A Flexible Interconnected Distribution Network Dispatch Method and System Based on Gaussian Mixture Model

Abstract

A flexible interconnected distribution network scheduling method and system based on a Gaussian mixture model is proposed. This method establishes a source-load power probabilistic model for the flexible interconnected distribution network, determining the random variable of injected power using the predicted value of injected power and the sampled value of the injected power prediction error. With the objective function being the minimum operating loss cost of the flexible interconnected distribution network, constraints are established for the objective function. Based on the source-load power probabilistic model, the inverse function of the cumulative distribution function of the injected power random variable is determined. The inverse function and the node injected power adjustment amount are used to transform the probabilistic constraints of node voltage not exceeding limits and branch power not exceeding limits. The AC / DC system power balance constraint is relaxed, and together with the objective function, they form a flexible interconnected distribution network scheduling optimization model. The optimal value of the injected power adjustment amount for each node is obtained through iterative solution of the flexible interconnected distribution network scheduling optimization model. This optimal value serves as the power value exchanged by the flexible interconnected devices, meeting the scheduling requirements of the medium-voltage flexible interconnected system.

Description

Technical Field

[0001] This invention belongs to the field of power grid dispatching technology, and relates to the optimization dispatching technology of flexible interconnected distribution systems. Specifically, it relates to an optimization dispatching method and system for flexible interconnected distribution networks that considers the probability distribution characteristics of source and load power. Background Technology

[0002] Flexible interconnection technology for medium-voltage distribution networks, based on flexible interconnection devices, enhances system flexibility. The increasing availability of renewable energy and new electricity loads places higher demands on the flexibility of distribution systems, especially when source and load power exhibits strong uncertainty. The challenge lies in maximizing the flexibility potential of medium-voltage flexible interconnection systems during dispatch. Furthermore, for medium-voltage interconnected flexible distribution networks, the large number of source and load connections and the complex spatiotemporal distribution of power make solving the optimization model even more difficult when considering probability distributions. Therefore, a dispatch optimization method that considers the multidimensional stochasticity of source and load is needed.

[0003] In existing technologies, optimization scheduling schemes that consider voltage risk perception in AC / DC distribution networks prioritize economic efficiency in day-ahead decision-making scheduling, while intraday risk scheduling considers the characteristics of distributed photovoltaic power and ultra-short-term load fluctuations. Based on ultra-short-term prediction probability information, a probabilistic power flow calculation is performed using a stochastic response surface method combined with Nataf transform, and a voltage risk perception system is established based on the probabilistic power flow results; however, this method cannot achieve source-load probabilistic modeling of multidimensional random variables. An optimization strategy for low-voltage load shedding in AC / DC hybrid systems, constrained by static voltage stability indices, calculates system power flow using an alternating iterative method and establishes a static voltage stability index applicable to AC / DC transmission; based on an improved genetic algorithm, the optimal load shedding configuration strategy is solved with the objective function of minimizing low-voltage load shedding loss cost; however, this method only analyzes the optimal load shedding strategy and does not consider the impact of large-scale distributed photovoltaic power and electric vehicle integration. A distributed multi-PV coordinated control strategy based on the discrete consensus algorithm obtains the average value of PV controller power deviation and operating mode through the discrete consensus algorithm, updates the operating mode command and power reference command, and utilizes the complementary power between PVs to balance the power deviation, enabling the PVs to adaptively operate in maximum power point tracking mode or constant power mode. This method effectively smooths out the power fluctuations of PVs in different application scenarios, but it is not suitable for AC / DC distribution grid optimization considering uncertainties. Existing optimization scheduling methods that consider the randomness of source load power mainly use Monte Carlo methods or analytical methods based on probability distributions to overcome the influence of uncertainties. However, for medium-voltage flexible interconnected distribution systems, the number of random source loads is large and the dimensionality is high, and there are significant correlations between various power variables. Probabilistic modeling methods based on Monte Carlo methods take too long to model when dealing with such high-dimensional massive data, and cannot meet scheduling requirements. Robust optimization methods based on variable intervals can only obtain the optimal solution under the worst-case scenario, facing the problem of excessive conservatism. While traditional chance-constraint methods can calculate the optimal solution under certain confidence levels, the model solution also suffers from long computation times, especially in medium-voltage interconnected power distribution systems with complex source-load scenarios. Furthermore, for flexible interconnected systems, the correlation of random variables between interconnected systems cannot be ignored because optimization decisions regarding the switching power of flexible interconnected devices are required. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a flexible interconnected distribution network scheduling method and system based on a Gaussian mixture model. The Gaussian mixture model enables probabilistic modeling that considers the correlation of random variables in a flexible interconnected system, quickly and analytically characterizing the probability distribution and correlation of high-dimensional, large-scale random variables. Based on the cumulative distribution function of the Gaussian mixture model, the opportunity constraints are decomposed and transformed. A fourth-order polynomial is used to fit the cumulative distribution function curve, and the roots of this fourth-order polynomial are calculated to obtain the quantiles of the cumulative distribution function. This transforms the difficult-to-handle opportunity constraints into linear constraints, accelerating the solution of the optimization model and enabling it to meet the scheduling requirements of medium-voltage flexible interconnected systems.

[0005] The present invention adopts the following technical solution.

[0006] This invention proposes a flexible interconnected distribution network scheduling method based on a Gaussian mixture model, comprising:

[0007] The load power and the output power of distributed generation in the flexible interconnected distribution network are obtained as random variables. Based on the Gaussian mixture model, the superposition of multiple Gaussian distributions of the random variables is used as the source-load power probability model of the flexible interconnected distribution network.

[0008] The injection power prediction error is determined by using the actual and predicted values ​​of the injected power at each node in the flexible interconnected distribution network. The actual injected power value and its sampling time constitute the injection power time series value. Based on the source-load power probability model, the joint probability density function of the injection power prediction error and the injection power time series value is determined. Utilizing the invariant conditional probability property of the Gaussian mixture model, the conditional probability density function of the injection power prediction error is determined based on the joint probability density function of the injection power prediction error and the injection power time series value. Based on the conditional probability density function of the injection power prediction error, a sampled value of the injection power prediction error is obtained. The injection power random variable is determined using the injected power prediction value and the sampled value of the injection power prediction error.

[0009] The objective function is to minimize the operating loss cost of the flexible interconnected distribution network, which includes AC system loss cost, DC system loss cost, and converter loss cost. Constraints are established for the objective function, including: probabilistic constraints on node voltage and branch power limits established using chance-constrained programming, AC / DC system power balance constraints, and converter operation constraints. Based on the source-load power probability model, the inverse function of the cumulative distribution function of the injected power random variable is determined. The probabilistic constraints on node voltage and branch power limits are transformed using the inverse function and node injected power adjustment. The AC / DC system power balance constraints are relaxed based on the Distflow power flow model. The transformed node voltage and branch power limits, the processed AC / DC system power balance constraints, and the converter operation constraints, along with the objective function, constitute a flexible interconnected distribution network scheduling optimization model. This model is iteratively solved to obtain the optimal value of the injected power adjustment for each node, which serves as the power value exchanged by the flexible interconnected devices.

[0010] Preferably, the source-load power probability model of the flexible interconnected distribution network satisfies the following relationship:

[0011]

[0012] In the formula, f X (x) represents the marginal probability density of the random variable X, M is the number of Gaussian components in the Gaussian mixture model; x is a sample of the random variable; ω m N represents the weight of the m-th Gaussian component; m () represents the m-th one-dimensional normal distribution; Let be the mean and covariance of the m-th Gaussian component of sample x, respectively.

[0013] Preferably, the injected power of W nodes in the flexible interconnected distribution network is random, and a first random vector X1 represents the actual value of the injected power of the W nodes, satisfying X1=[X 11 X 12 …X 1i …X 1W ] T , where X 1i Let X2 be the actual value of the injected power at the i-th node, and let the second random vector X2 represent the predicted values ​​of the injected power at the W nodes, satisfying X2=[X 21 X 22 … X 2i … X 2W ] T X 2iLet be the predicted injected power value of the i-th node. Then, the third random vector representing the predicted injected power error of the W nodes satisfies the following relationship:

[0014] X e =X1-X2 (3)

[0015] Satisfy X e =[X e1 X e2 …X ei …X eW ] T X ei Let be the prediction error of the injected power at the i-th node.

[0016] Preferably, the sampling times of the actual injected power values ​​of the W nodes constitute a time-series vector, satisfying T = [T1 T2…T i …T W ] T T i The sampling time is the actual value of the injected power at the i-th node;

[0017] Construct a matrix Y such that Y = [X1 T] T Y i The injection power timing value of the i-th node includes the actual value of the injection power of the i-th node and its sampling time;

[0018] Based on the Gaussian mixture model, the joint probability density function of the injection power prediction error of the i-th node and the injection power time series value of the i-th node satisfies the following relationship:

[0019]

[0020] In the formula, Let y be the joint probability density function of the injection power prediction error of the i-th node and the injection power time series value of the i-th node. i For Y i The sample, x ei For X ei The sample, Let be the mean and covariance of the m-th Gaussian component of the i-th node, respectively. Let be the weight of the m-th Gaussian component of the i-th node. Let the m-th one-dimensional normal distribution be the i-th node. Let be the covariance of the injection power prediction error of the i-th node with respect to the m-th Gaussian component of the injection power prediction error. Let be the covariance of the injection power prediction error at the i-th node with respect to the m-th Gaussian component of the injection power time series value. Let be the covariance of the injection power time series value at the i-th node with respect to the m-th Gaussian component of the injection power time series value. Let be the mean of the m-th Gaussian component of the injection power prediction error for the i-th node. Let W be the mean of the m-th Gaussian component of the injection power time series value of the i-th node, and W be the number of nodes.

[0021] Preferably, the conditional probability density function of the injected power prediction error satisfies the following relationship:

[0022]

[0023] In the formula, Let be the joint probability density function of the injection power prediction error of the i-th node and the injection power time series value of the i-th node. Let m be the weight of the m-th Gaussian component of the injection power prediction error at the i-th node, given the time-series distribution of the actual injection power values. Let the m-th one-dimensional normal distribution be the i-th node. Let m be the mean of the m-th Gaussian component of the conditional probability distribution of the injection power prediction error at the i-th node, given the time-series distribution of the actual injection power values. Let m be the covariance of the conditional probability distribution of the injection power prediction error of the i-th node, given the time-series distribution of the actual injection power value.

[0024] Preferably, the objective function is to minimize the operating loss cost of the flexible interconnected distribution network, which includes AC system loss cost, DC system loss cost, and converter loss cost; the objective function satisfies the following relationship:

[0025] C loss =C loss，AC +C loss，DC +C loss，VSC (6)

[0026]

[0027] In the formula, C loss For the operating loss cost of flexible interconnected distribution networks, C loss，AC For the loss cost of the AC system; C loss，DC For DC system loss costs, C loss，VSC For converter loss cost; N AC N represents the number of nodes in the communication system. DC Let be the number of nodes in the DC system network; Ω(i) be the set of neighboring nodes of node i; r ij，AC The resistance of AC branch ij; r ij，DC I is the resistance of the DC branch ij;ij，AC I is the square of the current flowing through the AC branch ij; ij，DC is the square of the current flowing through the DC branch ij.

[0028] Preferably, the constraints for establishing the objective function include: probabilistic constraints on node voltage not exceeding limits and branch power not exceeding limits established using the chance-constrained programming method, AC / DC system power balance constraints, and converter operation constraints.

[0029] Preferably, the probabilistic constraint condition for ensuring that the node voltage does not exceed the limit satisfies the following relationship:

[0030] P{U i,min ≤U i (ξ)≤U i,max}≥β U

[0031] In the formula, U i (ξ) represents the voltage of node i under the operating state ξ of the distribution network; U i,min and U i,max Let P{U} be the lower and upper limits of the voltage at node i; i,min ≤U i (ξ)≤U i,max} represents the probability that the voltage of node i will not exceed the limit under the operating state ξ of the distribution network; β U This represents the confidence level at which the node voltage does not exceed the limit.

[0032] The probabilistic constraint condition for branch power not exceeding the limit satisfies the following relationship:

[0033] P{P k (ξ)≤P k,max}≥β P

[0034] In the formula, P k (ξ) represents the active power of branch k under the operating state ξ of the distribution network; P k,max P{P is the upper limit of active power in branch k; k (ξ)≤P k,max} represents the probability that the active power of branch k will not exceed the limit under the operating state ξ of the distribution network; β P This represents the confidence level that the branch power will not exceed the limit.

[0035] Preferably, the power balance constraint condition of the AC / DC system satisfies the following relationship:

[0036]

[0037] In the formula, P AC,i and Q AC,iThese represent the active and reactive power injected into node i of the AC system, respectively; G AC,ij B ij θ ij These represent the conductance, susceptance, and voltage phase difference between node i and node j in the AC system, respectively; U AC,i and U AC,j P represents the voltage amplitudes at nodes i and j in the AC system, respectively. DC,i Active power injected into node i of the DC system; U DC,i and U DC,j Let G be the voltages at nodes i and j in the DC system, respectively; DC,ij Let N be the conductance between node i and node j in the DC system. AC N represents the number of nodes in the communication system. DC This represents the number of nodes in the DC system network.

[0038] Preferably, the converter operating constraints satisfy the following relationship:

[0039]

[0040] In the formula, P VSC and Q VSC These represent the active power and reactive power flowing through the converter, respectively; S VSC This refers to the capacity of the converter.

[0041] Preferably, the inverse function of the cumulative distribution function of the injected power random variable is determined based on the source-load power probability model. The inverse function and the node injected power adjustment amount are used to transform the probabilistic constraints on node voltage not exceeding limits and branch power not exceeding limits, including:

[0042] Based on the injected power random variable, the probabilistic constraints on node voltage not exceeding limits and branch power not exceeding limits are transformed using the following relationship:

[0043]

[0044] In the formula, P r () represents the probability of a specific event occurring, ΔV i,max ΔP is the upper limit of the voltage deviation at node i. i,max Let A1 be the upper limit of the branch power deviation, B1 be the conversion coefficient matrix between the node injected power adjustment and the node voltage deviation, A2 be the conversion coefficient matrix between the node injected power random variable and the node voltage deviation, and B3 be the conversion coefficient matrix between the node injected power random variable and the branch power deviation. Let ΔP be the upper limit of the branch power deviation. adj,t Let ΔP be the injection power adjustment at node t. ran,tLet α be the injection power random variable at time t. set For a given confidence level;

[0045] Based on the source-load power probability model, the cumulative distribution function of the node injected power random variable is determined. Based on the cumulative distribution function, the transformed probability constraints for node voltage not exceeding limits and branch power not exceeding limits are transformed for the first time, resulting in the following relationship:

[0046]

[0047] In the formula, Let be the cumulative distribution function of the injection power random variable at time t;

[0048] Based on the inverse function of the cumulative distribution function, the probabilistic constraints on node voltage not exceeding limits and branch power not exceeding limits are transformed a second time to obtain the following relationship:

[0049]

[0050] In the formula, It is the inverse function of the cumulative distribution function.

[0051] This invention also proposes a flexible interconnected distribution network dispatching system based on a Gaussian mixture model, comprising:

[0052] The load power modeling module is used to obtain the load power and the output power of distributed generation in the flexible interconnected distribution network as random variables. Based on the Gaussian mixture model, the superposition of multiple Gaussian distributions of the random variables is used as the source-load power probability model of the flexible interconnected distribution network.

[0053] The power prediction error modeling module is used to determine the injection power prediction error by using the actual value and predicted value of the injected power at each node in the flexible interconnected distribution network; the actual value of the injected power and its sampling time constitute the injection power time series value; based on the source-load power probability model, the joint probability density function of the injection power prediction error and the injection power time series value is determined; using the conditional probability invariance property of the Gaussian mixture model, the conditional probability density function of the injection power prediction error is determined based on the joint probability density function of the injection power prediction error and the injection power time series value.

[0054] The flexible interconnected distribution network scheduling optimization module aims to minimize the operating loss cost of the flexible interconnected distribution network, which includes AC system loss cost, DC system loss cost, and converter loss cost. It establishes constraints on the objective function, including probabilistic constraints on node voltage and branch power limits established using chance-constrained programming, AC / DC system power balance constraints, and converter operation constraints. A flexible interconnected distribution network scheduling optimization model is constructed using the objective function and its constraints. The model is iteratively solved to obtain the optimal value of the injected power adjustment for each node, which serves as the power value exchanged by the flexible interconnected devices.

[0055] A terminal includes a processor and a storage medium; the storage medium is used to store instructions; the processor is used to perform operations according to the instructions to execute the steps of a method.

[0056] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of a method.

[0057] The beneficial effects of this invention, compared with the prior art, include at least the following: First, this invention considers the uncertain resource access to the flexible interconnected distribution network on the source-load side, such as photovoltaics and electric vehicles. It characterizes the probability distribution characteristics of source-load power using a Gaussian mixture model. Based on this, it establishes an optimal scheduling model for the AC-Central Voltage Flexible Interconnected Distribution System based on chance-constrained optimization. The objective is to maximize the comprehensive operating benefits of AC / DC distribution substations. The constraints include power balance constraints, equipment operation constraints, and probabilistic constraints on node voltage and branch power. Utilizing the analytically expressible property of the cumulative distribution function of the Gaussian mixture model, the quantile function is used to transform the chance constraints containing probability values ​​into deterministic constraints. Then, the power flow equation constraints are relaxed to second-order cone constraints, thereby transforming the probabilistic optimization scheduling model considering uncertainty into a deterministic second-order cone optimization model, enabling rapid model solution. Attached Figure Description

[0058] Figure 1 This is a typical medium-voltage power distribution network wiring diagram in an embodiment of the present invention;

[0059] Figure 2 This is a wiring diagram of an AC / DC hybrid power distribution network including SOP and VSC in an embodiment of the present invention;

[0060] Figure 3 This is a flowchart of the flexible interconnected distribution network scheduling method based on Gaussian mixture model proposed in this invention;

[0061] Figure 4 This is a wiring diagram of the modified IEEE 33-node system in this embodiment of the invention;

[0062] Figure 5This is a diagram showing the power curves of distributed power sources and loads in an embodiment of the present invention;

[0063] Figure 6 This is a graph showing the active and reactive power output curves of two SOPs in an embodiment of the present invention.

[0064] Figure 7 This is a voltage distribution diagram of substation outgoing line 1 before optimization in this embodiment of the invention;

[0065] Figure 8 This is the optimized voltage distribution diagram of substation outgoing line 1 in this embodiment of the invention. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of this invention. The embodiments described in this application are merely some embodiments of this invention, and not all embodiments. Based on the spirit of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of this invention.

[0067] Figure 1 The diagram shows a typical medium-voltage distribution network wiring diagram. Line 1 and Line 2 are connected to the 10kV AC busbars, and the distribution networks connected to Line 1 and Line 2 are respectively connected to a photovoltaic (PV) power station and a wind farm (WT). Line 1 has five normally open tie switches, such as... Figure 1 The dashed lines between nodes 8 and 21, 12 and 22, 25 and 29, 9 and 15, and 18 and 33 on line 1 all represent tie switches.

[0068] right Figure 1 The medium-voltage distribution network wiring shown is modified to obtain the following result: Figure 2 The AC / DC hybrid distribution network wiring diagram shows the following: the tie switch between nodes 25 and 29 on line 1 is replaced with a smart soft switch SOP1, and the tie switch between nodes 12 and 22 is replaced with a smart soft switch SOP2. A voltage source converter VSC1 is installed at the beginning of line 2, and a voltage source converter VSC2 is installed between line 1 and line 2 to convert the entire AC line of line 2 into a DC line. Figure 2As shown by the midpoint line. Through the above modifications, an AC / DC hybrid distribution network containing SOPs and VSCs is formed. Considering that the cost of flexible equipment such as converters and smart soft switches is still relatively high, converting lines with a large number of DC source loads such as distributed photovoltaic power generation and electric vehicles into DC lines, and replacing some tie switches in the AC distribution network with smart soft switches, is a feasible solution that balances investment costs and distribution network operation efficiency. This is beneficial for absorbing distributed clean energy and improving the asset utilization rate of the distribution network. In this AC / DC hybrid distribution network, power flow control and operation optimization can be achieved by coordinating tie switches and SOPs. The exchange power of the flexible interconnection device is the decision variable of the method proposed in this invention, representing the active power exchanged between interconnected systems through SOPs and the reactive power generated or absorbed by SOPs in the interconnected systems on both sides during the scheduling process. Compared with the random fluctuation power in the system, the above decision variable belongs to adjustable power, and is therefore uniformly defined as ΔP. adj,t , is used to represent the switching power of flexible interconnect devices in the system, i.e., the decision variable.

[0069] Taking a flexible interconnected distribution network containing SOPs and VSCs as the object, this invention provides a flexible interconnected distribution network scheduling method based on a Gaussian mixture model, such as... Figure 3 As shown, it includes:

[0070] Step 1: Obtain the load power and the output power of distributed generation in the flexible interconnected distribution network as random variables. Based on the Gaussian mixture model, use the superposition of multiple Gaussian distributions of the random variables as the source-load power probability model of the flexible interconnected distribution network.

[0071] Specifically, taking the load power of a node in a flexible interconnected distribution network and the output power of distributed generation as random variables X, and based on a Gaussian mixture model (GMM), the probability distribution of random variable X is characterized by the superposition of several Gaussian distributions. The established source-load power probability model satisfies the following relationship:

[0072]

[0073] In the formula, f X (x) represents the marginal probability density of the random variable X, M is the number of Gaussian components in the Gaussian mixture model; x is a sample of the random variable; ω m N represents the weight of the m-th Gaussian component; m () represents the m-th one-dimensional normal distribution; Let be the mean and covariance of the m-th Gaussian component of sample x, respectively.

[0074] Using random variable X and its conjugate matrix Construct random variables Because GMMs possess marginal probability invariance and conditional probability invariance, random variables If a probability follows a GMM, then its marginal probability distribution and conditional probability distribution also follow a GMM, satisfying the following relationship:

[0075]

[0076] In the formula, Let random variable X be in event Conditional probability under given conditions. For the event The sample, ω′ m Let random variable X be in event The weight of the m-th Gaussian component of the conditional probability. Let m be the conditional probability of the m-th one-dimensional normal distribution.

[0077] Step 2: Using the actual and predicted values ​​of injected power at each node in the flexible interconnected distribution network, determine the injected power prediction error; the actual injected power value and its sampling time constitute the injected power time series value; based on the source-load power probability model, determine the joint probability density function of the injected power prediction error and the injected power time series value; utilizing the invariant conditional probability property of the Gaussian mixture model, determine the conditional probability density function of the injected power prediction error based on the joint probability density function of the injected power prediction error and the injected power time series value; based on the conditional probability density function of the injected power prediction error, obtain the sampled value of the injected power prediction error; use the injected power prediction value and the sampled value of the injected power prediction error to determine the injected power random variable.

[0078] Specifically, step 2 includes:

[0079] Step 2.1: Determine the injection power prediction error by using the actual value and predicted value of the injection power of each node in the flexible interconnected distribution network;

[0080] Specifically, in a flexible interconnected distribution network, the injected power of W nodes is random. A first random vector X1 represents the actual injected power value of the W nodes, satisfying X1 = [X...]. 11 X 12 …X 1i …X 1W ] T , where X 1i Let X2 be the actual value of the injected power at the i-th node, and let the second random vector X2 represent the predicted values ​​of the injected power at the W nodes, satisfying X2=[X 21 X 22 … X 2i … X 2W ] T X 2iLet be the predicted injected power value of the i-th node. Then, the third random vector representing the predicted injected power error of the W nodes satisfies the following relationship:

[0081] X e =X1-X2 (3)

[0082] Satisfy X e =[X e1 X e2 …X ei …X eW ] T X ei Let be the prediction error of the injected power at the i-th node.

[0083] Step 2.2: The actual value of injected power and its sampling time constitute the time series value of injected power. Based on the source-load power probability model, the joint probability density function of the injected power prediction error and the time series value of injected power is determined.

[0084] The sampling times of the actual injected power values ​​of W nodes constitute a time-series vector, satisfying T = [T1 T2 … T i …T W ] T T i The sampling time is the actual value of the injected power at the i-th node.

[0085] Construct a matrix Y such that Y = [X1 T] T Y i Let y be the injection power timing value of the i-th node, including the actual value of the injection power of the i-th node and its sampling time. i For Y i The sample, x ei For X ei Therefore, based on the Gaussian mixture model, the joint probability density function of the injection power prediction error of the i-th node, the injection power prediction error of the i-th node, and the injection power time series value satisfies the following relationship:

[0086]

[0087] In the formula, Let be the joint probability density function of the injection power prediction error of the i-th node and the injection power time series value of the i-th node. Let be the mean and covariance of the m-th Gaussian component of the i-th node, respectively. Let be the weight of the m-th Gaussian component of the i-th node. Let the m-th one-dimensional normal distribution be the i-th node. Let be the covariance of the injection power prediction error of the i-th node with respect to the m-th Gaussian component of the injection power prediction error. Let be the covariance of the injection power prediction error at the i-th node with respect to the m-th Gaussian component of the injection power time series value. Let be the covariance of the injection power time series value at the i-th node with respect to the m-th Gaussian component of the injection power time series value. Let be the mean of the m-th Gaussian component of the injection power prediction error for the i-th node. Let W be the mean of the m-th Gaussian component of the injection power time series value of the i-th node, and W be the number of nodes.

[0088] Furthermore, based on the joint probability density function of the injected power prediction error and the injected power time series value, the sampling expectation-maximization algorithm is used to obtain the parameters in equation (4) by fitting historical data of the injected power time series value. and This allows us to determine the relationship between the injection power prediction error and the injection power timing value.

[0089] Step 2.3: Utilizing the invariant conditional probability property of the Gaussian mixture model, determine the conditional probability density function of the injection power prediction error based on the joint probability density function of the injection power prediction error and the injection power time series value.

[0090] Given the time-series distribution of the actual injected power values, by the conditional probability invariance of the GMM, the conditional probability of the prediction error still follows the GMM. That is, for the i-th node, given the time-series distribution of the actual injected power values, the conditional probability density function of the injected power prediction error satisfies the following relationship:

[0091]

[0092] In the formula, Let be the joint probability density function of the injection power prediction error of the i-th node and the injection power time series value of the i-th node. Let m be the weight of the m-th Gaussian component of the injection power prediction error at the i-th node, given the time-series distribution of the actual injection power values. Let the m-th one-dimensional normal distribution be the i-th node. Let m be the mean of the m-th Gaussian component of the conditional probability distribution of the injection power prediction error at the i-th node, given the time-series distribution of the actual injection power values. Let m be the covariance of the conditional probability distribution of the injection power prediction error of the i-th node, given the time-series distribution of the actual injection power value.

[0093] Step 2.4: Based on the conditional probability density function of the injection power prediction error, obtain the sampled value of the injection power prediction error, and use the injection power prediction value and the sampled value of the injection power prediction error to determine the injection power random variable.

[0094] This invention characterizes the correlation between various power variables of random source load as the probability distribution characteristics of source load power. The injected power random variable determined accordingly conforms to the probability distribution characteristics of source load power. Moreover, when faced with high-dimensional massive data, it can efficiently obtain the injected power random variable that characterizes the correlation between various power variables. Therefore, it has good application prospects in medium-voltage interconnected power distribution systems with complex source load scenarios.

[0095] Step 3: The objective function is to minimize the operating loss cost of the flexible interconnected distribution network, which includes AC system loss cost, DC system loss cost, and converter loss cost. Constraints are established for the objective function, including: probabilistic constraints on node voltage and branch power limits established using chance-constrained programming, AC / DC system power balance constraints, and converter operation constraints. Based on the source-load power probability model, the inverse function of the cumulative distribution function of the injected power random variable is determined. The inverse function and the node injected power adjustment amount are used to determine the probability of node voltage not exceeding limits. The power balance constraints of the AC / DC system are relaxed based on the Distflow power flow model by transforming the rate constraints and the probabilistic constraints of branch power not exceeding the limits. The transformed probabilistic constraints of node voltage not exceeding the limits and branch power not exceeding the limits, the processed AC / DC system power balance constraints, and the converter operation constraints are combined with the objective function to form a flexible interconnected distribution network scheduling optimization model. The flexible interconnected distribution network scheduling optimization model is iteratively solved to obtain the optimal value of the injected power adjustment of each node, which is used as the power value exchanged by the flexible interconnected device.

[0096] Specifically, step 3 includes:

[0097] Step 3.1: The objective function is to minimize the operating loss cost of the flexible interconnected distribution network. The operating loss cost includes the AC system loss cost, DC system loss cost, and converter loss cost.

[0098] The objective function satisfies the following relationship:

[0099] C loss =C loss，AC +C loss，DC +C loss，VSC (6)

[0100]

[0101] In the formula, C loss For the operating loss cost of flexible interconnected distribution networks, C loss，AC For the loss cost of the AC system; C loss，DC For DC system loss costs, C loss，VSC For converter loss cost; NAC N represents the number of nodes in the communication system. DC Let be the number of nodes in the DC system network; Ω(i) be the set of neighboring nodes of node i; r ij，AC The resistance of AC branch ij; r ij，DC I is the resistance of the DC branch ij; ij，AC I is the square of the current flowing through the AC branch ij; ij，DC is the square of the current flowing through the DC branch ij.

[0102] In the embodiment, for the low-voltage distribution area converter, since the power flowing through it is relatively small, the converter loss cost C is low. loss，VSC The calculation is based on 2% of the power flowing through it.

[0103] Step 3.2: Establish the constraints of the objective function, including: probabilistic constraints on node voltage not exceeding limits and branch power not exceeding limits established by using the chance-constrained programming method, AC / DC system power balance constraints, and converter operation constraints.

[0104] In chance-constrained programming models, the probabilistic constraints on the objective function satisfy the following relationship:

[0105]

[0106] In the formula, N max f(X,ξ) represents the total number of states in the system. i ) indicates that in state ξ i A function of the physical quantity X; α is the confidence level; F represents f(X, ξ). i The maximum value obtained when the probability level is at least α.

[0107] 1) The probabilistic constraint condition for ensuring that the node voltage does not exceed the limit satisfies the following relationship:

[0108] P{U i,min ≤U i (ξ)≤U i,max}≥β U (9)

[0109] In the formula, U i (ξ) represents the voltage of node i under the operating state ξ of the distribution network; U i,min and U i,max Let P{U} be the lower and upper limits of the voltage at node i; i,min ≤U i (ξ)≤U i,max} represents the probability that the voltage of node i will not exceed the limit under the operating state ξ of the distribution network; β U This represents the confidence level at which the node voltage does not exceed the limit.

[0110] 2) The probabilistic constraint condition for ensuring that the branch power does not exceed the limit satisfies the following relationship:

[0111] P{P k (ξ)≤P k,max}≥β P (10)

[0112] In the formula, P k (ξ) represents the active power of branch k under the operating state ξ of the distribution network; P k,max P{P is the upper limit of active power in branch k; k (ξ)≤P k,max} represents the probability that the active power of branch k will not exceed the limit under the operating state ξ of the distribution network; β P This represents the confidence level that the branch power will not exceed the limit.

[0113] 3) The power balance constraints of the AC / DC system satisfy the following relationship:

[0114]

[0115] In the formula, P AC,i and Q AC,i These represent the active and reactive power injected into node i of the AC system, respectively; G AC,ij B ij θ ij These represent the conductance, susceptance, and voltage phase difference between node i and node j in the AC system, respectively; U AC,i and U AC,j P represents the voltage amplitudes at nodes i and j in the AC system, respectively. DC,i Active power injected into node i of the DC system; U DC,i and U DC,j Let G be the voltages at nodes i and j in the DC system, respectively; DC,ij Let N be the conductance between node i and node j in the DC system. AC N represents the number of nodes in the communication system. DC This represents the number of nodes in the DC system network.

[0116] 4) The converter's operating constraints satisfy the following relationship:

[0117]

[0118] In the formula, P VSC and Q VSC These represent the active power and reactive power flowing through the converter, respectively; S VSC This refers to the capacity of the converter.

[0119] Step 3.3: Based on the source-load power probability model, determine the inverse function of the cumulative distribution function of the injected power random variable. Use the inverse function and the node injected power adjustment amount to transform the probability constraints of node voltage not exceeding the limit and branch power not exceeding the limit. Based on the Distflow power flow model, relax the AC / DC system power balance constraints. The transformed probability constraints of node voltage not exceeding the limit and branch power not exceeding the limit, the processed AC / DC system power balance constraints, and the converter operation constraints, together with the objective function, constitute a flexible interconnected distribution network scheduling optimization model.

[0120] The probabilistic constraints on node voltage and branch power limits, AC / DC system power balance, and converter operation established using the opportunity-constrained programming method, together with the objective function, constitute a flexible interconnected distribution network scheduling optimization model. This model is an opportunity-constrained model. The difficulty in solving opportunity-constrained models lies in the fact that the constraints on node voltage and branch power limits are probabilistic, and traditional model solving methods cannot handle such probabilistic constraints. Therefore, equations (9) and (10) need to be transformed.

[0121] Specifically, step 3.3 includes:

[0122] Step 3.3.1: Based on the injected power random variable, transform the probabilistic constraint condition for node voltage not exceeding the limit and the probabilistic constraint condition for branch power not exceeding the limit using the following relationship:

[0123]

[0124] In the formula, P r () represents the probability of a specific event occurring, ΔV i,max ΔP is the upper limit of the voltage deviation at node i. i,max Let A1 be the upper limit of the branch power deviation, B1 be the conversion coefficient matrix between the node injected power adjustment and the node voltage deviation, A2 be the conversion coefficient matrix between the node injected power random variable and the node voltage deviation, and B3 be the conversion coefficient matrix between the node injected power random variable and the branch power deviation. Let ΔP be the upper limit of the branch power deviation. adj,t Let ΔP be the injection power adjustment at node t. ran,t Let α be the injection power random variable at time t. set For a given confidence level.

[0125] Step 3.3.2: Based on the source-load power probability model, determine the cumulative distribution function of the node injected power random variable; based on the cumulative distribution function, perform the first transformation on the transformed node voltage limit-free probability constraint and branch power limit-free probability constraint, obtaining the following relationship:

[0126]

[0127] In the formula, Let be the cumulative distribution function of the injection power random variable at time t;

[0128] Step 3.3.3: Based on the inverse function of the cumulative distribution function, the probabilistic constraints on node voltage not exceeding the limit and branch power not exceeding the limit are transformed a second time to obtain the following relationship:

[0129]

[0130] In the formula, It is the inverse function of the cumulative distribution function.

[0131] In the embodiment, the mean of the node injection power random variable is μ. m The variance is σ m The cumulative distribution function of the Gaussian distribution satisfies the following fourth-order polynomial:

[0132]

[0133] In the formula, h0 = -0.0005, h1 = 0.424, h2 = -0.06211, h3 = -0.02918, h4 = 0.00709, v is the voltage variable, and x is the given voltage limit. For comparison variables given a voltage limit relative to the mean of a random variable,

[0134] Therefore, inverse function The function value can be obtained by solving the above fourth-order polynomial.

[0135] The key to solving the above chance-constrained optimization problem lies in the handling of equation (14). After obtaining the inverse function... After obtaining the function value, equation (14) is transformed into a linear constraint on the decision variables as shown in equation (15), where the decision variables include the node's injection power adjustment.

[0136] Step 3.3.4: Based on the Distflow power flow model, relax the power balance constraints of the AC / DC system.

[0137] Step 3.3.5: Using the transformed probability constraints of no-limit node voltage and no-limit branch power, the processed AC / DC system power balance constraints, and the converter operation constraints, a flexible interconnected distribution network scheduling optimization model is constructed with the objective function.

[0138] The flexible interconnected distribution network scheduling optimization model, formed by the transformed and processed constraints and the objective function, is a second-order cone optimization model. Furthermore, the decision variables of the second-order cone optimization model include: the active power and reactive power exchanged by the flexible interconnection devices, which is ΔP in equation (15). adj,t and the corresponding ΔQ adj,t (Since the formulas are exactly the same, they are not given in the text.) The state variables of the second-order cone optimization model include: node voltage distribution and branch power distribution.

[0139] Step 3.4: Solve the flexible interconnected distribution network scheduling optimization model to obtain the optimal value of the injected power adjustment of each node, which is used as the power value exchanged by the flexible interconnected device;

[0140] The flexible interconnected distribution network dispatch scheme includes the power values ​​exchanged by the flexible interconnected devices.

[0141] This invention is based on the IEEE 33-node example and modified accordingly. Its topology diagram is as follows: Figure 4 As shown in the diagram. Substation outgoing line 1 has a high proportion of clean energy units connected, while substation outgoing line 2 has fewer clean energy units connected, but two sets of Standard Operating Procedures (SOPs) are used for intra-line power transfer and inter-line power exchange, respectively. Both outgoing lines are equipped with energy storage. The parameters of each device are shown in Tables 1 to 3.

[0142] Table 1 Power Supply Side Equipment Parameters

[0143]

[0144]

[0145] Table 2 Energy Storage Equipment Parameters

[0146] serial number line Device Name node Capacity / kWh Maximum charge / discharge power / kW 9 Qualifying 1 ESS1 30 900 300 10 Qualifying 2 ESS2 13 600 150

[0147] Table 3 Parameters of Flexible Interconnection Devices

[0148]

[0149] Adopting such Figure 5 The distributed power source and load power curves shown are used to optimize the active and reactive power of the smart soft switch and the charging and discharging power of the energy storage based on the proposed day-ahead optimization scheduling model.

[0150] The following three optimization schemes were compared:

[0151] Option 1: No optimization.

[0152] Option 2: Optimize using a second-order cone linear programming method;

[0153] Option 3: Optimize using the method proposed in this paper;

[0154] Table 4 shows the system operation under the three schemes. Without distribution network optimization, the total daily network loss is 4764.5 kWh. As can be seen from Table 4, Scheme 2 has the best loss reduction effect, but due to the large scale of the optimization model, the solution time is long. Scheme 3, using the method proposed in this invention, can achieve a similar optimization effect to Scheme 2 while shortening the solution time.

[0155] Table 4 Comparison of Results of the Three Schemes

[0156] plan System losses / kWh Loss reduction percentage / % System operating cost / yuan Solution time / s Option 1 4764.5 - 7360.1 - Option 2 3839.7 19.4％ 8372.2 568.3 Option 3 3921.6 17.6％ 8391.9 14.2

[0157] In Scheme 3, the active and reactive power outputs of the two SOPs are as follows: Figure 6 As shown, substation outgoing line 1 has a lighter load and more distributed power sources, while substation outgoing line 2 has a heavier load. Therefore, SOP2 injects active power into node 33 of substation outgoing line 2. At midday, photovoltaic output is higher, and the power transmitted by SOP2 also increases accordingly. SOP1 connects to 25 industrial load nodes on one side, whose load power varies little over time, and to 29 residential load nodes on the other side, whose load power varies greatly over time. During the morning and evening when residential load is lower, SOP1 injects active power into the industrial load; at midday, SOP1 injects active power into the residential load. In summary, SOPs transfer active power and generate reactive power, balancing the power distribution across different lines in the network, thereby reducing network losses.

[0158] Furthermore, due to the high degree of source-load mismatch in substation outgoing line 1, the system exhibits severe voltage exceeding the upper limit when not optimized, such as... Figure 7 As shown. After optimization, the SOP performs power transfer within and between lines, broadening the pathways for distributed power absorption. Simultaneously, it can generate reactive power to regulate voltage, eliminating the voltage over-limit problem at substation outgoing line 1. Figure 8 As shown.

[0159] This invention also proposes a flexible interconnected distribution network dispatching system based on a Gaussian mixture model, comprising:

[0160] The load power modeling module is used to obtain the load power and the output power of distributed generation in the flexible interconnected distribution network as random variables. Based on the Gaussian mixture model, the superposition of multiple Gaussian distributions of the random variables is used as the source-load power probability model of the flexible interconnected distribution network.

[0161] The power prediction error modeling module is used to determine the injection power prediction error by using the actual value and predicted value of the injected power at each node in the flexible interconnected distribution network; the actual value of the injected power and its sampling time constitute the injection power time series value; based on the source-load power probability model, the joint probability density function of the injection power prediction error and the injection power time series value is determined; using the conditional probability invariance property of the Gaussian mixture model, the conditional probability density function of the injection power prediction error is determined based on the joint probability density function of the injection power prediction error and the injection power time series value.

[0162] The flexible interconnected distribution network scheduling optimization module aims to minimize the operating loss cost of the flexible interconnected distribution network, which includes AC system loss cost, DC system loss cost, and converter loss cost. It establishes constraints on the objective function, including probabilistic constraints on node voltage and branch power limits established using chance-constrained programming, AC / DC system power balance constraints, and converter operation constraints. A flexible interconnected distribution network scheduling optimization model is constructed using the objective function and its constraints. The model is iteratively solved to obtain the optimal value of the injected power adjustment for each node, which serves as the power value exchanged by the flexible interconnected devices.

[0163] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0164] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example—but not limited to—electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination of the foregoing. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0165] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0166] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0167] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A flexible interconnected distribution network scheduling method based on a Gaussian mixture model, characterized in that, include: The load power and the output power of distributed generation in the flexible interconnected distribution network are obtained as random variables. Based on the Gaussian mixture model, the superposition of multiple Gaussian distributions of the random variables is used as the source-load power probability model of the flexible interconnected distribution network. The injection power prediction error is determined by using the actual and predicted values ​​of the injected power at each node in the flexible interconnected distribution network; the actual value of the injected power and its sampling time constitute the injection power time series value; based on the source-load power probability model, the joint probability density function of the injection power prediction error and the injection power time series value is determined. By utilizing the invariance of conditional probability in Gaussian mixture models, the conditional probability density function of the injection power prediction error is determined based on the joint probability density function of the injection power prediction error and the injection power time series value. Based on the conditional probability density function of the injection power prediction error, the sampled value of the injection power prediction error is obtained, and the injection power random variable is determined using the injection power prediction value and the sampled value of the injection power prediction error. The objective function is to minimize the operating loss cost of the flexible interconnected distribution network. The operating loss cost includes the AC system loss cost, DC system loss cost, and converter loss cost. The constraints for the objective function are established, including: probabilistic constraints on node voltage and branch power not exceeding limits, AC / DC system power balance constraints, and converter operation constraints established using the chance-constrained programming method; the inverse function of the cumulative distribution function of the injected power random variable is determined based on the source-load power probability model, and the probabilistic constraints on node voltage and branch power not exceeding limits are transformed using the inverse function and the node injected power adjustment amount; the AC / DC system power balance constraints are relaxed based on the Distflow power flow model; the transformed probabilistic constraints on node voltage and branch power not exceeding limits, the processed AC / DC system power balance constraints, and the converter operation constraints, together with the objective function, constitute a flexible interconnected distribution network scheduling optimization model. The scheduling optimization model of the flexible interconnected distribution network is iteratively solved to obtain the optimal value of the injected power adjustment of each node, which is used as the power value exchanged by the flexible interconnected device.

2. The flexible interconnected distribution network scheduling method based on Gaussian mixture model according to claim 1, characterized in that, The source-load power probability model of a flexible interconnected distribution network satisfies the following relationship: In the formula, f X (x) represents the marginal probability density of the random variable X, M is the number of Gaussian components in the Gaussian mixture model; x is a sample of the random variable; ω m N represents the weight of the m-th Gaussian component; m () represents the m-th one-dimensional normal distribution; Let be the mean and covariance of the m-th Gaussian component of sample x, respectively.

3. The flexible interconnected distribution network scheduling method based on Gaussian mixture model according to claim 1, characterized in that, In a flexible interconnected distribution network, the injected power of W nodes is random. A first random vector X1 represents the actual injected power value of the W nodes, satisfying X1 = [X...]. 11 X 12 … X 1i … X 1W ] T , where X 1i Let X2 be the actual value of the injected power at the i-th node, and let the second random vector X2 represent the predicted values ​​of the injected power at the W nodes, satisfying X2=[X 21 X 22 …X 2i …X 2W ] T X 2i Let be the predicted injected power value of the i-th node. Then, the third random vector representing the predicted injected power error of the W nodes satisfies the following relationship: Satisfy X e =[X e1 X e2 …X ei …X eW ] T X ei Let be the prediction error of the injected power at the i-th node.

4. The flexible interconnected distribution network scheduling method based on Gaussian mixture model according to claim 3, characterized in that, The sampling times of the actual injected power values ​​of W nodes constitute a time-series vector, satisfying T = [T1 T2 … T i …T W ] T T i The sampling time is the actual value of the injected power at the i-th node; Construct a matrix Y such that Y = [X1 T] T Y i The injection power timing value of the i-th node includes the actual value of the injection power of the i-th node and its sampling time; Based on the Gaussian mixture model, the joint probability density function of the injection power prediction error of the i-th node and the injection power time series value of the i-th node satisfies the following relationship: In the formula, Let y be the joint probability density function of the injection power prediction error of the i-th node and the injection power time series value of the i-th node. i For Y i The sample, x ei For X ei The sample, Let be the mean and covariance of the m-th Gaussian component of the i-th node, respectively. Let be the weight of the m-th Gaussian component of the i-th node. Let the m-th one-dimensional normal distribution be the i-th node. Let be the covariance of the injection power prediction error of the i-th node with respect to the m-th Gaussian component of the injection power prediction error. Let be the covariance of the injection power prediction error at the i-th node with respect to the m-th Gaussian component of the injection power time series value. Let be the covariance of the injection power time series value at the i-th node with respect to the m-th Gaussian component of the injection power time series value. Let be the mean of the m-th Gaussian component of the injection power prediction error for the i-th node. Let W be the mean of the m-th Gaussian component of the injection power time series value of the i-th node, and W be the number of nodes.

5. The flexible interconnected distribution network scheduling method based on Gaussian mixture model according to claim 4, characterized in that, The conditional probability density function of the injected power prediction error satisfies the following relationship: In the formula, Let be the joint probability density function of the injection power prediction error of the i-th node and the injection power time series value of the i-th node. Let m be the weight of the m-th Gaussian component of the injection power prediction error at the i-th node, given the time-series distribution of the actual injection power values. Let the m-th one-dimensional normal distribution be the i-th node. Let m be the mean of the m-th Gaussian component of the conditional probability distribution of the injection power prediction error at the i-th node, given the time-series distribution of the actual injection power values. Let m be the covariance of the conditional probability distribution of the injection power prediction error of the i-th node, given the time-series distribution of the actual injection power value.

6. The flexible interconnected distribution network scheduling method based on Gaussian mixture model according to claim 1, characterized in that, The objective function is to minimize the operating loss cost of the flexible interconnected distribution network, which includes AC system loss cost, DC system loss cost, and converter loss cost. The objective function satisfies the following relationship: C loss =C loss,AC +C loss,DC +C loss,VSC (6) In the formula, C loss For the operating loss cost of flexible interconnected distribution networks, C loss，AC For the loss cost of the AC system; C loss，DC For DC system loss costs, C loss，VSC For converter loss cost; N AC N represents the number of nodes in the communication system. DC Let be the number of nodes in the DC system network; Ω(i) be the set of neighboring nodes of node i; r ij，AC The resistance of AC branch ij; r ij，DC I is the resistance of the DC branch ij; ij，AC I is the square of the current flowing through the AC branch ij; ij，DC is the square of the current flowing through the DC branch ij.

7. The flexible interconnected distribution network scheduling method based on Gaussian mixture model according to claim 6, characterized in that, The constraints for establishing the objective function include: probabilistic constraints on node voltage and branch power not exceeding limits established using the chance-constrained programming method, AC / DC system power balance constraints, and converter operation constraints.

8. The flexible interconnected distribution network scheduling method based on Gaussian mixture model according to claim 7, characterized in that, The probabilistic constraint that the node voltage does not exceed the limit satisfies the following relationship: P{U i,min ≤U i (ξ)≤U i,max }≥β U In the formula, U i (ξ) represents the voltage of node i under the operating state ξ of the distribution network; U i,min and U i,max Let be the lower and upper limits of the voltage at node i; P{U i,min ≤U i (ξ)≤U i,max } represents the probability that the voltage of node i will not exceed the limit under the operating state ξ of the distribution network; β U This represents the confidence level at which the node voltage does not exceed the limit. The probabilistic constraint condition for branch power not exceeding the limit satisfies the following relationship: P{P k (ξ)≤P k,max }≥β P In the formula, P k (ξ) represents the active power of branch k under the operating state ξ of the distribution network; P k,max P{P is the upper limit of active power in branch k; k (ξ)≤P k,max } represents the probability that the active power of branch k will not exceed the limit under the operating state ξ of the distribution network; β P This represents the confidence level that the branch power will not exceed the limit.

9. The flexible interconnected distribution network scheduling method based on Gaussian mixture model according to claim 7, characterized in that, The power balance constraints of an AC / DC system satisfy the following relationship: In the formula, P AC,i and Q AC,i These represent the active and reactive power injected into node i of the AC system, respectively; G AC,ij B ij θ ij These represent the conductance, susceptance, and voltage phase difference between node i and node j in the AC system, respectively; U AC,i and U AC,j P represents the voltage amplitudes at nodes i and j in the AC system, respectively. DC,i Active power injected into node i of the DC system; U DC,i and U DC,j Let G be the voltages at nodes i and j in the DC system, respectively; DC,ij Let N be the conductance between node i and node j in the DC system. AC N represents the number of nodes in the communication system. DC This represents the number of nodes in the DC system network.

10. The flexible interconnected distribution network scheduling method based on Gaussian mixture model according to claim 7, characterized in that, The converter's operating constraints satisfy the following relationship: In the formula, P VSC and Q VSC These represent the active power and reactive power flowing through the converter, respectively; S VSC This refers to the capacity of the converter.

11. The flexible interconnected distribution network scheduling method based on Gaussian mixture model according to claim 8, characterized in that, Based on the source-load power probability model, the inverse function of the cumulative distribution function of the injected power random variable is determined. The inverse function and the node injected power adjustment amount are used to transform the probabilistic constraints on node voltage not exceeding limits and branch power not exceeding limits, including: Based on the injected power random variable, the probabilistic constraints on node voltage not exceeding limits and branch power not exceeding limits are transformed using the following relationship: In the formula, P r () represents the probability of a specific event occurring, ΔV i,max ΔP is the upper limit of the voltage deviation at node i. i,max Let A1 be the upper limit of the branch power deviation, B1 be the conversion coefficient matrix between the node injected power adjustment and the node voltage deviation, A2 be the conversion coefficient matrix between the node injected power random variable and the node voltage deviation, and B3 be the conversion coefficient matrix between the node injected power random variable and the branch power deviation. Let ΔP be the upper limit of the branch power deviation. adj,t Let ΔP be the injection power adjustment at node t. ran,t Let α be the injection power random variable at time t. set For a given confidence level; Based on the source-load power probability model, the cumulative distribution function of the node injected power random variable is determined. Based on the cumulative distribution function, the transformed probability constraints for node voltage not exceeding limits and branch power not exceeding limits are transformed for the first time, resulting in the following relationship: In the formula, Let be the cumulative distribution function of the injection power random variable at time t; Based on the inverse function of the cumulative distribution function, the probabilistic constraints on node voltage not exceeding limits and branch power not exceeding limits are transformed a second time to obtain the following relationship: In the formula, It is the inverse function of the cumulative distribution function.

12. A flexible interconnected distribution network dispatching system based on a Gaussian mixture model, characterized in that, include: The load power modeling module is used to obtain the load power and the output power of distributed generation in the flexible interconnected distribution network as random variables. Based on the Gaussian mixture model, the superposition of multiple Gaussian distributions of the random variables is used as the source-load power probability model of the flexible interconnected distribution network. The power prediction error modeling module is used to determine the injection power prediction error by using the actual value and predicted value of the injected power at each node in the flexible interconnected distribution network; the actual value of the injected power and its sampling time constitute the injection power time series value; based on the source-load power probability model, the joint probability density function of the injection power prediction error and the injection power time series value is determined. By utilizing the invariant conditional probability property of the Gaussian mixture model, the conditional probability density function of the injection power prediction error is determined based on the joint probability density function of the injection power prediction error and the injection power time series value. The flexible interconnected distribution network scheduling optimization module is used to minimize the operating loss cost of the flexible interconnected distribution network as the objective function. The operating loss cost includes AC system loss cost, DC system loss cost, and converter loss cost. The constraints for the objective function are established, including: probabilistic constraints on node voltage and branch power not exceeding limits established using the chance-constrained programming method, AC / DC system power balance constraints, and converter operation constraints; a flexible interconnected distribution network scheduling optimization model is constructed using the objective function and its constraints; the flexible interconnected distribution network scheduling optimization model is iteratively solved to obtain the optimal value of the injected power adjustment for each node, which is used as the power value exchanged by the flexible interconnected device.

13. A terminal, comprising a processor and a storage medium; characterized in that: The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method according to any one of claims 1-11.

14. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1-11.

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