1 is reduced by approximately 5.6%. When the measurement loss probability Prob{λ i,k = 0} is large, it can also ensure that the logarithm of the mean square error log(MSE i,k ) is below its upper bound. Description of the Drawings

[0047] Figure 1 It is a flowchart of the event scheduling distributed estimation method for a renewable microgrid system under a sensor network framework;

[0048] Figure 2 When and ε i,k = 0.05, it is a comparison graph of the second component of the actual state trajectory of the system and the state estimation of the sensor node;

[0049] Figure 3 When and ε i,k = 0.05, it is a comparison graph of the second component of the actual state trajectory of the system and the state estimation of the sensor node;

[0050] Figure 4 When and ε i,k = 0.05, it is a comparison graph of the second component of the actual state trajectory of the system and the state estimation of the sensor node;

[0051] Figure 5 When and ε i,k = 0.05, it is a comparison graph of the second component of the actual state trajectory of the system and the state estimation of the sensor node;

[0052] Figure 6 When and ε i,k = 0, it is a comparison graph of the logarithm of the mean square error log(MSE i,k ) of four sensor nodes and the logarithm of the corresponding upper bound trace of the minimum estimation error covariance log(tr{X i,k|k});

[0053] Figure 7 It is the logarithm of the mean square error log(MSE 1,k) and the logarithm of the upper bound trace of the corresponding minimum estimation error covariance log(tr{X 1,k|k}). Detailed implementation mode

[0054] The technical solution of the present invention will be further described below in conjunction with the accompanying drawings, but it is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.

[0055] The present invention provides an event scheduling distributed estimation method for a renewable microgrid system under a sensor network framework, as Figure 1 shown. The method includes the following steps:

[0056] Step 1: Establish a dynamic model of the renewable microgrid system under the sensor network framework based on event scheduling. The specific steps are as follows:

[0057] Step 1-1: Establish a dynamic model of the distributed generation units in the renewable microgrid:

[0058] Consider a renewable microgrid with two distributed generation units, denoted as DGU r and DGU s . The two distributed generation units are connected by a three-phase line with non-zero impedance. Each distributed generation unit consists of a DC voltage source representing renewable energy, a voltage source converter, a series filter, and a step-up transformer. The step-up transformer connects the distributed generation unit to the rest of the grid through a common coupling point. Assume that the renewable microgrid operates under balanced conditions. For the distributed generation units DGU r and DGU s , the model in the dq coordinate system rotating at ω 0 is given by the following state equations:

[0059]

[0060] In the formula, j is the imaginary unit, used to represent the phasor relationship in the rotating coordinate system; and are the derivatives of (V r,dq , V s,dq ) and (V tr,dq , V ts,dq ) with respect to time, representing the rate of change of voltage with time; and are the derivatives of (I tr,dq , I ts,dq ) and (I rs,dq , I sr,dq ) with respect to time, representing the rate of change of current with time; (Vr,dq , V s,dq ), (V tr,dq , V ts,dq ), (I tr,dq , I ts,dq ) and (I rs,dq , I sr,dq ) are the dq components of the common coupling point voltage of DGU r and DGU s , the voltage across the voltage source converter, the current through the series filter, and the three-phase line current connecting two distributed generation units; (R tr , R ts ) and (L tr , L ts ) are the resistance and inductance of the series filter in DGU r and DGU s respectively; (k r , k s ) is the transformer voltage ratio of DGU r and DGU s ; (R rs , L rs ) are the resistance and inductance of the three-phase line connecting DGU r and DGU s , satisfying R rs = R sr and L rs = L sr ; in the relevant area of each common coupling point, capacitors C tr and C ts are used to attenuate the influence of high-frequency harmonics of the load voltage.

[0061] Step 1: Construct the state-space model of the renewable microgrid:

[0062]

[0063] In the formula, x(t k ) represents the derivative of x(t k ) with respect to time; x(t k ) = [V r,d V r,q I tr,d I tr,q I rs,d I rs,q I sr,d I sr,q V s,d V s,q I ts,d I ts,q T is the state vector of the renewable microgrid at time t k ; (V​r,d , V s,d ), (I tr,d , I ts,d ), and (I rs,d , I sr,d ) are the d-components of the common coupling point voltage of DGU r and DGU s , the series filter current, and the three-phase line current connecting two distributed generation units; (V r,q , V s,q ), (I tr,q , I ts,q ), and (I rs,q , I sr,q ) are the q-components of the common coupling point voltage of DGU r and DGU s , the series filter current, and the three-phase line current connecting two distributed generation units; u(t k ) = [V tr,d V tr,q V ts,d V ts,q ) T is the known input vector at time t k ; (V tr,d , V ts,d ) is the d-component of the voltage across the voltage source converters of DGU r and DGU s ; (V tr,q , V ts,q ) is the q-component of the voltage across the voltage source converters of DGU r and DGU s ; A and B are matrices obtained from the state equations of the distributed generation units.

[0064] Step 13. Construct the dynamic model of the renewable microgrid system under the sensor network framework:

[0065] Discretize the state space model of the renewable microgrid with a state update period Δt, and the following dynamic model of the renewable microgrid system under the sensor network framework can be obtained:

[0066] x k+1 = A d x k + B d u k + n k

[0067] y i,k = λ i,k C i,k x k + v i,k

[0068] In the formula, k is the state update time of the renewable microgrid system under the sensor network framework. The difference between any two adjacent state update times k + 1 and k is Δt, and Δt is the state update period of the renewable microgrid system under the sensor network framework; x k+1 represents the state vector of the renewable microgrid system under the sensor network framework at the (k + 1)-th moment; A d = e AΔt and are the matrices obtained after discretizing matrices A and B respectively; x k represents the state vector of the renewable microgrid system under the sensor network framework at the k-th moment; u k represents the known input vector after discretization at the k-th moment; n k is the system noise sequence at the k-th moment with zero mean and covariance S k ; i represents the sensor node label, i = 1, 2,..., N, and N represents the number of sensor nodes; y i,k represents the measurement output of the i-th sensor node in the renewable microgrid system under the sensor network framework at the k-th moment; C i,k is the measurement matrix of the i-th sensor node in the renewable microgrid system under the sensor network framework at the k-th moment, diag{·} represents the diagonal matrix composed of elements "·", where,

[0069]

[0070] ω k = ω 0 k

[0071] sin(·) and cos(·) represent the sine function and cosine function of "·" respectively; v i,k is the measurement noise of the i-th sensor node in the renewable microgrid system under the sensor network framework at the k-th moment, and its mean is zero and covariance is R i,k ; The initial state x 0 is a random variable with mean η 0 = 0 and covariance Σ 0 ; λ i,k is used to describe the missing measurement phenomenon with inaccurate occurrence probability of the i-th sensor node at the k-th moment, and its variance is σ i,k , satisfying:

[0072]

[0073] where, Prob{λ i,k = 1} represents the probability that λ i,k takes the value of 1, and λ i,k= 1 indicates that the i-th sensor has no missing measurement at the k-th moment; Prob{λ i,k = 0} represents the probability that λ i,k takes the value of 0, and λ i,k = 0 indicates that the i-th sensor has a missing measurement at the k-th moment; represents the mathematical expectation of "·"; represents the nominal mathematical expectation of λ i,k ; |Δλ i,k | ≤ ε i,k , where ε i,k is a known positive scalar.

[0074] Step 14. Introduce a dynamic event-triggering strategy:

[0075] For sensor node i:

[0076]

[0077] In the formula, the superscript "T" represents taking the transpose of the matrix; is the transpose of ; represents the measurement output of the i-th sensor received by the estimator at the k-th moment in the renewable microgrid system under the sensor network framework based on event scheduling; s t is the event triggering moment; represents the measurement output of the i-th sensor at the event triggering moment s t in the renewable microgrid system under the sensor network framework based on event scheduling; s t+1 is the next triggering moment after the triggering moment s t ; Θ(y i,k , π i,k ) represents the triggering function defined in the renewable microgrid system under the sensor network framework based on event scheduling. Only when Θ(y i,k , π i,k ) > 0, the measurement output of the i-th sensor node will be transmitted to the estimator; is the triggering threshold of the i-th sensor at the moment k in the renewable microgrid system under the sensor network framework based on event scheduling, and τ i,1 , τ i,2 and τ i,3 are known positive scalars.

[0078] Step 2. Based on the measurements in Step 14, construct a distributed estimator:

[0079]

[0080] In the formula, represents the one-step prediction of the i-th sensor node at the k-th moment; Denote the state estimate of the \(i\)-th sensor node at the \(k\)-th moment; Denote the state estimate of the \(i\)-th sensor node at the \((k + 1)\)-th moment; \(u\) k Denote the known input vector after discretization at the \(k\)-th moment; \(\psi\) i Denote the pre-given consensus parameter of the \(i\)-th sensor node, satisfying \(\max\{\cdot\}\) represents the maximum value of "\(\cdot\)"; \(\zeta\) i Denote the number of adjacent nodes of the \(i\)-th node; "\(\sum\)" is the summation symbol; is the set of adjacent nodes of the \(i\)-th sensor node; \(w\) ij Denote the connection coefficient between the \(i\)-th sensor node and the \(j\)-th sensor node; \(K\) i,k+1 Denote the distributed estimator parameter of the \(i\)-th sensor node at the \((k + 1)\)-th moment; Denote the one-step prediction of the \(j\)-th sensor node at the \(k\)-th moment; Denote the measurement output of the \(i\)-th sensor received by the estimator at the \((k + 1)\)-th moment in the renewable microgrid system under the sensor network framework based on event scheduling; is the nominal mathematical expectation of the missing measurement of the \(i\)-th sensor node at the \((k + 1)\)-th moment; \(C\) i,k+1 is the measurement matrix of the renewable microgrid system under the sensor network framework for the \(i\)-th sensor node at the \((k + 1)\)-th moment; Denote \(\lambda\) i,k+1 the nominal mathematical expectation of \(\lambda\); \(\lambda\) i,k+1 is used to describe the missing measurement phenomenon with inaccurate occurrence probability of the \(i\)-th sensor node at the \((k + 1)\)-th moment.

[0081] Step 3. Based on Derive the one-step prediction of the \(i\)-th sensor node at the \(k\)-th moment

[0082] Step 4. By solving the matrix difference equation, calculate the upper bound \(X\) of the one-step prediction error covariance of the \(i\)-th sensor node at the \(k\)-th moment i,k+1|k :

[0083]

[0084] In the formula, Denote \(A\) d the transpose of \(A\); \(X\) i,k|k Denote the upper bound of the estimation error covariance of the \(i\)-th sensor node at the \(k\)-th moment; \(S\) k is the covariance matrix of the system noise \(n\) k at the \(k\)-th moment.

[0085] Step 5. According to the \(X\) obtained in Step 4 i,k+1|k, the distributed estimator parameter K of the i-th sensor node at the (k + 1)-th moment is derived by minimizing the trace of the upper bound of the estimation error covariance i,k+1 :

[0086]

[0087] where,

[0088]

[0089] In the formula, the superscript "-1" represents matrix inversion or taking the reciprocal of the logarithm; I is the identity matrix; the superscript "2" represents squaring; represents squared; represents the square of ε i,k+1 ; μ 1 , μ 2 , μ 3 , μ 4 , μ 5 , μ 6 , μ 7 , μ 8 , μ 9 are known scaling parameters; are the reciprocals of μ 2 , μ 3 , μ 4 , μ 5 , μ 6 , μ 7 , μ 9 respectively; is the transpose of C i,k+1 ; is the inverse of Φ i,k+1 ; is transpose; represents the minimum value between 0.25 and both.

[0090] Step 6. According to the K i,k+1 obtained in Step 5, derive the state estimate

[0091] of the i-th sensor node at the (k + 1)-th moment i,k+1 Step 7. According to the K i,k+1|k+1 obtained in Step 5, solve the upper bound X

[0092]

[0093] of the estimation error covariance of the i-th sensor node at the (k + 1)-th moment:

[0094]

[0095] In the formula, and are the reciprocals of μ 1 and μ 8 respectively; is 's transpose; is the transpose of K i,k+1 ; is the transpose of Λ i,k+1|k ; R i,k+1 is the covariance matrix of the measurement noise v i,k+1 at the (k + 1)-th moment of the i-th sensor node in the renewable microgrid system under the sensor network framework; Let k = k + 1, and return to step two.

[0096] In this step, calculate X i,k+1|k+1 for each sensor node, so that P i,k+1|k+1 ≤X i,k+1|k+1 holds, where P i,k+1|k+1 is the estimated error covariance of the i-th sensor node at the (k + 1)-th moment. Next, design the distributed estimator parameter K i,k+1|k+1 at the (k + 1)-th moment by minimizing the trace of X i,k+1 .

[0097] Example:

[0098] In this example, a sensor network with four sensor nodes is selected for simulation, and its edge set can be expressed as:

[0099] ε = {(1,3),(1,4),(3,4),(4,1),(4,3)}

[0100] In the formula, each ordered pair represents the information interaction behavior between sensor nodes. For example, (1,3) means that the 3rd sensor node can transmit information to the 1st sensor node. For any (i,j) (i,j = 1,2,3,4), if (i,j) ∈ ε, then the connection coefficient w ij between the i-th sensor node and the j-th sensor node is 1, otherwise w ij = 0.

[0101] The parameters of the renewable microgrid system are:

[0102] R ti = 1.4 mΩ, R tj = 1.5 mΩ

[0103] L ti = 83.7 μH, L tj = 84.8 μH

[0104] C ti= 77.86 μF, C tj = 76.31 μF

[0105] R ij = 1.2 mΩ, R ji = 1.2 mΩ

[0106] L ij = 500 mH, L ji = 500 mH

[0107] k i = 0.048, k j = 0.048

[0108] f = 50 Hz, Δt = 1e -5 s

[0109] Where mΩ is the unit of resistance, representing milliohm; mH and μH are the units of inductance, representing millihenry and microhenry respectively; μF is the unit of capacitance, representing microfarad; Hz is the basic unit of frequency in the International System of Units, representing the number of periodic variations per second, used to describe the frequency of periodic motion; s is the symbol of second, representing the unit of time; 1e -5 represents 1×10 -5 , that is, 0.00001.

[0110] The remaining selected parameters are:

[0111] ω 0 = 314, S k = 0.03I 12 , R 1,k = 0.17I 18

[0112] R 2,k = 0.13I 18 , R 3,k = 0.12I 18 , R 4,k = 0.15I 18

[0113] Σ 0 = 0.03I 12 , τ 1,k = 0.2, τ 2,k = 0.03, τ 3,k = 0.3

[0114] ψ i = 0.03, ε i,k ∈(0, 0.2)

[0115] Where I 12 represents the 12×12 identity matrix, I18 Represents an 18-by-18 identity matrix.

[0116] log(MSE i,k ) represents the logarithm of the mean square error of the i-th sensor node at the k-th moment, where log(·) represents the logarithm of “·” and MSE i,k represents the mean square error of the i-th sensor node at the k-th moment. The present invention uses the mean square error to demonstrate the superiority of the state estimation method, and its calculation formula is:

[0117]

[0118] where L is the number of simulation runs (L = 50 simulation runs in this embodiment), and respectively represent the true state and the estimated state of the l-th run, is the transpose of. In addition, the average mean square error is introduced to further measure the performance change of the state estimation method under different measurement loss probabilities, and its calculation method is: In this embodiment, M = 50 is the total running time.

[0119] Effect of the distributed state estimation algorithm:

[0120] Figure 2 , Figure 3 , Figure 4 and Figure 5 are respectively the trajectories of the actual state and the estimated state under different loss probabilities, Figure 6 depicts the logarithm log(MSE i,k ) of the mean square error of four sensor nodes and the logarithm log(tr{X i,k|k}) of the corresponding upper bound trace of the minimum estimation error covariance. The experimental results verify the effectiveness of the method proposed in the present invention. Let ε 1,k = 0. When the nominal mathematical expectation of the lost measurement is 0.80, 0.85, 0.90, the average mean square errors of sensor node 1 are -2.10, -2.31, and -2.44 respectively. That is, when the nominal mathematical expectation of the lost measurement changes from 0.80 to 0.85, the average mean square error decreases by about 10%; when the nominal mathematical expectation of the lost measurement changes from 0.85 to 0.90, the average mean square error decreases by about 5.6%.

[0121] Figure 7 gives log(MSE 1,k ) of sensor node 1 and the logarithm of the corresponding upper bound trace of the minimum estimation error covariance log(tr{X1,k|k ) comparison chart. It can be seen from the figure that as the triggering threshold π 1,k increases, the corresponding upper bound increases accordingly, which indicates that the increase in the triggering threshold may lead to a decrease in the estimation accuracy. The introduction of the event-triggering mechanism sacrifices part of the estimation performance to reduce the impact of limited network resources.

[0122] In summary, the method of the present invention can also effectively estimate the system state in the presence of a dynamic event-triggering mechanism and inaccurate occurrence probability loss measurements.

Claims

1. A distributed estimation method for event scheduling of a renewable microgrid system in a sensor network framework, characterized in that The method comprises the following steps: Step 1: Establish a dynamic model of the renewable microgrid system under the sensor network framework based on event scheduling. The specific steps are as follows: Step 1. Establish a dynamic model of distributed generation units in a renewable microgrid: Consider a renewable microgrid with two distributed generation units, denoted as DGU r and DGU s , two distributed generation units are connected through a three-phase line with non-zero impedance. Each distributed generation unit consists of a DC voltage source representing renewable energy, a voltage source converter, a series filter and a step-up transformer, where the step-up transformer connects the distributed generation unit to the rest of the grid through a common coupling point; assuming that the renewable microgrid operates under balanced conditions, for the distributed generation unit DGU r and DGU s , the model in the dq coordinate system rotated to ω0 is given by the following state equation: In the formula, j is an imaginary unit, which is used to express the phasor relationship in the rotating coordinate system; and They are (V r,dq , V s,dq )、(V tr,dq , V ts,dq ) is the derivative of voltage with respect to time, which represents the rate of change of voltage with time; and They are (I tr,dq , I ts,dq ) and (I rs,dq , I sr,dq ) is the derivative with respect to time, which represents the rate of change of current with time; (V r,dq , V s,dq )、(V tr,dq , V ts,dq )、(I tr,dq , I ts,dq ) and (I rs,dq , I sr,dq ) are DGU r and DGU s The voltage at the common coupling point, the voltage across the voltage source converter, the series filter current and the dq components of the three-phase line current connecting the two distributed generation units; (R tr ,R ts ) and (L tr , L ts ) are composed of DGU r and DGU s The resistance and inductance of the upper series filter; (k r , k s ) is DGU r and DGU s Upper transformer voltage ratio; (R rs , L rs ) to connect DGU r and DGU s The resistance and inductance of the three-phase line satisfy R rs =R sr and L rs =L sr ; In the relevant area of ​​each common coupling point, the capacitor C tr and C ts It is used to attenuate the influence of high-frequency harmonics of load voltage; Step 1 and 2: Construct the state space model of the renewable microgrid: In the formula, represents x(t k ) with respect to time; x(t k ) is the renewable microgrid at t k The state vector at the moment; u(t k ) is at t k The known input vector at the time; A and B are matrices obtained from the state equation of the distributed generation unit; Step 13: Construct a dynamic model of the renewable microgrid system under the sensor network framework: The state space model of the renewable microgrid is discretized with a state update period Δt, and the dynamic model of the renewable microgrid system under the sensor network framework is obtained as follows: x k+1 =A d x k +B d u k +n k y i,k =λ i,k C i,k x k +v i,k In the formula, x k+1 A represents the state vector of the renewable microgrid system under the sensor network framework at the k+1th moment; d and B d are the matrices obtained after discretization of matrices A and B; x k represents the state vector of the renewable microgrid system under the sensor network framework at the kth moment; u k represents the known input vector after discretization at the kth moment; n k is the k-th time point with zero mean and covariance S k The system noise sequence; i represents the sensor node number, i = 1, 2, ..., N, N represents the number of sensor nodes; y i,k represents the measurement output of the i-th sensor node in the renewable microgrid system under the sensor network framework at the k-th time; C i,k is the measurement matrix of the renewable microgrid system in the sensor network framework at the i-th sensor node at the k-th time; v i,k is the measurement noise sequence of the i-th sensor node in the renewable microgrid system under the sensor network framework at the k-th time; i,k It is used to describe the phenomenon of lost measurement with inaccurate probability at the i-th sensor node at the k-th time; Step 14: Introduce dynamic event triggering strategy: For sensor node i: In the formula, the superscript "T" means taking the transpose of the matrix; for The transpose of represents the measurement output of the ith sensor received by the estimator at the kth time in the renewable microgrid system under the event-based scheduling sensor network framework; s t It is the event triggering moment; represents the i-th sensor in the renewable microgrid system under the sensor network framework based on event scheduling at the event triggering time s t The measurement output; s t+1 is the triggering time s t The next triggering moment after θ(y i,k ,π i,k ) represents the trigger function defined in the renewable microgrid system under the sensor network framework based on event scheduling; π i,k is the triggering threshold of the ith sensor at time k in the renewable microgrid system under the sensor network framework based on event scheduling; Step 2: Based on the measurements in step 14, construct a distributed estimator: In the formula, represents the one-step prediction of the i-th sensor node at the k-th time; represents the state estimation of the i-th sensor node at the k-th moment; represents the state estimation of the i-th sensor node at the k+1th time; ψ i represents the pre-given consistency parameter of the i-th sensor node; "Σ" is the summation symbol; is the set of neighboring nodes of the ith sensor node; w ij represents the connection coefficient between the i-th sensor node and the j-th sensor node; K i,k+1 represents the distributed estimator parameters of the i-th sensor node at the k+1th time; represents the one-step prediction of the j-th sensor node at the k-th time; represents the measurement output of the i-th sensor received by the estimator at the k+1th time in the renewable microgrid system under the event-based sensor network framework; C i,k+1 is the measurement matrix of the renewable microgrid system in the sensor network framework at the i-th sensor node at the k+1th time; Represents λ i,k+1 The nominal mathematical expectation of ; λ i,k+1 It is used to describe the phenomenon of lost measurement with inaccurate probability at the i-th sensor node at the k+1th time; Step 3: Based on Derive the one-step prediction of the i-th sensor node at the k-th time Step 4: Calculate the upper bound of the one-step prediction error covariance X of the i-th sensor node at the k-th time by solving the matrix difference equation i,k+1|k : In the formula, Indicates A d The transpose of X i,k|k represents the upper bound of the estimation error covariance of the i-th sensor node at the k-th time; S k is the system noise n k The covariance matrix at the kth moment; Step 5: According to X obtained in step 4 i,k+1|k , the distributed estimator parameter K of the i-th sensor node at the k+1th time is derived by minimizing the trace of the upper bound of the estimation error covariance i,k+1 : in, In the formula, express The square of Represents ε i,k+1 The square of; μ1, μ2, μ3, μ4, μ5, μ6, μ7, μ8, μ9 are known scaling parameters; They are the reciprocals of μ2, μ3, μ4, μ5, μ6, μ7 and μ9 respectively; C i,k+1 The transpose of Φ i,k+1 The inverse of for The transpose of Indicates 0.25 and The minimum value between the two; Step 6: According to K obtained in step 5 i,k+1 , derive the state estimate of the i-th sensor node at the k+1th time Step 7: According to K obtained in step 5 i,k+1 , solve the upper bound X of the estimation error covariance of the i-th sensor node at the k+1th time i,k+1|k+1 : in, In the formula, and are the reciprocals of μ1 and μ8 respectively; for The transpose of K i,k+1 The transpose of For i,k+1|k The transpose of R i,k+1 is the measurement noise v of the i-th sensor node in the renewable microgrid system at the k+1th time in the sensor network framework i,k+1 covariance matrix; let k = k + 1, and return to step 2.

2. The event scheduling distributed estimation method for renewable microgrid system under the sensor network framework according to claim 1 is characterized in that In the steps 1 and 2, x(t k )=[V r,d V r,q I tr,d I tr,q I rs,d I rs,q I sr,d I sr,q V s,d V s,q I ts,d I ts,q ] T , where (V r,d , V s,d )、(I tr,d , I ts,d ) and (I rs,d , I sr,d ) are DGU r and DGU s The voltage at the common coupling point, the series filter current and the d component of the three-phase line current connecting the two distributed generation units; (V r,q , V s,q )、(I tr,q , I ts,q ) and (I rs,q , I sr,q ) are DGU r and DGU s The voltage at the common coupling point, the series filter current and the q component of the three-phase line current connecting the two distributed generation units; u(t k )=[V tr,d V tr,q V ts,d V ts,q ] T , where (V tr,d , V ts,d ) is DGU r and DGU s The d component of the voltage across the voltage source converter; (V tr,q , V ts,q ) is DGU r and DGU s The q component of the voltage across the voltage source converter.

3. The event scheduling distributed estimation method for renewable microgrid system under the sensor network framework according to claim 1 is characterized in that Among the above three, A d =e AΔt , 4. The event scheduling distributed estimation method for a renewable microgrid system under a sensor network framework according to claim 1 is characterized in that In the steps 1 and 3, diag{·} represents a diagonal matrix consisting of elements "·", where oh k =ω0k sin(·) and cos(·) represent the sine function and cosine function of "·" respectively.

5. The event scheduling distributed estimation method for renewable microgrid system under the sensor network framework according to claim 1 is characterized in that In the steps 1 and 3, λ i,k satisfy: Among them, Prob{λ i,k =1} means λ i,k The probability of taking the value 1, λ i,k =1 means that the i-th sensor has no missing measurement at the k-th time; Prob{λ i,k =0} means λ i,k The probability of taking the value 0, λ i,k =0 means that the i-th sensor has a missing measurement at the k-th time; represents the mathematical expectation of "·"; Represents λ i,k The nominal mathematical expectation of |Δλ i,k |≤ε i,k , ε i,k is a known positive scalar.

6. The event scheduling distributed estimation method for a renewable microgrid system under a sensor network framework according to claim 1 is characterized in that In the step 1-4, when Θ(y i,k ,π i,k )>0, the measurement output of the i-th sensor node will be transmitted to the estimator.

7. The event scheduling distributed estimation method for a renewable microgrid system under a sensor network framework according to claim 1 is characterized in that In the steps 1 to 4, τ i,1 , τ i,2 and τ i,3 is a known positive scalar.

8. The event scheduling distributed estimation method for a renewable microgrid system under a sensor network framework according to claim 1 is characterized in that In the step 2, max{·} represents the maximum value of "·", ζ i Represents the number of adjacent nodes of the i-th node.

9. The event scheduling distributed estimation method for a renewable microgrid system under a sensor network framework according to claim 1 is characterized in that In step 7, calculate the X of each sensor node i,k+1|k+1 , so that P i,k+1|k+1 ≤X i,k+1|k+1 Established, where P i,k+1|k+1 is the estimated error covariance of the i-th sensor node at the k+1th time, by minimizing X i,k+1|k+1 The trace of the distributed estimator parameter K at the k+1th moment is designed i,k+1 .

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