Distributed voltage regulation method for photovoltaic and transformer coordination in low-voltage distribution network

Abstract

The present application relates to the technical field of voltage regulation of medium and low voltage distribution network, and particularly relates to a kind of distributed voltage regulation method of low voltage distribution network photovoltaic and transformer coordination, by constructing objective function based on multi-dimensional cost, and constructing constraint condition of objective function, and then the distributed voltage regulation of multiple low voltage distribution network is carried out, that is, the augmented Lagrangian form of objective function is constructed;Discrete variable OLTC and CB are optimized and controlled in outer layer;Augmented Lagrangian function is split into upper and lower two layers, the result obtained by lower layer optimization iteration is transmitted to upper layer for optimization again, through the continuous iteration between upper distribution network dispatching center and each aggregate of lower layer, until the convergence condition is satisfied, so that the optimal output of each distributed unit is obtained.The present application effectively realizes the accurate regulation of distributed voltage.

Description

Technical Field

[0001] This invention relates to the field of voltage regulation technology for medium and low voltage distribution networks, and specifically to a distributed voltage regulation method that coordinates photovoltaic and transformer operations in multiple low voltage distribution networks. Background Technology

[0002] With the escalating global energy crisis and the advancement of new energy system construction, renewable energy sources, represented by photovoltaics, are being widely applied, and the proportion of distributed photovoltaic (PV) power connected to low-voltage users continues to increase. However, distributed PV power generation is characterized by significant intermittency, volatility, and randomness. High penetration rates can easily lead to problems such as voltage fluctuations in medium- and low-voltage distribution networks and voltage exceeding limits due to reverse power feed-through. Furthermore, medium- and low-voltage distribution networks belong to different stakeholders with conflicting operational optimization objectives. Traditional centralized control methods place stringent demands on communication and computing resources and struggle to balance the privacy and collaborative optimization needs of each stakeholder, posing a significant challenge to the safe and stable operation of the distribution network. Summary of the Invention

[0003] To address the aforementioned technical problems, the present invention aims to provide a distributed voltage regulation method for the coordinated operation of photovoltaic and transformer systems in multiple low-voltage distribution networks. The specific technical solution adopted is as follows: In a first aspect, the present invention provides a distributed voltage regulation method for the coordinated operation of photovoltaic and transformer systems in multiple low-voltage distribution networks, comprising the following steps: An objective function is constructed based on multi-dimensional costs, and constraints on the objective function are also constructed. Based on the objective function and the constraints, a distributed optimization control model for the power distribution network is constructed. Based on the constructed distributed optimization control model of the power grid, distributed voltage control of multiple low-voltage distribution networks is carried out. The process includes: Construct the augmented Lagrangian form of the objective function; The discrete variables OLTC and CB are optimized and controlled in the outer layer. The augmented Lagrangian function is split into two layers, and the result of the optimization iteration of the lower layer is passed to the upper layer for further optimization. Through continuous iteration between the upper-layer distribution network dispatch center and the lower-layer aggregates, the optimal output of each distributed unit can be obtained until the convergence condition is met.

[0004] In conjunction with the first aspect mentioned above, in some possible implementations, the multi-dimensional cost includes at least the following two costs: electricity purchase cost, photovoltaic grid integration cost, and network loss cost.

[0005] In conjunction with the first aspect mentioned above, among some possible implementation methods, an objective function is constructed based on multi-dimensional costs, and the corresponding calculation formula is as follows: In the formula: These represent the magnitude correction factors for network loss costs, photovoltaic integration costs, and electricity purchase costs, respectively. , , These represent network loss costs, photovoltaic integration costs, and electricity purchase costs, respectively. Indicates the power distribution network dispatching cycle; This represents the set of all node numbers in a medium-voltage distribution network; Represents a node Place The active power flowing out at all times; express Active power network losses within the medium-voltage distribution network at all times; express The price at which a medium-voltage distribution network purchases a unit of active power from the upper-level power grid at any given time; This represents the set of node numbers for all photovoltaic (PV) connections in a low-voltage distribution network. Indicates the first Each node The theoretical power injected into the photovoltaic system at any given moment; Indicates the first Each node at time... The actual photovoltaic power consumption; This represents the set of all node numbers in a medium-voltage distribution network; express Constant active power network losses within the low-voltage distribution network; express The price at which a medium-voltage distribution network purchases a unit of active power from the upstream power grid at any given time; F represents the objective function; This represents the function that takes the minimum value.

[0006] In conjunction with the first aspect above, in some possible implementations, the constraints of the objective function include at least the following two types of constraints: power flow constraints of the distribution network, node voltage constraints, line current constraints, active and reactive power constraints of photovoltaic equipment, transformer tap constraints, reactive power compensation equipment constraints, and node power constraints.

[0007] In conjunction with the first aspect above, in some possible implementations, the calculation formula corresponding to the power flow constraints of the distribution network is as follows: The calculation formula corresponding to the node voltage constraint is: The calculation formula corresponding to the line current constraint is: The calculation formulas corresponding to the active and reactive power constraints of the photovoltaic equipment are as follows: The calculation formula corresponding to the transformer tap constraint is: The calculation formula corresponding to the constraints of the reactive power compensation equipment is: The calculation formula corresponding to the node power constraint is: In the formula: , Let each represent a branch in the z-th scenario. exist Active and reactive power flowing through during a given time period; In the z-th scenario, Distribution network nodes at all times The voltage amplitude; Represents a set of random scenarios in the operation of the distribution network; superscript Indicates time; subscript and These respectively represent the node number and line number of the distribution network. Represents a node The set of nodes in the downstream region that are connected to it; Indicates the current in each line; These represent the active power and reactive power of each load, respectively. These represent the active power and reactive power of each distributed energy source, respectively. This represents the voltage amplitude at each node; These represent the resistance and reactance of each line, respectively. These represent the upper and lower limits of the allowable voltage amplitude at each node within the medium-voltage distribution network, respectively. express Time Node The actual operating voltage amplitude; Indicates the maximum allowable current for the circuit; express Timetable The actual operating current amplitude; Indicates the first Each photovoltaic unit in Apparent power at any given moment; Indicates the first Each photovoltaic unit in Predicted power at time; Indicates the first The rated apparent power of each photovoltaic unit; They represent the first Each photovoltaic unit in The actual active and reactive power at any given time; They represent the first Gear adjustment range, The square of the time period variation Time-of-use level, maximum level; This indicates the operating tap position of the OLTC on-load tap-changing transformer during the t-1 time period; These respectively represent the OLTC (On-Load Tap Changer, transformer tap changer) at... Time period Gear position action variable, increase gear position 0-1 auxiliary variable, decrease gear position 0-1 auxiliary variable; , They represent At time m-1, the gear position action variables of the m-th gear and the 0-1 gear of the m-th gear in the OLTC; These represent the minimum ratio of OLTC and the maximum number of adjustments allowed within the scheduling time, respectively; T represents the total number of time periods for scheduling optimization. Indicates the OLTC access point during the time period The square of the voltage amplitude; Indicates the reference voltage amplitude; express The square of the turns ratio of the on-load tap-changing transformer in the OLTC during the specified time period; Indicates the number of adjustable gears in the OLTC; They represent Device in Reactive power output during the time period, total number of output groups, and maximum number of groups; Indicates the first The number of reactive power compensation capacitor banks put into operation during the t-1 period; , They represent Time of the first 0-1 switching variables of the m-1th and mth groups of capacitors in a CB device; This indicates the maximum number of capacitor banks that can be put into operation in a single reactive power compensation capacitor bank. They represent Device exist Time period Gear position action variable, increase gear position 0-1 auxiliary variable, decrease gear position 0-1 auxiliary variable; express Each group of devices The reactive power compensation power; This represents the maximum total number of switching operations allowed for a single reactive power compensation capacitor bank within the entire dispatch cycle T. Indicates participation in the scheduling cluster middle Access node set; express Adjustable number of gears; They represent Time Node The net injected active power, load active power, and active power generated by the photovoltaic unit; , , , They represent Time Node The net injected reactive power, load reactive power, reactive power generated by photovoltaic units, and reactive power generated by reactive power compensation capacitor banks.

[0008] In conjunction with the first aspect mentioned above, in some possible implementations, the augmented Lagrangian form of the objective function is constructed based on the ADMM algorithm, and the corresponding calculation formula is as follows: In the formula: L represents the augmented Lagrangian objective function corresponding to ADMM; , They represent Medium-voltage distribution network nodes at all times Net injected active power, The total active power loss of the medium-voltage distribution network at any given time; express Time-of-use electricity pricing at any given moment; express The total active power loss of the low-voltage distribution network at all times; , , These represent the weight coefficients of different objectives in a multi-objective optimization problem; This is the set of node numbers for a medium-voltage distribution network. This is the set of node numbers for a low-voltage distribution network. This is the set of node numbers for nodes connected to a low-voltage distribution network under a medium-voltage distribution network. They are nodes exist The Lagrange multipliers corresponding to the equation constraints of active power, reactive power, and boundary voltage at each moment; These represent the penalty parameters corresponding to the equation constraints of node active power, reactive power, and boundary voltage, respectively.

[0009] In conjunction with the first aspect mentioned above, some possible implementations involve optimizing and controlling the discrete variables OLTC and CB at the outer layer, including: The outer iteration interval of OLTC is set, and the update triggering condition of OLTC adjustment decision is controlled by the preset outer iteration interval; When the OLTC regulation decision update trigger condition is met, if the voltage of any node in the low-voltage network exceeds the safety limit for any time period, the OLTC regulation decision process will be initiated. During the OLTC regulation decision-making process, if the node voltage exceeds the upper limit, the OLTC turns ratio is increased to reduce the low-voltage side voltage; if there is no overvoltage phenomenon but there is undervoltage, the OLTC turns ratio is decreased to increase the voltage. The updated OLTC turns ratio is mapped to the boundary conditions of the inner low-voltage subnet through voltage transformation relationship, so as to directly affect the voltage constraints and feasible region of the inner optimization model. The outer iteration period of the CB is set, and the triggering condition for the switching decision of the CB is controlled by the preset outer iteration period; When the outer iteration cycle trigger condition is met, the outer optimization function calculates the reactive power deficit based on the node voltage level, local reactive power injection and load information. Based on the aforementioned reactive power deficit, the switching action of CB is determined according to a preset heuristic rule; After the CB switching action is updated, the equivalent reactive power compensation generated is used as a fixed node injection amount and directly participates in the reactive power balance equation in the inner continuous optimization model, thereby adjusting the reactive power distribution of the low-voltage distribution network and improving the system voltage quality.

[0010] In conjunction with the first aspect mentioned above, in some possible implementations, the augmented Lagrangian function is split into upper and lower layers. The result obtained from the optimization iteration of the lower layer is passed to the upper layer for further optimization. Through continuous iteration between the upper-layer distribution network dispatch center and the various lower-layer aggregates until the convergence condition is met, the optimal output of each distributed unit can be obtained, including: The augmented Lagrange function is decomposed into two sub-problems, one for medium-voltage and one for low-voltage, and optimized separately. The low-voltage sub-problem aims to maximize the photovoltaic absorption rate, while the medium-voltage sub-problem aims to minimize the overall electricity purchase cost of the medium-voltage distribution network. When optimizing the low-voltage layer, the active and reactive power output of the photovoltaic units in the low-voltage layer and the boundary voltage of the low-voltage layer are used as optimization variables. The relevant parameters obtained from the optimization iteration of the medium-voltage layer are used as known quantities and substituted into the optimization objective function of the low-voltage layer for iterative optimization to obtain the optimization iteration result of the low-voltage layer. The optimization iteration results of the low-voltage layer are transferred to the medium-voltage layer. The distribution network of the medium-voltage layer uses these optimization iteration results as a basis, substitutes them into the optimization objective function of the medium-voltage layer, and performs optimization again to obtain the optimization iteration results of the medium-voltage layer. During the iteration of each sub-problem in the medium-pressure and low-pressure layers, the Lagrange multipliers are updated synchronously; Within the framework of the ADMM algorithm, the convergence condition of the iterative process is evaluated based on the original residual and dual residual at each iteration. The iteration stops when the convergence condition is met, and the output of each photovoltaic and reactive power compensation device unit obtained after stopping the iteration is taken as the optimal output of each distributed unit.

[0011] In conjunction with the first aspect above, in some possible implementations, the calculation formula corresponding to the objective function of the low-pressure layer optimization is as follows: In the formula: They represent Low-voltage distribution network nodes at all times At this point, the active power output optimization variables and reactive power output optimization variables of the photovoltaic unit are... Low-voltage interconnection nodes at all times Voltage amplitude optimization variables; , , They represent the first During the next ADMM iteration, the low-pressure node The Lagrange multipliers corresponding to the active power balance equation constraints, the Lagrange multipliers corresponding to the reactive power balance equation constraints, and the boundary nodes of medium and low voltage interconnections. The Lagrange multipliers corresponding to the voltage equality constraints; , They represent the first During the next ADMM iteration, the low-pressure node The iterative values ​​of net injected active power and net injected reactive power; , , These represent the low- and medium-voltage interconnection nodes to be determined in this iteration of the low-voltage layer. Voltage amplitude squared optimization variable, the first During the next ADMM iteration, the corresponding interconnection node on the medium-voltage side The iterative value of the square of the voltage amplitude, Low-voltage interconnection nodes at all times The voltage amplitude squared optimization variable; The calculation formula corresponding to the objective function of the intermediate-pressure layer optimization is as follows: In the formula: , They represent the first , The next iteration; Indicates the first In the next iteration, the node The iterative value of the active power output of the photovoltaic unit; , , They represent the first In the next iteration, the node The reactive power output iteration value of the photovoltaic unit, the reactive power output iteration value of the reactive power compensation capacitor bank, and the reactive power of the load; express Low-voltage interconnection nodes at all times The voltage amplitude squared optimization variable; Indicates the first In the next iteration, the low-voltage side interconnection node The iterative value of the squared voltage amplitude; , , All indicate the first Lagrange multipliers in the next iteration.

[0012] In conjunction with the first aspect above, in some possible implementations, the calculation formulas for the original residual and dual residual at each iteration of the iterative process are as follows: In the formula: Indicates the iteration step size; Indicates the first The set of optimization variables at the next iteration ; , They represent the first In the next iteration, the interconnection nodes on the medium-voltage side... The iterative value of the boundary voltage dual variable; Indicates the first The set of optimization variables for the entire system at the next iteration.

[0013] Secondly, the present invention also provides a distributed voltage regulation system for the coordinated operation of photovoltaic and transformer systems in multiple low-voltage distribution networks, including a memory and a processor. The memory is used to store executable computer program code, and the processor is used to call and run the executable computer program code from the memory, so that the system performs a distributed voltage regulation method for the coordinated operation of photovoltaic and transformer systems in multiple low-voltage distribution networks, as described in the first aspect or any possible implementation thereof.

[0014] Thirdly, the present invention also provides a computer program product comprising: computer program code, which, when executed on a computer, causes the computer to execute a distributed voltage regulation method for the coordinated operation of photovoltaic and transformer in a low-voltage distribution network, as described in the first aspect or any possible implementation thereof.

[0015] Fourthly, the present invention also provides a computer-readable storage medium storing computer program code, which, when executed on a computer, causes the computer to perform a distributed voltage regulation method for the coordinated operation of photovoltaic and transformer systems in a low-voltage distribution network, as described in the first aspect or any possible implementation thereof.

[0016] This invention offers the following advantages: By constructing an objective function based on multi-dimensional costs and establishing constraints for that objective function, it achieves precise voltage control of medium- and low-voltage distribution networks while simultaneously addressing multiple objectives such as balancing distribution network operating costs and ensuring balanced power distribution between distribution stations. By splitting the augmented Lagrangian function into two layers, the results of the lower layer's optimization iterations are passed to the upper layer for further optimization. Through continuous iteration between the upper-layer distribution network dispatch center and the various lower-layer aggregates until convergence conditions are met, the optimal output of each distributed unit is obtained. This enables dynamic adaptive adjustment of voltage regulation, effectively suppressing voltage overshoot caused by reverse power feedback, achieving high regulation efficiency, and possessing broader application scenarios. Attached Figure Description

[0017] To more clearly illustrate the technical solutions and advantages 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 these drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of a multi-objective optimization framework for a power distribution network according to an embodiment of the present invention; Figure 2 This is a flowchart illustrating the steps of a distributed voltage regulation method for photovoltaic and transformer coordination in multiple low-voltage distribution networks according to an embodiment of the present invention. Figure 3 This is a flowchart illustrating the algorithm for distributed voltage regulation in multiple low-voltage distribution networks according to an embodiment of the present invention. Figure 4 This is a topology diagram of an IEEE 33-7 node multi-low voltage distribution network example according to an embodiment of the present invention; Figure 5 This is a residual convergence graph of the ADMM algorithm in an embodiment of the present invention; Figure 6 This is a low-voltage distribution network node voltage curve diagram according to an embodiment of the present invention; Figure 7 This is a voltage curve diagram of a medium-voltage distribution network node according to an embodiment of the present invention. Detailed Implementation

[0019] To clearly illustrate the technical features of this solution, the invention will be described in detail below through specific embodiments and in conjunction with the accompanying drawings.

[0020] Embodiments of the present invention will now be described in more detail with reference to the accompanying drawings. While some embodiments of the invention are shown in the drawings, it should be understood that the invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the invention. It should be understood that the accompanying drawings and embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the invention.

[0021] It should be understood that the various steps described in the method embodiments of the present invention may be performed in different orders and / or in parallel. Furthermore, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present invention is not limited in this respect.

[0022] The term "comprising" and its variations as used herein are open-ended inclusions, meaning "including but not limited to". The term "based on" means "at least partially based on". The term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments". Definitions of other terms will be given in the description below.

[0023] It should be noted that the concepts of "first" and "second" mentioned in this invention are only used to distinguish different devices, modules or units, and are not used to limit the order of functions performed by these devices, modules or units or their interdependencies.

[0024] Although operations or steps are described in a specific order in the accompanying drawings in the embodiments of the present invention, this should not be construed as requiring these operations or steps to be performed in the specific order or serial order shown, or requiring all of the shown operations or steps to be performed to obtain the desired result. In the embodiments of the present invention, these operations or steps may be performed serially; they may be performed in parallel; or a portion of these operations or steps may be performed.

[0025] Furthermore, it is understood that the data involved in the technical solutions of this invention (including but not limited to the data itself, the acquisition or use of the data) shall comply with the requirements of relevant laws, regulations, and provisions. Unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0026] To address the problems existing in the prior art, this invention provides a scientific, reasonable, highly applicable, and effective distributed voltage regulation method for the coordinated operation of photovoltaic and transformer systems in low-voltage distribution networks. This method controls the output of distributed power sources to achieve the optimal power flow target within the distribution network while responding to frequency and voltage regulation commands from the upper-level distribution network, thus cooperating with the upper-level distribution network to achieve the goals of frequency and voltage regulation.

[0027] The following will describe in detail, with reference to the accompanying drawings, a distributed voltage regulation method for the coordinated operation of photovoltaic and transformer in a multi-low voltage distribution network provided by an embodiment of the present invention.

[0028] This invention provides a distributed voltage regulation method for the coordinated operation of photovoltaic and transformer systems in multiple low-voltage distribution networks. A schematic diagram of the optimized framework of this method is shown below. Figure 1 As shown, the process includes: First, each low-voltage distribution network feeds back its own photovoltaic output potential, voltage operating status, and adjustable resource capabilities to the medium-voltage distribution network. The medium-voltage distribution network, combining global voltage stability requirements with the actual operating characteristics of the low-voltage distribution network, generates voltage regulation guidance signals based on a long-term coordination strategy. Then, based on the established hierarchical time-varying optimization model and distributed solution principle of the medium- and low-voltage distribution networks, a tracking mechanism for the coordinated goals of voltage limit suppression and photovoltaic absorption is incorporated. Next, based on the boundary measurement feedback principle, the response characteristics of node voltage to photovoltaic injected power are calculated, thereby achieving dynamic and rapid correction of photovoltaic output within the low-voltage distribution network, reducing the impact of photovoltaic volatility and model simplification on voltage regulation accuracy. Following this, a coordinated control strategy is designed that comprehensively considers the voltage and current operating indicators of the medium- and low-voltage distribution networks, balances distribution network power flow optimization, and aims for precise voltage regulation, thereby reducing frequent and significant adjustments in photovoltaic output. Figure 2 As shown, the specific steps include: Step S100: Construct a distributed optimization control model for the power distribution network.

[0029] The process of constructing a distributed optimization control model for a power distribution network includes: constructing an objective function based on multi-dimensional costs, and constructing constraints on the objective function.

[0030] In a specific example, multi-dimensional costs include at least the following two types of costs: electricity purchase cost, photovoltaic integration cost, and network loss cost.

[0031] In a specific example, this multi-dimensional cost includes electricity purchase cost, photovoltaic (PV) grid integration cost, and network loss cost. The objective function is to minimize these three costs. Therefore, the objective function is constructed based on the multi-dimensional cost, and the corresponding calculation formula is as follows: In the formula: These represent the magnitude correction factors for network loss costs, photovoltaic integration costs, and electricity purchase costs, respectively. , , These represent network loss costs, photovoltaic integration costs, and electricity purchase costs, respectively. Indicates the power distribution network dispatching cycle; This represents the set of all node numbers in a medium-voltage distribution network; Represents a node Place The active power flowing out at all times; express Active power network losses within the medium-voltage distribution network at all times; express The price at which a medium-voltage distribution network purchases a unit of active power from the upper-level power grid at any given time; This represents the set of node numbers for all photovoltaic (PV) connections in a low-voltage distribution network. Indicates the first Each node The theoretical power injected into the photovoltaic system at any given moment; Indicates the first Each node at time... The actual photovoltaic power consumption; This represents the set of all node numbers in a medium-voltage distribution network; express Constant active power network losses within the low-voltage distribution network; express The price at which a medium-voltage distribution network purchases a unit of active power from the upstream power grid at any given time; F represents the objective function; This represents the function that takes the minimum value.

[0032] In a specific example, the constraints of the objective function include at least the following two types of constraints: power flow constraints of the distribution network, node voltage constraints, line current constraints, active and reactive power constraints of photovoltaic equipment, transformer tap constraints, reactive power compensation equipment constraints, and node power constraints.

[0033] In a specific example, the constraints of the objective function include distribution network power flow constraints, node voltage constraints, line current constraints, active and reactive power constraints of photovoltaic equipment, transformer tap changer constraints, reactive power compensation equipment constraints, and node power constraints. The calculation formula for the distribution network power flow constraints is as follows: The calculation formula corresponding to the node voltage constraint is: The calculation formula corresponding to the line current constraint is: The calculation formulas corresponding to the active and reactive power constraints of the photovoltaic equipment are as follows: The calculation formula corresponding to the transformer tap constraint is: The calculation formula corresponding to the constraints of the reactive power compensation equipment is: The calculation formula corresponding to the node power constraint is: In the formula: , Let each represent a branch in the z-th scenario. exist Active and reactive power flowing through during a given time period; In the z-th scenario, Distribution network nodes at all times The voltage amplitude; Represents a set of random scenarios in the operation of the distribution network; superscript Indicates time; subscript and These respectively represent the node number and line number of the distribution network. Represents a node The set of nodes in the downstream region that are connected to it; Indicates the current in each line; These represent the active power and reactive power of each load, respectively. These represent the active power and reactive power of each distributed energy source, respectively. This represents the voltage amplitude at each node; These represent the resistance and reactance of each line, respectively. These represent the upper and lower limits of the allowable voltage amplitude at each node within the medium-voltage distribution network, respectively. express Time Node The actual operating voltage amplitude; Indicates the maximum allowable current for the circuit; express Timetable The actual operating current amplitude; Indicates the first Each photovoltaic unit in Apparent power at any given moment; Indicates the first Each photovoltaic unit in Predicted power at time; Indicates the first The rated apparent power of each photovoltaic unit; They represent the first Each photovoltaic unit in The actual active and reactive power at any given time; They represent the first Gear adjustment range, The square of the time period variation Time-of-use level, maximum level; This indicates the operating tap position of the OLTC on-load tap-changing transformer during the t-1 time period; They represent OLTC in Time period Gear position action variable, increase gear position 0-1 auxiliary variable, decrease gear position 0-1 auxiliary variable; , They represent At time m-1, the gear position action variables of the m-th gear and the 0-1 gear of the m-th gear in the OLTC; These represent the minimum ratio of OLTC and the maximum number of adjustments allowed within the scheduling time, respectively; T represents the total number of time periods for scheduling optimization. Indicates the OLTC access point during the time period The square of the voltage amplitude; Indicates the reference voltage amplitude; express The square of the turns ratio of the on-load tap-changing transformer in the OLTC during the specified time period; Indicates the number of adjustable gears in the OLTC; They represent Device in Reactive power output during the time period, total number of output groups, and maximum number of groups; Indicates the first The number of reactive power compensation capacitor banks put into operation during the t-1 period; , They represent Time of the first The 0-1 switching variables of the m-1th and m-th groups of capacitors in a CB (Capacitor Bank, reactive power compensation device); This indicates the maximum number of capacitor banks that can be put into operation in a single reactive power compensation capacitor bank. They represent Device exist Time period Gear position action variable, increase gear position 0-1 auxiliary variable, decrease gear position 0-1 auxiliary variable; express Each group of devices The reactive power compensation power; This represents the maximum total number of switching operations allowed for a single reactive power compensation capacitor bank within the entire dispatch cycle T. Indicates participation in the scheduling cluster middle Access node set; express Adjustable number of gears; They represent Time Node The net injected active power, load active power, and active power generated by the photovoltaic unit; , , , They represent Time Node The net injected reactive power, load reactive power, reactive power generated by photovoltaic units, and reactive power generated by reactive power compensation capacitor banks.

[0034] Step S200: Based on the constructed distributed optimization control model of the distribution network, perform distributed voltage control of multiple low-voltage distribution networks.

[0035] The distributed voltage regulation online tracking solution algorithm requires continuous interaction between distributed collaborative units in the medium and low voltage layers, including voltage information, line current data, photovoltaic output, and transformer operating status of each low-voltage distribution network node. Combined with the global voltage stability guidance signal of the medium-voltage distribution network, the algorithm achieves precise voltage regulation and solution for multiple low-voltage distribution networks through distributed iterative calculation of photovoltaic output and transformer tap adjustment allocation schemes.

[0036] Specifically, such as Figure 3 As shown, the implementation process of distributed voltage regulation of multiple low-voltage distribution networks based on the constructed distributed optimization control model of the distribution network includes: 1) Construct the augmented Lagrangian form of the objective function.

[0037] When dealing with complex optimization problems, the Alternating Directional Multiplier Method (ADMM) employs a divide-and-conquer strategy. This method first introduces an extended Lagrangian function to reformulate the initial objective, then decomposes this function into several more manageable independent submodules. Each submodule is optimized independently, and once all submodules have reached a stable state, the Lagrangian multipliers are adjusted to update the global information. When all submodules tend to equilibrium, the solution to the original complex problem naturally emerges. Thanks to the rapid solution capability of the submodules, ADMM achieves a highly efficient computational flow. This method can easily adapt to diverse optimization scenarios, and the parameter setting process is intuitive and simple. Therefore, ADMM has gained widespread research interest and practical applications in the field of computational optimization.

[0038] In a specific example, the augmented Lagrangian form of the objective function is constructed according to the ADMM algorithm, and the corresponding calculation formula is as follows: In the formula: L represents the augmented Lagrangian objective function corresponding to ADMM; , They represent Medium-voltage distribution network nodes at all times Net injected active power, The total active power loss of the medium-voltage distribution network at any given time; express Time-of-use electricity pricing at any given moment; express The total active power loss of the low-voltage distribution network at all times; , , These represent the weight coefficients of different objectives in a multi-objective optimization problem; This is the set of node numbers for a medium-voltage distribution network. This is the set of node numbers for a low-voltage distribution network. This is the set of node numbers for nodes connected to a low-voltage distribution network under a medium-voltage distribution network. They are nodes exist The Lagrange multipliers corresponding to the equation constraints of active power, reactive power, and boundary voltage at each moment; These represent the penalty parameters corresponding to the equation constraints of node active power, reactive power, and boundary voltage, respectively.

[0039] 2) Perform optimal control on the discrete variables OLTC and CB in the outer layer.

[0040] In a specific example, the discrete variable OLTC is optimized and controlled at the outer layer, including: setting the outer layer iteration interval of OLTC, and the update triggering condition of OLTC regulation decision is controlled by the preset outer layer iteration interval; when the update triggering condition of OLTC regulation decision is reached, if the voltage of any node in the low-voltage network exceeds the safety limit for any time period, the OLTC regulation decision process is initiated; during the OLTC regulation decision process, if a node voltage exceeds the upper limit, the OLTC ratio is increased to reduce the low-voltage side voltage; if there is no overvoltage phenomenon and there is undervoltage, the OLTC ratio is decreased to increase the voltage; the updated OLTC ratio is mapped to the boundary conditions of the inner low-voltage subnet through voltage transformation relationship, so as to directly affect the voltage constraints and feasible region of the inner optimization model.

[0041] Specifically, the outer optimization function of OLTC uses the voltage distribution of the entire low-voltage distribution network as the basis for decision-making, rather than relying solely on the boundary node voltages. When the update trigger condition for OLTC regulation decision is met, for any given time period... If the voltage at any node in the low-voltage network exceeds the safety limit, the regulation decision process begins. If a node voltage exceeds the upper limit, the turns ratio is increased (upgrading) to reduce the low-voltage side voltage. When there is no overvoltage and undervoltage exists, the turns ratio is decreased (downgrading) to increase the voltage. OLTC regulation is performed on a slower time scale, and its update triggering condition is controlled by a preset outer iteration interval. During each update, the outer function judges the voltage over-limit trend and regulation needs based on real-time information of the medium-voltage node voltage and the low-voltage boundary voltage. Turns ratio adjustments typically follow a "single-step" principle. The updated turns ratio is determined through voltage transformation relationships. The boundary conditions of the inner low-voltage subnet are mapped onto the network, thus directly affecting the voltage constraints and feasible region of its optimization model.

[0042] In a specific example, the discrete variable CB is optimized and controlled at the outer layer, including: setting the outer layer iteration period of CB, and the triggering condition for CB switching decision is controlled by the preset outer layer iteration period; when the triggering condition of the outer layer iteration period is reached, the outer layer optimization function calculates the reactive power deficit based on the node voltage level, local reactive power injection and load information; based on the reactive power deficit, the switching action of CB is determined according to the preset heuristic rule; after the CB switching action is updated, the equivalent reactive power compensation amount generated is used as a fixed node injection amount and directly participates in the reactive power balance equation in the inner layer continuous optimization model, thereby adjusting the reactive power distribution of the low-voltage distribution network and improving the system voltage quality.

[0043] Specifically, the switching decision of the CB is also based on the outer iteration cycle trigger. The outer function calculates the reactive power deficit based on information such as node voltage level, local reactive power injection, and load, and determines the switching action according to preset heuristic rules. After the update, the equivalent reactive power compensation generated by the CB... As a fixed node injection quantity, it directly participates in the reactive power balance equation in the inner continuous optimization model. This is to adjust the reactive power distribution of the system and improve voltage quality.

[0044] 3) The augmented Lagrangian function is split into two layers, and the result obtained from the optimization iteration of the lower layer is passed to the upper layer for further optimization. Through continuous iteration between the upper-level distribution network dispatch center and the lower-level aggregates, the convergence condition is met, thereby obtaining the optimal output of each distributed unit.

[0045] The augmented Lagrangian function is split into two layers for optimization. The lower layer optimizes to minimize low-voltage network loss and curtailment. The results of the lower layer optimization are passed to the upper layer. The upper layer optimizes again to minimize distribution network operating costs and network loss. Through continuous iteration between the upper distribution network dispatch center and the lower aggregates, the optimal output of each distributed unit can be obtained until the convergence condition is met.

[0046] In a specific example, the augmented Lagrangian function is split into two layers. The result of the optimization iteration in the lower layer is passed to the upper layer for further optimization. Through continuous iteration between the upper-layer distribution network dispatch center and the various aggregates in the lower layer, the convergence condition is met, thereby obtaining the optimal output of each distributed unit. This includes: splitting the augmented Lagrangian function into two sub-problems, a medium-voltage layer and a low-voltage layer, for optimization. The low-voltage layer aims to maximize the photovoltaic absorption rate, while the medium-voltage layer aims to minimize the overall electricity purchase cost of the medium-voltage distribution network. It should be understood that maximizing the photovoltaic absorption rate is equivalent to minimizing curtailment; the higher the photovoltaic absorption rate, the smaller the curtailed photovoltaic power. Minimizing the overall electricity purchase cost of the medium-voltage distribution network is equivalent to minimizing the distribution network operating cost and network losses. The distribution network electricity purchase cost is the most critical operating cost, while line network losses directly increase the amount of electricity purchased and the cost of electricity purchase for the distribution network. Therefore, minimizing the electricity purchase cost naturally includes minimizing the operating cost plus minimizing the network losses. When optimizing the low-voltage layer, the active and reactive power outputs of the photovoltaic units and the boundary voltage of the low-voltage layer are used as optimization variables. The relevant parameters obtained from the optimization iteration of the medium-voltage layer are used as known quantities and substituted into the optimization objective function of the low-voltage layer for iterative optimization to obtain the optimization iteration result of the low-voltage layer. The optimization iteration result of the low-voltage layer is then transferred to the medium-voltage layer. The distribution network of the medium-voltage layer uses this optimization iteration result as a basis and substitutes it into the optimization objective function of the medium-voltage layer for further optimization to obtain the optimization iteration result of the medium-voltage layer. During the iteration process of each sub-problem in the medium-voltage and low-voltage layers, the Lagrange multipliers are updated synchronously. Under the framework of the ADMM algorithm, based on the original residual and dual residual at each iteration, the convergence condition of the iteration process is evaluated. The iteration stops when the convergence condition is met, and the output of each photovoltaic and reactive power compensation equipment unit obtained after stopping the iteration is taken as the optimal output of each distributed unit.

[0047] Specifically, due to the complexity of the problem, to improve the solution speed of the model, the overall augmented Lagrangian function is split into two layers, low-voltage and medium-voltage, for separate solutions. The active and reactive power output of the photovoltaic units in the low-voltage layer and the boundary voltage of the low-voltage layer are the optimization variables, while the optimization iteration of the medium-voltage layer yields the results. All quantities are known. The objective is to maximize the photovoltaic absorption rate. The objective function for optimizing the low-voltage layer is: In the formula: They represent Low-voltage distribution network nodes at all times At this point, the active power output optimization variables and reactive power output optimization variables of the photovoltaic unit are... Low-voltage interconnection nodes at all times Voltage amplitude optimization variables; , , They represent the first During the next ADMM iteration, the low-pressure node The Lagrange multipliers corresponding to the active power balance equation constraints, the Lagrange multipliers corresponding to the reactive power balance equation constraints, and the boundary nodes of medium and low voltage interconnections. The Lagrange multipliers corresponding to the voltage equality constraints; , They represent the first During the next ADMM iteration, the low-pressure node The iterative values ​​of net injected active power and net injected reactive power; , , These represent the low- and medium-voltage interconnection nodes to be determined in this iteration of the low-voltage layer. Voltage amplitude squared optimization variable, the first During the next ADMM iteration, the corresponding interconnection node on the medium-voltage side The iterative value of the square of the voltage amplitude, Low-voltage interconnection nodes at all times The voltage amplitude squared optimization variable; The medium-voltage distribution network is then optimized and iterated based on the low-voltage layer. The objective function for optimizing the medium-voltage distribution network is: To minimize the overall electricity purchase cost of the medium-voltage distribution network. In the formula: , They represent the first , iteration; Indicates the first In the next iteration, the node The iterative value of the active power output of the photovoltaic unit; , , They represent the first In the next iteration, the node The reactive power output iteration value of the photovoltaic unit, the reactive power output iteration value of the reactive power compensation capacitor bank, and the reactive power of the load; express Low-voltage interconnection nodes at all times The voltage amplitude squared optimization variable; Indicates the first In the next iteration, the low-voltage side interconnection node The iterative value of the squared voltage amplitude; , , All indicate the first Lagrange multipliers in the next iteration.

[0048] While iterating among the subproblems in the medium and low pressure layers, the Lagrange multipliers are continuously refined. The algorithm is updated until it gradually converges, yielding the optimal output of each photovoltaic and reactive power compensation unit. The update formula for the Lagrange multipliers, i.e., the dual variables, is as follows: In the formula: They represent the first During the nth iteration The sum of active power and reactive power of photovoltaics at each node; , They represent the first During the next ADMM iteration, the interconnection nodes on the medium-voltage side... The iterative values ​​of the boundary voltage dual variables and the iterative values ​​of the boundary voltage dual variables of the low-voltage side interconnection node i; , , They represent the first During the next ADMM iteration, the net injected active power iteration value, the net injected reactive power iteration value, and the total reactive power output of the distributed voltage regulation device at node i are calculated. , , All indicate the first Lagrange multipliers in the next iteration.

[0049] Within the framework of the Alternating Directional Multiplier Method (ADMM), the core criterion for evaluating whether its iterative process has terminated is the value of the residual terms. Here, we mainly examine two types of residuals: the original residual, which reflects the power balance (covering active and reactive power) and voltage matching degree of the medium- and low-voltage distribution networks at the boundary nodes; and the dual residual, defined as the change in the algorithm's key variables between the current iteration and the previous iteration. The convergence criterion is that both of the above residuals decrease to a sufficiently small level. Once this condition is met, ADMM can be considered to have successfully approximated the theoretical optimal solution of the original optimization problem. Original Residual and dual residual The formula is: In the formula: Indicates the iteration step size; Indicates the first The set of optimization variables at the next iteration ; , They represent the first In the next iteration, the interconnection nodes on the medium-voltage side... The iterative value of the boundary voltage dual variable; Indicates the first The set of optimization variables for the entire system at the next iteration.

[0050] The convergence criteria for the original residuals and dual residuals are: In the formula: These are the residual vectors. The number of elements contained therein; This represents the absolute error value allowed for algorithm convergence.

[0051] Based on the distributed voltage regulation method for photovoltaic and transformer coordination in multi-low-voltage distribution networks provided in this embodiment, an IEEE 33-7 node multi-low-voltage distribution network case study is selected to verify its effectiveness. The case study topology is as follows: Figure 4As shown in the figure. In this example, the medium-voltage side adopts the IEEE 33-node distribution system (voltage level 12.66kV), and each of its 15 nodes (2, 4, 7, 9, 11) is connected to a 7-node low-voltage distribution system (voltage level 0.4kV). Each low-voltage system with load nodes is connected to distributed photovoltaic (PV) power sources. The PV penetration rate is defined as the ratio of the maximum PV output to the maximum connected load. In the example, the PV penetration rate of each low-voltage distribution network is distributed between 118% and 284%, reflecting the high penetration rate connection characteristics. The power base capacity is set to 1MVA, the medium-voltage system node 1 is the balancing node, the maximum load is (3.715+j2.3)MVA, and the allowable voltage range of each node is 0.95~1.05pu.

[0052] Distributed solution is achieved using the Alternating Direction Multiplier Method (ADMM), and the residual convergence performance of the algorithm is as follows: Figure 5 As shown. The example sets the penalty parameter. =0.5、 =0.5、 =0.5, iteration step size =1, the allowable absolute error for algorithm convergence is... .like Figure 5 As shown, after 700 iterations, both the original residual and the dual residual decreased to [a value missing]. The convergence rate is on the order of magnitude, meets the convergence criterion, and is faster than the traditional Lagrange function method, verifying the efficiency and stability of the distributed voltage regulation method provided in this embodiment.

[0053] After adopting the distributed voltage regulation method provided in this embodiment, as follows: Figure 6 , Figure 7 As shown, the voltage at each node of the low-voltage distribution network is controlled within the allowable range of 0.95~1.05 pu, with uniform voltage distribution, effectively suppressing voltage surges caused by photovoltaic fluctuations. Similarly, the voltage at all nodes of the medium-voltage distribution network meets the constraints, and the voltage peak during peak photovoltaic periods is precisely controlled, avoiding the risk of voltage exceeding limits due to reverse power feed-through. Furthermore, this method achieves distributed coordination through limited boundary information exchange between the medium and low-voltage layers, improving photovoltaic absorption rate and reducing distribution network operating costs while ensuring voltage quality. This fully verifies its applicability and control effect in high-penetration photovoltaic access scenarios.

[0054] Based on the same inventive concept, embodiments of the present invention also provide a distributed voltage regulation system for the coordinated operation of photovoltaic and transformer systems in multiple low-voltage distribution networks. The system includes: a memory, a processor, and computer program code stored in the memory and running on the processor. When the processor executes the computer program code, the system can execute any of the aforementioned distributed voltage regulation methods for the coordinated operation of photovoltaic and transformer systems in multiple low-voltage distribution networks.

[0055] In this embodiment of the invention, the system can be divided into functional modules according to the above method example. For example, each module can correspond to a separate functional module, or two or more functions can be integrated into one processing module. The integrated module can be implemented in hardware. It should be noted that the module division in this embodiment is illustrative and only represents one logical functional division. In actual implementation, there may be other division methods.

[0056] Based on the same inventive concept, embodiments of the present invention also provide a computer program product, which includes: computer program code, which, when run on a computer, causes the computer to execute any of the aforementioned distributed voltage regulation methods for the coordinated operation of photovoltaic and transformer systems in low-voltage distribution networks.

[0057] Based on the same inventive concept, embodiments of the present invention also provide a computer-readable storage medium storing computer program code, which, when executed on a computer, causes the computer to perform any of the aforementioned distributed voltage regulation methods for the coordinated operation of photovoltaic and transformer systems in low-voltage distribution networks.

[0058] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A distributed voltage regulation method for the coordinated operation of photovoltaic and transformer systems in multiple low-voltage distribution networks, characterized in that, Includes the following steps: An objective function is constructed based on multi-dimensional costs, and constraints on the objective function are also constructed. Based on the objective function and the constraints, a distributed optimization control model for the power distribution network is constructed. Based on the constructed distributed optimization control model of the power grid, distributed voltage control of multiple low-voltage distribution networks is carried out. The process includes: Construct the augmented Lagrangian form of the objective function; The discrete variables OLTC and CB are optimized and controlled in the outer layer. The augmented Lagrangian function is split into two layers, and the result of the optimization iteration of the lower layer is passed to the upper layer for further optimization. Through continuous iteration between the upper-layer distribution network dispatch center and the lower-layer aggregates, the convergence condition is met, thereby obtaining the optimal output of each distributed unit.

2. The distributed voltage regulation method for photovoltaic and transformer coordination in multi-low-voltage distribution networks according to claim 1, characterized in that, The multi-dimensional costs include at least the following two types of costs: electricity purchase cost, photovoltaic power consumption cost, and network loss cost.

3. The distributed voltage regulation method for photovoltaic and transformer coordination in multiple low-voltage distribution networks according to claim 2, characterized in that, The objective function is constructed based on multi-dimensional costs, and the corresponding calculation formula is as follows: In the formula: These represent the magnitude correction factors for network loss costs, photovoltaic integration costs, and electricity purchase costs, respectively. , , These represent network loss costs, photovoltaic integration costs, and electricity purchase costs, respectively. Indicates the power distribution network dispatching cycle; This represents the set of all node numbers in a medium-voltage distribution network; Represents a node Place The active power flowing out at all times; express Active power network losses within the medium-voltage distribution network at all times; express The price at which a medium-voltage distribution network purchases a unit of active power from the upper-level power grid at any given time; This represents the set of node numbers for all photovoltaic (PV) connections in a low-voltage distribution network. Indicates the first Each node The theoretical power injected into the photovoltaic system at any given moment; Indicates the first Each node at time... The actual photovoltaic power consumption; This represents the set of all node numbers in a medium-voltage distribution network; express Constant active power network losses within the low-voltage distribution network; express The price at which a medium-voltage distribution network purchases a unit of active power from the upper-level power grid at any given time; F represents the objective function; This represents the function that takes the minimum value.

4. The distributed voltage regulation method for photovoltaic and transformer coordination in multi-low-voltage distribution networks according to claim 2, characterized in that, The constraints of the objective function include at least the following two types of constraints: power flow constraints of the distribution network, node voltage constraints, line current constraints, active and reactive power constraints of photovoltaic equipment, transformer tap constraints, reactive power compensation equipment constraints, and node power constraints.

5. The distributed voltage regulation method for photovoltaic and transformer coordination in multiple low-voltage distribution networks according to claim 4, characterized in that, The calculation formula for the power flow constraints of the distribution network is as follows: The calculation formula corresponding to the node voltage constraint is: The calculation formula corresponding to the line current constraint is: The calculation formulas corresponding to the active and reactive power constraints of the photovoltaic equipment are as follows: The calculation formula corresponding to the transformer tap constraint is: The calculation formula corresponding to the constraints of the reactive power compensation equipment is: The calculation formula corresponding to the node power constraint is: In the formula: , Let each represent a branch in the z-th scenario. exist Active and reactive power flowing through during a given time period; In the z-th scenario, Distribution network nodes at all times The voltage amplitude; Represents a set of random scenarios in the operation of the distribution network; superscript Indicates time; subscript and These respectively represent the node number and line number of the distribution network. Represents a node The set of nodes in the downstream region that are connected to it; Indicates the current in each line; These represent the active power and reactive power of each load, respectively. These represent the active power and reactive power of each distributed energy source, respectively. This indicates the voltage amplitude at each node; These represent the resistance and reactance of each line, respectively. These represent the upper and lower limits of the allowable voltage amplitude at each node within the medium-voltage distribution network, respectively. express Time Node The actual operating voltage amplitude; Indicates the maximum allowable current for the circuit; express Timetable The actual operating current amplitude; Indicates the first Each photovoltaic unit in Apparent power at any given moment; Indicates the first Each photovoltaic unit in Predicted power at time; Indicates the first The rated apparent power of each photovoltaic unit; They represent the first Each photovoltaic unit in The actual active and reactive power at any given time; They represent the first Gear adjustment range, The square of the time period variation Time-of-use level, maximum level; This indicates the operating tap position of the OLTC on-load tap-changing transformer during the t-1 time period; They represent OLTC in Time period Gear position action variable, gear increase 0-1 auxiliary variable, gear decrease 0-1 auxiliary variable; , They represent At time m-1, the gear position action variables of the m-th gear and the 0-1 gear of the m-th gear in the OLTC; These represent the minimum ratio of OLTC and the maximum number of adjustments allowed within the scheduling time, respectively; T represents the total number of time periods for scheduling optimization. Indicates the OLTC access point during the time period The square of the voltage amplitude; Indicates the reference voltage amplitude; express The square of the turns ratio of the on-load tap-changing transformer in the OLTC during the specified time period; Indicates the number of adjustable gears in the OLTC; They represent Device in Reactive power output during the time period, total number of output groups, and maximum number of groups; Indicates the first The number of reactive power compensation capacitor banks put into operation during the t-1 period; , They represent Time of the first 0-1 switching variables of the m-1th and mth groups of capacitors in a CB device; This indicates the maximum number of capacitor banks that can be put into operation in a single reactive power compensation capacitor bank. They represent Device exist Time period Gear position action variable, increase gear position 0-1 auxiliary variable, decrease gear position 0-1 auxiliary variable; express Each group of devices The reactive power compensation power; This represents the maximum total number of switching operations allowed for a single reactive power compensation capacitor bank within the entire dispatch cycle T. Indicates participation in the scheduling cluster middle Access node set; express Adjustable number of gears; They represent Time Node The net injected active power, load active power, and active power generated by the photovoltaic unit; , , , They represent Time Node The net injected reactive power, load reactive power, reactive power generated by photovoltaic units, and reactive power generated by reactive power compensation capacitor banks.

6. The distributed voltage regulation method for photovoltaic and transformer coordination in multiple low-voltage distribution networks according to claim 5, characterized in that, The augmented Lagrangian form of the objective function is constructed using the ADMM algorithm, and the corresponding calculation formula is as follows: In the formula: L represents the augmented Lagrangian objective function corresponding to ADMM; , They represent Medium voltage distribution network nodes at all times Net injected active power, The total active power loss of the medium-voltage distribution network at any given time; express Time-of-use electricity pricing at any given moment; express The total active power loss of the low-voltage distribution network at all times; , , These represent the weight coefficients of different objectives in a multi-objective optimization problem; This is the set of node numbers for a medium-voltage distribution network. This is the set of node numbers for a low-voltage distribution network. This is the set of node numbers for nodes connected to a low-voltage distribution network under a medium-voltage distribution network. They are nodes exist The Lagrange multipliers corresponding to the equation constraints of active power, reactive power, and boundary voltage at each moment; These represent the penalty parameters corresponding to the equation constraints of node active power, reactive power, and boundary voltage, respectively.

7. The distributed voltage regulation method for photovoltaic and transformer coordination in multi-low-voltage distribution networks according to claim 1, characterized in that, The discrete variables OLTC and CB are optimized and controlled at the outer layer, including: The outer iteration interval of OLTC is set, and the update triggering condition of OLTC adjustment decision is controlled by the preset outer iteration interval; When the OLTC regulation decision update trigger condition is met, if the voltage of any node in the low-voltage network exceeds the safety limit for any time period, the OLTC regulation decision process will be initiated. During the OLTC regulation decision-making process, if the node voltage exceeds the upper limit, the OLTC turns ratio is increased to reduce the low-voltage side voltage; if there is no overvoltage phenomenon but there is undervoltage, the OLTC turns ratio is decreased to increase the voltage. The updated OLTC turns ratio is mapped to the boundary conditions of the inner low-voltage subnet through voltage transformation relationship, so as to directly affect the voltage constraints and feasible region of the inner optimization model. The outer iteration period of the CB is set, and the triggering condition for the switching decision of the CB is controlled by the preset outer iteration period; When the outer iteration cycle trigger condition is met, the outer optimization function calculates the reactive power deficit based on the node voltage level, local reactive power injection and load information. Based on the aforementioned reactive power deficit, the switching action of CB is determined according to a preset heuristic rule; After the CB switching action is updated, the equivalent reactive power compensation generated is used as a fixed node injection amount and directly participates in the reactive power balance equation in the inner continuous optimization model, thereby adjusting the reactive power distribution of the low-voltage distribution network and improving the system voltage quality.

8. The distributed voltage regulation method for photovoltaic and transformer coordination in multi-low-voltage distribution networks according to claim 6, characterized in that, The augmented Lagrangian function is split into two layers. The result of the optimization iteration in the lower layer is passed to the upper layer for further optimization. Through continuous iteration between the upper-layer distribution network dispatch center and the various aggregates in the lower layer, the convergence condition is met, thereby obtaining the optimal output of each distributed unit, including: The augmented Lagrange function is decomposed into two sub-problems, one for medium-voltage and one for low-voltage, and optimized separately. The low-voltage sub-problem aims to maximize the photovoltaic absorption rate, while the medium-voltage sub-problem aims to minimize the overall electricity purchase cost of the medium-voltage distribution network. When optimizing the low-voltage layer, the active and reactive power output of the photovoltaic units in the low-voltage layer and the boundary voltage of the low-voltage layer are used as optimization variables. The relevant parameters obtained from the optimization iteration of the medium-voltage layer are used as known quantities and substituted into the optimization objective function of the low-voltage layer for iterative optimization to obtain the optimization iteration result of the low-voltage layer. The optimization iteration results of the low-voltage layer are transferred to the medium-voltage layer. The distribution network of the medium-voltage layer uses these optimization iteration results as a basis, substitutes them into the optimization objective function of the medium-voltage layer, and performs optimization again to obtain the optimization iteration results of the medium-voltage layer. During the iteration of each sub-problem in the medium-pressure and low-pressure layers, the Lagrange multipliers are updated synchronously; Within the framework of the ADMM algorithm, the convergence condition of the iterative process is evaluated based on the original residual and dual residual at each iteration. The iteration stops when the convergence condition is met, and the output of each photovoltaic and reactive power compensation device unit obtained after stopping the iteration is taken as the optimal output of each distributed unit.

9. The distributed voltage regulation method for photovoltaic and transformer coordination in multi-low-voltage distribution networks according to claim 8, characterized in that, The calculation formula corresponding to the objective function of the low-pressure layer optimization is as follows: In the formula: They represent Low-voltage distribution network nodes at all times At this point, the active power output optimization variables and reactive power output optimization variables of the photovoltaic unit are... Low-voltage interconnection nodes at all times Voltage amplitude optimization variables; , , They represent the first During the next ADMM iteration, the low-pressure node The Lagrange multipliers corresponding to the active power balance equation constraints, the Lagrange multipliers corresponding to the reactive power balance equation constraints, and the boundary nodes of medium and low voltage interconnections. The Lagrange multipliers corresponding to the voltage equality constraints; , They represent the first During the next ADMM iteration, the low-pressure node The iterative values ​​of net injected active power and net injected reactive power; , , These represent the low- and medium-voltage interconnection nodes to be determined in this iteration of the low-voltage layer. Voltage amplitude squared optimization variable, the first During the next ADMM iteration, the corresponding interconnection node on the medium-voltage side The iterative value of the square of the voltage amplitude, Low-voltage interconnection nodes at all times The voltage amplitude squared optimization variable; The calculation formula corresponding to the objective function of the intermediate-pressure layer optimization is as follows: In the formula: , They represent the first , The next iteration; Indicates the first In the next iteration, the node The iterative value of the active power output of the photovoltaic unit; , , They represent the first In the next iteration, the node The reactive power output iteration value of the photovoltaic unit, the reactive power output iteration value of the reactive power compensation capacitor bank, and the reactive power of the load; express Low-voltage interconnection nodes at all times The voltage amplitude squared optimization variable; Indicates the first In the next iteration, the low-voltage side interconnection node The iterative value of the squared voltage amplitude; , , All indicate the first Lagrange multipliers in the next iteration.

10. The distributed voltage regulation method for photovoltaic and transformer coordination in multi-low-voltage distribution networks according to claim 8, characterized in that, The calculation formulas for the original residual and dual residual at each iteration of the iterative process are as follows: In the formula: Indicates the iteration step size; Indicates the first The set of optimization variables at the next iteration ; , They represent the first In the next iteration, the interconnection nodes on the medium-voltage side... The iterative value of the boundary voltage dual variable; Indicates the first The set of optimization variables for the entire system at the next iteration.

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