A power distribution network voltage optimization control method based on a non-parametric iteration framework

Abstract

The application discloses a power distribution network voltage optimization control method based on a non-parametric iteration framework, and steps are as follows: generating an uncertainty sample set based on a photovoltaic output GMM; decomposing a joint opportunity constraint of a node voltage amplitude into a single opportunity constraint based on a Boole inequality uniform risk allocation, solving an optimization model, and obtaining an initial conservative feasible solution; calculating the voltage amplitude of each node in combination with a current operation solution and the uncertainty sample, and statistically calculating the edge default probability of each node and the joint default event empirical probability; according to the edge default level of each node constraint, updating the risk budget of the single opportunity constraint by using an ARA strategy, and reconstructing the constraint form; based on the updated risk constraint, the power distribution network optimization model is solved again, if a termination condition is met, the final optimization result is output. While retaining the ability to depict the uncertainty statistical characteristics, the application reduces the conservativeness and the calculation burden of the joint risk estimation, and improves the matching degree between the optimization result and the actual operation risk.

Description

Technical Field

[0001] This invention relates to a method for optimizing the operation of a distribution network, and more particularly to a method for optimizing the voltage control of a distribution network based on a nonparametric iterative framework. Background Technology

[0002] With the deepening implementation of the green and low-carbon transformation strategy and the rapid construction of new power systems, the penetration rate of renewable energy sources such as distributed photovoltaic and wind power in distribution networks is continuously increasing. The large-scale integration of distributed power sources has significantly altered the power flow distribution characteristics of traditional single-source radial distribution networks, causing the system's operating state to gradually evolve from a relatively stable deterministic mode to a stochastic operating mode influenced by multiple sources of disturbance. Especially when photovoltaic output fluctuations, load changes, and network coupling effects coexist, node voltages are more prone to fluctuations and exceeding limits, thus posing a significant challenge to the safe and stable operation of the distribution network.

[0003] To address the voltage risk problem in distribution networks with a high proportion of distributed generation, existing research has proposed various optimization control methods that consider uncertainties. Among these, opportunity-constrained optimization methods have received widespread attention due to their ability to strike a trade-off between operational safety and economy. By introducing node voltage constraints at a given confidence level into the optimization model, voltage exceedance risk can be controlled to some extent. However, when multiple node voltage constraints in the system need to be satisfied simultaneously, the problem further transforms into a joint opportunity-constrained optimization problem. Since different node voltage exceedance events are usually significantly correlated, the joint default probability is difficult to calculate directly. If traditional inequality decomposition methods based on union upper bounds are used, the overlapping relationships between events are often ignored, leading to overly conservative constraints, significant shrinkage of the feasible region, and increased system operating costs.

[0004] Furthermore, existing methods for handling joint opportunity constraints typically suffer from the following shortcomings: On the one hand, some methods rely on explicit analytical assumptions about the probability distribution of random disturbances, which may lead to biased risk characterization when actual photovoltaic output exhibits complex statistical characteristics such as non-Gaussian and multimodal output. On the other hand, some methods perform a one-time estimation and risk allocation of the joint default probability at a fixed operating point, making it difficult to accurately reflect the true voltage risk level corresponding to the final optimal solution, thus causing inconsistencies between the optimal solution, the default event identification results, and the probability estimation results. Especially in high-dimensional uncertain scenarios, directly calculating the joint default probability accurately also faces problems such as large sample requirements, high computational complexity, and insufficient solution efficiency. Therefore, there is an urgent need to propose an efficient solution method for joint opportunity constraints of distribution network node voltages, which leads to this proposal. Summary of the Invention

[0005] The purpose of this invention is to provide a distribution network voltage optimization control method based on a nonparametric iterative framework. This method can solve the problems of traditional joint opportunity constraint processing methods under high-proportion distributed renewable energy access conditions, such as strong dependence on distribution assumptions, difficulty in accurately reflecting the final operating state by one-time probability correction, conservative risk allocation, and inconsistency between the optimization solution and the risk estimation results. While retaining the ability to characterize the statistical features of uncertainty, this method reduces the conservatism and computational burden of joint risk estimation, and improves the matching degree between the optimization results and the actual operating risks, so as to meet the needs of safe and economical operation of distribution networks under high-proportion distributed power access conditions.

[0006] To achieve the above objectives, the solution of the present invention is:

[0007] A distribution network voltage optimization control method based on a nonparametric iterative framework includes the following steps:

[0008] Step 1: Generate an uncertainty sample set based on the photovoltaic output GMM to obtain the sample basis required for nonparametric probability assessment;

[0009] Step 2: Decompose the joint chance constraint of node voltage magnitude into a single chance constraint based on uniform risk allocation according to Boole's inequality, and solve the optimization model to obtain the initial conservative feasible solution.

[0010] Step 3: Combine the current running solution with the uncertainty sample to calculate the voltage amplitude of each node and identify the set of constraints that may cause voltage overruns;

[0011] Step 4: Calculate the edge default probability of each node and the empirical probability of the joint default event to obtain the joint default probability correction term;

[0012] Step 5: Based on the marginal default level of each node constraint, update the risk budget of the single opportunity constraint using the ARA strategy and reconstruct the constraint form;

[0013] Step 6: Resolve the distribution network optimization model based on the updated risk constraints, and check whether the objective function, the set of default events, and the joint default probability correction term converge. If the termination condition is met, output the final optimization result; otherwise, return to step 3 to continue iterating.

[0014] The specific process of step 1 above is as follows:

[0015] Step 11, assume that generation occurs in each runtime segment. A random sample of photovoltaic power output is denoted as... ,in, For the first If the total number of samples is distributed among the Gaussian components according to their respective weights, then the nth random sample is... The number of samples corresponding to each Gaussian component is denoted as:

[0016]

[0017] Step 12, for the first The covariance matrix of each Gaussian component is decomposed and modeled using the full covariance form. If we consider it as a positive definite matrix, then there exists a matrix... , making

[0018]

[0019] make for If a standard normal random vector is given by dimension 1, then the 1st dimension is... The first Gaussian component Each sample is represented as,

[0020]

[0021] This generates the first The sample set corresponding to each Gaussian component.

[0022]

[0023] Step 13, for all After sampling each Gaussian component, the sample sets of each component are merged to obtain the final photovoltaic output sample set.

[0024]

[0025] Right now,

[0026]

[0027] in, Indicates the first A random sample of photovoltaic power output.

[0028] In step 11 above, the first Number of samples corresponding to each Gaussian component The data is processed by rounding down, and a final fine-tuning of the total sample size is performed to ensure...

[0029]

[0030] in, The number of Gaussian components. This represents the number of sets of random samples of photovoltaic output generated during each operating period.

[0031] In step 1 above, the number of Gaussian components is determined according to the following method:

[0032] For photovoltaic power output 3D random vector Its joint probability density function Use several The Gaussian distribution is approximated by linear superposition.

[0033]

[0034] in, The number of Gaussian components. , and They represent the first The weights, mean, and covariance of each Gaussian component; It is a multidimensional Gaussian distribution with a probability density function. for,

[0035]

[0036] In the formula, Represents the determinant of a matrix;

[0037] The weights of each Gaussian component satisfy the normalization condition, that is,

[0038]

[0039] The number of Gaussian components is determined using the Akaike Information Content Criterion (AIC), denoted as:

[0040]

[0041] in, It is the maximum likelihood function.

[0042] In step 2 above, the constraints include branch DisFlow power flow constraints, distribution network current security constraints, PV output constraints, SVC compensation constraints, OLTC constraints, and joint opportunity constraints of distribution network voltage amplitude. The objective function for solving the optimization model includes electricity purchase cost, network loss penalty cost, and PV curtailment cost.

[0043] In step 2 above, the joint chance constraint of node voltage magnitude is decomposed into a single chance constraint based on uniform risk allocation according to Boole's inequality, including:

[0044] The joint opportunity constraint of distribution network voltage amplitude is expressed as follows:

[0045]

[0046] In the formula, The upper limit of the joint default probability of node voltage amplitude represents the time period. The probability that the voltage amplitudes of all nodes simultaneously meet the upper and lower limits is not less than ; These are the squares of the upper limit of the voltage amplitude at node j;

[0047] To ensure that the overall risk does not exceed Assign a local tolerance level to each node. ,satisfy,

[0048]

[0049] Thus, the original joint opportunity constraint is transformed into,

[0050]

[0051] set up Indicates in the sample The decision variables are as follows: Time node During the period If the square of the voltage amplitude is given, then the above formula can be approximated by an empirical distribution as follows:

[0052]

[0053] set up Indicates sample Whether the voltage constraint at this node is allowed to be violated, then...

[0054]

[0055]

[0056] In the formula, It is a sufficiently large positive number.

[0057] The specific process of step 3 above is as follows:

[0058] Step 31, in the In this iteration, let the solution obtained by the current optimization model be... ,Will Substituting the uncertainty sample set into the distribution network operation model, we obtain the NCVSI values ​​for each node under each sample scenario; for each node... Record its position in the sample. The corresponding squared voltage amplitude result is ;

[0059] Step 32, the first Node in the next iteration The voltage constraint default event is defined as follows:

[0060]

[0061] Nodes are obtained based on sample statistics. The estimated marginal default probability in the current iteration

[0062]

[0063] in: Indicates events obtained based on sample statistics Marginal default probability estimation;

[0064] Step 33: Organize the constraint events with a marginal default probability greater than zero into a set of possible default events for the current iteration, i.e.

[0065]

[0066] gather That is, the first The set of active default events that need to be addressed in this iteration, and its cardinality This indicates the number of constraints at the current operating point that pose a risk of sample default.

[0067] The specific process of step 4 above is as follows:

[0068] Step 41, define the joint default event on the active event set in the current iteration as,

[0069]

[0070] Step 42, based on MC sample statistics, estimate their joint default probability as follows:

[0071]

[0072] in, Indicates the currently running solution The empirical probability that at least one node in the active event set will experience a voltage over-limit.

[0073] Step 43, the first The joint default probability correction term in the next iteration is defined as follows:

[0074]

[0075] Obviously, when there is overlap between active events, If the events hardly overlap in the sample, then Approaching zero; therefore, using Measure the strength of the correlation between default events at the current operating point and adjust the risk budget in the JCC decomposition;

[0076] Step 44, write the JCC on the active set as follows:

[0077]

[0078] Using a uniform distribution method, it is further transformed into a set of SCCs.

[0079] .

[0080] In step 5 above, for any The risk allocation weight is defined as follows:

[0081]

[0082]

[0083] Total risk budget allowed by JCC By weight Assigned to each active constraint, resulting in the first... Node in the next iteration Single-constraint risk budget,

[0084]

[0085] The original JCC is further refactored into a set of SCCs on the active event set.

[0086] .

[0087] The specific process of step 6 above is as follows:

[0088] Step 61, let the first... The optimization objective function value corresponding to the next iteration is Then its relative change is defined as,

[0089]

[0090] Given target convergence tolerance Then the convergence criterion for the objective is,

[0091]

[0092] Step 62, set the set of active events to remain unchanged between two adjacent iterations, that is,

[0093]

[0094] At the same time, it is required that changes in the joint default probability correction term be controlled within a given tolerance range, that is,

[0095]

[0096] in, This represents the convergence tolerance for the joint probability correction term;

[0097] Step 63: If all three conditions are met simultaneously, the current closed-loop iteration process is considered to have reached a stable state, and the update is terminated; otherwise, return to step 3 to continue the iteration, and set the maximum number of iterations. ,like,

[0098]

[0099] Regardless of whether the termination condition is met, the iteration stops and the current optimal result is output.

[0100] After adopting the above scheme, this invention takes the joint opportunity constraint of distribution network node voltage amplitude as the research object. First, it generates an uncertainty sample set based on the Gaussian mixture model (GMM) of photovoltaic output, and constructs an initial single opportunity constraint using uniform risk allocation based on Boole's inequality to obtain an initial conservative feasible solution. Subsequently, during the iteration process, it identifies a set of possible default events by combining the current running solution and the uncertainty sample, and calculates the marginal default probability and the empirical probability of joint default events to obtain a joint default probability correction term. Further, based on the marginal default level of each constraint, it updates the risk budget of the single opportunity constraint using an adaptive risk allocation (ARA) strategy and reconstructs its deterministic constraint form, thereby updating the distribution network optimization model. Finally, it determines whether to terminate the iteration based on the convergence of the objective function, the set of default events, and the joint default probability correction term, and outputs an optimization result that balances node voltage security and operational economy. In summary, this invention provides a new approach and key technical support for distribution network voltage optimization control under high-dimensional uncertainty conditions.

[0101] Compared with existing technologies, the advantages of this invention are as follows: This invention proposes a distribution network voltage optimization control method based on a nonparametric iterative framework, which can uniformly characterize and optimize the risk of node voltage exceedance under conditions of high proportion of distributed generation access. By leveraging the modeling capability of Gaussian power output stochastic characteristics through Gaussian Models (GMM), this invention can better reflect the complex uncertainty characteristics of distributed generation, such as non-Gaussian and multimodal behavior, and generate an uncertainty sample set that conforms to actual statistical laws, providing a reliable foundation for subsequent probability assessment. Furthermore, this invention no longer relies on the one-time static estimation of the joint default probability in traditional methods, but instead dynamically identifies constraints that may lead to voltage exceedances by combining the current operating solution, statistically analyzes the marginal default probability and the empirical probability of joint default events, and constructs a joint default probability correction term, thereby improving the consistency between the risk characterization results and the actual operating state. Further, this invention introduces an ARA strategy to dynamically update the risk budget of a single opportunity constraint based on the actual default level of each node constraint, avoiding the problems of excessively tight local constraints and overly conservative overall behavior caused by traditional uniform risk allocation methods. Through the above-described sample generation, risk identification, constraint reconstruction, and iterative solution process, this invention can reduce the conservatism and computational burden of joint opportunity constraint processing while ensuring the effective validity of node voltage risk constraints, thereby improving the solution efficiency, operational economy, and matching degree between the optimization solution and risk estimation results of the optimization model. Attached Figure Description

[0102] Figure 1 This is a flowchart of the present invention;

[0103] Figure 2 This is a simulation analysis diagram of the power distribution system topology in this invention;

[0104] Figure 3 This is a graph showing the iterative changes of the objective function value in this invention;

[0105] Figure 4 This is a graph showing how the probability of stable system operation changes over time in this invention;

[0106] Figure 5 This is a diagram illustrating the effect of reducing conservatism in this invention;

[0107] Figure 6 This is the NCVSI probability distribution diagram in this invention. Detailed Implementation

[0108] The technical solution and beneficial effects of the present invention will be described in detail below with reference to the accompanying drawings.

[0109] like Figure 1 As shown, this invention provides a distribution network voltage optimization control method based on a nonparametric iterative framework, comprising the following steps:

[0110] Step 1: Generate an uncertainty sample set based on the photovoltaic output GMM to obtain the sample basis required for nonparametric probability assessment;

[0111] Step 2: Decompose the joint chance constraint of node voltage magnitude into a single chance constraint based on uniform risk allocation according to Boole's inequality, and solve the optimization model to obtain the initial conservative feasible solution.

[0112] Step 3: Combine the current running solution with the uncertainty sample to calculate the voltage amplitude of each node and identify the set of constraints that may cause voltage overruns;

[0113] Step 4: Calculate the edge default probability of each node and the empirical probability of the joint default event to obtain the joint default probability correction term;

[0114] Step 5: Based on the marginal default level of each node constraint, update the risk budget of the single opportunity constraint using the ARA strategy and reconstruct the constraint form;

[0115] Step 6: Resolve the distribution network optimization model based on the updated risk constraints, and check whether the objective function, the set of default events, and the joint default probability correction term converge. If the termination condition is met, output the final optimization result; otherwise, return to step 3 to continue iterating.

[0116] Step 1, which generates an uncertainty sample set based on the photovoltaic output GMM, obtains the sample basis required for nonparametric probability assessment. This is relevant to photovoltaic output. 3D random vector Its joint probability density function Several can be used Gaussian distribution linear superposition approximation:

[0117] (1)

[0118] In the formula: The number of Gaussian components. , and They represent the first The weights, mean, and covariance of each Gaussian component. It is a multidimensional Gaussian distribution with a probability density function. for:

[0119] (2)

[0120] In the formula, This represents the determinant of the matrix. The weights of each Gaussian component must satisfy the normalization condition, i.e.:

[0121] (3)

[0122] Estimating the number of Gaussian components using the Expectation-Maximization (EM) algorithm based on historical photovoltaic data yields better results in reflecting the statistical characteristics of the input variables, thus improving fitting accuracy. However, this also increases computational complexity. Therefore, to balance the trade-off between model complexity and fitting accuracy, the Akaike Information Content Criterion (AIC) is used to determine the number of Gaussian components, which can be expressed as:

[0123] (4)

[0124] In the formula: The maximum likelihood function (AIC) is used to calculate the maximum likelihood. The AIC value directly reflects the goodness of fit of the GMM model to the data; a smaller AIC value means a better model fit. Generally, as the number of model components increases... As the number of components increases, the AIC value will continuously decrease. However, when the number of components is sufficiently large, the downward trend of the AIC value will gradually slow down. Therefore, when selecting the number of model components, one should choose a number that makes the AIC value sufficiently small and no longer significantly decreases. The value is adjusted to achieve a balance between model fitting performance and complexity.

[0125] Step 1, which generates an uncertainty sample set based on the photovoltaic output GMM, obtains the sample basis required for nonparametric probability assessment. It is assumed that this is generated in each operating segment. A random sample of photovoltaic power output is denoted as... .in, For the first A total of 10 random samples are distributed among the Gaussian components according to their respective weights. The number of samples corresponding to each Gaussian component is denoted as:

[0126] (5)

[0127] In actual calculations, This can be handled by rounding down, and a final fine-tuning of the total sample size can be performed to ensure that:

[0128] (6)

[0129] For the The covariance matrix of each Gaussian component is decomposed. Since the covariance matrix of each Gaussian component is estimated from continuous photovoltaic power output samples and modeled using full covariance, it can be decomposed... If we consider it as a positive definite matrix, then there exists a matrix... , so that:

[0130] (7)

[0131] make for If a standard normal random vector is given by dimension 1, then the 1st dimension is... The first Gaussian component A sample can be represented as:

[0132] (8)

[0133] This can generate the first... The sample set corresponding to each Gaussian component:

[0134] (9)

[0135] For all After sampling each Gaussian component, the sample sets of each component are merged to obtain the final photovoltaic output sample set:

[0136] (10)

[0137] Right now:

[0138] (11)

[0139] in, Indicates the first A random sample of photovoltaic power output.

[0140] The physical meaning of the above sampling process is as follows: Since GMM is essentially a mixture distribution formed by the weighted superposition of multiple Gaussian components, it is only necessary to allocate the number of samples according to the proportion of each component in the overall distribution, generate samples independently from each Gaussian component, and then aggregate these samples to obtain a sample set that satisfies the original GMM distribution. This method has strict distribution consistency. This sampling method can directly generate samples in the target variable space, thus it is simpler to implement and more computationally efficient.

[0141] Step 2 involves decomposing the joint chance constraint of node voltage magnitude into a single chance constraint based on uniform risk allocation using Boole's inequality, and solving the optimization model to obtain an initial conservative feasible solution. The optimization model, specifically the objective function of the new distribution network... This includes electricity purchase costs, network loss penalty costs, and PV curtailment costs. Among these, network loss costs, as an increasing function of branch currents, are a sufficient condition to ensure accurate second-order cone relaxation in the distribution network. It can be represented as:

[0142] (12)

[0143] (13)

[0144] (14)

[0145] (15)

[0146] In the formula, , , , These represent the total cost of distribution network operation optimization, the cost of electricity purchase from the upstream power grid, the network loss penalty cost, and the cost of photovoltaic curtailment, respectively; T, B, E, and M represent the operating interval of 24 hours, the set of OLTC nodes, the set of network lines, and the set of PV grid-connected nodes, respectively; and t represents the operating time of the distribution network. , , The unit electricity purchase cost coefficient, network loss cost coefficient, and unit cost price of curtailed photovoltaic power are for the distribution network. , , These represent the electricity purchased from the upper-level grid by node j at time t, the active power output by the PV of node j at time t, and the maximum output power of the PV connected to node j at time t, respectively. , Let be the resistance of line ij and the current flowing through line ij at time t, respectively.

[0147] The second-order cone expression for branch DisFlow power flow constraints:

[0148] (16)

[0149] (17)

[0150] In the formula: Let j be the set of the first and last nodes. Let j be the set of end nodes. and These represent the active power and reactive power flowing through line ij at time t, respectively. Let be the square of the voltage amplitude at node j at time t; and Let be the active power and reactive power of the load at node j at time t, respectively. , Let PV be the PV of node j at time t, and WT be the reactive power output. The power compensation of the static var compensator (SVC) at node j at time t; and These represent the charging and discharging power of the energy storage system (ESS) connected to node j at time t; Let be the actual turns ratio of the on-load tap changer (OLTC) connected to line ij at time t, defined as the ratio of the secondary side to the primary side. If line ij is connected to an OLTC, then... For the actual ratio of OLTC, and vice versa =1; Let be the reactance of line ij.

[0151] The current safety constraint of the distribution network can be expressed as:

[0152] (18)

[0153] In the formula, It is the square of the upper limit of the current amplitude of line ij.

[0154] PV output constraints:

[0155] (19)

[0156] In the formula, Let be the PV power factor angle at time t for node j.

[0157] SVC compensation constraints can be expressed as:

[0158] (20)

[0159] In the formula, , Let be the upper and lower limits of the SVC compensation power at time t for node j, respectively. To address potential distribution network overvoltage issues after large-scale DG integration, the following settings are defined: .

[0160] OLTC constraints can be expressed as:

[0161] (twenty one)

[0162] In the formula, and The upper and lower limits of the adjustable ratio for OLTC; It is the difference between the square of the ratio of OLTC gear s and gear s-1 on line ij; Use 0-1 variables to indicate OLTC gear positions; This is the set of lines that include OLTCs. Considering that the distribution network is subject to constraints such as the number of adjustments during actual operation, the following OLTC constraints are further added:

[0163] (twenty two)

[0164] In the formula, and Add and remove flag variables for the OLTC gear position, which are 0-1 variables. If the OLTC shifts gears from time (t-1) to time t, then the shift will shift gears; otherwise, if the OLTC shifts gears... Then the OLTC will decrease the gear from time (t-1) to time t; This is the highest gear setting for OLTC; This represents the maximum number of OLTC gear adjustments allowed within the time period T.

[0165] The joint opportunity constraint of distribution network voltage amplitude can be expressed as:

[0166] (twenty three)

[0167] In the formula, The upper limit of the joint default probability of node voltage amplitude represents the time period. The probability that the voltage amplitudes of all nodes simultaneously meet the upper and lower limits is not less than ; These are the squares of the upper limit of the voltage amplitude at node j.

[0168] A uniform risk allocation strategy based on Boolean inequalities is adopted to perform initial decomposition of the joint opportunity constraints of distribution network voltage amplitude, in order to ensure that the overall risk does not exceed A local permissible risk level can be assigned to each node. ,satisfy:

[0169] (twenty four)

[0170] In the formula, n represents the number of nodes.

[0171] Therefore, the original joint opportunity constraint is transformed into:

[0172] (25)

[0173] set up Indicates in the sample The decision variables are as follows: Time node During the period If the square of the voltage amplitude is given, then equation (25) can be approximated by an empirical distribution as follows:

[0174] (26)

[0175] set up Indicates sample Whether the voltage constraint at this node is allowed to be violated depends on the following:

[0176] (27)

[0177] (28)

[0178] In the formula, A sufficiently large positive constant is used to achieve the equivalent transformation of chance constraints into mixed-integer deterministic constraints. Equation (29) limits the number of samples allowed to default in all samples to no more than [a certain value]. This ensures that the node voltage constraint meets the given confidence level requirement in the sense of the sample.

[0179] Solving the optimization model yields an initial conservative feasible solution. It should be noted that although the initial solution is somewhat conservative, it can guarantee the satisfaction of the original joint chance constraints in a probabilistic sense, thus providing a strictly probabilistically feasible initial operating point for subsequent iterations. The reason for using conservative initialization is that the true set of active events and their joint risk structure are not accurately known in the early stages of iteration; if optimization is started directly based on overly aggressive decomposition results, the initial operating point may fall into a high-risk region, thereby weakening the effectiveness of subsequent sample statistics and probability corrections. In contrast, although the conservative feasible region provides a certain redundancy margin, it can provide a stable baseline state for subsequent default event identification, joint probability estimation, and optimization model reconstruction, allowing the closed-loop iteration to start from a safe and reliable operating point and gradually release the redundancy margin brought by the conservative upper bound in subsequent updates.

[0180] Step 3 involves combining the current running solution with uncertainty samples to calculate the voltage amplitude at each node and identify the set of constraints where voltage exceedances may occur. In this iteration, let the solution obtained by the current optimization model be... ,Will Substituting the NCVSI values ​​of each node into the distribution network operation model along with the uncertainty sample set yields the values ​​for each node under each sample scenario. For each node... Record its position in the sample. The corresponding squared voltage amplitude result is .

[0181] Therefore, the first Node in the next iteration The voltage constraint default event is defined as:

[0182] (29)

[0183] Furthermore, nodes can be obtained based on sample statistics. The estimated marginal default probability in the current iteration:

[0184] (30)

[0185] in: Indicates events obtained based on sample statistics Marginal default probability estimation.

[0186] Based on this, the constraint events with a marginal default probability greater than zero are grouped into a set of possible default events for the current iteration, namely:

[0187] (31)

[0188] gather That is, the first The set of active default events that need to be addressed in this iteration, and its cardinality This indicates the number of constraints at the current running point that pose a risk of sample default. If This indicates that no voltage exceedance events exist under the current sample set evaluation, and the current running solution can be considered to meet the voltage risk requirements in the sample sense. In engineering implementation, if the sample size is large and the influence of extremely small sample noise needs to be suppressed, it is also possible to... The criteria were further extended to The form exceeds a given tiny threshold, but does not change the overall framework of the method of the present invention.

[0189] Step 4 involves calculating the edge default probability of each node and the empirical probability of the joint default event to obtain the joint default probability correction term. The joint default event on the active event set in the current iteration is defined as:

[0190] (32)

[0191] Based on the statistics of the MC sample, their joint default probability can be estimated as follows:

[0192] (33)

[0193] in, Indicates the currently running solution The empirical probability that at least one node in the active event set will experience a voltage over-limit.

[0194] According to the inclusion-exclusion principle, the difference between the sum of marginal default probabilities and the joint default probability reflects the probability correction effect corresponding to the overlapping regions of events. Based on this, the first... The joint default probability correction term in the next iteration is defined as:

[0195] (34)

[0196] Obviously, when there is overlap between active events, If the events hardly overlap in the sample, then It is close to zero. Therefore, It can be used to measure the correlation strength between default events at the current running point and to adjust the risk budget in JCC decomposition. JCC on the active set can be written as:

[0197] (35)

[0198] Using a uniform distribution method, it is further transformed into a set of SCCs:

[0199] (36)

[0200] Step 5 involves updating the risk budget of the single opportunity constraint using the ARA strategy based on the marginal default level of each node constraint, and reconstructing the constraint form. For any The risk allocation weight is defined as follows:

[0201] (37)

[0202] (38)

[0203] Based on this, the total risk budget allowed by JCC will be... By weight Assigned to each active constraint, resulting in the first... Node in the next iteration Single-constraint risk budget:

[0204] (39)

[0205] Therefore, the original JCC can be further refactored into a set of SCCs on the active event set:

[0206] (40)

[0207] Step 6 involves resolving the distribution network optimization model based on the updated risk constraints and verifying the convergence of the objective function, the set of default events, and the joint default probability correction term. If the termination condition is met, the final optimization result is output; otherwise, the process returns to step 3 to continue iterating. Let the... The optimization objective function value corresponding to the next iteration is Then its relative change is defined as:

[0208] (41)

[0209] when A sufficiently small convergence tolerance indicates that the optimization results of two adjacent iterations have essentially converged. Based on this, a given convergence tolerance is established. The convergence criterion for the objective can be written as:

[0210] (42)

[0211] On the other hand, to avoid a situation where the objective function changes only slightly but the set of default events or the joint risk structure still fluctuates, it is necessary to further examine the stability of the constraint set and the probability correction term. Therefore, it is required that the set of active events remains unchanged between two adjacent iterations, i.e.:

[0212] (43)

[0213] At the same time, it is required that changes in the joint default probability correction term be controlled within a given tolerance range, that is:

[0214] (44)

[0215] in, This represents the convergence tolerance of the joint probability correction term.

[0216] If all three conditions are met simultaneously, the current closed-loop iterative process is considered to have reached a stable state, and the update can be terminated; otherwise, return to step 3 to continue the iteration. At this point, the obtained solution has not only basically converged in the sense of the objective function, but the corresponding default event identification results and joint default probability correction results have also tended to stabilize.

[0217] In addition, to avoid continuous oscillations or excessively long computation times during the iteration process in extreme cases, a maximum number of iterations is also set. If the following conditions are met:

[0218] (45)

[0219] Regardless of whether the termination condition is met, the iteration stops and the current optimal result is output.

[0220] The present invention will be further illustrated below through specific embodiments.

[0221] like Figure 2The diagram shows the topology of the power distribution system simulated in this invention. This power distribution system is an IEEE-123 node power distribution network test system. In this system, photovoltaic (PV) systems are installed at each of the 12 nodes, with a PV power factor of 0.98. The PV time-series output curves use open-source data from an actual power system. Four capacitors are installed at nodes 20, 59, 66, and 114, each with a capacity of 40 kvar. Four energy storage systems are installed at nodes 56, 83, 96, and 116, each with a maximum capacity of 600 kWh and a rated charge / discharge power of 100 kW. The substation outlet is connected to the main transformer OLTC (On-Line Control Center), with a main transformer capacity of 100 MW. The OLTC adjustment step size is 0.01, and the maximum number of adjustment levels is 10. To reduce the number of OLTC adjustments, the maximum number of OLTC adjustments per day is 6.

[0222] like Figure 3 The figure shows the iterative change of the objective function value. In this embodiment, a confidence level is set. The proposed iterative + ARA method exhibits good convergence in four typical time periods: 11:00, 12:00, 13:00, and 14:00. The objective function values ​​in each time period gradually decrease with the number of iterations and tend to stabilize after a finite number of iterations, indicating that the method can gradually reduce the initial conservatism and obtain a stable solution by iteratively correcting the joint risk estimation and probability allocation results.

[0223] Comparing the convergence curves at different time points reveals that the trends across the four time periods are largely consistent, exhibiting a rapid decline in the early stages followed by gradual stabilization, without significant oscillations. This indicates that the iterative method proposed in this invention possesses good convergence characteristics. Meanwhile, the objective function value is generally higher at 12:00 and relatively lower at 14:00, which is largely consistent with the differences in daily photovoltaic power output and system operating status.

[0224] like Figure 4 The figure shows the change in the probability of stable system operation over time. In this embodiment, Method I is set as follows: The nonparametric iterative JCC decomposition method of ARA is not used; Method II is set as follows: The nonparametric iterative JCC decomposition method of ARA is used; Confidence levels are set. The system's probability of safe operation (PoS) is defined as the joint probability that all voltage constraints are simultaneously satisfied during a given period. The system's probability of stable operation remains constant at 1 during nighttime periods with no photovoltaic output fluctuations. Differences are mainly concentrated in critical periods where photovoltaic fluctuations and load changes are significant. At these times, different risk allocation methods have a more pronounced impact on the system's operating state. Both Method I and Method II can meet the preset safety margin requirements. However, the overall system stability probability corresponding to Method I is significantly higher than the safety margin line, indicating that the operating scheme obtained under uniform risk allocation still has strong conservatism. In contrast, the overall system stability probability of Method II is closer to the set safety margin, indicating that, under the premise of meeting JCC requirements, the ARA strategy can effectively reduce the additional conservatism brought about by uniform allocation.

[0225] like Figure 5 The diagram illustrates the effect of reducing conservatism. In this embodiment, Method II is defined as the nonparametric iterative JCC decomposition method using ARA; Method III is the JCC decomposition method based on constraint activity discrimination and phased upper bound provided by this invention; and Method IV is the traditional JCC decomposition method based on Boole upper bound. Throughout the entire scheduling cycle, the PoS curves obtained by the three decomposition methods are all strictly above the set safety margin, verifying the fundamental effectiveness of each method in ensuring system voltage safety. However, the different methods exhibit significant step-like differences in the degree of constraint feasible region release. The traditional Boole upper bound method (Method IV), due to completely ignoring the spatial coupling relationship between individual constraints, has a PoS curve close to 1.0 throughout the entire cycle, exhibiting extremely strong static conservatism. Method III, by introducing constraint activity discrimination and phased upper bound technology, effectively weakens this redundancy, causing the overall PoS curve to move closer to the safety lower bound. In contrast, Method II proposed in this invention achieves deeper conservative control. Thanks to the combination of nonparametric iteration mechanism and ARA strategy, Method II can accurately match the actual risk distribution of the system, and its PoS curve almost completely follows the set safety bottom line during the period when the system is under pressure.

[0226] like Figure 6The figure shows the NCVSI probability distribution. In this embodiment, the peak photovoltaic output period of 13:00 was selected, and the probability density distribution of NCVSI was reconstructed under the operating points of Method IV, Method III, and Method II proposed in this invention through MC simulation. The tail integral area of ​​each method in the instability risk region was calculated. All three decomposition algorithms can control the main distribution of NCVSI probability density to the left of the safety upper limit of 0.8, effectively ensuring the voltage stability of the system. However, in the right tail region that determines the feasible region, the different methods show significant differences. The traditional Boole method, due to its static average allocation, ignores the spatial coupling effect between constraints, and its tail integral area is only 1.50%, resulting in a large amount of idle risk budget and a severe shrinkage of the feasible region. The improved method based on constraint activity discrimination and stage upper bound increases the tail area to 2.64%, but still has obvious conservatism. In contrast, the probability density curve of the proposed iterative and ARA collaborative strategy approaches the safety boundary as a whole, with a tail integral area of ​​4.99%, which closely matches the 5% risk budget boundary set by the system. The physical essence of this tail feature lies in the fact that the nonparametric iterative process can dynamically capture the true joint default probability state of the system as the running point is updated, while the ARA mechanism achieves adaptive allocation of the risk budget based on the actual tendency of nodes to exceed limits. Through the synergistic effect of these two mechanisms, the proposed algorithm maximizes the safe operating boundary of the system while strictly satisfying voltage safety constraints. This deep release of the feasible region fundamentally avoids unnecessary voltage stability adjustment actions, providing a robust mechanistic support for improving the economic efficiency of system operation.

[0227] This invention provides a distribution network voltage optimization control method based on a nonparametric iterative framework. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment of the invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A distribution network voltage optimization control method based on a nonparametric iterative framework, characterized in that... Includes the following steps: Step 1: Generate an uncertainty sample set based on the photovoltaic output GMM to obtain the sample basis required for nonparametric probability assessment; Step 2: Decompose the joint chance constraint of node voltage magnitude into a single chance constraint based on uniform risk allocation according to Boole's inequality, and solve the optimization model to obtain the initial conservative feasible solution. Step 3: Combine the current running solution with the uncertainty sample to calculate the voltage amplitude of each node and identify the set of constraints that may cause voltage overruns; Step 4: Calculate the edge default probability of each node and the empirical probability of the joint default event to obtain the joint default probability correction term; Step 5: Based on the marginal default level of each node constraint, update the risk budget of the single opportunity constraint using the ARA strategy and reconstruct the constraint form; Step 6: Resolve the distribution network optimization model based on the updated risk constraints, and check whether the objective function, the set of default events, and the joint default probability correction term converge. If the termination condition is met, output the final optimization result; otherwise, return to step 3 to continue iterating.

2. The method as described in claim 1, characterized in that: The specific process of step 1 is as follows: Step 11, assume that generation occurs in each runtime segment. A random sample of photovoltaic power output is denoted as... ,in, For the first If the total number of samples is distributed among the Gaussian components according to their respective weights, then the nth random sample is... The number of samples corresponding to each Gaussian component is denoted as: ， Step 12, for the first The covariance matrix of each Gaussian component is decomposed and modeled using the full covariance form. If we consider it as a positive definite matrix, then there exists a matrix... , making ， make for If a standard normal random vector is given by dimension 1, then the 1st dimension is... The first Gaussian component Each sample is represented as, ， This generates the first The sample set corresponding to each Gaussian component. ， Step 13, for all After sampling each Gaussian component, the sample sets of each component are merged to obtain the final photovoltaic output sample set. ， Right now, ， in, Indicates the first A random sample of photovoltaic power output.

3. The method as described in claim 2, characterized in that: In step 11, the first Number of samples corresponding to each Gaussian component The data is processed by rounding down, and a final fine-tuning of the total sample size is performed to ensure... ， in, The number of Gaussian components. This represents the number of sets of random samples of photovoltaic output generated during each operating period.

4. The method as described in claim 2, characterized in that: In step 1, the number of Gaussian components is determined according to the following method. For photovoltaic power output 3D random vector Its joint probability density function Use several The Gaussian distribution is approximated by linear superposition. ， in, The number of Gaussian components. , and They represent the first The weights, mean, and covariance of each Gaussian component; It is a multidimensional Gaussian distribution with a probability density function. for, ， In the formula, Represents the determinant of a matrix; The weights of each Gaussian component satisfy the normalization condition, that is, ， The number of Gaussian components is determined using the Akaike Information Content Criterion (AIC), denoted as: ， in, It is the maximum likelihood function.

5. The method as described in claim 1, characterized in that: In step 2, the constraints include branch DisFlow power flow constraints, distribution network current security constraints, PV output constraints, SVC compensation constraints, OLTC constraints, and distribution network voltage amplitude joint opportunity constraints. The objective function for solving the optimization model includes electricity purchase cost, network loss penalty cost, and PV curtailment cost.

6. The method as described in claim 1, characterized in that: In step 2, the joint chance constraint of node voltage magnitude is decomposed into a single chance constraint based on uniform risk allocation according to Boole's inequality, including: The joint opportunity constraint of distribution network voltage amplitude is expressed as follows: ， In the formula, The upper limit of the joint default probability of node voltage amplitude represents the time period. The probability that the voltage amplitudes of all nodes simultaneously meet the upper and lower limits is not less than ; These are the squares of the upper limit of the voltage amplitude at node j; To ensure that the overall risk does not exceed Assign a local tolerance level to each node. ,satisfy, ， Thus, the original joint opportunity constraint is transformed into, ， set up Indicates in the sample The decision variables are as follows: Time node During the period If the square of the voltage amplitude is given, then the above formula can be approximated by an empirical distribution as follows: ， set up Indicates sample Whether the voltage constraint at this node is allowed to be violated, then... ， ， In the formula, It is a sufficiently large positive number.

7. The method as described in claim 1, characterized in that: The specific process of step 3 is as follows: Step 31, in the In this iteration, let the solution obtained by the current optimization model be... ,Will Substituting the uncertainty sample set into the distribution network operation model, we obtain the NCVSI values ​​for each node under each sample scenario; for each node... Record its position in the sample. The corresponding squared voltage amplitude result is ; Step 32, the first Node in the next iteration The voltage constraint default event is defined as follows: ， Nodes are obtained based on sample statistics. The estimated marginal default probability in the current iteration ， in: Indicates events obtained based on sample statistics Marginal default probability estimation; Step 33: Organize the constraint events with a marginal default probability greater than zero into a set of possible default events for the current iteration, i.e. ， gather That is, the first The set of active default events that need to be addressed in this iteration, and its cardinality This indicates the number of constraints at the current operating point that pose a risk of sample default.

8. The method as described in claim 7, characterized in that: The specific process of step 4 is as follows: Step 41, define the joint default event on the active event set in the current iteration as, ， Step 42, based on MC sample statistics, estimate their joint default probability as follows: ， in, Indicates the currently running solution The empirical probability that at least one node in the active event set will experience a voltage over-limit. Step 43, the first The joint default probability correction term in the next iteration is defined as follows: ， Obviously, when there is overlap between active events, If the events hardly overlap in the sample, then Approaching zero; therefore, using Measure the strength of the correlation between default events at the current operating point and adjust the risk budget in the JCC decomposition; Step 44, write the JCC on the active set as follows: ， Using a uniform distribution method, it is further transformed into a set of SCCs. 。 9. The method as described in claim 8, characterized in that: In step 5, for any The risk allocation weight is defined as follows: ， ， Total risk budget allowed by JCC By weight Assigned to each active constraint, resulting in the first... Node in the next iteration Single-constraint risk budget, ， The original JCC is further refactored into a set of SCCs on the active event set. 。 10. The method as described in claim 1, characterized in that: The specific process of step 6 is as follows: Step 61, let the first... The optimization objective function value corresponding to the next iteration is Then its relative change is defined as, ， Given target convergence tolerance Then the convergence criterion for the objective is, ， Step 62, set the set of active events to remain unchanged between two adjacent iterations, that is, ， At the same time, it is required that changes in the joint default probability correction term be controlled within a given tolerance range, that is, ， in, This represents the convergence tolerance for the joint probability correction term; Step 63: If all three conditions are met simultaneously, the current closed-loop iteration process is considered to have reached a stable state, and the update is terminated; otherwise, return to step 3 to continue the iteration, and set the maximum number of iterations. ,like, ， Regardless of whether the termination condition is met, the iteration stops and the current optimal result is output.

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