Impedance weight-based distribution network photovoltaic load capacity optimization method and system

Abstract

The application provides a kind of impedance weight-based distribution network photovoltaic carrying capacity optimization method and system, method includes: based on distribution network topology and branch impedance parameter, impedance weight theory model is constructed, respectively the photovoltaic impedance product of each photovoltaic power supply and the load impedance product of each load are calculated;Based on impedance weight theory model, impedance space integral model is constructed, the mapping relationship of node voltage change and the cumulative effect of power on impedance path is established;With minimizing photovoltaic light rejection as optimization goal, and with impedance balance constraint and node voltage safety constraint as limiting condition, photovoltaic carrying capacity optimization model is constructed;Photovoltaic carrying capacity optimization model is solved, and the optimal photovoltaic power reduction strategy of each photovoltaic power supply is obtained;According to optimal photovoltaic power reduction strategy, the active output of each photovoltaic power supply in distribution network is coordinated and controlled, the application can not only consider the impedance physical characteristics of distribution network, but also efficiently, real-time accurately calculate the carrying capacity of distributed photovoltaic.

Description

Technical Field

[0001] This invention relates to the field of distribution network planning and operation control technology, and in particular to a method and system for optimizing the photovoltaic carrying capacity of distribution networks based on impedance weight. Background Technology

[0002] With the deepening implementation of dual-carbon power generation, a high proportion of distributed photovoltaic (PV) power grid integration has become a prominent feature of the new power system. However, the randomness and volatility of distributed PV output have altered the traditional unidirectional power flow operation mode of the distribution network, posing multiple challenges to power grid planning and operation.

[0003] First, at the physical operation level, the temporal and spatial mismatch between peak solar power generation and off-peak loads can easily lead to voltage overshooting at end nodes and reverse power flow fluctuations, increasing grid losses and threatening the reliability of protection devices. Second, at the planning and evaluation level, accurately quantifying the maximum solar power absorption capacity under a specific topology is a prerequisite for ensuring the safe operation of the power grid. Finally, at the real-time control level, there is an urgent need to achieve collaborative optimization of solar power clusters on a second- or minute-level scale to balance absorption rate and voltage security.

[0004] While existing technologies have proposed various assessment and control schemes to address the above needs, they still have the following limitations in practical applications:

[0005] Inaccurate characterization of physical characteristics: Methods based on moment difference analysis focus on overall power balance, neglecting the differences in voltage sensitivity of grid impedance distribution to different access points, leading to a disconnect between the assessment results and the actual physical process. Methods based on distributed voltage control often lack precise quantification of grid impedance weights, making it difficult to reflect the impact of electrical distance between nodes on the control effect, and easily causing under- or over-control.

[0006] Poor adaptability to dynamic and complex operating conditions: Static analysis methods based on eigenvalue indices often rely on linearized models, which overly idealize the handling of dynamic characteristics such as reactive power regulation of photovoltaic inverters. Under complex operating conditions, they are prone to underestimating the risk of system instability and cannot support instantaneous control.

[0007] The contradiction between computational efficiency and global optimization: Although methods based on traditional intelligent search algorithms have the ability to find global optimization, they face a serious "curse of dimensionality", with high computational complexity and slow convergence, making it difficult to meet the stringent requirements of real-time operation decision-making in distribution networks for response speed.

[0008] Therefore, there is an urgent need for a distribution network photovoltaic carrying capacity optimization method and system based on impedance weight, which can take into account the physical characteristics of the distribution network impedance and calculate the carrying capacity of distributed photovoltaics in a high-efficiency, real-time and accurate manner. Summary of the Invention

[0009] To address the aforementioned deficiencies in the prior art, the present invention aims to provide a method and system for optimizing the photovoltaic carrying capacity of distribution networks based on impedance weights. This method and system are intended to solve the technical problems of inaccurate assessment of photovoltaic carrying capacity of distribution networks and lagging real-time control caused by the neglect of impedance characteristics or low computational efficiency in the prior art.

[0010] To achieve the above objectives, in a first aspect, the present invention provides a method for optimizing the carrying capacity of photovoltaic distribution networks based on impedance weights, applicable to distribution networks with high penetration of distributed photovoltaic access, comprising the following steps:

[0011] S1. Based on the distribution network topology and branch impedance parameters, an impedance weighting theoretical model is constructed to calculate the photovoltaic impedance product of each photovoltaic power source and the load impedance product of each load, which is used to quantify the weighted influence of photovoltaic output and load power on the grid impedance path.

[0012] S2. Based on the impedance weighting theoretical model, an impedance space integral model is constructed to establish a mapping relationship between node voltage changes and the cumulative effect of power on the impedance path, which is used to quickly characterize the impact of photovoltaic power changes on node voltage.

[0013] S3. With minimizing photovoltaic curtailment as the optimization objective and impedance balance constraints and node voltage safety constraints as limitations, a photovoltaic carrying capacity optimization model is constructed.

[0014] S4. Solve the photovoltaic carrying capacity optimization model to obtain the optimal photovoltaic power reduction strategy for each photovoltaic power source;

[0015] S5. Based on the optimal photovoltaic power reduction strategy, coordinate and control the active power output of each photovoltaic power source in the distribution network to improve the distribution network's carrying capacity for distributed photovoltaics while meeting voltage safety constraints.

[0016] As a further improvement to the above scheme, in step S4, when solving the photovoltaic carrying capacity optimization model, the photovoltaic carrying capacity optimization model is first linearized and transformed into a quadratic programming problem. Combining the sparsity characteristics of the distribution network topology, the optimal photovoltaic power reduction strategy is obtained by using a solution method based on sparse matrix decomposition.

[0017] As a further improvement to the above scheme, the process of transforming the model into a quadratic programming problem in step S4 includes:

[0018] The impedance balance constraint is expanded using a first-order Taylor series at the initial operating point, transforming it into a function relating to the photovoltaic power reduction P. curt Linear inequality constraints;

[0019] Using the impedance space integral model, the voltage stability term in the objective function is expressed as a function of P. curtGiven a quadratic form, construct a standard quadratic programming model:

[0020] ;

[0021] ;

[0022] Where c is the linear cost vector, Q is the positive semi-definite weight matrix, b is the constraint boundary vector, and A is the constraint matrix.

[0023] ;

[0024] ;

[0025] in For a linear cost vector, its elements This reflects the economic cost of reducing photovoltaic output, and its element c i It is related to the levelized cost of electricity (LCOE) of photovoltaic power sources and the operating efficiency of inverters;

[0026] Let be the photovoltaic power reduction vector, with dimension . , Indicates the total number of photovoltaic nodes;

[0027] The weighting matrix is ​​a positive semi-definite matrix, constructed from the voltage sensitivity matrix:

[0028] ;

[0029] in This is the voltage stability weighting coefficient. For node voltage vectors, This is the photovoltaic output vector;

[0030] This is the constraint coefficient matrix, which includes linearized impedance balance constraints and voltage safety constraints;

[0031] b is the constraint boundary vector, whose physical meaning is the safety boundary threshold for system operation. This indicates that each element in the vector satisfies the less than or equal to relation.

[0032] As a further improvement to the above scheme, the steps of obtaining the optimal photovoltaic power reduction strategy based on the sparse matrix decomposition method include:

[0033] Constructing a Karouch-Kun-Tucker KKT linear system based on the distribution network topology:

[0034] ;

[0035] Where A is the constraint matrix. These are Lagrange multiplier vectors;

[0036] Taking advantage of the sparsity of the distribution network topology, a sparse Cholesky decomposition or LDL is performed on the coefficient matrix of the KKT linear system. T break down;

[0037] The matrix row and column order for reducing filler elements is determined through symbolic analysis. The KKT linear system is then solved using numerical decomposition and back-supplication operations to obtain the optimal power reduction vector. .

[0038] As a further improvement to the above scheme, the photovoltaic impedance product is the product of the photovoltaic power injection power and the equivalent impedance path between the photovoltaic grid connection point and the power node. The equivalent impedance path is obtained by the complex summation of the impedances of each branch on the path from the grid connection point to the power node.

[0039] As a further improvement to the above scheme, the load impedance product is the product of the load power and the equivalent impedance path between the load node and the power supply node, which is used to characterize the impedance cancellation effect of the load power on the photovoltaic injection power.

[0040] As a further improvement to the above scheme, the impedance balance constraint is constructed based on the sensitivity relationship between node voltage and photovoltaic active power output. By limiting the net change of the photovoltaic impedance product and the load impedance product to not exceed the system impedance balance threshold, the node voltage is prevented from exceeding the limit.

[0041] The node voltage safety constraint ensures that the voltage of each node in the distribution network is within the allowable deviation range of the rated voltage.

[0042] As a further improvement to the above scheme, the impedance space integral model is established based on the approximate expansion of the power flow model of the distribution network. By integrating the power along the impedance path, the voltage change of each node can be quickly estimated.

[0043] Secondly, the present invention also provides a distribution network photovoltaic carrying capacity optimization system based on impedance weight, comprising:

[0044] The impedance weighting modeling module is used to calculate the photovoltaic impedance product and the load impedance product based on the distribution network topology and branch impedance parameters.

[0045] Impedance space integration module is used to construct the mapping relationship between node voltage changes and power-impedance paths;

[0046] The optimization modeling module is used to build an optimization model with the goal of minimizing photovoltaic curtailment and constraints of impedance balance and voltage security.

[0047] A fast solution module is used to transform the optimization model into a quadratic programming problem and solve it based on the sparse matrix factorization method;

[0048] The control output module is used to output the optimal power reduction strategy for each photovoltaic power source.

[0049] As a further improvement to the above scheme, the fast solution module constructs a sparse matrix based on the node-branch association relationship of the distribution network, and utilizes the structural characteristics of the sparse matrix to improve the optimization solution efficiency.

[0050] As a further improvement to the above scheme, the control output module is communicatively connected to the distributed photovoltaic inverter and is used to send the optimal power reduction strategy to the corresponding photovoltaic inverter for execution.

[0051] Because the present invention adopts the above technical solutions, the beneficial effects of this application are as follows:

[0052] This invention provides a method for optimizing the photovoltaic (PV) carrying capacity of a distribution network based on impedance weighting. First, an impedance weighting theoretical model is constructed in step S1. Then, using the impedance space integral model in step S2, a physical mapping relationship between node voltage changes and power accumulation along the impedance path is established. Compared to traditional methods that neglect impedance distribution characteristics and rely on fuzzy estimation, this invention quantifies the contribution of power to voltage fluctuations through the "PV impedance product" and the "load impedance product." This modeling approach, based on the physical topology characteristics of the power grid, can more accurately characterize the impact of PV power inflow on the voltage of specific nodes, thus providing more precise data support for assessing PV carrying capacity and avoiding voltage violations or resource waste caused by assessment bias. This impedance-based modeling approach effectively improves the accuracy of voltage change prediction. Practical case studies show that in the IEEE 33-node system, the average voltage prediction error of this method can be controlled below 0.6%, which is approximately 42.9% lower than the traditional second-order cone programming method, significantly improving the accuracy of PV carrying capacity assessment.

[0053] Secondly, addressing the "curse of dimensionality" and computational lag issues inherent in existing technologies for handling high-penetration distribution networks, the optimization model constructed in this invention possesses clear physical meaning and sparsity characteristics. Because the impedance space integral model transforms complex power flow equations into a more linear mapping relationship, it significantly reduces the search space and iteration count of the optimization algorithm. This feature enables the system to achieve solution responses in the order of seconds or even milliseconds, ensuring the real-time performance of the control strategy and allowing the distribution network to quickly track fluctuations in photovoltaic output, effectively solving the technical pain point of real-time control lag. Test results on the same IEEE 33-bus system show that the time to complete one optimization solution using the method of this invention can be reduced to 0.8 seconds, with a computational efficiency more than 3200 times that of the traditional particle swarm optimization algorithm. This fully meets the speed requirements for online analysis and real-time decision-making in engineering sites, providing strong support for rapid coordinated control of photovoltaic output.

[0054] Furthermore, an impedance balance constraint is introduced into the optimization model, a feature that combines the structural strength and operating status of the power grid itself. Through impedance weight allocation, the adjustment of photovoltaic output can better conform to the natural distribution of the power grid topology, avoiding excessive regulation of local nodes. Verification through N-1 fault scenario testing shows that the method of this invention can effectively maintain optimization and control capabilities under various operating modes and fault conditions, ensuring that voltage safety constraints are always met and photovoltaic curtailment is controlled at an optimal level, demonstrating good robustness and operational stability.

[0055] Furthermore, through the optimal power reduction strategy output in step S5, this invention can achieve global coordination with the goal of minimizing curtailment while strictly adhering to the node voltage safety limit. This impedance-weighted allocation mechanism ensures that each power reduction achieves the optimal voltage improvement effect, thereby maximizing the potential of the distribution network to absorb distributed photovoltaic power. This method has simple computational logic, low hardware requirements, and high engineering application value, providing dispatching departments with a management tool that balances accuracy and execution efficiency. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art 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 the structures shown in these drawings without creative effort.

[0057] Figure 1 This is a flowchart illustrating a distribution network photovoltaic carrying capacity optimization method based on impedance weighting disclosed in Embodiment 1 of the present invention.

[0058] Figure 2This is a structural schematic diagram of the IEEE 33-node power distribution system test case disclosed in this invention.

[0059] The realization of the objective, functional characteristics and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. 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.

[0061] It should be noted that the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0062] Example 1

[0063] See Figure 1 This invention provides a method for optimizing the carrying capacity of photovoltaic distribution networks based on impedance weights, which is used in distribution networks with high penetration distributed photovoltaic access. Its structure includes multiple photovoltaic power sources, several load nodes and corresponding distribution lines. Each line has known or measured impedance parameters, and real-time operating data can be obtained through a monitoring and data acquisition system or a measurement system.

[0064] S1. Constructing the impedance weighting theoretical model:

[0065] First, based on the topology of the distribution network and the impedance parameters (including resistance R and reactance X) of each branch, an impedance weighting theoretical model is established. For each photovoltaic power source, the photovoltaic impedance product of its branch is calculated, which is the product of the photovoltaic power source's injected power and the equivalent impedance path between the photovoltaic grid connection point and the power source node; the equivalent impedance path is obtained by the complex summation of the impedances of each branch on the path from the grid connection point to the power source node.

[0066] Specifically, the photovoltaic impedance product (PV-IP) is used to quantify the weighted impact of the k-th photovoltaic power source on the grid, as shown in the following formula:

[0067] ;

[0068] For the first The photovoltaic impedance product of a photovoltaic power source, in units of It is a complex quantity that comprehensively reflects the active power injected by photovoltaics and the intensity of the impedance through which it flows; For the first The active power injected into the distribution network by a photovoltaic power source, in units of ; For the first The equivalent complex impedance path from each photovoltaic grid-connected point to the system balance node (power source point), in units of ; The resistance component of the equivalent impedance path, in units of ; The reactance component of the equivalent impedance path, in units of ; It is the imaginary unit.

[0069] The impedance parameters are calculated through power flow tracking: , To represent the distance from the equilibrium node to the th The set of all branches on the path of a photovoltaic node. For the first on the path The impedance of each branch, in units of .

[0070] For each load, the load impedance product (LD-IP) of its branch is calculated, which is the product of the load power and the equivalent impedance path between the load node and the power supply node. The LD-IP is used to quantify the weighted cancellation effect of the load, as shown in the following formula:

[0071] ;

[0072] For the first The product of the load impedances of each load, in units of It is a complex quantity that comprehensively reflects the apparent power consumed by the load and the strength of its power supply impedance path;

[0073] For the first Apparent power consumed by a load, in units of ;

[0074] For the first The equivalent complex impedance path from each load node to the system slack node, in units of... ;

[0075] The resistance component of the equivalent impedance path, in units of ;

[0076] The reactance component of the equivalent impedance path, in units of ;

[0077] By using the impedance weighting theory model, the weighted impact of photovoltaic output and load power on the grid impedance path can be quantified, enabling subsequent analysis to reflect the differences in the contribution of power sources and loads at different locations to voltage changes, and avoiding errors caused by evaluating only based on capacity ratio.

[0078] S2. Constructing the impedance space integral model:

[0079] Based on the impedance weighting theoretical model, an impedance space integral model is further established. This model establishes a mapping relationship between node voltage changes and the cumulative effect of power along the impedance path. By integrating the power-impedance product of each branch along the impedance path, the impact of photovoltaic power changes on node voltage can be quickly characterized.

[0080] Compared to traditional node-by-node power flow calculation, this model can obtain an approximate voltage response without explicitly solving the power flow equations of the entire system, thereby improving computational efficiency and making it suitable for scenarios requiring rapid evaluation and real-time control.

[0081] S3. Construct a photovoltaic load-bearing capacity optimization model:

[0082] With minimizing photovoltaic curtailment as the optimization objective, Pareto front analysis is used to determine the weights. The specific objective function is shown in the following equation:

[0083] ;

[0084] in This refers to the set of all nodes connected to the distributed photovoltaic system. For the first The active power reduction required for each photovoltaic node, in units of ; For the first The levelized cost of electricity (LCOE) of a photovoltaic power source, expressed in yuan / kWh, is used to measure the economics of the reduction. For the first Operating efficiency of a photovoltaic inverter; This is the weighting coefficient for the voltage stability term, used to balance economy and stability; The L2 norm of the voltage sensitivity vector is used to characterize the overall voltage stability of the system. The smaller the value, the lower the overall sensitivity of the node voltage to changes in photovoltaic power, and the more stable the system voltage.

[0085] Two types of constraints are introduced: impedance balance constraints and node voltage safety constraints. The impedance balance constraints are constructed based on the sensitivity relationship between node voltage and photovoltaic active power output. By limiting the net change of the photovoltaic impedance product and the load impedance product to not exceed the system impedance balance threshold, the node voltage is prevented from exceeding the limit, thereby ensuring that the power distribution under the impedance weight of each branch meets the overall power balance requirements of the distribution network.

[0086] Specifically, the impedance balance constraint is shown in the following equation:

[0087] ;

[0088] For the first The power reduction factor of a photovoltaic power source is a factor between... Variables between;

[0089] ( ) indicates the number after reduction The remaining photovoltaic impedance product of the photovoltaic power source;

[0090] This constraint requires that the net value of the adjusted total grid photovoltaic impedance product and load impedance product must be less than the system impedance balance index. This ensures the static safety of the system from a mechanistic perspective.

[0091] The node voltage safety constraint ensures that the voltage of each node in the distribution network is within the allowable deviation range of the rated voltage, thus limiting the voltage of each node to a safe range.

[0092] Specifically, the node voltage safety constraints are as follows:

[0093] ;

[0094] This is the rated voltage of the distribution network; this constraint ensures that the voltage at all nodes is within the safe range specified by national standards, that is... to Within the range.

[0095] Based on the above objective function and constraints, a photovoltaic load-bearing capacity optimization model is formed to maximize the absorption of photovoltaic power output while ensuring voltage safety.

[0096] S4. Solve the optimization model:

[0097] Numerical methods suitable for engineering applications, such as linear programming or quadratic programming, are used to solve the above-mentioned photovoltaic carrying capacity optimization model, yielding the optimal photovoltaic power reduction strategy for each photovoltaic power source. This strategy clarifies the active power output that each photovoltaic power source should reduce under given operating conditions, ensuring that the system satisfies voltage safety while minimizing curtailment.

[0098] S5. Coordinated control of photovoltaic power output:

[0099] Based on the optimal photovoltaic power reduction strategy obtained in step S4, the active power output of each photovoltaic power source in the distribution network is coordinated and controlled. The control method can be remote dispatch commands or local controller adjustments to ensure that the node voltage is maintained within a safe range during real-time operation and to maximize the photovoltaic absorption capacity.

[0100] As a preferred embodiment, in step S4, to address the technical challenges of low computational efficiency and lagging real-time control in the nonlinear model of large-scale distribution network photovoltaic carrying capacity assessment, this embodiment employs a fast solution strategy based on topological sparsity characteristics to solve the photovoltaic carrying capacity optimization model. The specific implementation steps are as follows:

[0101] S41. Model linearization and quadratic programming transformation:

[0102] First, considering the significant nonlinear characteristics of distribution network operation constraints, direct solutions are difficult to meet real-time requirements. Therefore, the photovoltaic carrying capacity optimization model constructed in step S3 is expanded using a first-order Taylor series at the initial operating point.

[0103] Transform the impedance balance constraint into a relationship with the photovoltaic power reduction factor P. curt The linear inequality constraint. Simultaneously, using the impedance space integral model, the voltage sensitivity term in the objective function is approximated as being related to P. curt The relevant quadratic forms are used to transform the original load-bearing capacity optimization problem into a standard quadratic programming (QP) model.

[0104] Specifically, first, the impedance balance constraint... At the initial running point (corresponding to the reduction coefficient vector) Perform a first-order Taylor expansion. Define the net impedance product vector. Its change is related to the power reduction. Approximately linear relationship:

[0105] ;

[0106] Net impedance product Photovoltaic power The Jacobian matrix, calculated at the initial point, characterizes the impact of reducing unit photovoltaic power on the net impedance product of the system. It is a vector consisting entirely of 1s; This means that each element in the vector is less than or equal to the element to its right.

[0107] Then the objective function The voltage sensitivity term in the equation, using the impedance space integral model, is approximately expressed as... The quadratic form. Ultimately, the original problem is transformed into a quadratic programming problem of the following form:

[0108] ;

[0109] ;

[0110] For a linear cost vector, its elements This corresponds to the economic part of the objective function; The weighting matrix is ​​a positive semi-definite matrix, corresponding to the voltage stability part of the objective function, and can be derived from the sensitivity matrix. It is deduced that, i.e. ; This is the constraint matrix, which includes the coefficients of the linearized impedance balance constraint and the voltage safety constraint. These are the constraint boundary vectors.

[0111] Through the above transformation, the original problem is reconstructed into a standard quadratic programming problem. Compared to nonlinear models, quadratic programming problems are supported by mature convex optimization theory, ensuring that a globally optimal photovoltaic reduction strategy is found in a very short time, avoiding the problem of traditional algorithms easily getting trapped in local optima.

[0112] S42. When solving the above quadratic programming problem, considering the inherent sparsity of the distribution network in its physical structure, graph theory techniques are introduced for matrix optimization:

[0113] As a radial or weakly looped network structure, the distribution network exhibits extremely high sparsity in its node-branch correlation matrix and Laplace matrix. This embodiment constructs a Karouch-Kuhn-Tucker (KKT) linear system using graph theory, allowing the core equations for solving the quadratic programming problem to inherit this sparsity.

[0114] Specifically, matrix sparsification mapping: representing the distribution network as... Construct a node-branch association matrix and the corresponding Laplace matrix ;

[0115] KKT System Construction: Based on the Karouch-Kun-Tucker (KKT) conditions of the quadratic programming problem, a system containing Lagrange multiplier vectors is constructed. The system of linear equations. Due to the sparse properties of the topology inherited by the coefficient matrix Q and the constraint matrix A, the entire KKT linear system exhibits highly sparsity characteristics.

[0116] By utilizing sparse matrix storage and computation, memory usage during the computation process can be significantly reduced, and invalid zero elements can be eliminated, providing a computational foundation for handling complex power distribution networks with thousands of nodes.

[0117] S43. Sparse Matrix Decomposition and Optimal Strategy Acquisition:

[0118] For the constructed sparse KKT system, a solution method based on sparse matrix factorization is adopted. The core step is to solve the linear system derived from its corresponding Karouch-Kun-Tucker conditions:

[0119] ;

[0120] Let be the Lagrange multiplier vector, corresponding to the dual variables of the constraint. This is a linear cost vector, corresponding to the economic penalty term for photovoltaic power reduction in the objective function. During the solution process... The guiding model prioritizes retaining photovoltaic power output with high economic benefits and high efficiency, thereby minimizing the economic losses of curtailment across the entire grid while ensuring safety. The constraint boundary vector corresponds to the linearized system safety constraint limits. It defines the "red line" of power fluctuations that the power grid can tolerate under the current topology, ensuring that the optimized photovoltaic power will not cause voltage over-limit or reverse power flow, which would lead to protection malfunctions.

[0121] Due to the coefficient matrix and It is sparse, and the coefficient matrix of the above linear system is also sparse. This invention uses Cholesky decomposition or LDL. T Efficient solutions are obtained using sparse matrix decomposition techniques. The specific steps are as follows:

[0122] Symbolic analysis: Determine the matrix row and column order for reducing filler elements based on the system topology.

[0123] Numerical decomposition: Perform sparse Cholesky decomposition on the coefficient matrix, i.e. ,in It is a permutation matrix. It is a sparse lower triangular matrix. It is a diagonal matrix.

[0124] Previous generation and back generation: utilizing the decomposed and The system of equations is solved quickly through forward and backward substitution operations to obtain the optimal photovoltaic power reduction vector.

[0125] S44. Algorithm Convergence and Output:

[0126] Set the convergence tolerance to When satisfied The iteration terminates when the time is reached. The final output parameters are:

[0127] Optimal power reduction vector This vector contains information about each photovoltaic node. The optimal active power value that should be reduced.

[0128] Optimal power reduction coefficient vector It can be accessed through The calculated values ​​are then directly distributed to each photovoltaic inverter for execution.

[0129] This method significantly improves the system's computational efficiency. Taking the IEEE 33-bus system as an example, the solution time can be reduced to 0.8 seconds, representing a computational efficiency more than 3200 times higher than the traditional particle swarm optimization algorithm. This millisecond-level response capability effectively addresses the problem of instantaneous voltage exceedances caused by photovoltaic power output fluctuations, truly achieving real-time assessment and control.

[0130] It should be noted that the system impedance balance index (IBI) is based on the voltage sensitivity obtained by inverting the Jacobian matrix of the power flow calculation, and is used to define the system-level carrying capacity threshold. This serves as a criterion for determining whether a system is safe and stable.

[0131] ;

[0132] The system impedance balance index is the threshold value for the maximum change in impedance product that the system can withstand under its current state, measured in units of... or ; Total number of distribution network nodes; Node index, ; For the first The voltage of the first node is related to the first node voltage. The sensitivity of a photovoltaic power source's active power output, measured in units of... ; For the first The change in active power of a photovoltaic power source, in units of ; : No. The voltage at each node, in units of or ; The upper limit of the allowable node voltage is usually set according to the standard. .

[0133] As a preferred embodiment, the impedance space integral model is established based on the approximate expansion of the power flow model of the distribution network. By integrating the power along the impedance path, the voltage change of each node can be quickly estimated.

[0134] First, based on the pre-established impedance weighting theoretical model, an impedance space integral model is further constructed. The impedance weighting theoretical model has clearly defined the basic correlation between the impedance of each branch of the power grid and the node voltage response. This embodiment strengthens the characterization of the cumulative effect of power on the impedance path by introducing space integral operations, breaking through the limitation of traditional models that can only reflect the local impedance influence, and realizing a global and continuous description of the impact of photovoltaic power changes on node voltage.

[0135] The impedance space integral model uses the node voltage change as the dependent variable and the cumulative effect of power along the impedance path as the independent variable, establishing a one-to-one mapping relationship between the two. Specifically, by continuously integrating the power-impedance product of each branch along the grid impedance path, the discrete branch power and impedance parameters are transformed into continuous spatial integral variables. This allows for the rapid capture of the comprehensive impact of photovoltaic power fluctuations on the target node voltage after power changes in each branch are transmitted through the impedance path, significantly improving the timeliness and accuracy of voltage response characterization.

[0136] To derive the spatial mapping relationship between voltage change and power-impedance integral, this embodiment is based on the DistFlow power flow model. By Taylor expansion and ignoring higher-order terms, the model complexity is simplified while ensuring calculation accuracy.

[0137] The DistFlow power flow model is a classic model for power flow calculation in distribution networks. Its core equations accurately describe the nonlinear relationship between node power, branch impedance, and node voltage. However, the integration of photovoltaic power causes node power fluctuations, leading to nonlinear voltage changes. Directly solving the DistFlow model is complex and time-consuming, failing to meet the need for rapid characterization. Therefore, this embodiment performs a Taylor expansion on the DistFlow power flow model, transforming the nonlinear equations into linear approximations. The specific process is as follows:

[0138] The steady-state operating point before photovoltaic power fluctuations is selected as the reference point for the Taylor expansion. Let the voltage at node i at the reference point be U. i0 The branch power is P0, Q0, and the branch resistance is R. i The reactance is X i The relationship equations between node voltage, power, and impedance in the DistFlow model are expanded using a first-order Taylor series at the baseline. First-order terms are retained, while second-order and higher-order terms (O(ΔU²), where ΔU is the second-order term representing the voltage change) are ignored. This eliminates the impact of nonlinear terms on computational efficiency, resulting in the following voltage recursive relationship:

[0139] ;

[0140] In the formula: For the first Voltage amplitude at each node; For the first The node (the first) The voltage amplitude of the upstream adjacent nodes of each node; For the branch road Net active power ( ), unit is ; For the branch road Net reactive power, in units of ; branch road The resistance, in units of ; branch road Reactance, in units of ; Voltage amplitude at the reference node (balance node) These are higher-order terms in the Taylor expansion, which are ignored in this embodiment to simplify the model and improve computation speed.

[0141] Based on the linear approximation equation obtained from the Taylor expansion above, the impedance space integral variable is further introduced to derive the node voltage change ΔU. i Spatial mapping relationship with power-impedance integral. Define the impedance path integral variable W as the cumulative impedance parameter along the power grid impedance path. Its physical meaning is the cumulative impedance value from the reference node to the target node i, reflecting the comprehensive impact of the impedance path on power transfer.

[0142] Combined with net active power ( Injecting power into photovoltaics, (For the node load power), a differential transformation is performed on the voltage recursive equation, transforming the discrete node voltage recursive relationship into a continuous spatial integral relationship. This is achieved by integrating the power-impedance product of each branch along the impedance path W, taking into account the denominator in the linearization approximation. Since it is a constant, the voltage change ΔU is finally derived. i The expression for (i.e., the impedance space integral model) is as follows:

[0143] ;

[0144] in, The voltage change of the i-th node relative to the reference node; W i-1 W represents the cumulative impedance from the reference node to the (i-1)th node. iLet be the cumulative impedance from the reference node to the i-th node; To travel along the impedance path from the first The node to the first The power-impedance integral of each node represents the cumulative contribution of net power to voltage change along that path segment.

[0145] This model intuitively represents the change in node voltage as the integral effect of net power on the impedance path, providing a theoretical basis for rapid estimation of voltage changes.

[0146] Through the above derivation, the impedance space integral model is constructed. The impedance space integral model closely correlates the power-impedance characteristics of each branch with node voltage changes through integration operations. Compared with the traditional impedance weight model, it has the following advantages: First, by ignoring higher-order terms in Taylor expansion, the computational complexity of the model is significantly reduced, enabling rapid characterization of the impact of photovoltaic power changes on node voltage; second, based on space integration operations, it can fully capture the cumulative effect of power on the impedance path, avoiding errors caused by neglecting local parameters, thus improving the accuracy of voltage response characterization; third, the model expression is concise and can be directly embedded into photovoltaic grid-connected voltage regulation algorithms, providing theoretical support for real-time voltage optimization.

[0147] It should be noted that higher-order terms are ignored in this embodiment. In scenarios where photovoltaic power fluctuations are relatively small, the impact of calculation errors can usually be controlled within an acceptable range, such as... If the photovoltaic power fluctuates significantly, the influence of higher-order terms can be corrected through iterative calculations to further improve the model accuracy.

[0148] To further illustrate the inventive concept of this invention, the following example uses the modification and optimization of a typical IEEE 33-node power distribution system. Figure 2 The diagram illustrates the specific implementation process of the method of this invention. The system has a rated voltage of 12.66kV and a total load of 3.715MW + j2.300Mvar. Distributed photovoltaic (PV) power sources are connected to nodes 10, 14, 16, 18, 19, 22, 24, 27, 31, and 32, with a total installed capacity of 1000kW. The PV daily output curve is generated using the PVWatts model, with 14:00 being the peak output time; therefore, this time is selected for load-bearing capacity assessment and optimization. The specific steps include:

[0149] Step 1: Data Preparation and Initialization

[0150] Obtain distribution network topology parameters: including the resistance of all branches in the system. and reactance .

[0151] Obtain operating status parameters: including load power of each node. And the initial output of each photovoltaic node. .

[0152] Initialization optimization parameters: including the levelized cost of electricity (LCOE) for photovoltaic power. (Can be set to a uniform or differential value based on local data), Inverter efficiency (usually set to 0.98), and voltage stability weighting factor. This can be initially set through preliminary Pareto front analysis, for example, 0.1.

[0153] Step 2: Construct the impedance weighting model:

[0154] Calculate the photovoltaic / load impedance product: Use forward-backward power flow calculation or power flow tracking method to determine the photovoltaic nodes. and load nodes Equivalent photovoltaic impedance to the equilibrium node and equivalent load impedance For example, for node 18, its It is the sum of the impedances of branches 1-2, 2-3, 3-4, ..., 17-18.

[0155] According to the formula and The impedance product of all photovoltaic and load components is calculated. This process transforms the abstract power injection into a weighted quantity with explicit physical meaning that is closely related to the grid structure.

[0156] Determine the system impedance balance index (IBI): On platforms such as MATLAB, use toolkits such as MATPOWER to perform power flow calculations on the initial state and obtain the Jacobian matrix.

[0157] By obtaining the inverse of the Jacobian matrix, the sensitivity matrix of each node voltage to each photovoltaic output can be obtained. .

[0158] Set voltage upper limit constraint The goal is to find the power change that ensures the maximum voltage deviation just doesn't exceed a certain limit by solving an optimization problem. Therefore, the bearing capacity threshold of this system is determined. .

[0159] Step 3: Establish and solve the optimization model:

[0160] Constructing the objective function and constraints: Substitute the data obtained in steps one and two into the following model:

[0161] Objective function: ;

[0162] Constraint 1 (Impedance Balance): ,in Let be the power reduction factor to be determined. .

[0163] Constraint 2 (Voltage Safety): .

[0164] Model solution: Construct the node-branch correlation matrix of the system, and then obtain its Laplace matrix. .

[0165] The above optimization model is solved quickly using a sparse matrix solving algorithm based on Cholesky decomposition; the convergence tolerance is set to... When satisfied When the iteration terminates, the optimal power reduction decision vector is output. .

[0166] Step 4: Results Analysis and Execution Control

[0167] Results Verification: The photovoltaic curtailment commands obtained from the optimization solution for each node were sent to each photovoltaic inverter or set in its local controller, and then power flow calculation was performed again. The results show that before optimization, the voltage of nodes 15-18 exceeded the limit; however, after optimization using the method of this invention, the voltage of all nodes could be restored to the safe range, and the total curtailment was minimized.

[0168] To verify the superiority of this invention, it is compared with traditional particle swarm optimization (PSO) and second-order cone programming (SOCP) methods. The method of this invention has significant advantages in voltage control accuracy, impedance product deviation, and computation time.

[0169] The final Commands are sent to the corresponding distributed photovoltaic inverters via the power communication network. Hardware-in-the-loop testing shows that the entire dynamic response process, from detecting a voltage over-limit to completing optimization calculations and issuing commands, can be completed within 200 milliseconds, meeting real-time control requirements.

[0170] This specific embodiment clearly demonstrates how the technical solution of the present invention can be applied to a specific power distribution network case, and through detailed steps and data analysis, it confirms the effectiveness, accuracy and efficiency of the present invention in improving the distributed photovoltaic absorption capacity.

[0171] Example 2

[0172] This invention also provides a distributed photovoltaic (PV) carrying capacity optimization system for distribution networks based on impedance weighting theory. This system, through the collaboration of hardware and software modules, transforms the physical topology characteristics of the power grid into quantitative decision commands, aiming to solve the voltage exceedance and regulation lag problems caused by high-penetration PV integration. Specifically, it includes:

[0173] The impedance weighting modeling module first obtains the topology parameters of the distribution network and identifies the resistance R and reactance X of each branch. The module then calculates a weighted average of the active power injected by the photovoltaic / load and its equivalent complex impedance path to the power source by defining the photovoltaic impedance product and the load impedance product.

[0174] This module not only considers the power level, but also more accurately quantifies the coupling relationship between the access location and the grid impedance path, thus solving the evaluation bias caused by the neglect of differences in electrical distance between nodes in existing technologies.

[0175] The impedance space integration module, based on the Taylor expansion of the DistFlow power flow model, constructs a spatial mapping relationship between node voltage changes and the "power-impedance" path integral. This mapping relationship reveals the underlying mechanism of voltage fluctuations, enabling high-precision sensing of node voltage changes, and allowing voltage prediction errors to be controlled below 0.6% in typical systems.

[0176] The optimization modeling module constructs a multi-objective optimization model with the goal of minimizing photovoltaic curtailment, and sets impedance balance index and voltage range specified by national standards as core constraints. By introducing the IBI index as a balance criterion, the system possesses a clear stability boundary, significantly improving control robustness under different operating modes.

[0177] The fast solution module first linearizes the nonlinear impedance balance constraint and transforms the objective function into a quadratic programming problem using an impedance space integral model. In this linear system, a linear cost vector *c* is introduced to reflect cost reduction, and a constraint boundary vector *b* reflects safety limits. Based on the natural radial topology of the distribution network, the module constructs the node-branch correlation matrix and Laplace matrix using graph theory. Due to the large number of zero elements in the matrix, the module optimizes the matrix row and column order through symbolic analysis and employs sparse Cholesky decomposition or LDL. T Decomposition techniques are used to solve KKT linear systems. By utilizing the structural properties of sparse matrices, the system avoids the redundant overhead of full matrix operations.

[0178] The control output module outputs the optimal power reduction vector and its corresponding reduction coefficient. This module is connected in real time to the distributed photovoltaic inverters in the field via a power communication network, directly sending decision commands to the inverter's actuators.

[0179] Hardware-in-the-loop testing shows that the entire dynamic response process, from detecting a voltage over-limit to issuing a command, can be completed within 200 milliseconds. This efficient closed-loop control mechanism ensures that the grid's absorption capacity of distributed photovoltaic power is maximized while guaranteeing grid security.

[0180] The above are merely preferred embodiments of the present invention and do not limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention's specification and drawings under the inventive concept of the present invention, or direct or indirect applications in other related technical fields, are within the patent protection scope of the present invention.

Claims

1. A method for optimizing the carrying capacity of photovoltaic distribution networks based on impedance weights, applied to distribution networks with high penetration of distributed photovoltaic (PV) access, characterized in that, The steps include: S1. Based on the distribution network topology and branch impedance parameters, an impedance weighting theoretical model is constructed to calculate the photovoltaic impedance product of each photovoltaic power source and the load impedance product of each load, which is used to quantify the weighted influence of photovoltaic output and load power on the grid impedance path. The photovoltaic impedance product is the product of the photovoltaic power source injection power and the equivalent impedance path between the corresponding photovoltaic grid connection point and the power source node. The equivalent impedance path is obtained by the complex summation of the branch impedances on the path from the grid connection point to the power source node. The load impedance product is the product of the load power and the equivalent impedance path between the load node and the power source node. S2. Based on the impedance weighting theoretical model, an impedance space integral model is constructed to establish a mapping relationship between node voltage changes and the cumulative effect of power along the impedance path, which is used to quickly characterize the impact of photovoltaic power changes on node voltage; wherein, the impedance space integral model is established based on the approximate expansion of the distribution network power flow model, and the voltage change of each node is quickly estimated by integrating the power along the impedance path. S3. With minimizing photovoltaic curtailment as the optimization objective and impedance balance constraints and node voltage safety constraints as limitations, a photovoltaic carrying capacity optimization model is constructed. The impedance balance constraints are constructed based on the sensitivity relationship between node voltage and photovoltaic active power output, and the node voltage safety constraints limit the voltage of each node in the distribution network to be within the allowable deviation range of the rated voltage. S4. Solve the photovoltaic carrying capacity optimization model to obtain the optimal photovoltaic power reduction strategy for each photovoltaic power source; S5. Based on the optimal photovoltaic power reduction strategy, coordinate and control the active power output of each photovoltaic power source in the distribution network.

2. The method for optimizing the photovoltaic carrying capacity of a distribution network based on impedance weighting according to claim 1, characterized in that, In step S4, when solving the photovoltaic carrying capacity optimization model, the photovoltaic carrying capacity optimization model is first linearized and transformed into a quadratic programming problem. Combining the sparsity characteristics of the distribution network topology, the optimal photovoltaic power reduction strategy is obtained by using a solution method based on sparse matrix decomposition.

3. The method for optimizing the photovoltaic carrying capacity of a distribution network based on impedance weighting according to claim 2, characterized in that, Step S4, which transforms the model into a quadratic programming problem, includes: The impedance balance constraint is expanded using a first-order Taylor series at the initial operating point, transforming it into a function relating to the photovoltaic power reduction. P curt Linear inequality constraints; Using the impedance space integral model, the voltage stability term in the objective function can be expressed as... P curt Given a quadratic form, construct a standard quadratic programming model: ； ； in It is a linear cost vector, reflecting the economic cost of reducing photovoltaic output; Let be the photovoltaic power reduction vector, with dimension . , Represents the total number of photovoltaic nodes; Q is a positive semi-definite weight matrix. b is the constraint coefficient matrix, including the linearized impedance balance constraint and voltage safety constraint; b is the constraint boundary vector. This indicates that each element in the vector satisfies the less than or equal to relation.

4. The method for optimizing the photovoltaic carrying capacity of a distribution network based on impedance weights according to claim 3, characterized in that, The steps of obtaining the optimal photovoltaic power reduction strategy using the sparse matrix decomposition-based solution method include: Constructing a Karouch-Kun-Tucker KKT linear system based on the distribution network topology: ； Where A is the constraint matrix. These are Lagrange multiplier vectors; Taking advantage of the sparsity of the distribution network topology, a sparse Cholesky decomposition or LDL is performed on the coefficient matrix of the KKT linear system. T break down; The matrix row and column order for reducing filler elements is determined through symbolic analysis. The KKT linear system is then solved using numerical decomposition and back-supplication operations to obtain the optimal power reduction vector. .

5. A distribution network photovoltaic carrying capacity optimization system based on impedance weight, based on the distribution network photovoltaic carrying capacity optimization method based on impedance weight as described in any one of claims 1-4, characterized in that, include: The impedance weighting modeling module is used to calculate the photovoltaic impedance product and the load impedance product based on the distribution network topology and branch impedance parameters. Impedance space integration module is used to construct the mapping relationship between node voltage changes and power-impedance paths; The optimization modeling module is used to build an optimization model with the goal of minimizing photovoltaic curtailment and constraints of impedance balance and voltage security. A fast solution module is used to transform the optimization model into a quadratic programming problem and solve it based on the sparse matrix factorization method; The control output module is used to output the optimal power reduction strategy for each photovoltaic power source.

6. The distribution network photovoltaic carrying capacity optimization system based on impedance weight according to claim 5, characterized in that, The fast solution module constructs a sparse matrix based on the node-branch relationship of the distribution network, and utilizes the structural characteristics of the sparse matrix to improve the optimization solution efficiency; The control output module is communicatively connected to the distributed photovoltaic inverter and is used to send the optimal power reduction strategy to the corresponding photovoltaic inverter for execution.

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