A power distribution network photovoltaic active and reactive power collaborative control method and system

Abstract

The present application relates to power distribution network operation control technical field, disclose a kind of power distribution network photovoltaic active and reactive power collaborative control method and system, according to the control variable of power distribution network under current operating point and the voltage measurement of key monitoring node, the control space of power distribution network is orthogonally decomposed into voltage sensitive subspace and approximate voltage insensitive subspace;Based on voltage sensitive subspace, with the voltage safety constraint as hard constraint, with the minimum adjustment of control variable as target to build first objective function and solve, obtain voltage sensitive control increment;Based on approximate voltage insensitive subspace, with the minimum loss of network as target to build second objective function and solve, obtain network loss optimization control increment;Two increments are added after stacking into ac power flow equation to execute nonlinear complex review, and when complex review passes, issue power distribution network photovoltaic active and reactive power collaborative control instruction, on the premise of strictly guaranteeing voltage constraint hard feasibility, the accurate regulation and control of photovoltaic power in power distribution network is realized.

Description

Technical Field

[0001] This invention relates to the field of power distribution network operation control technology, and in particular to a method and system for coordinated control of photovoltaic active and reactive power in power distribution networks. Background Technology

[0002] As the penetration rate of distributed photovoltaic power generation in the distribution network continues to increase, the traditional radial passive distribution network is gradually being transformed into a complex active distribution network containing a large number of distributed power sources. The randomness and volatility of photovoltaic output cause the distribution network to frequently experience voltage over-limit problems, which seriously threaten equipment safety and power supply quality.

[0003] Existing technologies treat the voltage-power coupling relationship of the distribution network as a static, offline-sampleable function mapping and construct a piecewise linearized model through offline Monte Carlo sampling. However, when the photovoltaic output fluctuates rapidly and the operating point crosses the segment boundary, the hard switching of the sensitivity matrix will cause a step jump in the control command. Frequent inverter operation will aggravate equipment losses and may induce voltage oscillations at the moment of switching. Moreover, the optimization calculation of this technology is highly complex, making it impossible to accurately control the photovoltaic power in the distribution network.

[0004] Therefore, how to achieve precise control of photovoltaic power in the distribution network under the premise of strictly ensuring the hard feasibility of voltage constraints has become a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] This invention provides a method and system for coordinated control of active and reactive power of photovoltaic power in distribution networks, which solves the problem of how to achieve precise control of photovoltaic power in distribution networks under the premise of strictly ensuring the hard feasibility of voltage constraints.

[0006] To address the aforementioned technical problems, the first aspect of this invention provides a method for coordinated control of active and reactive power in a distribution network, comprising: The control variables of the distribution network at the current operating point and the voltage measurement values ​​of key monitoring nodes are obtained so as to orthogonally decompose the control space of the distribution network into a voltage-sensitive subspace and an approximately voltage-insensitive subspace. Based on the voltage-sensitive subspace, with the voltage security constraints in the distribution network as hard constraints, and with the goal of minimizing the adjustment amount of the control variables, a first objective function is constructed and solved to obtain the voltage-sensitive control increment; Based on the approximate voltage-insensitive subspace, a second objective function is constructed and solved with the goal of minimizing the network loss of the distribution network, thereby obtaining the network loss optimization control increment; The voltage-sensitive control increment and the network loss optimization control increment are superimposed to obtain a candidate total control increment, which is then substituted into the AC power flow equation to perform nonlinear verification. When the verification is successful, a photovoltaic active and reactive power coordinated control command for the distribution network is issued.

[0007] A second aspect of the present invention provides a photovoltaic active and reactive power coordinated control system for a power distribution network, comprising: The control space decomposition module is used to obtain the control variables of the distribution network at the current operating point and the voltage measurement values ​​of key monitoring nodes, so as to orthogonally decompose the control space of the distribution network into a voltage-sensitive subspace and an approximately voltage-insensitive subspace. The first function solving module is used to construct and solve a first objective function based on the voltage-sensitive subspace, with the voltage security constraints in the distribution network as hard constraints and the minimization of the adjustment amount of the control variables as the objective, to obtain the voltage-sensitive control increment; The second function solving module is used to construct and solve a second objective function based on the approximate voltage-insensitive subspace, with the goal of minimizing the network loss of the distribution network, to obtain the network loss optimization control increment; The control command issuing module is used to superimpose the voltage-sensitive control increment and the network loss optimization control increment to obtain a candidate total control increment, which is then substituted into the AC power flow equation to perform nonlinear verification. When the verification is successful, the module issues a photovoltaic active and reactive power coordinated control command for the distribution network.

[0008] Compared with the prior art, the beneficial effects of the embodiments of the present invention are as follows: By decomposing the control space of the distribution network into a voltage-sensitive subspace and an approximately voltage-insensitive subspace, and prioritizing voltage safety as a hard constraint to ensure the system does not exceed limits in the voltage-sensitive subspace, while independently optimizing network losses in the insensitive subspace, this "layered and divide-and-conquer" strategy mathematically avoids the mutual interference between voltage regulation and economic regulation, ensures absolute priority protection for grid safety, and fully explores the potential for loss reduction within the safety margin. By solving the voltage correction problem in the low-dimensional voltage-sensitive subspace and the economic dispatch problem in the approximately voltage-insensitive subspace, the originally high-dimensional, highly nonlinear mixed integer / nonlinear programming problem is decomposed into two smaller, more linearized problems. The sub-problems not only significantly reduce the computation time of a single control operation, meeting the real-time control requirements of distribution networks with second-level / minute-level rapid response, but also reduce the dependence on underlying computing hardware. After superimposing the candidate total control increment, it is forcibly substituted into the accurate AC power flow equation for nonlinear verification, effectively overcoming the model error caused by linearization decomposition. This ensures that the final issued commands strictly meet the safety boundaries of node voltage and branch power flow in the actual physical power grid, eliminating the risk of "theoretical safety, actual limit violation" caused by approximate calculations. This greatly improves the reliability of the engineering implementation of the control strategy. Under the premise of strictly ensuring the hard feasibility of voltage constraints, it also realizes the precise regulation of photovoltaic power in the distribution network. Attached Figure Description

[0009] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is a flowchart of a photovoltaic active and reactive power coordinated control method for a power distribution network according to a certain embodiment of the present invention; Figure 2 This is a structural diagram of a low-voltage power distribution network simulation system provided in a certain embodiment of the present invention; Figure 3 This is a photovoltaic 24-hour active power output curve provided in a certain embodiment of the present invention; Figure 4 This is a photovoltaic 24-hour reactive power output curve provided in a certain embodiment of the present invention; Figure 5 This is a structural diagram of a photovoltaic active and reactive power coordinated control system for a power distribution network provided in a certain embodiment of the present invention; Figure label: Among them, 10 is the control space decomposition module; 20 is the first function solving module; 30 is the second function solving module; and 40 is the control command issuing module. Detailed Implementation

[0011] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings and examples. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0012] It should be understood that the step numbers used in the text are for ease of description only and are not intended to limit the order in which the steps are performed.

[0013] It should be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0014] The terms “comprising” and “including” indicate the presence of the described feature, whole, step, operation, element and / or component, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0015] The term “and / or” refers to any combination of one or more of the associated listed items, as well as all possible combinations, and includes these combinations.

[0016] In one embodiment, such as Figure 1 As shown, the first aspect of the present invention provides a method for coordinated control of active and reactive power in a distribution network, comprising: S1. Obtain the control variables of the distribution network at the current operating point and the voltage measurements of key monitoring nodes, so as to orthogonally decompose the control space of the distribution network into a voltage-sensitive subspace and an approximately voltage-insensitive subspace; specifically, the distribution network in this invention is preferably a radial active distribution network, with feeders connected to several distributed photovoltaic power stations (all equipped with intelligent inverters with continuous active and reactive power regulation capabilities), that is, there are One photovoltaic access node, and at the end of the feeder and on the heavy-load branch. Voltage measurement devices are installed at key monitoring nodes. Edge computing terminals (including power flow calculation engines and quadratic programming solvers) are deployed on the distribution network side, with a control cycle set to execute once every 5 minutes.

[0017] At the start of any control cycle, data from the distribution network at the current operating point is collected: the current active and reactive power outputs of each photovoltaic power station are obtained, and a vector consisting of the reduction in active power output data and the adjustment in reactive power output data is defined as the control variable. ( To control the cycle, the initial value of this variable is set to zero; at the same time, real-time voltage measurement values ​​of key monitoring nodes, voltage measurement data of non-key monitoring nodes other than key monitoring nodes, and line topology data of the distribution network (line impedance, ground admittance, topology composition, etc.) are acquired, and these data are preprocessed such as cleaning to improve the accuracy of the data.

[0018] In one embodiment, the orthogonal decomposition of the control space of the distribution network into a voltage-sensitive subspace and an approximately voltage-insensitive subspace includes: The Jacobian matrix of the voltage measurement values ​​against the control variables is used as the voltage drive coefficient matrix; Perform truncated singular value decomposition on the voltage drive coefficient matrix to obtain a right singular vector matrix and a singular value diagonal matrix; Set an adaptive truncation threshold and determine the effective rank by combining it with the singular value diagonal matrix; By decomposing the right singular vector matrix using the effective rank, the voltage-sensitive subspace and the approximately voltage-insensitive subspace are obtained.

[0019] Specifically, this invention uses the Jacobian matrix of voltage versus control variables as the voltage driving coefficient matrix, which is expressed by the following formula: In the formula, For the first Voltage drive coefficient matrix at each control cycle It quantifies the local linear coupling strength between power injection and voltage response in the distribution network. In this matrix, the row space corresponds to the control direction that can cause voltage changes, and the column space corresponds to the voltage response mode that can be realized. For voltage measurements at key monitoring nodes, ; For controlling the periodic index; This represents the total number of photovoltaic (PV) access nodes in the distribution network. This represents the total number of critical voltage monitoring nodes.

[0020] The numerical calculation method for the voltage drive coefficient matrix is ​​as follows: At the current operating point of the distribution network, a small disturbance (0.1% of the rated capacity) is applied to each control variable. The corresponding voltage change is obtained through a single AC power flow calculation. The matrix value is then the quotient of the voltage change and the small disturbance. Essentially, this method utilizes a finite difference approximation of the Jacobian matrix. The calculation accuracy improves as the disturbance step size decreases, but an excessively small step size may be affected by numerical noise. In practical implementation, using 0.1% of the rated capacity as the disturbance step size achieves a balance between accuracy and numerical stability. The voltage drive coefficient matrix defines a linear approximate mapping from the control space to the voltage space. Its row space corresponds to the control direction that can cause changes in the monitored voltage, and its right singular vector gives the orthogonal modes in the control space; the column space represents the achievable monitored voltage response modes.

[0021] Subsequently, a truncated singular value decomposition is performed on the voltage drive coefficient matrix to obtain the right singular vector matrix and the singular value diagonal matrix. This process is expressed by the following equation: In the formula, , , For the first The left singular vector matrix (corresponding to the voltage measurement space), the right singular vector matrix (whose row vectors correspond to the orthonormal basis of the control variable space), and the singular value diagonal matrix for each control cycle; where... , , Additionally, the diagonal elements of the singular value diagonal matrix are arranged in descending order as follows: The elements in this matrix reflect the voltage drive efficiency of different control modes. Large singular values ​​correspond to efficient control modes, while small singular values ​​correspond to inefficient control modes.

[0022] Set adaptive cutoff threshold The effective rank is determined by combining the singular value diagonal matrix with the rank, and this process is expressed by the following formula: In the formula, The dimension of the voltage regulation tangent space, its physical meaning is the number of independently controllable voltage modes at the current operating point, typically... ; These are the singular values ​​at the effective rank truncation point; This is the first singular value to be truncated.

[0023] Therefore, based on the effective rank, the row vectors of the right singular vector matrix can be divided into two groups. The space spanned by the right singular vectors of the first effective rank rows is the voltage-sensitive subspace (corresponding to the direction of large singular values, where unit control changes will cause significant node voltage fluctuations), and the space spanned by the right singular vectors of the remaining rows is the approximately voltage-insensitive subspace (corresponding to the direction of small singular values, where control changes have negligible impact on node voltage). The block partitioning result of the right singular vector matrix is ​​expressed by the following formula: In the formula, This is the orthonormal basis corresponding to the voltage-sensitive subspace. Its column vectors span the direction that directly affects the voltage in the control space, corresponding to the set of all voltage-sensitive control modes in the distribution network; This forms the orthonormal basis corresponding to the approximate voltage-insensitive subspace. Its column vectors span the directions in the control space that have a smaller impact on the voltage. This decomposition satisfies orthogonality: In the formula, for The physical essence of the above decomposition lies in the fact that the high-dimensional control space of the distribution network is not isotropic, but rather exhibits strong anisotropy determined by the topology of the power flow equations. Voltage-sensitive subspace directions correspond to voltage-efficient control modes, while approximately voltage-insensitive subspace directions correspond to voltage-inefficient control modes. It is important to note that... The direction of the truncated small singular value has a small impact on the voltage only under the first-order local linear model approximation and is not a zero space in the strict sense. When the control increment is large or the operating point changes significantly, this subspace direction may still have a non-negligible impact on the voltage.

[0024] This invention directly defines the Jacobian matrix of the voltage measurement on the control variable as the voltage driving coefficient matrix, and orthogonals it using singular value decomposition (SVD). Based on the physical power flow characteristics of the power grid itself, it strictly distinguishes between control directions that have a strong driving effect on voltage and those that have almost no driving effect on voltage. It introduces an adaptive threshold, which has the ability to track operating conditions and resist noise. Based on the decomposition of the right singular vector matrix, it directly corresponds to the modulation direction of the control variable.

[0025] In one embodiment, the step of orthogonally decomposing the control space of the distribution network into a voltage-sensitive subspace and an approximately voltage-insensitive subspace includes: The remaining reactive power data of each inverter is determined based on the current power output data and rated apparent power data of each inverter in the power distribution network. When the reactive power margin of the distribution network is determined to be sufficient based on the remaining reactive power data, a key node weight diagonal matrix is ​​constructed according to the voltage measurement value and the voltage security constraint, and the active power reduction marginal utility data of the distribution network is determined through the voltage driving coefficient matrix and the key node weight diagonal matrix.

[0026] Specifically, this invention defines the proportion of projected energy of each inverter control dimension on the voltage-sensitive subspace basis using the following formula: In the formula, For the first The energy percentage of the voltage-sensitive subspace for each control dimension reflects the total energy of that control dimension in each basis direction of the voltage-sensitive subspace. The element in the i-th row and m-th column of the basis matrix of the voltage-sensitive subspace; Corresponding to the active dimension, This corresponds to the reactive power dimension. It should be noted that the i-th row in the voltage-sensitive subspace basis matrix corresponds one-to-one with the i-th control dimension. Therefore, the row index i in the formula and the control dimension number i represent the same object, used only for matrix representation and physical meaning description, respectively.

[0027] The leverage of the control dimension in the selected subspace can serve as an indicator of control effectiveness. However, the inverter approaching the apparent power circle boundary represents a change in feasible control margin. The reactive power will not automatically decrease due to reactive power saturation. Therefore, the remaining reactive power capacity of the inverter must be calculated directly, and saturated devices must be handled through dynamic upper and lower bounds. This invention determines the remaining reactive power data of these inverters based on their current power output data and rated apparent power data in the distribution network. This process is expressed by the following formula: In the formula, This represents the remaining reactive power data for the nth inverter. , S represents the current active and reactive power output data of the nth inverter; rated,n This represents the rated apparent power data for the nth inverter.

[0028] The calculated residual reactive power data is not less than the preset threshold. (Pick When the reactive power regulation margin of the inverter is deemed sufficient, the marginal utility data of active power reduction for each inverter in the distribution network is calculated based on the sensitivity norm index. First, a key node weight diagonal matrix is ​​constructed by combining the voltage measurements of each monitoring node and the upper and lower voltage limits in the voltage safety constraints. This process is expressed by the following formula: In the formula, Let be the key node weight corresponding to the j-th key monitoring node; The voltage measurement value of the j-th critical monitoring node; , These are the upper and lower limits of the node voltage; This is a diagonal matrix of key node weights, in which nodes with higher risk of exceeding limits are assigned greater weights.

[0029] Subsequently, based on the constructed key node weight diagonal matrix and voltage drive coefficient matrix, the active power reduction marginal utility data of the distribution network can be calculated. This process is expressed by the following formula: In the formula, The active power reduction marginal utility of the i-th control dimension is used to characterize the comprehensive regulation efficiency of the i-th control dimension on the voltage of all monitoring nodes. The standard basis vector corresponding to the i-th control dimension has its i-th component being 1.

[0030] If the calculated residual reactive power data is less than the preset threshold If the inverter's reactive power regulation margin is insufficient, its upper and lower bounds in the reactive power dimension will be tightened to... (δ) Q The convergence coefficient (preferably 0.1) forms upper and lower bound constraints on reactive power and allows it to participate in subsequent economic optimization.

[0031] This invention fully explores the potential of reactive power regulation and minimizes the loss of curtailed solar power. By calculating the marginal utility data of active power reduction, it accurately quantifies the actual voltage improvement contribution of reducing a unit of active power to the most dangerous node. This guides subsequent control strategies to prioritize the removal of active power components with the lowest marginal utility (i.e., small contribution to voltage improvement) or the highest (depending on the objective, usually pursuing high efficiency, but actually identifying the active power node most sensitive to voltage) to achieve the maximum voltage security benefit with the minimum power generation sacrifice.

[0032] S2. Based on the voltage-sensitive subspace, with the voltage security constraints in the distribution network as hard constraints, and with the goal of minimizing the adjustment amount of the control variables, a first objective function is constructed and solved to obtain the voltage-sensitive control increment; In one embodiment, step S2 includes: The control variables are decomposed to obtain voltage-sensitive subspace components and approximately voltage-insensitive subspace components; Based on the voltage-sensitive subspace components, the voltage security constraints in the distribution network are transformed into the hard constraints; Using the hard constraints as the first constraint condition, and minimizing the adjustment amount of the control variables as the objective, the first objective function is constructed and solved to obtain the optimal voltage-sensitive subspace coordinates; The voltage-sensitive control increment is determined based on the optimal voltage-sensitive subspace coordinates and the voltage-sensitive subspace.

[0033] Specifically, at the current operating point, let the measured voltage of the monitoring node be... Therefore, the voltage safety constraint can be expressed as: In the formula, The current operating point relative to the control variable The optimized control increment is used to update the active and reactive power control quantities of the inverter, and its update relationship is as follows: This invention decomposes the control variables to obtain voltage-sensitive subspace components and approximately voltage-insensitive subspace components, a process expressed by the following equation: In the formula, For voltage-sensitive subspace components; For voltage-sensitive subspace coordinates; This is an approximate voltage-insensitive subspace component; These are approximate voltage-insensitive subspace coordinates.

[0034] because The direction has a relatively small effect on the voltage under the first-order approximation, because It is guaranteed that voltage changes are primarily determined by the voltage-sensitive subspace components: In the formula, The front of the left singular vector List, ; It is a diagonal matrix with non-zero singular values. .

[0035] To reserve a safety margin for model errors, a margin factor is introduced into the voltage constraints. (Taking 0.005 pu), and based on the voltage-sensitive subspace component, it is transformed into the hard constraint, which is expressed by the following formula: In the formula, It is a vector consisting entirely of 1s; This provides a safety margin to compensate for linear approximation errors and measurement noise.

[0036] Subsequently, using hard constraints as the first constraint condition, a first objective function is constructed with the goal of minimizing the adjustment amount of the control variables. In one embodiment, constructing the first objective function with the goal of minimizing the adjustment amount of the control variables includes: An initial objective function is constructed by minimizing the adjustment amount of the control variables, and a subspace coordinate transformation is performed on the initial objective function based on the voltage-sensitive subspace to obtain the transformed objective function; Based on the marginal utility data of active power reduction, a control quantity weight matrix is ​​constructed, and the transformation objective function is modified by the control quantity weight matrix to obtain the modified objective function; The modified objective function is combined with a regularization term based on voltage-sensitive subspace coordinates to form the first objective function.

[0037] This invention first constructs an initial objective function based on minimizing the adjustment amount of the control variables: The physical meaning of this initial objective function is to minimize the overall active power reduction and reactive power regulation of all inverters while satisfying voltage constraints.

[0038] Subsequently, the voltage-sensitive subspace is used to perform a subspace coordinate transformation on the initial objective function, that is, to transform the initial objective function into subspace coordinates. Projected to Soon Substituting into the initial objective function, we form the transformed objective function. The physical meaning of the objective remains unchanged after the transformation; it is simply transformed from Cartesian coordinates in the original control space to orthogonal base coordinates in the voltage-sensitive subspace. Optimizing α is equivalent to optimizing the control increment in the Tα direction.

[0039] However, photovoltaic (PV) control in the distribution network has a clear priority strategy: reactive power regulation has low costs (the inverter only changes the current phase, without losing power generation) and should be used first; active power reduction has high costs (direct curtailment of solar power, resulting in lost power generation revenue) and should be avoided as much as possible. Therefore, all control dimensions cannot be treated equally; a control weight matrix needs to be introduced to assign different penalties to different dimensions. The control weight matrix... The weight matrix consists of two parts: basic weights and marginal utility correction weights; in the basic weights, the active reduction dimension weight is set as follows: The reactive power adjustment dimension weight is set to This reflects a physical strategy of prioritizing reactive power adjustment and reducing active power when necessary. Subsequently, the marginal utility adjustment weight is determined based on the marginal utility data of active power reduction, a process expressed by the following formula: In the formula, The weight of the i-th control variable; The marginal utility adjustment coefficient is used to control the correction range, and 0.5 is preferred. This is the maximum value of the marginal utility of all active dimensions, used for normalization.

[0040] Multiplying the control weight matrix by the transformation objective function yields the modified objective function. This modification increases the weight penalty for control dimensions with higher marginal utility of active power reduction, thus prioritizing active power reduction of dimensions with higher marginal utility during optimization, achieving precise targeting and minimizing curtailment loss. Finally, the modified objective function is combined with a regularization term based on voltage-sensitive subspace coordinates to form the first objective function, expressed as follows: In the formula, Let this be the first objective function; This is a regularization term based on the voltage-sensitive subspace coordinates; This is the regularization coefficient, which guarantees the uniqueness of the solution.

[0041] The first constraint also includes inverter physical constraints: In the formula, , To control the minimum and maximum values ​​of variables.

[0042] It also includes the apparent power circle constraint: In the formula, For the first Active power reduction of each inverter; and The first The active and reactive power settings of each inverter; For the first The current maximum active power output of each inverter.

[0043] This invention constructs a control weight matrix by introducing active power reduction marginal utility data, enabling the first objective function to assign different cost weights to the active / reactive power adjustment actions of different inverters. This maximizes the retention of photovoltaic power generation, which has a weak effect on voltage support, and minimizes the economic losses of safety correction. By using the orthogonal basis of the voltage-sensitive subspace to perform coordinate transformation on the initial objective, the coupled active / reactive power adjustment quantities in the original physical space are mapped to independent coordinate variables in the sensitive subspace. This ensures that the optimization direction is strictly aligned with the actual leverage effect of voltage control, avoiding power waste in ineffective control actions. The introduction of a regularization term significantly improves the numerical stability and disease resistance of the solution process.

[0044] The first objective function, after transformation and correction, is a convex quadratic constrained quadratic programming problem (QCQP). It has a unique global optimum and can be efficiently solved using a standard convex optimization solver, with a computational complexity of O(n log n). Far below the original space Then, the optimal voltage-sensitive subspace coordinates are obtained by solving the problem. Finally, the coordinates are multiplied by the orthonormal basis corresponding to the voltage-sensitive subspace to obtain the voltage-sensitive control increment.

[0045] This invention decomposes the control variables into subspaces and constructs hard constraints based solely on the voltage-sensitive subspace components, thereby avoiding the triggering of false safety limits due to adjustments of irrelevant control variables. This makes the application of voltage constraints highly physically targeted and mathematically rigorous. After decomposing the control variables, the objective function and constraint conditions are constructed only on the low-dimensional voltage-sensitive subspace coordinate axes, significantly reducing the solution dimensionality and computation time of hard-constraint optimization problems.

[0046] S3. Based on the approximate voltage-insensitive subspace, construct a second objective function with the goal of minimizing the network loss of the distribution network and solve it to obtain the network loss optimization control increment; In one embodiment, step S3 includes: Power flow calculations are performed on the distribution network to obtain network loss data; Based on the approximate voltage-insensitive subspace component, the second constraint conditions are: the inverter apparent power circle constraint determined according to the rated apparent power data of each inverter; the upper and lower bounds of reactive power determined according to the residual reactive power data of each inverter; the ramp rate constraint determined by the optimal voltage-sensitive subspace coordinates; the total upper and lower bounds of the control quantity corresponding to the control variable; the trust region constraint; and the hard constraint. The second objective function is constructed with the goal of minimizing the network loss data. Expanding the second objective function at the current running point yields a quadratic approximate objective function; Based on the approximate voltage-insensitive subspace, the quadratic approximate objective function is subjected to subspace dimensionality reduction projection to obtain the dimensionality-reduced optimized objective function; The dimensionality reduction optimization objective function is approximated by Hessian diagonalization, and the result is combined with the Tikhonov regularization term to form the final objective function for solving, thereby obtaining the optimal approximate voltage-insensitive subspace coordinates. The network loss optimization control increment is determined based on the optimal approximate voltage-insensitive subspace coordinates and the approximate voltage-insensitive subspace.

[0047] Specifically, the physical objective of the approximate voltage-insensitive subspace optimization is to further reduce the total active power loss of the distribution network and improve operational economy by utilizing the remaining control degrees of freedom (approximate voltage-insensitive direction) after voltage correction has been completed in the voltage-sensitive subspace. This invention performs a precise Newton-Raphson three-phase power flow calculation based on the power data of each inverter at the start of the current cycle, the calculated voltage-sensitive control increment, and the complete distribution network topology and load data. This yields the total active power loss at the current feeder outlet and in each branch, which is then used as the network loss data.

[0048] This invention uses the inverter apparent power circle constraint determined based on the rated apparent power data of each inverter, the upper and lower bounds of reactive power determined based on the residual reactive power data of each inverter, the ramp rate constraint determined by the optimal voltage-sensitive subspace coordinates, the total upper and lower bounds of the control variables corresponding to the control variables, the trust region constraint, and the hard constraint as the second constraint conditions; wherein, the ramp rate constraint is expressed by the following formula: In the formula, The optimal voltage-sensitive subspace coordinates; For approximately voltage-insensitive subspace components, The variable to be determined; The maximum allowable control increment change amplitude within the control cycle is set to 10% of the inverter's rated capacity.

[0049] The total upper and lower bounds of the control quantity are expressed by the following formula: In the formula, This is the control variable for the current running point.

[0050] Trust region constraints are expressed by the following formula: In the formula, The value is the trust region radius, used to limit the norm of the approximate voltage-insensitive subspace control increment, ensuring the effectiveness of the linear approximation, and is set to 5% of the inverter's rated capacity.

[0051] The network loss optimization control increment (also known as the economic optimization control increment) corresponding to the approximate voltage insensitive subspace has a small impact on the monitoring node voltage under the first-order approximation, but it does affect the power flow distribution and network loss of the distribution network. Therefore, this invention solves the optimization problem with the goal of minimizing network loss within the approximate voltage insensitive subspace: In the formula, This is network loss data (which is calculated from the power flow equations and is essentially a quadratic / higher-order function of power injection). This is the voltage-sensitive control increment.

[0052] The optimization problem model is combined with the second constraint to form the second objective function. Because The direction has a small but not strictly zero effect on the voltage under the first-order approximation, and the unconstrained analytical solutions are superimposed. This may lead to control variables going out of bounds, requiring the second objective function to be expanded at the current running point: In the formula, To optimize and control network loss increments, = ; This is the network loss value at the baseline point (a constant term that can be ignored during optimization and does not affect the location of the optimal solution). The gradient vector of network loss with respect to control quantity The first-order term is used to reflect the slope of network loss as the control quantity changes; The Hessian matrix of network loss versus control quantity The second-order term is used to reflect the curvature of the network loss function.

[0053] After removing the constant term from the above function, a quadratic approximate objective function is formed: a first term (gradient-driven descent direction) + a second term (curvature-controlled step size).

[0054] Will = Substituting the quadratic approximation objective function into the subspace dimension reduction projection, we obtain the dimension reduction optimization objective function: The above describes the variable dimensions from 2N. PV The dimension drops to (2N) PV -r) dimension (the larger r is, the more obvious the dimensionality reduction), and only optimizes network loss in directions with little impact on voltage, avoiding economic optimization that interferes with voltage safety, while matrix multiplication is used. Compress large-scale Hessian into small-scale subspace Hessian.

[0055] The objective function for dimensionality reduction optimization is approximated using Hessian diagonalization—only the diagonal elements of the Hessian matrix are retained, while all off-diagonal elements are set to zero. Specifically, each diagonal element takes the absolute value of the second-order partial derivative of the network loss in the corresponding control dimension, ensuring that the approximated Hessian is positive semi-definite. A Tikhonov regularization term consisting of the identity matrix is ​​added to the quadratic term of the diagonalization approximation result, forming the final objective function. In the formula, It is the identity matrix; The coefficient is a normalization factor, and its value is greater than 0, preferably 10. -5 .

[0056] The resulting objective function is a strictly convex quadratic function. Combined with the second constraint, the whole constitutes a convex quadratic programming problem with a unique global optimal solution. The optimal approximate voltage-insensitive subspace coordinates can be obtained by using a constrained quadratic programming solver or the projection gradient method. Multiplying these coordinates by the approximate voltage-insensitive subspace coordinates yields the incremental control for network loss optimization.

[0057] When constructing the second objective function, this invention does not only focus on network losses, but also forcibly incorporates the inverter's apparent power circle constraint (capacity boundary), the upper and lower bounds of remaining reactive power (dynamic reactive power reserve), the ramp rate constraint (connecting to safety correction results), the upper and lower bounds of the total control variables (hard limits on equipment), the trust region constraint (ensuring the effectiveness of the approximate model), and the hard voltage constraint. This ensures that even in the process of pursuing loss reduction through economic optimization, all obtained control increments are physically absolutely executable and will not conflict with the safety correction actions of the previous stage. By projecting the quadratic approximate objective function onto the approximate voltage-insensitive subspace, the original high-dimensional physical control variable optimization problem is reduced to a coordinate axis optimization with a dimension equal to that of the insensitive subspace. This greatly reduces the search space of the solver, enabling the quadratic programming problem, which carries a large number of constraints, to close the loop quickly within milliseconds.

[0058] S4. The voltage-sensitive control increment and the network loss optimization control increment are superimposed to obtain a candidate total control increment, which is then substituted into the AC power flow equation to perform nonlinear verification. Upon successful verification, a photovoltaic active and reactive power coordinated control command for the distribution network is issued. Specifically, the voltage-sensitive control increment and the network loss optimization control increment are added to obtain the candidate total control increment. Since the above calculation is based on a first-order linear approximation, and... The direction is not strictly unaffected by the voltage. The combined candidate total control increment needs to undergo nonlinear verification to ensure that all node voltages and equipment constraints meet the requirements under actual AC power flow.

[0059] In one embodiment, the step of performing nonlinear verification by substituting into the AC power flow equations includes: Based on the topology data of the distribution network, the weighted least squares method is used to perform state estimation on the voltage measurement values, as well as the load forecast data and photovoltaic output data of non-critical monitoring nodes, to obtain the voltage data of all nodes. Substitute the candidate total control increment into the AC power flow equation and solve it using the Newton-Raphson method to obtain the power setpoints for all inverters. Based on the second constraint, a feasibility assessment is performed on the full node voltage data and the power setting value, and if the feasibility assessment is passed, the review is deemed successful.

[0060] This invention retrieves voltage measurements from key monitoring nodes and load forecast data (which can be obtained by fitting historical data) and photovoltaic output data (calculated from a lighting model trained on historical data) from non-key monitoring nodes. Based on the complete topology and line impedance parameters of the distribution network, a weighted least squares state estimation model is constructed: high weights are assigned to voltage measurements at key nodes (e.g., a weight coefficient of 1.0), while lower weights are assigned to load / PV forecast data at non-key nodes (e.g., 0.1), reflecting that measured data has higher reliability than forecast data. Through iterative solving, the weighted sum of squared measurement residuals is minimized, ultimately outputting estimated voltage amplitudes and phase angles for all nodes, providing reliable initial values ​​for accurate power flow calculations.

[0061] The initial power setpoints of each inverter are element-wise superimposed with the candidate total control increment to form experimental power setpoints. Using the estimated voltage amplitude and phase angle of all nodes as initial values ​​for iteration, node power deviation equations are constructed, forming the Jacobian matrix, and Newton-Raphson iterative solutions are performed. In each iteration, the power deviation vector is calculated, and the corrected equations are solved to update the voltage amplitude and phase angle. The convergence criterion is set as the absolute value of the maximum power deviation being less than... After about 3-4 iterations, the residual rapidly decreased to below the convergence threshold, and the solution process ended stably. Thus, the actual voltage distribution of the entire network under the candidate power setting value was obtained. At the same time, the injected power at each inverter access node was directly collected, which is the actual physically achievable power setting value at the inverter end under the test condition (since the inverter node is set as a PV / PQ node in the processing, this value is the solution result, and it confirms that the system has a physically feasible solution under this setting).

[0062] The system checks whether the calculated voltage amplitudes of all nodes and the power setpoints of all inverters satisfy the inverter apparent power circle constraint and hard constraint (i.e., voltage safety constraint) in the second constraint condition. If all are satisfied, the verification status is marked as "verification passed," and the calculated inverter power setpoints are converted into standardized inverter power setpoint instructions, encapsulated into communication messages (such as IEC 61850-8-1 GOOSE messages), and sent to each photovoltaic inverter for execution via fiber optic Ethernet, completing the full closed loop of this control cycle. Furthermore, after verification, the control instructions sent to the photovoltaic inverters are as follows: In the formula, , To issue active and reactive power control commands to the nth photovoltaic inverter; The first candidate total control increment Each component corresponds to an active power reduction; The first candidate total control increment Each component corresponds to a reactive power regulation.

[0063] This invention employs the weighted least squares method, fusing limited critical node measurements with global load / photovoltaic forecast data to calculate the voltage amplitude and phase angle of non-critical nodes with high confidence. This provides necessary initial values ​​and benchmarks for subsequent accurate Newton-Raphson iterations, fundamentally solving the engineering pain point of unsolvable power flow problems due to insufficient measurements. By substituting candidate total control increments into rigorous AC power flow equations and using the Newton-Raphson method to solve for the actual physical power distribution, this invention ensures that any pseudo-optimal solution that is feasible in the approximate model but infeasible in the real physical network is rejected, greatly improving the success rate of real-world implementation of control commands.

[0064] In one embodiment, the method further includes: If the review fails, the first-level rollback mechanism is triggered, and the voltage-sensitive control increment is used as the updated candidate total control increment to re-execute the nonlinear review; If the first-level rollback fails the verification, the second-level rollback mechanism is triggered, the first objective function is updated and solved again, and the candidate total control increment is re-verified based on the re-solved result to re-execute the nonlinear verification. If the second-level rollback fails the review, the third-level rollback mechanism is triggered, and all inverters in the distribution network are switched to the local reactive power droop control mode.

[0065] Specifically, if the review fails, a multi-layered rollback mechanism is triggered: If the review fails, the first-level rollback mechanism is triggered to cancel the network loss optimization control increment, and the voltage-sensitive control increment calculated above is used as the updated candidate total control increment. The AC power flow nonlinearity review is then re-executed based on the updated candidate total control increment.

[0066] If the verification still fails after the first-level backoff, the second-level backoff mechanism is triggered, increasing the safety margin in the first objective function by 0.0005 pu to update the first objective function. The voltage-sensitive control increment is re-solved using the updated first objective function, and the candidate total control increment is updated by combining it with the network loss optimization control increment obtained from the previous calculation. The AC power flow nonlinear verification is then re-executed using the updated candidate total control increment.

[0067] If the second-level rollback verification still fails (either due to communication failure or controller malfunction), the third-level rollback mechanism is triggered. A "switch to local reactive power droop mode" flag command is broadcast to all photovoltaic inverters in the distribution network via the high-speed communication channel. Simultaneously, subsequent periodic optimization calculations are stopped at the local end, and the system enters an abnormal monitoring state. Specifically, each inverter switches to local voltage reactive power droop control as follows: In the formula, Let n be the rated reactive power capacity of the nth photovoltaic inverter; Let s be the droop factor of the nth photovoltaic inverter; The voltage amplitude of the nth photovoltaic inverter; This is the reference voltage.

[0068] Upon receiving this command (or automatically entering QV droop control if no valid command is received from the master station within a certain time window), each inverter's internal control logic automatically switches to QV droop control. Each inverter responds independently and quickly based on its local voltage deviation at its grid connection point, without needing to communicate with each other or rely on global measurement data provided by the master station. This mode can spontaneously form a distributed reactive voltage support. Although it cannot guarantee global optimization across the entire network, it can effectively clamp the voltage of each node within an acceptable engineering safety range. Simultaneously, an emergency alarm signal indicating "cooperative control failure, switched to local droop protection mode" is sent to the distribution network dispatch center. After maintenance personnel intervene to troubleshoot and repair communication or measurement problems, they can manually or remotely reset the system to exit the third-level mode and return to the normal cyclical rolling optimization startup process.

[0069] When the current invention fails the review, it often discards all optimization results or switches back to fixed parameters, resulting in excessively large actions and a lack of intermediate buffers. This solution innovatively designs a three-layer gradient backoff: the first layer sacrifices economy but retains safety; the second layer modifies the safety model itself; and the third layer enables local autonomy. This gradual process from "soft adjustment" to "hard fallback" maximizes the controllability of the system and avoids a precipitous drop from high-performance optimization to a state of no optimization.

[0070] In one embodiment, the method further includes: When the distribution network meets the safety gating conditions of the active detection mechanism, a sinusoidal detection disturbance sequence is applied to all inverters in the distribution network to obtain the voltage response data of each monitoring node; Based on the voltage response data, a voltage response matrix and a detection disturbance matrix are constructed to perform sensitivity identification and obtain a candidate sensitivity matrix. Data evaluation is performed based on the candidate sensitivity matrix, the voltage response matrix, and the detection perturbation matrix. When the evaluation is successful, a subspace drift metric is calculated based on the candidate voltage sensitive subspace determined by the candidate sensitivity matrix and the voltage sensitive subspace. When the subspace drift metric reaches a preset drift threshold, the voltage driving coefficient moment and the voltage sensitive subspace are updated based on the candidate sensitivity matrix.

[0071] Specifically, the piecewise linearization model commonly used in existing technologies relies on offline sampling and cannot adapt to the rapid random fluctuations in photovoltaic output. Therefore, this invention proposes an active detection mechanism for inverters, which utilizes the natural adjustment process of the control cycle to update the voltage drive coefficient matrix in real time. The active detection mechanism is configured such that, within the steady-state measurement window of the control cycle, the central controller applies a sinusoidal disturbance sequence with extremely small amplitude and short duration to each inverter based on its current setpoint. Frequency domain filtering is then used to decouple the voltage response of each node, thereby identifying the increment of the voltage sensitivity matrix in real time.

[0072] The active detection mechanism requires the distribution network to meet the following safety gating conditions: the voltage margin of all monitoring nodes is not less than 0.03 pu, i.e., max(V min -V,0)≤0.03 and max(VV) max The following conditions must be met: 0 ≤ 0.03; all inverter capacity margins must be no less than 10% of rated capacity; load change rate must be below the threshold (0.05 pu / s); communication status must be normal, with no packet loss or excessive latency. When the distribution network simultaneously meets the above safety threshold conditions, an active detection mechanism is triggered, and a sinusoidal detection disturbance sequence with extremely small amplitude and extremely short duration is applied to all inverters in the distribution network based on the current set value. This sequence is expressed by the following formula: In the formula, For the first Each control dimension at time The detected disturbance signal; For the first The detection amplitude of each control dimension is taken as a value of the inverter's rated capacity. to To ensure that the transient effect of the disturbance on the voltage is less than pu; To detect the frequency, each inverter uses a non-overlapping frequency band, so that the voltage response of each node can be decoupled and separated through frequency domain filtering; To control the cycle duration (s); The duration of the steady-state measurement window (in seconds) is given. It should be noted that after the control command for the τth control cycle is executed, the system enters the steady-state measurement window Δt, within which active probing is performed. Probing and normal control are performed in a time-sharing manner and do not interfere with each other.

[0073] Simultaneously, the voltage amplitude data of each monitoring node at the detection frequency is measured to form the voltage response data of each node. Since the detection frequencies of each control dimension do not overlap, bandpass filtering (or FFT spectrum analysis) is performed on the voltage time-domain signal of each monitoring node to extract the response amplitude and phase corresponding to each detection frequency component, and the voltage response matrix is ​​constructed based on this. (The complex amplitude of the voltage response at the detection frequency of the j-th key monitoring node in the ith control dimension, i.e., amplitude + phase) and the detection disturbance matrix ( The number of sampling points within the window (each row of this matrix corresponds to a perturbation time-domain sampling sequence for a control dimension) is then used to identify the estimated value of the sensitivity matrix through regularized least squares, forming a candidate sensitivity matrix (sensitivity estimated from the data in this window): In the formula, is the candidate sensitivity matrix; ρ is the regularization parameter, used to suppress noise amplification and collinearity problems, and its value is greater than 0.

[0074] Before deciding whether to update the model with the newly identified Ŝ, it is necessary to evaluate the quality of the identified data and the model's fit to avoid contaminating the model with poor-quality data. This invention evaluates data quality from three aspects: the candidate sensitivity matrix, the voltage response matrix, and the probe perturbation matrix. The residual rate is calculated (the ratio between the Frobenius norm of the difference between the actual response and the model's predicted response and the Frobenius norm of the actual response itself). A result below a preset residual threshold indicates that this aspect of the evaluation is passed. The condition number of the probe perturbation matrix is ​​also calculated. In the formula, To detect the condition number of the perturbation matrix, if the calculated condition number is less than a preset condition threshold, the evaluation of that aspect is deemed to have passed.

[0075] Calculate the number of valid sampling points (whether the number of available valid sampling points within the window reaches the preset valid number) and the proportion of outliers (whether the proportion of outliers after removing outliers is lower than the 10% threshold, with the threshold value set to 1000). If both meet the corresponding requirements, the evaluation in this aspect is considered to have passed. Only when all three evaluations pass is the identification result considered reliable and can proceed to the next step of drift determination. If at least one evaluation fails, the identification is discarded, and the active detection is terminated.

[0076] Full SVD has high computational overhead, so it's unnecessary to re-decompose the subspace every cycle. Updating the two orthogonal bases is only necessary when the subspace structure has changed significantly (e.g., runpoint drift causing a change in the sensitivity structure). Otherwise, only fine-tuning the matrix values ​​is needed, while keeping the bases unchanged.

[0077] This invention, based on the candidate sensitivity matrix, uses a small number of subspaces for iteration to obtain the candidate basis corresponding to the candidate voltage-sensitive subspace. Alternatively, the first r right singular vectors of Ŝ can be directly used as candidate bases corresponding to the candidate voltage-sensitive subspaces, and combined with the voltage-sensitive subspaces calculated above, the normalized projection matrix can be used to calculate the subspace drift metric. In the formula, This is a measure of subspace drift.

[0078] The calculated subspace drift metric reaches the preset drift threshold. When the value is (preferably 0.05), it indicates a significant shift in the subspace structure, requiring a basis update. This involves updating the voltage driving coefficient matrix using an exponential moving average method based on the candidate sensitivity matrix. This process is expressed by the following equation: In the formula, For the first The voltage drive coefficient matrix for each control cycle, which is the updated voltage drive coefficient matrix; To update the gain, a Kalman filter framework is used for adaptive determination to balance the confidence levels of historical models and current identification results. .

[0079] Simultaneously, based on the updated voltage driving coefficient matrix, a new voltage-sensitive subspace basis T is obtained through truncated SVD or subspace iteration. new At the same time, determine the new effective rank r new Based on T new The orthogonal basis N is completed using the QR basis completion method or the null space method. new ; Verify T new N new If the orthogonality is determined, the old S, T, N, and r are replaced for use in the next cycle of subspace optimization; otherwise, only the confidence level is updated or the process waits for the next window, where the confidence level is defined as... The weights are used to weight the historical model and the current identification results in subsequent optimizations.

[0080] If any of the above safety gating conditions are not met, active detection is suspended, and an alternative route estimated by natural control increment or historical data is used instead. Predictive verification is required before disturbance. If voltage or capacity exceeds limits is detected during disturbance, the disturbance is immediately terminated and the system is restored to the pre-disturbance set value.

[0081] This invention triggers an active detection mechanism under safety gating conditions to achieve online active excitation of the distribution network. This ensures that all control channels to be identified receive sufficient frequency domain excitation, thereby obtaining measurement data with high signal-to-noise ratio and high information content, fundamentally guaranteeing the accuracy and reliability of sensitivity identification. By calculating the drift metric between the candidate subspace and the existing subspace, updates are only performed when this metric exceeds a preset threshold. This ensures that the system can track significant changes caused by seasonal changes, line aging, or topology fine-tuning, while filtering out high-frequency noise interference, giving the control strategy good temporal consistency and smoothness. It also ensures that the orthogonal decomposition based on SVD always approximates the real physical characteristics, extending the validity period of the control strategy.

[0082] Synchronous phasor measurement units (PMUs) are deployed in the terminal meter boxes of the low-voltage distribution transformer area, and AEC controllers are installed at the photovoltaic access points to acquire voltage and current phasor data of the observed nodes. The control host processes the data, and when a node voltage exceeds the limit, the host calculates the photovoltaic output to bring the observed node voltage within a safe range based on the sensitivity matrix, and the AEC controller executes the adjustment command.

[0083] To verify the effectiveness of this invention, the following methods were employed: Figure 2 The power simulation system of a low-voltage distribution network with distributed photovoltaic (PV) power shown has 16 nodes. Node 0 is the slack node with a constant voltage of 220V, which serves as the reference voltage of 1.0 pu. Measuring devices are installed on nodes 7-14 and connected to the PV system, resulting in a total of 8 PV connection nodes. The PV systems have the same maximum capacity. The nodes are assumed to be equidistant, have the same cable type, and the same load capacity. The simulation parameters are shown in the table below: Table 1 Simulation System Parameter Table Supplementary simulation parameters: The simulation software is MATLAB / Simulink (version R2023b), the power flow algorithm uses the Newton-Raphson method, and the solver is the interior-point method (IPOPT). Control period T s =5s, steady-state measurement window Δt=2s, active detection frequency set is allocated in the range of 0.5-5Hz according to non-overlapping frequency bands, sampling frequency is 100Hz, window length is 200 sampling points, minimum number of complete cycles is not less than 3 cycles, frequency band spacing is not less than 0.2Hz, and Hanning window is used to suppress spectral leakage.

[0084] Acquire measurement data from each node of the system via a synchronous phasor measurement device, including the current time and several previous historical sampling points. Each set of measurement data includes active power, reactive power, and voltage amplitude data. Input the 24-hour active and reactive power output curves of the photovoltaic system under simulated cloud shading, as shown in the figure. Figure 3 , 4As shown, the photovoltaic output data is generated based on measured irradiance data of a typical summer day in a real low-voltage distribution network, with a time resolution of 1 minute, and Gaussian noise is superimposed to simulate measurement uncertainty (signal-to-noise ratio SNR = 30dB). The load curve is scaled proportionally using the IEEE European Low Voltage Test Feeder standard load model to obtain the 24-hour voltage of all observed nodes. Comparison schemes are set up: Scheme A is a photovoltaic active and reactive power coordinated control method for distribution networks based on voltage sensitivity subspace decomposition and online updating proposed in this invention; Scheme B is the standard particle swarm hard switching two-stage algorithm.

[0085] This invention uses the 16-node system of this embodiment as an example to illustrate the specific implementation process of the method of this invention: Step 1: Initialization At the initial operating point (τ=0), the voltage drive coefficient matrix S is calculated using the finite difference method. (0) ∈R 8×16 The specific operation is as follows: apply a small disturbance of 0.1% of the rated capacity to each of the 16 control variables one by one, perform an AC power flow calculation after each disturbance, record the voltage changes of the 8 monitoring nodes, and thus obtain the elements of each column of the sensitivity matrix.

[0086] Step 2: Subspace Decomposition For S (0) Perform truncated singular value decomposition. Calculate the singular value sequence and set a truncation threshold of 10. -3 The effective rank r is determined. In this embodiment, with 8 monitoring nodes and 16 control variables, r=3 is calculated, meaning the control space is reduced from 16 dimensions to a 3-dimensional voltage-sensitive subspace, a dimensionality reduction ratio of 81.25%. The right singular vector matrix is ​​divided into blocks to obtain T. (0) ∈R 16×3 N (0) ∈R 16×13 .

[0087] Step 3: Voltage-Sensitive Subspace Optimization Assume the safe voltage range is [0.95, 1.05] pu, with a safety margin μ = 0.005 pu. Construct a dimensionality-reduced optimization problem: the first objective function and its corresponding first constraint condition. Solve this 3D QCQP problem using the interior-point method to obtain the optimal voltage-sensitive subspace coordinates, and then correlate them with T. (0) Multiplying these together yields the voltage-sensitive control increment.

[0088] Step 4: Approximate Voltage Insensitive Subspace Optimization With the goal of minimizing network loss, an optimization problem is constructed in a 13-dimensional approximate voltage-insensitive subspace: a second objective function and its corresponding second constraint conditions are obtained by solving the problem to obtain the optimal approximate voltage-insensitive subspace coordinates, which are then compared with N.(0) Multiplying these together yields the incremental control for network loss optimization.

[0089] Step 5: Incremental merging and verification The voltage-sensitive control increment is added to the network loss optimization control increment to obtain the candidate total control increment. This increment is then substituted into the AC power flow equations to perform Newton-Raphson power flow calculations. The calculations verify whether the voltages of all 16 nodes are within the range of [0.95, 1.05] pu, whether all 8 inverters meet the apparent power constraints, and whether the lines are overloaded. If the verification passes, a control command is issued; if the verification fails, the hierarchical rollback process is followed.

[0090] Step 6: Online Update In each control cycle (T) s Within a steady-state measurement window (Δt=2s) of 5s, if all safety gating conditions are met, the active detection mechanism is triggered. Each inverter is subjected to a non-overlapping sinusoidal disturbance with an amplitude of 0.5%-1% of rated capacity and a frequency range of 0.5Hz-5Hz. The voltage response is measured, and the sensitivity increment is identified using regularized least squares. ,renew ( (Preferred value 0.3), calculate the subspace drift metric. If it is not less than the preset drift threshold, trigger the basis update and recalculate T and N; otherwise, retain the original basis.

[0091] Step 7: Execute repeatedly Repeat steps 2 through 6 to achieve continuous online optimization of the coordinated control of active and reactive power of photovoltaic power distribution network.

[0092] The quantitative results for these two schemes are shown in the table below: Table 2. Quantitative Comparison Results of Scheme A and Scheme B As shown in Table 2, the proposed solution outperforms existing technologies in terms of voltage limit elimination rate, light curtailment rate, network loss reduction rate, and computation time. Solution A achieves a 100% voltage limit elimination rate, with a light curtailment rate of only 2.1%, significantly lower than Solution B's 4.9%. In terms of computational efficiency, Solution A's average solution latency is 8.2 ms, approximately 95% lower than Solution B's 156.3 ms, fully demonstrating the computational advantages brought by subspace dimensionality reduction.

[0093] In the standard two-stage particle swarm optimization (PSO) hard switching algorithm of Scheme B, the particle swarm parameters are set as follows: population size 50, maximum number of iterations 200, inertia weight decreasing linearly from 0.6 to 0.4, and learning factors c1=c2=2. To further verify the acceleration effect of subspace dimensionality reduction, full-dimensional same-objective convex optimization (SOCP) is added as an equivalent accuracy baseline, with a solution latency of 142.7ms, a voltage limit violation elimination rate of 100%, a light abandonment rate of 2.3%, and a network loss reduction rate of 8.4%. Under the premise of maintaining the same control accuracy, the subspace dimensionality reduction scheme reduces the solution latency from 142.7ms to 8.2ms, a speedup of approximately 17.4 times, proving that the acceleration effect comes from subspace dimensionality reduction rather than differences in the objective, constraints, or solver. The statistical sample size for the 8.2ms average solution latency is 1000 consecutive control cycles, including the entire process time of state estimation, SVD decomposition, optimization solution, and power flow verification, with 50 warm-up cycles.

[0094] The results of the ablation test are shown in the table below: Table 3 Ablation Test Results Ablation experiments show that subspace dimensionality reduction significantly reduces computational complexity while maintaining control accuracy; economic optimization of the approximate voltage-insensitive subspace contributes the main reduction in network loss; the online update mechanism is crucial for maintaining model accuracy and voltage control performance; and AC power flow verification is a key step in ensuring the hard feasibility of voltage constraints. Robustness test scenarios include: topology changes (line N-1 disconnection), measurement noise (SNR = 20dB-40dB), communication packet loss (packet loss rate 5%-15%), parameter errors (line parameter deviation ±10%), and three-phase imbalance (imbalance degree 5%-10%). Under these scenarios, the voltage exceedance elimination rate of the proposed solution remains above 95%, verifying the robustness of the method.

[0095] This invention proposes introducing voltage sensitivity subspace decomposition of the control space into the photovoltaic coordinated control of the distribution network, realizing approximate decomposition and hierarchical coordination of voltage regulation and economic optimization based on first-order sensitivity. Existing technologies place all active and reactive power regulation dimensions in the same optimization space for mixed solution. This invention decomposes the control space into a voltage-sensitive control subspace (voltage regulation subspace) and an approximately voltage-insensitive control subspace (economic optimization subspace) by truncating SVD. This decomposition is based on the inherent sensitivity structure of the distribution network power flow equations: the voltage-sensitive subspace direction corresponds to efficient voltage control modes, while the approximately voltage-insensitive subspace direction corresponds to inefficient voltage control modes. The satisfaction of voltage constraints is transformed from a probabilistic penalty to a deterministic projection, reducing the risk of misjudgment during phase switching. Finally, residual coupling is handled through complete constraints and nonlinear verification.

[0096] This invention proposes an online adaptive update mechanism for the voltage drive coefficient matrix based on active inverter detection. Existing technologies rely on offline Monte Carlo sampling to construct segmented models, which cannot adapt to the randomness of photovoltaic power output. This invention utilizes the inverter's natural adjustment process within the control cycle to apply orthogonal frequency division multiplexing (SDM) detection perturbations, identifies the voltage drive coefficient matrix increment in real time, and updates the tangent space basis through incremental SVD. By using the inverter itself as the detection signal source, the steady-state window within the control cycle as the identification timing, and linking the incremental SVD update trigger to the tangent space drift metric, the computational load of model updates is reduced by more than 70%, and control command oscillations caused by segment boundary jumps are effectively suppressed.

[0097] This invention designs a control closed loop based on AC power flow verification and a safety backoff mechanism. Existing technologies rely solely on linear models to solve control commands, neglecting nonlinear errors and model mismatch risks. This invention, after merging the control increments of the voltage-sensitive subspace and the approximately voltage-insensitive subspace, performs AC power flow verification to validate the feasibility of all node voltages, inverter apparent power, and line constraints. When the verification fails, a hierarchical backoff and local fault degradation strategy is employed, improving the constraint feasibility under the verified model conditions.

[0098] This application proposes a method for coordinated active and reactive power control of photovoltaic power in a distribution network, addressing the challenge of achieving precise regulation of photovoltaic power in a distribution network while strictly ensuring hard feasibility under voltage constraints. The method utilizes real-time voltage sensitivity analysis to structurally orthogonally partition the high-dimensional control space according to its impact on voltage, decomposing it into a voltage-sensitive subspace and an approximately voltage-insensitive subspace. Low-dimensional deterministic optimization is performed in the voltage-sensitive subspace to strictly satisfy voltage constraints, while minimizing network losses in the approximately voltage-insensitive subspace improves operational economy. Finally, AC power flow verification is performed on the merged control increment to ensure safety and feasibility under nonlinear conditions. By leveraging the differential geometry of the voltage-power coupled manifold of the distribution network while strictly ensuring hard feasibility under voltage constraints, the high-dimensional non-convex coordinated control problem is reduced to a fundamentally low-dimensional subspace for solution, significantly improving solution efficiency and achieving precise regulation of photovoltaic power in the distribution network.

[0099] It should be noted that although the steps in the flowchart above are shown sequentially as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order requirement for the execution of these steps, and they can be executed in other orders.

[0100] In another embodiment, such as Figure 5 As shown, a second aspect of the present invention provides a photovoltaic active and reactive power coordinated control system for a power distribution network, comprising: The control space decomposition module 10 is used to obtain the control variables of the distribution network at the current operating point and the voltage measurement values ​​of key monitoring nodes, so as to orthogonally decompose the control space of the distribution network into a voltage-sensitive subspace and an approximately voltage-insensitive subspace. The first function solving module 20 is used to construct and solve a first objective function based on the voltage-sensitive subspace, with the voltage security constraints in the distribution network as hard constraints and the minimization of the adjustment amount of the control variables as the objective, so as to obtain the voltage-sensitive control increment; The second function solving module 30 is used to construct and solve a second objective function based on the approximate voltage-insensitive subspace, with the goal of minimizing the network loss of the distribution network, to obtain the network loss optimization control increment; The control command issuing module 40 is used to superimpose the voltage-sensitive control increment and the network loss optimization control increment to obtain a candidate total control increment, which is then substituted into the AC power flow equation to perform nonlinear verification, and when the verification is passed, the photovoltaic active and reactive power coordinated control command of the distribution network is issued.

[0101] It should be noted that each module in the aforementioned photovoltaic active and reactive power coordinated control system for a distribution network can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each module. For specific limitations regarding the photovoltaic active and reactive power coordinated control system for a distribution network, please refer to the limitations of the photovoltaic active and reactive power coordinated control method for a distribution network described above; both have the same function and role, and will not be repeated here.

[0102] In summary, this invention relates to the field of distribution network operation control technology, and discloses a method and system for coordinated control of photovoltaic active and reactive power in distribution networks. Based on the control variables of the distribution network at the current operating point and the voltage measurements of key monitoring nodes, the control space of the distribution network is orthogonally decomposed into a voltage-sensitive subspace and an approximately voltage-insensitive subspace. Based on the voltage-sensitive subspace, a first objective function is constructed and solved with the voltage safety constraint as a hard constraint and the adjustment of the control variables as the objective, yielding the voltage-sensitive control increment. Based on the approximately voltage-insensitive subspace, a second objective function is constructed and solved with the network loss minimization as the objective, yielding the network loss optimization control increment. The two increments are superimposed and substituted into the AC power flow equations for nonlinear verification. Upon successful verification, a coordinated control command for photovoltaic active and reactive power in the distribution network is issued. Under the premise of strictly ensuring the hard feasibility of the voltage constraint, precise regulation of photovoltaic power in the distribution network is achieved.

[0103] The various embodiments in this specification are described in a progressive manner. For directly identical or similar parts of the embodiments, refer to each other. Each embodiment focuses on its differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. It should be noted that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification.

[0104] The embodiments described above are merely preferred embodiments of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various improvements and substitutions without departing from the technical principles of this invention, and these improvements and substitutions should also be considered within the scope of protection of this application. Therefore, the scope of protection of this patent application should be determined by the scope of the claims.

Claims

1. A method for coordinated control of active and reactive power in photovoltaic power distribution networks, characterized in that, include: The control variables of the distribution network at the current operating point and the voltage measurement values ​​of key monitoring nodes are obtained so as to orthogonally decompose the control space of the distribution network into a voltage-sensitive subspace and an approximately voltage-insensitive subspace. Based on the voltage-sensitive subspace, with the voltage security constraints in the distribution network as hard constraints, and with the goal of minimizing the adjustment amount of the control variables, a first objective function is constructed and solved to obtain the voltage-sensitive control increment; Based on the approximate voltage-insensitive subspace, a second objective function is constructed and solved with the goal of minimizing the network loss of the distribution network, thereby obtaining the network loss optimization control increment; The voltage-sensitive control increment and the network loss optimization control increment are superimposed to obtain a candidate total control increment, which is then substituted into the AC power flow equation to perform nonlinear verification. When the verification is successful, a photovoltaic active and reactive power coordinated control command for the distribution network is issued.

2. The method for coordinated control of active and reactive power in a distribution network based on photovoltaic power generation according to claim 1, characterized in that, The orthogonal decomposition of the control space of the distribution network into a voltage-sensitive subspace and an approximately voltage-insensitive subspace includes: The Jacobian matrix of the voltage measurement values ​​against the control variables is used as the voltage drive coefficient matrix; Perform truncated singular value decomposition on the voltage drive coefficient matrix to obtain a right singular vector matrix and a singular value diagonal matrix; Set an adaptive truncation threshold and determine the effective rank by combining it with the singular value diagonal matrix; By decomposing the right singular vector matrix using the effective rank, the voltage-sensitive subspace and the approximately voltage-insensitive subspace are obtained.

3. The method for coordinated control of active and reactive power in a distribution network based on photovoltaic power generation according to claim 2, characterized in that, The step of orthogonally decomposing the control space of the distribution network into a voltage-sensitive subspace and an approximately voltage-insensitive subspace includes: The remaining reactive power data of each inverter is determined based on the current power output data and rated apparent power data of each inverter in the power distribution network. When the reactive power margin of the distribution network is determined to be sufficient based on the remaining reactive power data, a key node weight diagonal matrix is ​​constructed according to the voltage measurement value and the voltage security constraint, and the active power reduction marginal utility data of the distribution network is determined through the voltage driving coefficient matrix and the key node weight diagonal matrix.

4. The method for coordinated control of active and reactive power in a distribution network based on photovoltaic power generation according to claim 3, characterized in that, Based on the voltage-sensitive subspace, using the voltage security constraints in the distribution network as hard constraints, and aiming to minimize the adjustment amount of the control variables, a first objective function is constructed and solved to obtain the voltage-sensitive control increment, including: The control variables are decomposed to obtain voltage-sensitive subspace components and approximately voltage-insensitive subspace components; Based on the voltage-sensitive subspace components, the voltage security constraints in the distribution network are transformed into the hard constraints; Using the hard constraints as the first constraint condition, and minimizing the adjustment amount of the control variables as the objective, the first objective function is constructed and solved to obtain the optimal voltage-sensitive subspace coordinates; The voltage-sensitive control increment is determined based on the optimal voltage-sensitive subspace coordinates and the voltage-sensitive subspace.

5. The method for coordinated control of active and reactive power in a distribution network based on photovoltaic power generation according to claim 3, characterized in that, The construction of the first objective function with the goal of minimizing the adjustment amount of the control variable includes: An initial objective function is constructed by minimizing the adjustment amount of the control variables, and a subspace coordinate transformation is performed on the initial objective function based on the voltage-sensitive subspace to obtain the transformed objective function; Based on the marginal utility data of active power reduction, a control quantity weight matrix is ​​constructed, and the transformation objective function is modified by the control quantity weight matrix to obtain the modified objective function; The modified objective function is combined with a regularization term based on voltage-sensitive subspace coordinates to form the first objective function.

6. The method for coordinated control of active and reactive power in a distribution network based on photovoltaic power generation according to claim 3, characterized in that, Based on the approximate voltage-insensitive subspace, a second objective function is constructed and solved with the goal of minimizing the network loss of the distribution network, resulting in the network loss optimization control increment, including: Power flow calculations are performed on the distribution network to obtain network loss data; Based on the approximate voltage-insensitive subspace component, the second constraint conditions are: the inverter apparent power circle constraint determined according to the rated apparent power data of each inverter; the upper and lower bounds of reactive power determined according to the residual reactive power data of each inverter; the ramp rate constraint determined by the optimal voltage-sensitive subspace coordinates; the total upper and lower bounds of the control quantity corresponding to the control variable; the trust region constraint; and the hard constraint. The second objective function is constructed with the goal of minimizing the network loss data. Expanding the second objective function at the current running point yields a quadratic approximate objective function; Based on the approximate voltage-insensitive subspace, the quadratic approximate objective function is subjected to subspace dimensionality reduction projection to obtain the dimensionality-reduced optimized objective function; The dimensionality reduction optimization objective function is approximated by Hessian diagonalization, and the result is combined with the Tikhonov regularization term to form the final objective function for solving, thereby obtaining the optimal approximate voltage-insensitive subspace coordinates. The network loss optimization control increment is determined based on the optimal approximate voltage-insensitive subspace coordinates and the approximate voltage-insensitive subspace.

7. The method for coordinated control of active and reactive power in a distribution network based on photovoltaic power generation according to claim 6, characterized in that, The nonlinear verification by substituting into the AC power flow equations includes: Based on the topology data of the distribution network, the weighted least squares method is used to perform state estimation on the voltage measurement values, as well as the load forecast data and photovoltaic output data of non-critical monitoring nodes, to obtain the voltage data of all nodes. Substitute the candidate total control increment into the AC power flow equation and solve it using the Newton-Raphson method to obtain the power setpoints for all inverters. Based on the second constraint, a feasibility assessment is performed on the full node voltage data and the power setting value, and if the feasibility assessment is passed, the review is deemed successful.

8. The method for coordinated control of active and reactive power in a distribution network based on photovoltaic power generation according to claim 1, characterized in that, The method further includes: If the review fails, the first-level rollback mechanism is triggered, and the voltage-sensitive control increment is used as the updated candidate total control increment to re-execute the nonlinear review; If the first-level rollback fails the verification, the second-level rollback mechanism is triggered, the first objective function is updated and solved again, and the candidate total control increment is re-verified based on the re-solved result to re-execute the nonlinear verification. If the second-level rollback fails the review, the third-level rollback mechanism is triggered, and all inverters in the distribution network are switched to the local reactive power droop control mode.

9. A method for coordinated control of active and reactive power in a distribution network based on photovoltaic power according to claim 2, characterized in that, The method further includes: When the distribution network meets the safety gating conditions of the active detection mechanism, a sinusoidal detection disturbance sequence is applied to all inverters in the distribution network to obtain the voltage response data of each monitoring node; Based on the voltage response data, a voltage response matrix and a detection disturbance matrix are constructed to perform sensitivity identification and obtain a candidate sensitivity matrix. Data evaluation is performed based on the candidate sensitivity matrix, the voltage response matrix, and the detection perturbation matrix. When the evaluation is successful, a subspace drift metric is calculated based on the candidate voltage sensitive subspace determined by the candidate sensitivity matrix and the voltage sensitive subspace. When the subspace drift metric reaches a preset drift threshold, the voltage driving coefficient moment and the voltage sensitive subspace are updated based on the candidate sensitivity matrix.

10. A photovoltaic active and reactive power coordinated control system for a power distribution network, characterized in that, include: The control space decomposition module is used to obtain the control variables of the distribution network at the current operating point and the voltage measurement values ​​of key monitoring nodes, so as to orthogonally decompose the control space of the distribution network into a voltage-sensitive subspace and an approximately voltage-insensitive subspace. The first function solving module is used to construct and solve a first objective function based on the voltage-sensitive subspace, with the voltage security constraints in the distribution network as hard constraints and the minimization of the adjustment amount of the control variables as the objective, to obtain the voltage-sensitive control increment; The second function solving module is used to construct and solve a second objective function based on the approximate voltage-insensitive subspace, with the goal of minimizing the network loss of the distribution network, to obtain the network loss optimization control increment; The control command issuing module is used to superimpose the voltage-sensitive control increment and the network loss optimization control increment to obtain a candidate total control increment, which is then substituted into the AC power flow equation to perform nonlinear verification. When the verification is successful, the module issues a photovoltaic active and reactive power coordinated control command for the distribution network.

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