Low-voltage transformer area loss reduction optimization method suitable for photovoltaic grid connection

Abstract

The invention discloses a low-voltage transformer area loss reduction optimization method suitable for photovoltaic grid connection, belongs to the technical field of power system optimization and new energy grid connection, and aims at challenges such as voltage fluctuation and network loss increase caused by distributed photovoltaic grid connection to construct a load flow calculation model through multi-source data through processing. The investment construction cost, the operation maintenance cost and the network loss cost are comprehensively considered, an optimization model with loss reduction as a target is established, the model fuses conventional power flow constraints, power quality constraints and to-be-planned equipment operation constraints, and efficient solving is performed by adopting a mixed solving algorithm of generalized Benders decomposition and an external approximation algorithm; and finally, outputting energy storage, reactive power planning and other loss reduction optimization schemes and an optimized line loss result. The economical efficiency and safety of the low-voltage transformer area are effectively improved, and scientific support is provided for power distribution network line loss management.

Description

Technical Field

[0001] This invention belongs to the field of power system optimization and new energy grid connection technology, specifically a low-voltage distribution area loss reduction optimization method adapted to photovoltaic grid connection. Background Technology

[0002] With the deepening of the "dual carbon" goals and the full implementation of the rural revitalization strategy, distributed photovoltaic power generation has experienced explosive growth in vast rural areas. However, the randomness, intermittency, and "reverse power" output characteristics of photovoltaic power generation have brought unprecedented technical challenges and management pressures to the already weak rural power distribution networks.

[0003] Blindly and haphazardly connecting photovoltaic (PV) systems to the grid can easily lead to serious power quality problems. For example, during the midday hours when sunlight is abundant and load is low, a surge in PV power generation may cause the voltage in the distribution area to exceed the upper limit, endangering the safety of users' electrical equipment. Conversely, during the evening peak load period when PV systems are disconnected, it may cause a sudden voltage drop, resulting in a "cliff-like" voltage fluctuation.

[0004] Furthermore, reverse power flow significantly increases system network losses and can even lead to line overload. Traditional low-voltage distribution area loss reduction methods rely heavily on manual inspection and primarily address management line losses. Technical loss reduction methods often depend on single approaches such as equipment replacement, and a unified and effective method that considers multiple resource types, including energy storage, on-load tap-changing transformers, and reactive power regulating equipment, has not yet been developed. Regarding algorithms for solving loss reduction optimization problems, mixed-integer nonlinear programming, as a complex optimization model involving continuous variables, integer variables, and nonlinear relationships, still has room for improvement in the computational efficiency of traditional methods such as branch-and-bound and cutting-plane algorithms.

[0005] Therefore, an effective loss reduction optimization method is needed to adapt to the background of photovoltaic grid connection. At the same time, the MINLP efficient solution algorithm is used to achieve fast solution, which can improve the economy and safety of low-voltage distribution areas and help improve the level of distribution network line loss management. Summary of the Invention

[0006] To achieve the above objectives, this application provides the following technical solution:

[0007] According to a first aspect of the present invention, the present invention claims protection for a method for optimizing loss reduction in low-voltage distribution areas adapted to photovoltaic grid connection, comprising:

[0008] S1, acquire multi-source data of the distribution radio station area, and perform data interconnection processing on the multi-source data of the distribution radio station area;

[0009] S2, based on the API interface, perform data parsing on the multi-source data of the connected distribution substation, and according to the calculation requirements, splice the topology model to construct and splice the power flow calculation model required for theoretical line loss calculation.

[0010] S3, based on the investment and construction cost, operation and maintenance cost and network loss cost of low-voltage distribution area, constructs the objective function of the loss reduction optimization model, and combines conventional power flow constraints, power quality constraints and the operation constraints of the equipment to be planned to construct the loss reduction optimization model;

[0011] S4. Solve the loss reduction optimization model using a hybrid solution algorithm based on generalized Benders decomposition and external approximation algorithm;

[0012] S5. Based on the results of solving the loss reduction optimization model, output the loss reduction optimization scheme and the optimized line loss result.

[0013] Furthermore, S1 also includes:

[0014] Based on data from the same source system and the data acquisition system, the data of the transformer area archives, topology information and transformer area measurement information are integrated;

[0015] The transformer area files and topology information are from the same system as the State Grid Corporation of China and are uploaded to the data platform.

[0016] The transformer area measurement information comes from the State Grid Corporation's user electricity consumption information collection system and is uploaded to the enterprise-level real-time measurement center.

[0017] All data is accessed through API interfaces, enabling seamless data flow.

[0018] Furthermore, S2 also includes:

[0019] Data parsing is performed on the multi-source data of the distribution substation obtained through the API interface. According to the calculation requirements, the topology model is assembled, and the required resistance, reactance, and no-load loss parameters are bound based on the archive information.

[0020] Based on marketing profile information and user measurement information, the power flow calculation model required for theoretical line loss calculation is constructed.

[0021] During the parsing process, embedded data verification and repair logic is used to make numerical judgments on the equipment's resistance, reactance, and no-load loss parameters, and to repair abnormal parameters. The repair values ​​are referenced from a typical equipment parameter library.

[0022] The system identifies topological islands in the topology information, generates a list of loose equipment, and provides on-site personnel with the means to confirm, verify, and address them.

[0023] The measurement information is over-capacity assessed, and data repair is performed for abnormal measurement information. The repair values ​​are based on typical operating curves.

[0024] Furthermore, the objective function for constructing the loss reduction optimization model in S3 also includes:

[0025] Under the premise of ensuring power quality for users, an objective function is constructed with the optimization goal of minimizing the total network loss cost, the total investment and construction cost, and the total operation and maintenance cost of the system.

[0026] The total investment and construction cost of the system includes the investment costs of energy storage, parallel reactors, parallel capacitors, SVC, and OLTC;

[0027] The total system operation and maintenance cost is determined by the availability of power distribution lines, reactive power equipment, ESS and OLTC. If the equipment is in operation, the corresponding maintenance costs must be taken into account.

[0028] The total network loss cost of the system is determined by the network loss coefficient B and the branch power flow distribution.

[0029] Furthermore, the loss reduction optimization model constructed in S3 by combining conventional power flow constraints, power quality constraints, and operational constraints of the equipment to be planned also includes:

[0030] Branch power flow constraints are obtained using polar coordinates.

[0031] Construct node power balance constraints based on the active and reactive power outputs of the planned equipment at each node.

[0032] Power quality constraints are constructed based on three-phase imbalance, voltage deviation, and voltage fluctuation.

[0033] Energy storage constraints are constructed based on charge / discharge state constraints and charge / discharge power constraints.

[0034] Constraints for reactive voltage regulation equipment are constructed based on the operating constraints of parallel capacitors and reactors, SVC operating constraints, reactive power reserve constraints, equipment construction constraints, and OLTC operating constraints.

[0035] Controllable photovoltaic constraints are constructed based on the configuration capacity, photovoltaic output, reactive power output flowing into the system, and power factor angle of distributed photovoltaic systems.

[0036] Network reconfiguration constraints are constructed based on branch switch states and node power balance.

[0037] Furthermore, S4 also includes:

[0038] Set the maximum and minimum values ​​of the objective function for the MINLP problem, and initialize the set, variables, and algorithm iteration count record;

[0039] Solving NLP models with integer variables based on relaxed MINLP models, solving relaxed nonlinear problems, and setting the objective function value to a lower bound;

[0040] Determine whether the PNLP model is feasible or not, and solve the lower bound subproblem;

[0041] Construct the PBR-MIQP problem and the PLB-MILP problem, and solve the upper bound principal problem.

[0042] Furthermore, S5 also includes:

[0043] The energy storage and reactive power planning schemes obtained based on the loss reduction optimization model are the loss reduction optimization schemes. The simulation calculations are performed again according to the loss reduction optimization schemes to obtain the results after loss reduction.

[0044] Furthermore, the objective function for constructing the loss reduction optimization model in S3 also includes:

[0045] Under the premise of ensuring power quality for users, an objective function is constructed with the optimization goal of minimizing the total network loss cost, the total investment and construction cost, and the total operation and maintenance cost of the system.

[0046] C = C INV +C OM +C LOSS (1)

[0047] Among them, C INV It is the total investment and construction cost of the system, C OM It is the total system maintenance cost, C LOSS Total network loss cost of the system;

[0048]

[0049] Equation (2) represents the energy storage investment cost. and These represent the investment cost of energy storage at node n and the investment cost of a single energy storage unit, respectively; N ESS,n Let n be the number of energy storage units planned for node n, where n is an integer variable, and equation (3) represents the investment cost of the parallel capacitors. This indicates the investment cost of parallel capacitors; The unit investment cost of a single parallel capacitor; N C,n Let C be the number of parallel capacitors at node n, and Equation (4) is the investment cost of the SVC, where C SVC Indicates the investment cost of SVC; Q SVC,n The SVC capacity installed for n nodes; a, b, c, d are cost coefficients, and equation (5) represents the OLTC investment cost.

[0050]

[0051] Equation (6) represents the variable operation and maintenance cost of energy storage, where, and These are the total operation and maintenance cost and the unit operation and maintenance cost of energy storage, respectively; S ESS(t) represents the apparent power of the energy storage at time t; Δt is 1 hour; T is 8760 hours, and equation (7) represents the fixed operation and maintenance cost of the parallel capacitor, where, and These are the total maintenance cost and the unit maintenance cost of parallel capacitors, respectively; Q C Let be the total capacity of the capacitors, and Equation (8) be the fixed operation and maintenance cost of the OLTC;

[0052]

[0053] After obtaining the branch power equation expression, the power conservation equation for the active power loss of the branch is shown in equation (10):

[0054]

[0055] In the formula, C Loss B represents the system's network loss cost; B represents the system's electricity price. P represents the active power loss of branch ij at time t. ij (t),P ji (t) represents the power at the beginning and end of branch ij at time t.

[0056] Furthermore, the loss reduction optimization model constructed in S3 by combining conventional power flow constraints, power quality constraints, and operational constraints of the equipment to be planned also includes:

[0057] The polar coordinate form of the branch power flow constraint can be expressed as equations (11)-(12):

[0058]

[0059] In the formula, conductance is g, susceptance is b, phase angle difference is θ, ρ,k∈{a,b,c} represents phase, and U i U j Indicates the node voltage amplitude. and Let ρ and k represent the mutual coupling conductance and susceptance of phase ρ and phase k of the three-phase line ij, respectively. If ρ = k, then and These represent the conductance and susceptance of phases ij and ρ in a three-phase circuit, respectively. This represents the phase angle difference between phase ρ and phase k at node i; This represents the phase angle difference between the ρ phase of node i and the k phase of node j;

[0060] The node power balance constraint considers the active and reactive power outputs of the devices to be planned at the node. The node power balance constraint is expressed as:

[0061]

[0062] In the formula, the superscript ρ∈a,b,c} denotes phase, P i,load and Q i,load P represents the active and reactive loads of node i, respectively; i,ch and P i,dis Q represents the charging and discharging power of the energy stored at node i; i,C and Q i,L These represent the reactive power compensation power of the parallel capacitor and reactor at node i, respectively. G represents the reactive power compensation of the SVC; ij B ij ,θ ij These represent the branch conductance, susceptance, and phase angle difference between nodes i and j, respectively.

[0063] For power quality constraints, the three-phase imbalance at node n at any given time should satisfy the upper and lower bound requirements:

[0064]

[0065] In the formula, PVUR represents the three-phase unbalance; U a U b U c These are the three-phase voltage amplitudes; U avg This is the average value of the three-phase voltage;

[0066] The voltage deviation at node n at any given time should meet the upper and lower bound requirements:

[0067]

[0068] In the formula, ΔU is the voltage deviation, U N Rated voltage;

[0069] Voltage fluctuation is:

[0070]

[0071] In the formula, d ρ d represents the voltage fluctuation value of phase ρ. max This is the upper limit for voltage fluctuation; These are the maximum and minimum values ​​of the ρ-phase sequential voltage, respectively;

[0072] Regarding energy storage constraints, the charge / discharge state constraint, as shown in equation (18), restricts the energy storage battery from being charged and discharged simultaneously.

[0073]

[0074] In the formula, These represent the charging and discharging states of energy storage, respectively. When the energy storage battery is charging... =1, otherwise A value of 1 indicates a binary variable.

[0075] Excessive charge / discharge state transitions can shorten the lifespan of energy storage, so the number of charge / discharge state transitions should be limited.

[0076]

[0077] In the formula, This indicates the upper limit of the number of times the energy storage charge / discharge state transitions;

[0078] Using the absolute value linearization method, equation (19) is linearized by introducing an auxiliary variable that characterizes the charging and discharging state of energy storage, as shown in equation (20).

[0079]

[0080] Equation (19) can then be transformed into:

[0081]

[0082] Equation (20) is the problem of finding the absolute value of the subtraction of two binary variables. Therefore, equation (20) can be transformed into:

[0083]

[0084] Regarding charging and discharging power constraints:

[0085] E(t)=E(t-1)(1-δΔt)+P ch (t)η ch Δt-P dis (t) / η dis Δt (23);

[0086] SOC min N batt P rated，batt ≤E(t)≤SOC max N batt P rated，batt (twenty four);

[0087]

[0088] In equation (23): E(t) and Δt represent the remaining energy (kWh), charging / discharging power (kW), and time interval (h) of the energy storage battery at time t, respectively; δ and η ch η dis Represent the self-discharge rate and charge / discharge efficiency of the energy storage battery per hour, respectively; In equation (24): N batt S indicates the number of energy storage batteries; batt，unit It refers to the capacity of a single energy storage unit; SOC min and SOC maxThese represent the minimum and maximum values ​​for energy storage and percentage of electricity, respectively.

[0089] Constraints on reactive power regulation equipment, including operational constraints on parallel capacitors and reactors;

[0090] Parallel capacitors and reactors are used for reactive power compensation by switching, and the amount of reactive power compensation is a discrete variable.

[0091] Q i,C (t)=u i,C (t)N i,C Q C,unit (27);

[0092] Q i,L (t)=u i,L (t)N i,L Q L,unit (28);

[0093] In the formula, N i,C and N i,L Q represents the number of parallel capacitor and reactor groups at node i, respectively; C,unit and Q L,unit These represent the capacities of a single group of capacitors and reactors to be planned in parallel; u i,C (t) and u i,L (t) represents the switching states of the parallel capacitor and reactor at time t at node i, respectively, and are binary variables;

[0094] To extend the service life of parallel capacitors and reactors and improve economic efficiency, equations (29) and (30) limit the number of switching operations, and equations (20)-(22) are used for linearization. Equation (31) prevents capacitors and reactors from being put into operation at the same time.

[0095]

[0096] u C (t)+u L (t)≤1 (31);

[0097] In the formula, and These represent the upper limits of the number of switching states for the capacitor and reactor, respectively.

[0098] Regarding the operational constraints of SVC, SVC has the characteristic of continuously adjustable reactive power compensation.

[0099]

[0100] In the formula, This indicates the capacity configured in the i-node SVC;

[0101] Regarding reactive power reserve constraints:

[0102]

[0103] In the formula, Q res This is the reactive power reserve factor. For the maximum reactive load, the capacitive reactive power reserve capacity should be 7%-8% of the reactive load; N c Q is the number of parallel capacitor groups; C,unit It refers to the capacitance of a single capacitor bank.

[0104] In response to constraints on equipment deployment, energy storage and reactive power regulation equipment should be put into operation after construction.

[0105]

[0106] binary variable B i,ESS B i,C B i,L These represent whether energy storage is in the switching status of the device corresponding to node i, with 1 indicating yes;

[0107] Regarding the OLTC operating constraints, the OLTC model is equivalent to a transformer + voltage regulator. The following constraints control the OLTC's gear switching within the range and satisfy the limit on the number of gear switching times.

[0108]

[0109] In the formula, binary variables Indicates whether an OLTC is planned at line ij, with 1 indicating yes; set Ω ML Includes all backbone lines; U i U j These represent the voltages at both ends of line ij; Tap OLTC (t) represents the gear position of the OLTC at time t; VR max VR min Represent the maximum and minimum values ​​of the voltage across the OLTC, respectively; integer variable N OLTC The number of OLTCs to be planned is 1 by default; This indicates the maximum number of gear shifts.

[0110] Line transmission capacity constraints:

[0111]

[0112] In the formula P ij and Q ij These represent the active and reactive power flowing through the line, S. L This represents the maximum transmission power of the line.

[0113] Controllable photovoltaic constraints are based on applying a local control strategy to the distributed photovoltaic converter to ensure that active and reactive power meet the following constraints:

[0114]

[0115] Among them, S PV P represents the configuration capacity of distributed photovoltaic power; PV Q represents photovoltaic output. PV This represents the reactive power flowing into the system; The power factor angle;

[0116] The network reconfiguration constraints are similar to those of the aforementioned line type planning, based on the branch power flow equations (11) to (12), considering that n rc If there are several alternative routes, then the branch power flow equations are changed to n branch +n rc There are 1, and whether each line uses a decision variable R is determined by the decision variable R. ij Decision, R ij This is a binary variable; when it equals 1, the line is in use. The branch power flow constraint is represented as follows:

[0117]

[0118] Constraint (43) is a radial topological constraint, where φ l Let n represent the set of all routes. b and n s These represent the total number of nodes and the number of root nodes in the power distribution system, respectively.

[0119] According to R ij The network is reconstructed based on the variable calculation results; when the result equals 1, the line is put into use.

[0120] Beneficial effects

[0121] This invention addresses the challenges of voltage fluctuations and increased network losses brought about by distributed photovoltaic grid connection. It constructs a power flow calculation model through multi-source data processing and comprehensively considers investment and construction costs, operation and maintenance costs, and network loss costs to establish an optimization model aimed at reducing losses. The model integrates conventional power flow constraints, power quality constraints, and operational constraints of the planned equipment. It employs a hybrid solution algorithm combining generalized Benders decomposition and external approximation algorithms for efficient solution, ultimately outputting loss reduction optimization schemes such as energy storage and reactive power planning, as well as optimized line loss results. This invention effectively improves the economy and safety of low-voltage distribution areas and provides scientific support for distribution network line loss management. Attached Figure Description

[0122] Figure 1 A flowchart illustrating the workflow of a low-voltage distribution area loss reduction optimization method adapted to photovoltaic grid connection, as claimed in an embodiment of the present invention.

[0123] Figure 2 This is a schematic diagram of a simulation analysis design scheme for a low-voltage distribution area loss reduction optimization method adapted to photovoltaic grid connection, as claimed in an embodiment of the present invention. Detailed Implementation

[0124] The technical solutions of the embodiments of this application 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 this application, and not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0125] The terms "first," "second," and "third" in this application are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first," "second," or "third" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified. All directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of this application are only used to explain the relative positional relationships and movements between components in a specific orientation (as shown in the figures). If the specific orientation changes, the directional indications also change accordingly. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices.

[0126] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0127] According to the first embodiment of the present invention, referring to Figure 1 This invention claims protection for a low-voltage distribution area loss reduction optimization method adapted to photovoltaic grid connection, comprising:

[0128] S1, acquire multi-source data of the distribution radio area, and perform data integration processing on the multi-source data of the distribution radio area;

[0129] S2, based on the API interface, performs data parsing on the multi-source data of the connected distribution substation, and according to the calculation requirements, splices the topology model to construct and splice the power flow calculation model required for theoretical line loss calculation.

[0130] S3, based on the investment and construction cost, operation and maintenance cost and network loss cost of low-voltage distribution area, constructs the objective function of the loss reduction optimization model, and combines conventional power flow constraints, power quality constraints and the operation constraints of the equipment to be planned to construct the loss reduction optimization model;

[0131] S4, a hybrid solution algorithm based on generalized Benders decomposition and external approximation algorithm is used to solve the loss reduction optimization model;

[0132] S5 outputs the loss reduction optimization scheme and the optimized line loss result based on the results of solving the loss reduction optimization model.

[0133] Furthermore, S1 also includes:

[0134] Based on data from the same source system and the data acquisition system, the data of the transformer area archives, topology information and transformer area measurement information are integrated;

[0135] The transformer area files and topology information come from the State Grid Corporation's data source system and are uploaded to the data platform;

[0136] The transformer area measurement information comes from the State Grid Corporation's user electricity consumption information collection system and is uploaded to the enterprise-level real-time measurement center.

[0137] All data is accessed through API interfaces, enabling seamless data flow.

[0138] Furthermore, S2 also includes:

[0139] Data parsing is achieved based on multi-source data of distribution substations obtained through API interface. According to calculation requirements, topology model is assembled, and the required resistance, reactance, and no-load loss parameters are bound based on archive information.

[0140] Based on marketing profile information and user measurement information, the power flow calculation model required for theoretical line loss calculation is constructed.

[0141] During the parsing process, embedded data verification and repair logic is used to make numerical judgments on the equipment's resistance, reactance, and no-load loss parameters, and to repair abnormal parameters. The repair values ​​are referenced from a typical equipment parameter library.

[0142] The system identifies topological islands in the topology information, generates a list of loose equipment, and provides on-site personnel with the means to confirm, verify, and address them.

[0143] The measurement information is over-capacity assessed, and data repair is performed for abnormal measurement information. The repair values ​​are based on typical operating curves.

[0144] Furthermore, the objective function for constructing the loss reduction optimization model in S3 also includes:

[0145] Under the premise of ensuring power quality for users, an objective function is constructed with the optimization goal of minimizing the total network loss cost, the total investment and construction cost, and the total operation and maintenance cost of the system.

[0146] The total investment and construction cost of the system includes the investment costs of energy storage, shunt reactors, shunt capacitors, SVCs, and OLTCs;

[0147] The total system operation and maintenance cost is determined by the availability of power distribution lines, reactive power equipment, ESS and OLTC. If the equipment is in operation, the corresponding maintenance costs must be taken into account.

[0148] The total network loss cost of the system is determined by the network loss coefficient B and the branch power flow distribution.

[0149] Furthermore, S3 incorporates a loss reduction optimization model that combines conventional power flow constraints, power quality constraints, and operational constraints of the equipment to be planned. This model also includes:

[0150] Branch power flow constraints are obtained using polar coordinates.

[0151] Construct node power balance constraints based on the active and reactive power outputs of the planned equipment at each node.

[0152] Power quality constraints are constructed based on three-phase imbalance, voltage deviation, and voltage fluctuation.

[0153] Energy storage constraints are constructed based on charge / discharge state constraints and charge / discharge power constraints.

[0154] Constraints for reactive voltage regulation equipment are constructed based on the operating constraints of parallel capacitors and reactors, SVC operating constraints, reactive power reserve constraints, equipment construction constraints, and OLTC operating constraints.

[0155] Controllable photovoltaic constraints are constructed based on the configuration capacity, photovoltaic output, reactive power output flowing into the system, and power factor angle of distributed photovoltaic systems.

[0156] Network reconfiguration constraints are constructed based on branch switch states and node power balance.

[0157] Furthermore, S4 also includes:

[0158] Set the maximum and minimum values ​​of the objective function for the MINLP problem, and initialize the set, variables, and algorithm iteration count record;

[0159] Solving NLP models with integer variables based on relaxed MINLP models, solving relaxed nonlinear problems, and setting the objective function value to a lower bound;

[0160] Determine whether the PNLP model is feasible or not, and solve the lower bound subproblem;

[0161] Construct the PBR-MIQP problem and the PLB-MILP problem, and solve the upper bound principal problem.

[0162] Furthermore, S5 also includes:

[0163] The energy storage and reactive power planning schemes obtained based on the loss reduction optimization model are the loss reduction optimization schemes. The simulation calculations are performed again according to the loss reduction optimization schemes to obtain the results after loss reduction.

[0164] Furthermore, the objective function for constructing the loss reduction optimization model in S3 also includes:

[0165] Under the premise of ensuring power quality for users, an objective function is constructed with the optimization goal of minimizing the total network loss cost, the total investment and construction cost, and the total operation and maintenance cost of the system.

[0166] C = C INV +C OM +C LOSS (1)

[0167] Among them, C INV It is the total investment and construction cost of the system, C OM It is the total system maintenance cost, C LOSS Total network loss cost of the system;

[0168]

[0169] Equation (2) represents the energy storage investment cost. and These represent the investment cost of energy storage at node n and the investment cost of a single energy storage unit, respectively; N ESS,n Let n be the number of energy storage units planned for node n, where n is an integer variable, and equation (3) represents the investment cost of the parallel capacitors. This indicates the investment cost of parallel capacitors; The unit investment cost of a single parallel capacitor; N C,n Let C be the number of parallel capacitors at node n, and Equation (4) is the investment cost of the SVC, where C SVC Indicates the investment cost of SVC; Q SVC,n The SVC capacity installed for n nodes; a, b, c, d are cost coefficients, and equation (5) represents the OLTC investment cost.

[0170]

[0171] Equation (6) represents the variable operation and maintenance cost of energy storage, where, and These are the total operation and maintenance cost and the unit operation and maintenance cost of energy storage, respectively; S ESS(t) represents the apparent power of the energy storage at time t; Δt is 1 hour; T is 8760 hours, and equation (7) represents the fixed operation and maintenance cost of the parallel capacitor, where, and These are the total maintenance cost and the unit maintenance cost of parallel capacitors, respectively; Q C Let be the total capacity of the capacitors, and Equation (8) be the fixed operation and maintenance cost of the OLTC;

[0172]

[0173] After obtaining the branch power equation expression, the power conservation equation for the active power loss of the branch is shown in equation (10):

[0174]

[0175] In the formula, C Loss B represents the system's network loss cost; B represents the system's electricity price. P represents the active power loss of branch ij at time t. ij (t),P ji (t) represents the power at the beginning and end of branch ij at time t.

[0176] Furthermore, S3 incorporates a loss reduction optimization model that combines conventional power flow constraints, power quality constraints, and operational constraints of the equipment to be planned. This model also includes:

[0177] The polar coordinate form of the branch power flow constraint can be expressed as equations (11)-(12):

[0178]

[0179] In the formula, conductance is g, susceptance is b, phase angle difference is θ, ρ,k∈{a,b,c} represents phase, and U i U j Indicates the node voltage amplitude. and Let ρ and k represent the mutual coupling conductance and susceptance of phase ρ and phase k of the three-phase line ij, respectively. If ρ = k, then and These represent the conductance and susceptance of phases ij and ρ in a three-phase circuit, respectively. This represents the phase angle difference between phase ρ and phase k at node i; This represents the phase angle difference between the ρ phase of node i and the k phase of node j;

[0180] The node power balance constraint considers the active and reactive power outputs of the devices to be planned at the node. The node power balance constraint is expressed as:

[0181]

[0182] In the formula, the superscript ρ∈{a,b,c} denotes phase, and P i,load and Q i,load P represents the active and reactive loads of node i, respectively; i,ch and P i,dis Q represents the charging and discharging power of the energy stored at node i; i,C and Q i,L These represent the reactive power compensation power of the parallel capacitor and reactor at node i, respectively. G represents the reactive power compensation of the SVC; ij B ij ,θ ij These represent the branch conductance, susceptance, and phase angle difference between nodes i and j, respectively.

[0183] For power quality constraints, the three-phase imbalance at node n at any given time should satisfy the upper and lower bound requirements:

[0184]

[0185] In the formula, PVUR represents the three-phase unbalance; U a U b U c These are the three-phase voltage amplitudes; U avg This is the average value of the three-phase voltage;

[0186] The voltage deviation at node n at any given time should meet the upper and lower bound requirements:

[0187]

[0188] In the formula, ΔU is the voltage deviation, U N Rated voltage;

[0189] Voltage fluctuation is:

[0190]

[0191] In the formula, d ρ d represents the voltage fluctuation value of phase ρ. max This is the upper limit for voltage fluctuation; These are the maximum and minimum values ​​of the ρ-phase sequential voltage, respectively;

[0192] Regarding energy storage constraints, the charge / discharge state constraint, as shown in equation (18), restricts the energy storage battery from being charged and discharged simultaneously.

[0193]

[0194] In the formula, These represent the charging and discharging states of energy storage, respectively. When the energy storage battery is charging... =1, otherwise A value of 1 indicates a binary variable.

[0195] Excessive charge / discharge state transitions can shorten the lifespan of energy storage, so the number of charge / discharge state transitions should be limited.

[0196]

[0197] In the formula, This indicates the upper limit of the number of times the energy storage charge / discharge state transitions;

[0198] Using the absolute value linearization method, equation (19) is linearized by introducing an auxiliary variable that characterizes the charging and discharging state of energy storage, as shown in equation (20).

[0199]

[0200] Equation (19) can then be transformed into:

[0201]

[0202] Equation (20) is the problem of finding the absolute value of the subtraction of two binary variables. Therefore, equation (20) can be transformed into:

[0203]

[0204] Regarding charging and discharging power constraints:

[0205] E(t)=E(t-1)(1-δΔt)+P ch (t)η ch Δt-P dis (t) / η dis Δt (23);

[0206] SOC min N batt P rated，batt ≤E(t)≤SOC max N batt P rated，batt (twenty four);

[0207]

[0208] In equation (23): E(t) and Δt represent the remaining energy (kWh), charging / discharging power (kW), and time interval (h) of the energy storage battery at time t, respectively; δ and η ch η dis Represent the self-discharge rate and charge / discharge efficiency of the energy storage battery per hour, respectively; In equation (24): N batt S indicates the number of energy storage batteries; batt，unit It refers to the capacity of a single energy storage unit; SOC min and SOC maxThese represent the minimum and maximum values ​​for energy storage and percentage of electricity, respectively.

[0209] Constraints on reactive power regulation equipment, including operational constraints on parallel capacitors and reactors;

[0210] Parallel capacitors and reactors are used for reactive power compensation by switching, and the amount of reactive power compensation is a discrete variable.

[0211] Q i,C (t)=u i,C (t)N i,C Q C,unit (27);

[0212] Q i,L (t)=u i,L (t)N i,L Q L,unit (28);

[0213] In the formula, N i,C and N i,L Q represents the number of parallel capacitor and reactor groups at node i, respectively; C,unit and Q L,unit These represent the capacities of a single group of capacitors and reactors to be planned in parallel; u i,C (t) and u i,L (t) represents the switching states of the parallel capacitor and reactor at time t at node i, respectively, and are binary variables;

[0214] To extend the service life of parallel capacitors and reactors and improve economic efficiency, equations (29) and (30) limit the number of switching operations, and equations (20)-(22) are used for linearization. Equation (31) prevents capacitors and reactors from being put into operation at the same time.

[0215]

[0216] u C (t)+u L (t)≤1 (31);

[0217] In the formula, and These represent the upper limits of the number of switching states for the capacitor and reactor, respectively.

[0218] Regarding the operational constraints of SVC, SVC has the characteristic of continuously adjustable reactive power compensation.

[0219]

[0220] In the formula, This indicates the capacity configured in the i-node SVC;

[0221] Regarding reactive power reserve constraints:

[0222]

[0223] In the formula, Q res This is the reactive power reserve factor. For the maximum reactive load, the capacitive reactive power reserve capacity should be 7%-8% of the reactive load; N c Q is the number of parallel capacitor groups; C,unit It refers to the capacitance of a single capacitor bank.

[0224] In response to constraints on equipment deployment, energy storage and reactive power regulation equipment should be put into operation after construction.

[0225]

[0226] binary variable B i,ESS B i,C B i,L These represent whether energy storage is in the switching status of the device corresponding to node i, with 1 indicating yes;

[0227] Regarding the OLTC operating constraints, the OLTC model is equivalent to a transformer + voltage regulator. The following constraints control the OLTC's gear switching within the range and satisfy the limit on the number of gear switching times.

[0228]

[0229]

[0230] In the formula, binary variables Indicates whether an OLTC is planned at line ij, with 1 indicating yes; set Ω ML Includes all backbone lines; U i U j These represent the voltages at both ends of line ij; Tap OLTC (t) represents the gear position of the OLTC at time t; VR max VR min Represent the maximum and minimum values ​​of the voltage across the OLTC, respectively; integer variable N OLTC The number of OLTCs to be planned is 1 by default; This indicates the maximum number of gear shifts.

[0231] Line transmission capacity constraints:

[0232]

[0233] In the formula P ij and Q ij These represent the active and reactive power flowing through the line, S. L This represents the maximum transmission power of the line.

[0234] Controllable photovoltaic constraints are based on applying a local control strategy to the distributed photovoltaic converter to ensure that active and reactive power meet the following constraints:

[0235]

[0236] Among them, S PV P represents the configuration capacity of distributed photovoltaic power; PV Q represents photovoltaic output. PV This represents the reactive power flowing into the system; The power factor angle;

[0237] The network reconfiguration constraints are similar to those of the aforementioned line type planning, based on the branch power flow equations (11) to (12), considering that n rc If there are several alternative routes, then the branch power flow equations are changed to n branch +n rc There are 1, and whether each line uses a decision variable R is determined by the decision variable R. ij Decision, R ij This is a binary variable; when it equals 1, the line is in use. The branch power flow constraint is represented as follows:

[0238]

[0239]

[0240] Constraint (43) is a radial topological constraint, where φ l Let n represent the set of all routes. b and n s These represent the total number of nodes and the number of root nodes in the power distribution system, respectively.

[0241] According to R ij The network is reconstructed based on the variable calculation results; when the result equals 1, the line is put into use.

[0242] In this embodiment, step S4 further includes:

[0243] To address the inefficient solution of MINLP for non-convex, nonlinear problems with a large number of integer variables, a mixed integer programming algorithm based on GBD and OA is adopted. This algorithm gradually approximates the optimal solution by alternately solving nonlinear programming (NLP) and mixed integer programming (MIP). The detailed algorithm flow is as follows:

[0244] Step 1): Initialization:

[0245] Set the maximum and minimum values ​​of the objective function for the MINLP problem to UB = +∞ and LB = -∞, respectively; initialize the continuous and integer variables to x0 and y0, respectively; initialize two sets S and T as empty sets, respectively, to store the results of the iteration points of infeasible and feasible solutions found during the iteration process; initialize the variable V0 = 10000, which is used to adjust the size of Benders' feasible region to ensure that the search space is effectively reduced; initialize k = 0 to record the number of iterations of the algorithm.

[0246] Step 2): Calculate the lower bound (LB):

[0247] Relaxing the integer variables of the MINLP model and solving the NLP model:

[0248] NLP models:

[0249]

[0250] To solve the relaxed nonlinear problem, the objective function is set to a lower bound LB.

[0251] Step 3): Solve the lower boundary subproblem:

[0252] Step 3a): With a fixed integer solution, solving the PNLP model is feasible.

[0253]

[0254] Solving the above model yields the optimal solution x for the continuous variables. k Its objective function value is f(x) k ,y k Store the optimal solution in set T and the feasible solution information in the following dataset D. k :

[0255]

[0256] In the formula, D k Store information related to the optimal solution, where k represents the number of iterations, and x... k ,y k J(y) represents the optimal solution obtained in the k-th iteration. k () represents the objective function value obtained when the y-value is fixed. This represents the gradient at that point.

[0257] Determine f(x) k ,y k If ) < UB, update the upper bound (Upper Bound, UB) of the MINLP problem.

[0258] Step 3b): PNLP(y k The model is not feasible:

[0259] Constructing PFNLP issues:

[0260]

[0261] In the formula, for some PNLP(y k There may be situations where this is not feasible. In such cases, setting f(x,y) is... k Given f = +∞, construct a feasibility problem to find the closest y on the boundary of f. k For points that are not found, a new approximate solution can be obtained through the following PFNLP model, and this solution can be stored in set S, along with feasible solution information stored in the dataset.

[0262] By combining the solutions to the PNLP and PFNLP problems, b(k) is set as the index of the best solution in the k-th iteration.

[0263]

[0264] Step 4): Solve the upper bound master problem:

[0265] Step 4a): Constructing the PBR-MIQP problem:

[0266]

[0267] In the formula, the constraints include linearized inequalities and equality constraints, as well as feasible and infeasible cut constraints based on the Benders region. Where B... b(k) This represents the Hessian matrix based on the current best solution. A phasor represented as a set of Lagrange multipliers of integer variables. The threshold used to define the Benders region is dynamically adjusted according to equation (50):

[0268]

[0269] In the formula, LB is the lower bound of the current objective function value, α is the weight parameter (0≤α<1), and the objective function value of formula (49) is defined as V. MIQP These constraints ensure that the search process does not return to previously explored areas, but instead seeks possible better solutions in new areas.

[0270] Step 4b): Constructing the PLB-MILP problem

[0271] When the PBR-MIQP problem has an infeasible solution due to the empty set of the Benders region, and it is impossible to confirm whether the current optimal solution is the optimal solution of the MINLP problem, the PLB-MILP problem is introduced for verification. This method constructs a MILP solution based on the GBD and OA algorithms and determines whether to update the lower bound LB, thereby verifying whether the current solution is the optimal solution.

[0272] PLB-MILP problem:

[0273]

[0274] The objective function value of formula (51) is defined as V. MILP Determine V MILP <UB, update UB.

[0275] Step 5): Termination Criteria

[0276] During the iteration process, the algorithm needs to check whether the termination condition is met to determine whether to continue iterating. The termination condition is based on the difference between the lower bound LB and the upper bound UB, as well as a preset tolerance TOL.

[0277] Calculate absolute tolerance TOL ABS :

[0278]

[0279] Check termination conditions:

[0280] RET = (LB + TOL) ABS -UB)≥0 (53)

[0281] If the corresponding LB and UB satisfy formula (53), the algorithm terminates; otherwise, return to Step 3.

[0282] Reference Figure 2 Simulation analysis and design scheme:

[0283] There are 4 photovoltaic access points, as shown in the diagram above: "First End", "Middle End (Front)", "Middle End (Rear)" and "End End".

[0284] There are three typical grid connection conditions: 1) Full consumption by users, that is, the photovoltaic power is completely consumed locally; 2) Surplus power is fed into the grid, power is supplied to the loads of users near the transformer area, but not fed back to the 10kV feeder; 3) Photovoltaic power is fed into the grid, and the excess power is fed back to the 10kV feeder.

[0285] Two transformer area load rate conditions are set, with the transformer area load rate set at 30% and 80% respectively.

[0286] Under different operating scenarios, photovoltaic power was connected to four access points in succession, and the photovoltaic power generation changed continuously within a certain range. The continuous changes in the line loss rate of the distribution area were analyzed under different grid connection locations and different power generation.

[0287] By setting different operating conditions for typical transformer substations, a simulation analysis of the impact of grid-connected photovoltaic power on the line loss rate of the substations was conducted, and the conclusions are as follows:

[0288] 1) Within a certain range, the larger the grid-connected photovoltaic capacity, that is, the higher the on-grid electricity, the faster the line loss rate decreases, which is more beneficial to loss reduction; after exceeding the limit, the line loss will show an increasing trend; the specific limit depends on the load factor and impedance parameters.

[0289] 2) The closer the photovoltaic grid connection point is to the middle and later part of the line (load center), the faster the line loss rate decreases, which is more beneficial to loss reduction.

[0290] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces, or indirect coupling or communication connection between apparatuses or units, and may be electrical, mechanical, or other forms.

[0291] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated units described above can be implemented in hardware or as software functional units. The above are merely embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made based on the description and drawings of this application, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

[0292] The specific embodiments of the invention have been described in detail above, but they are only examples, and this application is not limited to the specific embodiments described above. For those skilled in the art, any equivalent modifications or substitutions to the invention are also within the scope of this application. Therefore, all equivalent changes, modifications, and improvements made without departing from the spirit and principles of this application should be covered within the scope of this application.

Claims

1. A method for optimizing loss reduction in low-voltage distribution areas adapted to photovoltaic grid connection, characterized in that, include: S1, acquire multi-source data of the distribution radio station area, and perform data interconnection processing on the multi-source data of the distribution radio station area; S2, based on the API interface, perform data parsing on the multi-source data of the connected distribution substation, and according to the calculation requirements, splice the topology model to construct and splice the power flow calculation model required for theoretical line loss calculation. S3, based on the investment and construction cost, operation and maintenance cost and network loss cost of low-voltage distribution area, constructs the objective function of the loss reduction optimization model, and combines conventional power flow constraints, power quality constraints and the operation constraints of the equipment to be planned to construct the loss reduction optimization model; S4. Solve the loss reduction optimization model using a hybrid solution algorithm based on generalized Benders decomposition and external approximation algorithm; S5. Based on the results of solving the loss reduction optimization model, output the loss reduction optimization scheme and the optimized line loss result.

2. The method for optimizing loss reduction in low-voltage distribution areas adapted to photovoltaic grid connection as described in claim 1, characterized in that, S1 further includes: Based on data from the same source system and the data acquisition system, the data of the transformer area archives, topology information and transformer area measurement information are integrated; The transformer area files and topology information are from the same system as the State Grid Corporation of China and are uploaded to the data platform. The transformer area measurement information comes from the State Grid Corporation's user electricity consumption information collection system and is uploaded to the enterprise-level real-time measurement center. All data is accessed through API interfaces, enabling seamless data flow.

3. The method for optimizing loss reduction in low-voltage distribution areas adapted to photovoltaic grid connection as shown in claim 2, characterized in that, The S2 further includes: Data parsing is performed on the multi-source data of the distribution substation obtained through the API interface. According to the calculation requirements, the topology model is assembled, and the required resistance, reactance, and no-load loss parameters are bound based on the archive information. Based on marketing profile information and user measurement information, the power flow calculation model required for theoretical line loss calculation is constructed. During the parsing process, embedded data verification and repair logic is used to make numerical judgments on the equipment's resistance, reactance, and no-load loss parameters, and to repair abnormal parameters. The repair values ​​are referenced from a typical equipment parameter library. The system identifies topological islands in the topology information, generates a list of loose equipment, and provides on-site personnel with the means to confirm, verify, and address them. The measurement information is over-capacity assessed, and data repair is performed for abnormal measurement information. The repaired values ​​are based on typical operating curves.

4. The method for optimizing loss reduction in low-voltage distribution areas adapted to photovoltaic grid connection as shown in claim 2, characterized in that, The objective function for constructing the loss reduction optimization model in S3 also includes: Under the premise of ensuring power quality for users, an objective function is constructed with the optimization goal of minimizing the total network loss cost, the total investment and construction cost, and the total operation and maintenance cost of the system. The total investment and construction cost of the system includes the investment costs of energy storage, parallel reactors, parallel capacitors, SVC, and OLTC; The total system operation and maintenance cost is determined by the availability of power distribution lines, reactive power equipment, ESS and OLTC. If the equipment is in operation, the corresponding maintenance costs must be taken into account. The total network loss cost of the system is determined by the network loss coefficient B and the branch power flow distribution.

5. The method for optimizing loss reduction in low-voltage distribution areas adapted to photovoltaic grid connection as shown in claim 2, characterized in that, The loss reduction optimization model constructed in S3 by combining conventional power flow constraints, power quality constraints, and operational constraints of the equipment to be planned also includes: Branch power flow constraints are obtained using polar coordinates. Construct node power balance constraints based on the active and reactive power outputs of the planned equipment at each node. Power quality constraints are constructed based on three-phase imbalance, voltage deviation, and voltage fluctuation. Energy storage constraints are constructed based on charge / discharge state constraints and charge / discharge power constraints. Constraints for reactive voltage regulation equipment are constructed based on the operating constraints of parallel capacitors and reactors, SVC operating constraints, reactive power reserve constraints, equipment construction constraints, and OLTC operating constraints. Controllable photovoltaic constraints are constructed based on the configuration capacity, photovoltaic output, reactive power output flowing into the system, and power factor angle of distributed photovoltaic systems. Network reconfiguration constraints are constructed based on branch switch states and node power balance.

6. The method for optimizing loss reduction in low-voltage distribution areas adapted to photovoltaic grid connection as shown in claim 2, characterized in that, The S4 further includes: Set the maximum and minimum values ​​of the objective function for the MINLP problem, and initialize the set, variables, and algorithm iteration count record; Solving NLP models with integer variables based on relaxed MINLP models, solving relaxed nonlinear problems, and setting the objective function value to a lower bound; Determine whether the PNLP model is feasible or not, and solve the lower bound subproblem; Construct the PBR-MIQP problem and the PLB-MILP problem, and solve the upper bound principal problem.

7. The method for optimizing loss reduction in low-voltage distribution areas adapted to photovoltaic grid connection as shown in claim 4, characterized in that, The S5 also includes: The energy storage and reactive power planning schemes obtained based on the loss reduction optimization model are the loss reduction optimization schemes. The simulation calculations are performed again according to the loss reduction optimization schemes to obtain the results after loss reduction.

8. The method for optimizing loss reduction in low-voltage distribution areas adapted to photovoltaic grid connection as shown in claim 4, characterized in that, The objective function for constructing the loss reduction optimization model in S3 also includes: Under the premise of ensuring power quality for users, an objective function is constructed with the optimization goal of minimizing the total network loss cost, the total investment and construction cost, and the total operation and maintenance cost of the system. C=C INV +C OM +C LOSS (1) Among them, C INV It is the total investment and construction cost of the system, C OM It is the total system maintenance cost, C LOSS Total network loss cost of the system; Equation (2) represents the energy storage investment cost. and These represent the investment cost of energy storage at node n and the investment cost of a single energy storage unit, respectively; N ESS,n Let n be the number of energy storage units planned for node n, where n is an integer variable, and equation (3) represents the investment cost of the parallel capacitors. This indicates the investment cost of parallel capacitors; The unit investment cost of a single parallel capacitor; N C,n Let C be the number of parallel capacitors at node n, and Equation (4) is the investment cost of the SVC, where C SVC Indicates the investment cost of SVC; Q SVC,n The SVC capacity installed for n nodes; a, b, c, d are cost coefficients, and equation (5) represents the OLTC investment cost. Equation (6) represents the variable operation and maintenance cost of energy storage, where, and These are the total operation and maintenance cost and the unit operation and maintenance cost of energy storage, respectively; S ESS (t) represents the apparent power of the energy storage at time t; Δt is 1 hour; T is 8760 hours, and equation (7) represents the fixed operation and maintenance cost of the parallel capacitor, where, and These are the total maintenance cost and the unit maintenance cost of parallel capacitors, respectively; Q C Let be the total capacity of the capacitors, and Equation (8) be the fixed operation and maintenance cost of the OLTC; After obtaining the branch power equation expression, the power conservation equation for the active power loss of the branch is shown in equation (10): In the formula, C Loss B represents the system's network loss cost; B represents the system's electricity price. P represents the active power loss of branch ij at time t. ij (t),P ji (t) represents the power at the beginning and end of branch ij at time t.

9. The method for optimizing loss reduction in low-voltage distribution areas adapted to photovoltaic grid connection as shown in claim 5, characterized in that, The loss reduction optimization model constructed in S3 by combining conventional power flow constraints, power quality constraints, and operational constraints of the equipment to be planned also includes: The polar coordinate form of the branch power flow constraint can be expressed as equations (11)-(12): In the formula, conductance is g, susceptance is b, phase angle difference is θ, ρ,k∈{a,b,c} represents phase, and U i U j Indicates the node voltage amplitude. and Let ρ and k represent the mutual coupling conductance and susceptance of phase ρ and phase k of the three-phase line ij, respectively. If ρ = k, then and These represent the conductance and susceptance of phases ij and ρ in a three-phase circuit, respectively. This represents the phase angle difference between phase ρ and phase k at node i; This represents the phase angle difference between the ρ phase of node i and the k phase of node j; The node power balance constraint considers the active and reactive power outputs of the devices to be planned at the node. The node power balance constraint is expressed as: In the formula, the superscript ρ∈{a,b,c} denotes phase, and P i,load and Q i,load P represents the active and reactive loads of node i, respectively; i,ch and P i,dis Q represents the charging and discharging power of the energy stored at node i; i,C and Q i,L These represent the reactive power compensation power of the parallel capacitor and reactor at node i, respectively. G represents the reactive power compensation of the SVC; ij B ij ,θ ij These represent the branch conductance, susceptance, and phase angle difference between nodes i and j, respectively. For power quality constraints, the three-phase imbalance at node n at any given time should satisfy the upper and lower bound requirements: In the formula, PVUR represents the three-phase unbalance; U a U b U c These are the three-phase voltage amplitudes; U avg This is the average value of the three-phase voltage; The voltage deviation at node n at any given time should meet the upper and lower bound requirements: In the formula, ΔU is the voltage deviation, U N Rated voltage; Voltage fluctuation is: In the formula, d ρ d represents the voltage fluctuation value of phase ρ. max This is the upper limit for voltage fluctuation; These are the maximum and minimum values ​​of the ρ-phase sequential voltage, respectively; Regarding energy storage constraints, the charge / discharge state constraint, as shown in equation (18), restricts the energy storage battery from being charged and discharged simultaneously. In the formula, These represent the charging and discharging states of energy storage, respectively. When the energy storage battery is charging... =1, otherwise A value of 1 indicates a binary variable. Excessive charge / discharge state transitions can shorten the lifespan of energy storage, so the number of charge / discharge state transitions should be limited. In the formula, This indicates the upper limit of the number of times the energy storage charge / discharge state transitions; Using the absolute value linearization method, equation (19) is linearized by introducing an auxiliary variable that characterizes the charging and discharging state of energy storage, as shown in equation (20). Equation (19) can then be transformed into: Equation (20) is the problem of finding the absolute value of the subtraction of two binary variables. Therefore, equation (20) can be transformed into: Regarding charging and discharging power constraints: E(t)=E(t-1)(1-δΔt)+P ch (t)h ch Δt-P dis (t) / h dis Δt (23); SOC min N batt P rated，batt ≤E(t)≤SOC max N batt P rated，batt (24); In equation (23): E(t) and Δt represent the remaining energy (kWh), charging / discharging power (kW), and time interval (h) of the energy storage battery at time t, respectively; δ and η ch η dis Represent the self-discharge rate and charge / discharge efficiency of the energy storage battery per hour, respectively; In equation (24): N batt S indicates the number of energy storage batteries; batt，unit It refers to the capacity of a single energy storage unit; SOC min and SOC max These represent the minimum and maximum values ​​for energy storage and percentage of electricity, respectively. Constraints on reactive power regulation equipment, including operational constraints on parallel capacitors and reactors; Parallel capacitors and reactors are used for reactive power compensation by switching, and the amount of reactive power compensation is a discrete variable. Q i,C (t)=u i,C (t)N i,C Q C,unit (27); Q i,L (t)=u i,L (t)N i,L Q L,unit (28); In the formula, N i,C and N i,L Q represents the number of parallel capacitor and reactor groups at node i, respectively; C,unit and Q L,unit These represent the capacities of a single group of capacitors and reactors to be planned in parallel; u i,C (t) and u i,L (t) represents the switching states of the parallel capacitor and reactor at time t at node i, respectively, and are binary variables; To extend the service life of parallel capacitors and reactors and improve economic efficiency, equations (29) and (30) limit the number of switching operations, and equations (20)-(22) are used for linearization. Equation (31) prevents capacitors and reactors from being put into operation at the same time. u C (t)+u L (t)≤1 (31); In the formula, and These represent the upper limits of the number of switching states for the capacitor and reactor, respectively. Regarding the operational constraints of SVC, SVC has the characteristic of continuously adjustable reactive power compensation. In the formula, This indicates the capacity configured in the i-node SVC; Regarding reactive power reserve constraints: In the formula, Q res This is the reactive power reserve factor. For the maximum reactive load, the capacitive reactive power reserve capacity should be 7%-8% of the reactive load; N c Q is the number of parallel capacitor groups; C,unit It refers to the capacitance of a single capacitor bank. In response to constraints on equipment deployment, energy storage and reactive power regulation equipment should be put into operation after construction. binary variable B i,ESS B i,C B i,L These represent whether energy storage is in the switching status of the device corresponding to node i, with 1 indicating yes; Regarding the OLTC operating constraints, the OLTC model is equivalent to a transformer + voltage regulator. The following constraints control the OLTC's gear switching within the range and satisfy the limit on the number of gear switching times. In the formula, binary variables Indicates whether an OLTC is planned at line ij, with 1 indicating yes; set Ω ML Includes all backbone lines; U i U j These represent the voltages at both ends of line ij; Tap OLTC (t) represents the gear position of the OLTC at time t; VR max VR min Represent the maximum and minimum values ​​of the voltage across the OLTC, respectively; integer variable N OLTC The number of OLTCs to be planned is 1 by default; This indicates the maximum number of gear shifts. Line transmission capacity constraints: In the formula P ij and Q ij These represent the active and reactive power flowing through the line, S. L This represents the maximum transmission power of the line. Controllable photovoltaic constraints are based on applying a local control strategy to the distributed photovoltaic converter to ensure that active and reactive power meet the following constraints: Among them, S PV P represents the configuration capacity of distributed photovoltaic power; PV Q represents photovoltaic output. PV This represents the reactive power flowing into the system; The power factor angle; The network reconfiguration constraints are similar to those of the aforementioned line type planning, based on the branch power flow equations (11) to (12), considering that n rc If there are several alternative routes, then the branch power flow equations are changed to n branch +n rc There are 1, and whether each line uses a decision variable R is determined by the decision variable R. ij Decision, R ij This is a binary variable; when it equals 1, the line is in use. The branch power flow constraint is represented as follows: Constraint (43) is a radial topological constraint, where φ l Let n represent the set of all routes. b and n s These represent the total number of nodes and the number of root nodes in the power distribution system, respectively. According to R ij The network is reconstructed based on the variable calculation results; when the result equals 1, the line is put into use.

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