An optimization method for joint planning of distributed generation and energy storage in active power distribution network

Abstract

The application discloses to belong to the technical field of power system planning and optimization, and particularly relates to an optimization method for distributed power generation and energy storage joint planning in an active distribution network, comprising: a double-layer robust planning model considering new energy output uncertainty is established, SOT is used to discretize the probability distribution of wind power and photovoltaic into a probability sequence and calculate the expected output, and an uncertainty processing mechanism is embedded to guide DG and energy storage capacity configuration; a DG and energy storage joint optimization model based on a double-layer planning framework is constructed, the upper layer optimizes site selection and capacity determination with the minimum annual total cost as the target, the lower layer optimizes energy storage scheduling with the minimum daily operation cost as the target, and planning and operation are coordinated; an improved BPSO monitoring population fitness variance based on chaos optimization is proposed, and Tent mapping chaos disturbance is dynamically introduced to realize efficient solution and global optimization of the model. On the PG&E 69 bus system, line loss can be reduced, voltage distribution can be improved, and new energy consumption capacity can be significantly improved.

Description

Technical Field

[0001] This invention belongs to the field of power system planning and optimization technology, and specifically relates to an optimization method for the joint planning of distributed generation and energy storage in an active distribution network. Background Technology

[0002] With the continuous and rapid growth of installed capacity of new energy power generation, the randomness, intermittency, and volatility of power output in the distribution network lead to difficulties in system power balance, increased risk of voltage exceeding limits, and prominent line congestion problems. Current distributed generation planning methods mainly suffer from the following technical limitations: First, traditional planning models are mostly based on deterministic scenarios, using typical days or extreme scenarios for optimization, failing to fully consider the probabilistic distribution characteristics of new energy output, resulting in significant risks in actual operation. Second, existing research often plans distributed generation and energy storage systems separately, lacking a collaborative optimization mechanism, and failing to fully leverage the role of energy storage in mitigating fluctuations and improving the absorption capacity of new energy. Third, regarding uncertainty handling, although existing research has employed robust optimization or stochastic programming methods, these methods are often too conservative or computationally too complex, making them difficult to apply in practical engineering. At the algorithmic level, existing research mostly uses traditional optimization algorithms such as genetic algorithms and particle swarm optimization to solve planning models, but these algorithms are prone to getting trapped in local optima when dealing with high-dimensional, non-convex joint planning problems, and their convergence speed is slow. Especially when considering planning-operation co-optimization across multiple time scales, traditional algorithms often struggle to provide effective solutions.

[0003] Existing planning methods have significant shortcomings in the following aspects: First, they fail to fully consider the impact of the spatiotemporal correlation of new energy output on the planning results; second, they lack refined modeling of the multiple operating modes (charging, discharging, standby) and their conversion characteristics of energy storage systems; and third, they fail to effectively resolve the coupling relationship between planning and operation, leading to potential feasibility issues in actual operation. Although some studies have attempted to address these problems using two-stage or bi-level planning methods, many challenges remain in model construction and algorithm design. Especially when dealing with large-scale, multi-node distribution network planning problems, existing methods are often computationally inefficient and fail to meet the needs of practical engineering applications.

[0004] Therefore, there is an urgent need for an optimization method for the joint planning of distributed generation and energy storage in active distribution networks. This method should effectively handle the uncertainty of new energy sources, achieve synergistic optimization of distributed generation and energy storage, and be computationally efficient. It should effectively solve the distribution network planning problem under the uncertainty of new energy sources and provide a complete technical solution for distribution network planning under high-proportion new energy integration. Summary of the Invention

[0005] The purpose of this invention is to provide an optimization method for the joint planning of distributed generation and energy storage in an active distribution network, comprising the following steps:

[0006] Step A: Establish a two-layer robust planning model that considers the uncertainty of new energy output. Apply sequence operation theory to discretize the probability distributions of wind power and photovoltaic power into probability sequences and calculate the expected output. Guide the configuration of DG and energy storage capacity by embedding an uncertainty handling mechanism.

[0007] Step B: Construct a joint optimization model for DG and energy storage based on a two-layer planning framework, including: the upper layer optimizes site selection and capacity setting with the goal of minimizing the total annual cost, and the lower layer optimizes energy storage scheduling with the goal of minimizing the daily operating cost, so as to achieve synergy between planning and operation;

[0008] Step C: Propose an improved binary particle swarm optimization algorithm based on chaos optimization, including: dynamically introducing Tent map chaotic perturbation by monitoring the population fitness variance, thereby achieving efficient solution and global optimization of the DG and energy storage joint optimization model based on the bi-level programming framework.

[0009] The establishment of the two-layer robust programming model considering the uncertainty of new energy output includes:

[0010] Based on the stochastic characteristics of wind and solar power output, a new energy output uncertainty model considering probability distribution is established to realize the modeling of new energy output uncertainty. The new energy output uncertainty model includes the Weibull distribution of wind power output and the Beta distribution of solar power output, providing a probabilistic basis for the subsequent application of sequence operation theory.

[0011] By statistically modeling the randomness of wind speed using the Weibull distribution, and based on the wind speed probability density function and the relationship between wind power output and wind speed, the wind power output probability density function is derived; by statistically modeling the randomness of photovoltaic power using the Beta distribution, and based on the light intensity probability density function and the relationship between photovoltaic power output and solar irradiance, the photovoltaic power output probability density function is derived.

[0012] The probability density function of the wind power output is derived as follows:

[0013] (1)

[0014] In the formula, , For wind power output, it represents the active power output of the wind turbine unit; This serves as a reference value, ensuring that when calculating wind speed from power, the cut-in wind speed can be correctly anchored. At this physical starting point;

[0015] The probability density function of the photovoltaic output is:

[0016] (2)

[0017] In the formula, Contribute to photovoltaic power To maximize photovoltaic output;

[0018] The desired output includes:

[0019] The probability sequence of wind power output is The expected output is calculated as follows:

[0020] (3)

[0021] In the formula, Let be the probability sequence of wind power output during the t-th sampling period. This is the discretization step size; Let be the probability density function of wind power output. The index is a discrete state and is an integer variable. This represents the total length of the sequence, i.e., the maximum index value.

[0022] The probability sequence of photovoltaic power output is The expected output is calculated as follows:

[0023] (4)

[0024] (5)

[0025] In the formula, To contribute to the aspirations of wind power For wind power sequence length, For wind power sequence index, This is a probability sequence of wind power output. Contributing to the photovoltaic industry's aspirations The length of the photovoltaic sequence. For photovoltaic sequence indexing, The probability sequence for photovoltaic power output. This is the discretization step size;

[0026] By planning 24-hour time intervals, the annual data is divided into seasons, and each season is represented by a typical day, resulting in 96 representative hours of expected output.

[0027] The upper-level optimization of site selection and capacity allocation with the goal of minimizing total annual cost includes:

[0028] The upper-level model aims to minimize the total annual cost and optimizes the site selection and capacity determination of distributed generation and energy storage. The upper-level model comprehensively considers equipment investment costs, operation and maintenance costs, and electricity purchase costs to form a complete framework for optimizing the total annual cost.

[0029] The objective function of the upper-level model is:

[0030] (6)

[0031] In the formula, C1 is the equipment investment cost, C2 is the operation and maintenance cost, and C3 is the electricity purchase cost;

[0032] (7)

[0033] (8)

[0034] (9)

[0035] In the formula, The present value factor for the wind turbine (WT) is... Unit investment cost for wind turbines, unit: $ / kW For the total planned capacity of the wind turbines, The present value factor for photovoltaic (PV) power generation. The unit investment cost for photovoltaic power generation is expressed in $ / kW. For the total planned photovoltaic capacity, The present value factor for energy storage. Energy storage investment costs associated with rated power, in $ / kW. Energy storage investment costs associated with installed capacity, in units of $ / kWh This is the rated power of the energy storage. For energy storage installation capacity, This is a fixed maintenance cost factor, a maintenance factor related to the rated power of wind and solar power. For the number of days in each season, This is a variable operating cost factor, representing the cost associated with the actual power generation of wind and solar power ($ / kWh). To contribute to the wind power industry, the first season Expected value for the time period Contributing to the photovoltaic industry's aspirations For the annual operation and maintenance cost coefficient of energy storage, s represents seasonal index pairs, and h represents hourly index pairs. For time-of-use electricity pricing, For the system active load, For system active power loss, This refers to the energy storage discharge power; it is positive during discharge to reduce the amount of electricity purchased. This refers to the charging power of the energy storage system. It is positive during charging and increases the purchased capacity.

[0036] The technical constraints of the upper-level model include: distributed generation capacity constraints and energy storage system capacity constraints.

[0037] The lower layer optimizes energy storage scheduling with the goal of minimizing intraday operating costs, including:

[0038] The lower-level model aims to minimize intraday operating costs and optimizes the charging and discharging strategy of the energy storage system, while also taking into account the uncertainty of distributed generation output.

[0039] The objective function of the lower-level model is:

[0040] (10)

[0041] In the formula, for Time-of-use electricity pricing for different time periods for System active power loss during the time period for The charging and discharging power of energy storage during a given time period;

[0042] The operational constraints of the lower-level model include: power balance equations, power flow equations, and energy storage system operational constraints.

[0043] The coordination between planning and operation includes:

[0044] The upper-level model optimizes the location and capacity of energy storage and distributed power sources to find the optimal annual economic objective function, and then passes the location and capacity of energy storage and distributed power sources to the lower-level model.

[0045] The lower-level model optimizes the intraday scheduling of energy storage for each season to obtain the optimal annual fluctuating operating cost, and then returns the annual fluctuating operating cost to the upper-level model to generate the annual economic objective function.

[0046] Achieve collaborative optimization between upper and lower level models and establish an effective connection mechanism between planning and operation.

[0047] The improved binary particle swarm optimization algorithm based on chaos optimization includes:

[0048] Based on the traditional binary particle swarm optimization algorithm, a chaotic optimization mechanism is introduced to enhance the global search capability and avoid premature convergence. The optimization search is performed by updating particle velocity and position, making it suitable for solving mixed-integer programming problems.

[0049] The formula for updating particle velocity is:

[0050] (11)

[0051] In the formula, Let represent the current velocity of particle n in the k-th dimension. For inertial weights, and Here, `rand` is the acceleration coefficient, and `rand` is a random number in the range [0,1]. and These are the individual historical optimal solution and the global historical optimal solution, respectively.

[0052] The position update algorithm for updating particle positions uses the Sigmoid function for binary conversion:

[0053] (12)

[0054] In the formula, For the Sigmoid function, The particle velocity;

[0055] The new position is determined based on a random number:

[0056] (13)

[0057] In the formula, The particle position represents the nth The particle in the first The position value of a dimension can only be 0 or 1.

[0058] The monitoring of population fitness variance dynamics includes:

[0059] Premature convergence is identified by dynamically monitoring the population fitness variance, and chaotic optimization is triggered accordingly; the formula for calculating the dynamically monitored population fitness variance is as follows:

[0060] (14)

[0061] In the formula, Let m be the fitness value of particle m. The average fitness of the population. The optimal fitness of the population is Np, where Np is the population size. The standard deviation of population fitness;

[0062] The premature convergence detection condition for identifying the premature convergence state is as follows:

[0063] (15)

[0064] in, and These are the PFV values ​​for the current iteration and the next iteration, respectively. and The threshold values ​​are set to 0.99 and 1.01 respectively.

[0065] When the premature convergence detection condition for identifying premature convergence states is met, the chaos optimization process is automatically started.

[0066] The introduced Tent mapping chaotic perturbation includes:

[0067] To address the premature convergence problem of the algorithm, a Tent mapping is introduced to perform chaotic perturbation, leveraging the ergodicity and randomness of chaotic motion to enhance population diversity.

[0068] The Tent mapping formula is as follows:

[0069] (16)

[0070] When periodic or fixed points appear in the iterative sequence, adding random perturbations causes the mapping to re-enter a chaotic state:

[0071] (17)

[0072] In the formula, For the chaotic variables mapped by Tent;

[0073] Chaotic variables are used to modify particle positions. By perturbing the current solution by mapping it to the chaotic space, and then mapping it back to the solution space, global exploration is achieved.

[0074] The efficient solution and global optimization of the DG and energy storage joint optimization model based on the two-level programming framework includes:

[0075] Step C31: Initialize the particle swarm, set the population size Np=50, and the maximum number of iterations iter max =100, Inertia Weight Range And randomly generate initial position and velocity;

[0076] Step C32: Calculate the fitness value of each particle, which is the objective function of the DG and energy storage joint optimization model based on the bi-level programming framework. In the formula, F1 is the objective function of the upper-level model, and F2 is the objective function of the lower-level model.

[0077] Step C33: Update the individual's historical best solution and the global historical optimal solution ;

[0078] Step C34: Update the particle velocity according to formula (11), and update the particle position according to formulas (12) and (13);

[0079] Step C35: Calculate the population fitness variance Use formula (14) and check the premature convergence condition formula (15); if the condition is met, apply the Tent map chaotic perturbation formula (16) and formula (17);

[0080] Step C36: Repeat steps C32-C35 until the convergence condition is met;

[0081] The convergence condition is: Or reach the maximum number of iterations

[0082] The beneficial effects of this invention are as follows:

[0083] This invention discloses an optimization method for joint planning of distributed generation and energy storage in an active distribution network. First, it introduces sequence operation theory to model the uncertainty of wind and solar power output, discretizing the probability distribution into a probability sequence and calculating the expected output, significantly improving the robustness of the planning scheme under intermittent power source access. Second, it proposes a joint optimization method based on a two-layer planning framework. The upper layer optimizes the site selection and capacity allocation of distributed generation and energy storage with the goal of minimizing the annual total cost, while the lower layer optimizes the energy storage scheduling strategy with the goal of minimizing the daily operating cost, achieving effective coordination between planning and operation. Finally, addressing the problems of high model solution complexity and susceptibility to local optima, an improved binary particle swarm optimization algorithm based on chaotic optimization is proposed. By dynamically monitoring the population fitness variance and introducing chaotic perturbations from the Tent mapping, the algorithm's global search capability and convergence performance are effectively enhanced. Simulation results show that this method can reduce line losses, improve voltage distribution, and significantly enhance the renewable energy absorption capacity on the PG&E 69 bus system. Taking full account of the uncertainty of new energy output, this solution effectively addresses the distribution network planning problem under the uncertainty of new energy, and provides a complete technical solution for distribution network planning under high proportion of new energy access. Attached Figure Description

[0084] Figure 1 This is a flowchart illustrating an optimization method for the joint planning of distributed generation and energy storage in an active distribution network according to the present invention.

[0085] Figure 2 This is a schematic diagram of time-of-use electricity pricing for different periods throughout the year in an embodiment of the present invention;

[0086] Figure 3 This is a schematic diagram illustrating the impact analysis of energy storage planning in an embodiment of the present invention;

[0087] Figure 4 This is a schematic diagram of the cumulative probability of the voltage amplitude of bus 27 in an embodiment of the present invention. Detailed Implementation

[0088] This invention provides an optimization method for the joint planning of distributed generation and energy storage in an active distribution network. The invention will be further described in detail below with reference to the accompanying drawings.

[0089] like Figure 1The embodiment of the present invention disclosed presents an optimization method for joint planning of distributed generation and energy storage in an active distribution network, comprising the following steps:

[0090] Step A: Establish a two-layer robust planning model that considers the uncertainty of new energy output. Apply sequence operation theory to discretize the probability distributions of wind power and photovoltaic power into probability sequences and calculate the expected output. Guide the configuration of DG and energy storage capacity by embedding an uncertainty handling mechanism.

[0091] Step B: Construct a joint optimization model for DG and energy storage based on a two-layer planning framework, including: the upper layer optimizes site selection and capacity setting with the goal of minimizing the total annual cost, and the lower layer optimizes energy storage scheduling with the goal of minimizing the daily operating cost, so as to achieve synergy between planning and operation;

[0092] Step C: Propose an improved binary particle swarm optimization algorithm based on chaos optimization, including: dynamically introducing Tent map chaotic perturbation by monitoring the population fitness variance, thereby achieving efficient solution and global optimization of the DG and energy storage joint optimization model based on the bi-level programming framework.

[0093] In this embodiment, an optimization method for joint planning of distributed generation and energy storage in the active distribution network is applied. First, sequence operation theory is introduced to model the uncertainty of wind and solar power output, discretizing the probability distribution into a probability sequence and calculating the expected output, significantly improving the robustness of the planning scheme under intermittent power source access. Second, a joint optimization method based on a two-layer planning framework is proposed. The upper layer optimizes the site selection and capacity determination of distributed generation and energy storage with the goal of minimizing the annual total cost, while the lower layer optimizes the energy storage scheduling strategy with the goal of minimizing the daily operating cost, achieving effective coordination between planning and operation. Finally, to address the problems of high model solution complexity and easy getting trapped in local optima, an improved binary particle swarm optimization algorithm based on chaotic optimization is proposed. By dynamically monitoring the population fitness variance and introducing chaotic perturbations from the Tent mapping, the global search capability and convergence performance of the algorithm are effectively enhanced. Simulation results show that this method can reduce line losses, improve voltage distribution, and significantly improve the renewable energy absorption capacity on the PG&E 69 bus system.

[0094] The following detailed explanation of each step, in conjunction with the accompanying drawings, is provided.

[0095] An optimization method for joint planning of distributed generation and energy storage in an active distribution network includes the following steps:

[0096] Step A: Establish a two-layer robust planning model that considers the uncertainty of new energy output. Apply sequence operation theory to discretize the probability distributions of wind power and photovoltaic power into probability sequences and calculate the expected output. Guide the configuration of DG and energy storage capacity by embedding an uncertainty handling mechanism.

[0097] In this embodiment, step A, which proposes a wind power and solar power expected output model considering uncertainties, is summarized as follows:

[0098] Step A1: Modeling the uncertainty of new energy output.

[0099] The establishment of the two-layer robust programming model considering the uncertainty of new energy output includes:

[0100] Based on the stochastic characteristics of wind and solar power output, a new energy output uncertainty model considering probability distribution is established to realize the modeling of new energy output uncertainty. The new energy output uncertainty model includes the Weibull distribution of wind power output and the Beta distribution of solar power output, providing a probabilistic basis for the subsequent application of sequence operation theory.

[0101] By statistically modeling the randomness of wind speed using the Weibull distribution, and based on the wind speed probability density function and the relationship between wind power output and wind speed, the wind power output probability density function is derived; by statistically modeling the randomness of photovoltaic power using the Beta distribution, and based on the light intensity probability density function and the relationship between photovoltaic power output and solar irradiance, the photovoltaic power output probability density function is derived.

[0102] The wind speed probability density function is:

[0103] ;

[0104] In the formula, v is the actual wind speed, ι is the shape factor (dimensionless), which describes the shape of the wind speed probability density function; γ is the scale factor;

[0105] The relationship between wind power output and wind speed is expressed as follows:

[0106] ;

[0107] In the formula, Rated output power, To cut into wind speed, To cut off the wind speed, This is the rated wind speed.

[0108] Based on the aforementioned wind power output probability density function and the relationship between wind power output and wind speed, the wind power output probability density function is derived as follows:

[0109] (1)

[0110] In the formula, , For wind power output, it represents the active power output of the wind turbine unit; This serves as a reference value, ensuring that when calculating wind speed from power, the cut-in wind speed can be correctly anchored. At this physical starting point;

[0111] The light intensity probability density function is:

[0112] ;

[0113] In the formula, This represents the actual light intensity. The maximum value, For the Gamma function, and It is a shape parameter used to characterize the random characteristics of light intensity. Control high-value areas, Controlling the low-value region determines the fluctuation characteristics of the simulated photovoltaic output curve;

[0114] The relationship between photovoltaic power output and solar irradiance is as follows:

[0115] ;

[0116] In the formula, Solar irradiance, For maximum power point tracking efficiency, For the radiation area, For conversion efficiency, The angle of incidence of the sun;

[0117] The probability density function of photovoltaic power output is:

[0118] (2)

[0119] In the formula, Contribute to photovoltaic power To maximize photovoltaic output;

[0120] Step A2: Uncertainty discretization processing based on sequence operation theory.

[0121] In this embodiment, a sequence operation processing method considering the discretization of probability distributions is proposed by introducing a discretization step size and a probability sequence. Sequence Operation Theory (SOT) is based on the concept of sequence convolution in digital signal processing, which discretizes continuous random variables into probability sequences and generates new sequences through interoperation.

[0122] The application of sequence operation theory discretizes the probability distributions of wind power and photovoltaic power into probability sequences and calculates the expected output, including:

[0123] Define the discretization step size This converts continuous random variables into probability sequences.

[0124] probability sequence Must meet:

[0125] ;

[0126] In the formula, The length of the probability sequence;

[0127] probability sequence The expected value is calculated as follows:

[0128] ;

[0129] In the formula, Let be the expected value of the probability sequence;

[0130] Sequence operations include additive convolution (ATC) and subtractive convolution (STC):

[0131] ;

[0132] ;

[0133] In the formula, It is an additive convolution (ATC). It is a subtractive convolution (STC). Let a be a probability sequence. Let b be the probability sequence. Let be the length of sequence 'a'. b. Sequence length;

[0134] Discretizing wind and solar power output using SOT: Let Let be the probability sequence of wind power output during the t-th sampling period, with a sequence length of . ,in This represents the maximum wind power output within time period t.

[0135] The specific process of probability sequence calculation is as follows:

[0136] The desired output includes:

[0137] The probability sequence of wind power output is The expected output is calculated as follows:

[0138] (3)

[0139] In the formula, Let be the probability sequence of wind power output during the t-th sampling period. This is the discretization step size; Let be the probability density function of wind power output. The index is a discrete state and is an integer variable. This represents the total length of the sequence, i.e., the maximum index value.

[0140] The probability sequence of photovoltaic power output is The expected output is calculated as follows:

[0141] (4)

[0142] (5)

[0143] In the formula, To contribute to the aspirations of wind power For wind power sequence length, For wind power sequence index, This is a probability sequence of wind power output. Contributing to the photovoltaic industry's aspirations The length of the photovoltaic sequence. For photovoltaic sequence indexing, The probability sequence for photovoltaic power output. This is the discretization step size;

[0144] By planning the 24-hour time interval, the annual data is divided into seasons (91 days per season), and each season is represented by a typical day to obtain the expected output of 96 representative hours.

[0145] Step B: Construct a joint optimization model for DG and energy storage based on a two-layer planning framework, including: the upper layer optimizes site selection and capacity setting with the goal of minimizing the total annual cost, and the lower layer optimizes energy storage scheduling with the goal of minimizing the daily operating cost, so as to achieve synergy between planning and operation;

[0146] In this embodiment, the process for step B, establishing the joint optimization model of DG and energy storage based on a two-layer planning framework, is as follows:

[0147] Step B1: Construction of the upper-level planning model.

[0148] The upper-level optimization of site selection and capacity allocation with the goal of minimizing total annual cost includes:

[0149] The upper-level model aims to minimize the total annual cost and optimizes the site selection and capacity determination of distributed generation and energy storage. The upper-level model comprehensively considers equipment investment costs, operation and maintenance costs, and electricity purchase costs to form a complete framework for optimizing the total annual cost.

[0150] Objective function of the upper-level model for:

[0151] (6)

[0152] In the formula, C1 is the equipment investment cost, C2 is the operation and maintenance cost, and C3 is the electricity purchase cost;

[0153] (7)

[0154] (8)

[0155] (9)

[0156] In the formula, The present value factor for the wind turbine (WT) is... Unit investment cost for wind turbines, unit: $ / kW For the total planned capacity of the wind turbines, The present value factor for photovoltaic (PV) power generation. The unit investment cost for photovoltaic power generation is expressed in $ / kW. For the total planned photovoltaic capacity, The present value factor for energy storage. Energy storage investment costs associated with rated power, in $ / kW. Energy storage investment costs associated with installed capacity, in units of $ / kWh This is the rated power of the energy storage. For energy storage installation capacity, This is a fixed maintenance cost factor, a maintenance factor related to the rated power of wind and solar power. For the number of days in each season, This is a variable operating cost factor, representing the cost associated with the actual power generation of wind and solar power ($ / kWh). To contribute to the wind power industry, the first season Expected value for the time period Contributing to the photovoltaic industry's aspirations For the annual operation and maintenance cost coefficient of energy storage, s represents seasonal index pairs, and h represents hourly index pairs. For time-of-use electricity pricing, For the system active load, For system active power loss, This refers to the energy storage discharge power; it is positive during discharge to reduce the amount of electricity purchased. This refers to the charging power of the energy storage system. It is positive during charging and increases the purchased capacity.

[0157] The technical constraints of the upper-level model include: distributed generation capacity constraints and energy storage system capacity constraints.

[0158] Distributed generation capacity constraints:

[0159] ;

[0160] ;

[0161] In the formula, The active power output of the DG at node i, i.e., the planned capacity, For nodes Active load, This represents the total active power loss of the system without DG. For nodes DG's efforts were in vain. For nodes reactive load, N represents the total reactive power loss of the system without DG, and N is the total number of system nodes.

[0162] Energy storage system capacity constraints:

[0163] ;

[0164] ;

[0165] In the formula, This is the lower limit for the rated power of energy storage. This is the rated power of the energy storage. The upper limit of the rated power of energy storage is planned. This serves as the lower limit for planned energy storage installation capacity. For energy storage installation capacity, The upper limit for energy storage installation capacity is planned;

[0166] Step B2: Run the optimization model at the lower level.

[0167] The lower layer optimizes energy storage scheduling with the goal of minimizing intraday operating costs, including:

[0168] The lower-level model aims to minimize intraday operating costs and optimizes the charging and discharging strategy of the energy storage system, while also taking into account the uncertainty of distributed generation output.

[0169] Objective function of the lower-level model for:

[0170] (10)

[0171] In the formula, for Time-of-use electricity pricing for different time periods for System active power loss during the time period for The charging and discharging power of energy storage during a given time period;

[0172] The operational constraints of the lower-level model include: power balance equations, power flow equations, and energy storage system operational constraints.

[0173] The power balance equation is:

[0174] ;

[0175] ;

[0176] In the formula, The active power of the balancing node (relaxed node), For nodes DG contributed significantly. For nodes Active load, For the total active power loss of the system, The reactive power of the balancing node (relaxed node), For nodes DG's efforts were in vain. For nodes reactive load, Let N be the total reactive power loss of the system, N be the total number of node pairs, and i be the node index;

[0177] The power flow equation constraints are:

[0178] ;

[0179] ;

[0180] ;

[0181] ;

[0182] ;

[0183] ;

[0184] In the formula, for Time period nodes Active power injection, branch road The admittance amplitude, for Time period nodes voltage amplitude, for Time period nodes voltage amplitude, For admittance phase angle, For nodes voltage phase angle, For nodes voltage phase angle, for Time period nodes reactive power injection branch road The resistance, for Time-of-day branch Active power flow, branch road Reactance, for Time-of-day branch reactive power flow, for Time-of-day branch The square of the current amplitude, This is the square of the lower limit of the allowable node voltage. The square of the maximum allowable node voltage. The square of the maximum allowable current of the branch;

[0185] The operating constraints of the energy storage system are:

[0186] ;

[0187] ;

[0188] ;

[0189] ;

[0190] In the formula, Time-of-use energy storage charging power, This is the maximum allowable charging power for energy storage. for Time-of-use energy storage discharge power, For the maximum allowable discharge power of energy storage, For the minimum allowable capacity / electricity of energy storage, for The remaining electricity stored during the time period, For the maximum allowable capacity / electricity of energy storage, For charging efficiency, For discharge efficiency;

[0191] Step B3: Two-layer model collaborative optimization mechanism.

[0192] The coordination between planning and operation includes:

[0193] The upper-level model optimizes the location and capacity of energy storage and distributed generation to find the optimal annual economic objective function, and then passes the location and capacity of energy storage and distributed generation (DG) to the lower-level model.

[0194] The lower-level model optimizes the intraday scheduling of energy storage for each season to obtain the optimal annual fluctuating operating cost, and then returns the annual fluctuating operating cost to the upper-level model to generate the annual economic objective function.

[0195] Achieve collaborative optimization between upper and lower level models and establish an effective connection mechanism between planning and operation.

[0196] Step C: Propose an improved binary particle swarm optimization algorithm based on chaos optimization, including: dynamically introducing Tent map chaotic perturbation by monitoring the population fitness variance, thereby achieving efficient solution and global optimization of the DG and energy storage joint optimization model based on the bi-level programming framework.

[0197] Step C1: Basic principles of the improved binary particle swarm optimization algorithm.

[0198] This algorithm, based on the traditional Binary Particle Swarm Optimization (BPSO) algorithm, introduces a chaotic optimization mechanism to enhance global search capabilities and avoid premature convergence. It optimizes the search by updating particle velocities and positions, and is suitable for solving mixed-integer programming problems.

[0199] The formula for updating particle velocity is:

[0200] (11)

[0201] In the formula, Let represent the current velocity of particle n in the k-th dimension. For inertial weights, and Here, `rand` is the acceleration coefficient, and `rand` is a random number in the range [0,1]. and These are the individual historical optimal solution and the global historical optimal solution, respectively.

[0202] The position update algorithm for updating particle positions uses the Sigmoid function for binary conversion:

[0203] (12)

[0204] In the formula, For the Sigmoid function, The particle velocity;

[0205] The new position is determined based on a random number:

[0206] (13)

[0207] In the formula, The particle position represents the nth The particle in the first The position value of a dimension can only be 0 or 1;

[0208] Step C2: Monitoring and dynamic optimization of population fitness variance.

[0209] The monitoring of population fitness variance (PFV) dynamics includes:

[0210] Premature convergence states are identified by dynamically monitoring the population fitness variance, and chaotic optimization is triggered.

[0211] The formula for calculating the dynamic monitoring population fitness variance (PFV) is as follows:

[0212] (14)

[0213] In the formula, Let m be the fitness value of particle m. The average fitness of the population. The optimal fitness of the population is Np, where Np is the population size. The standard deviation of population fitness;

[0214] The premature convergence detection condition for identifying the premature convergence state is as follows:

[0215] (15)

[0216] in, and These are the PFV values ​​for the current iteration and the next iteration, respectively. and The threshold values ​​are set to 0.99 and 1.01 respectively.

[0217] When the premature convergence detection condition for identifying premature convergence states is met, the chaos optimization process is automatically started.

[0218] Step C3: Chaotic optimization mechanism based on Tent mapping.

[0219] The introduced Tent mapping chaotic perturbation includes:

[0220] To address the premature convergence problem of the algorithm, a Tent mapping is introduced to perform chaotic perturbation, leveraging the ergodicity and randomness of chaotic motion to enhance population diversity.

[0221] The Tent mapping formula is as follows:

[0222] (16)

[0223] When periodic points (such as 0.2, 0.4, 0.6, 0.8) or fixed points (such as 0, 0.25, 0.5, 0.75) appear in the iterative sequence, a random perturbation is added to make the mapping re-enter a chaotic state:

[0224] (17)

[0225] In the formula, For the chaotic variables mapped by Tent;

[0226] Chaotic variables are used to modify particle positions. Specifically, this is achieved by perturbing the current solution by mapping it to the chaotic space, and then mapping it back to the solution space to realize global exploration.

[0227] Step C4: Algorithm implementation process and model solution.

[0228] The improved BPSO algorithm is applied to solve the bilevel programming model in step B. The specific process includes initialization, iterative optimization, and convergence judgment.

[0229] The efficient solution and global optimization of the DG and energy storage joint optimization model based on the two-level programming framework includes:

[0230] Step C31: Initialize the particle swarm, set the population size Np=50, and the maximum number of iterations iter max =100, Inertia Weight Range And randomly generate initial position and velocity;

[0231] Step C32: Calculate the fitness value of each particle, which is the objective function of the DG and energy storage joint optimization model based on the bi-level programming framework. In the formula, F1 is the objective function of the upper-level model, and F2 is the objective function of the lower-level model.

[0232] Step C33: Update the individual's historical best solution and the global historical optimal solution ;

[0233] Step C34: Update the particle velocity according to formula (11), and update the particle position according to formulas (12) and (13);

[0234] Step C35: Calculate the population fitness variance Use formula (14) and check the premature convergence condition formula (15); if the condition is met, apply the Tent map chaotic perturbation formula (16) and formula (17);

[0235] Step C36: Repeat steps C32-C35 until the convergence condition is met;

[0236] The convergence condition is: Or it may reach the maximum number of iterations.

[0237] In this embodiment, an optimization method for joint planning of distributed generation and energy storage in an active distribution network disclosed in this invention is applied. Sequence operation theory is introduced to model the uncertainty of wind and solar power output, discretizing the probability distribution into a probability sequence and calculating the expected output, significantly improving the robustness of the planning scheme under intermittent power source access. A joint optimization method based on a two-layer planning framework is proposed. The upper layer optimizes the site selection and capacity determination of distributed generation and energy storage with the goal of minimizing the annual total cost, while the lower layer optimizes the energy storage scheduling strategy with the goal of minimizing the daily operating cost, achieving effective coordination between planning and operation. To address the problems of high model solution complexity and susceptibility to local optima, an improved binary particle swarm optimization algorithm based on chaotic optimization is proposed. By dynamically monitoring the population fitness variance and introducing chaotic perturbations from the Tent mapping, the algorithm's global search capability and convergence performance are effectively enhanced.

[0238] To verify the effectiveness of the optimization method for joint planning of distributed generation and energy storage in an active distribution network disclosed in this invention, simulation experiments were conducted. The simulation results show that the method can reduce line losses, improve voltage distribution, and significantly enhance the renewable energy absorption capacity on the PG&E 69 bus system.

[0239] In this simulation experiment, the time-of-use electricity prices for different periods throughout the year are as follows: Figure 2 As shown, the impact analysis of energy storage planning is as follows: Figure 3 As shown, the cumulative probability of the voltage amplitude of bus 27 is as follows: Figure 4 As shown.

[0240] I. Simulation Environment and Parameter Settings

[0241] To verify the effectiveness of the "robust collaborative planning method for photovoltaic-storage power grids considering dynamic frequency security" described in this invention, this embodiment selects a standard PG&E 69-node distribution system as the test object for simulation analysis. The system's base voltage is set to 12.66 kV, the total active load is 3715 kW, and the total reactive load is 2300 kVar. Based on the network sensitivity index analysis results, this embodiment selects nodes 49, 50, 61, and 64 as candidate installation locations for distributed generation (DG) and energy storage devices. For energy storage selection, zinc-bromine redox flow batteries, which offer better economic benefits, are used, with investment costs and operation and maintenance parameters set based on market data. The solution algorithm adopts the improved binary particle swarm optimization (IBPSO) algorithm, with a population size of 50 and a maximum number of iterations of 100 to ensure the convergence and accuracy of the optimization.

[0242] II. Economic Analysis

[0243] This embodiment first introduces a time-of-use pricing mechanism through a lower-level operation model to guide energy storage operations. For example... Figure 2 As shown, the system input data includes two typical time-of-use electricity price curves for spring / summer and autumn / winter. The electricity price exhibits a significant peak-valley gradient characteristic over time, providing a price signal basis for the "low storage, high generation" arbitrage operation of energy storage systems. The planning results based on this price signal are as follows: Figure 3 As shown in the figure, the chart compares the annual cost indicators of the photovoltaic-storage collaborative planning model (with energy storage) proposed in this invention with the traditional distributed power generation planning model (without energy storage). The results show that although configuring energy storage slightly increases the system's equipment investment and operation and maintenance costs (investment cost increases from 0.08 M$ to 0.12 M$), the annual electricity purchase cost is significantly reduced from 1.83 M$ to 1.63 M$, thanks to the energy storage system's discharge support during peak electricity price periods and its effective suppression of network losses. After comprehensive calculation, the total annual cost of the model described in this embodiment is 1.94 M$, lower than the 2.11 M$ of the model without energy storage. This result demonstrates that this invention, through photovoltaic-storage collaborative planning, can effectively cover its investment cost by utilizing the peak-shaving and valley-filling benefits of energy storage, achieving global optimization of distribution network planning from an economic perspective.

[0244] III. Technical Security Analysis

[0245] In addition to economic benefits, this embodiment further verifies the effectiveness of the planning scheme in improving power quality. For example... Figure 4 As shown in the figure, this graph illustrates the cumulative probability distribution curve of voltage amplitude at the weakest node (node ​​27) at the end of the system during an 8760-hour operating cycle throughout the year. The circled curves represent the voltage distribution of the present invention (with energy storage model), while the solid lines represent the voltage distribution of the traditional method (without energy storage model). The graph results show that the cumulative probability curve of the model described in this invention is generally located to the right of the traditional model curve, and the curve slope is steeper. This result indicates that by coordinating the configuration of the energy storage system during the planning stage, the overall voltage amplitude level of the system nodes is improved, approaching the per-unit value of 1.0 pu; simultaneously, the voltage fluctuation range is significantly reduced, effectively solving the voltage limit exceedance problem caused by the uncertainty of photovoltaic output. In summary, this invention significantly enhances the voltage stability and operational resilience of the system while improving the economic efficiency of the distribution network operation.

[0246] Another embodiment of the present invention provides a computer device including a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes the optimization method for joint planning of distributed generation and energy storage in an active distribution network according to the present invention.

[0247] Another embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the processor performs an optimization method for the joint planning of distributed generation and energy storage in an active distribution network according to the present invention.

[0248] The above embodiments have provided a detailed description of the technical solution of the present invention. Obviously, the present invention is not limited to the described embodiments. Based on the embodiments of the present invention, those skilled in the art can make various modifications, but any modifications equivalent to or similar to the present invention fall within the scope of protection of the present invention.

Claims

1. An optimization method for joint planning of distributed generation and energy storage in an active distribution network, characterized in that, Includes the following steps: Step A: Establish a two-layer robust planning model that considers the uncertainty of new energy output. Apply sequence operation theory to discretize the probability distributions of wind power and photovoltaic power into probability sequences and calculate the expected output. Guide the configuration of DG and energy storage capacity by embedding an uncertainty handling mechanism. Step B: Construct a joint optimization model for DG and energy storage based on a two-layer planning framework, including: the upper layer optimizes site selection and capacity setting with the goal of minimizing the total annual cost, and the lower layer optimizes energy storage scheduling with the goal of minimizing the daily operating cost, so as to achieve synergy between planning and operation; Step C: Propose an improved binary particle swarm optimization algorithm based on chaos optimization, including: dynamically introducing Tent map chaotic perturbation by monitoring the population fitness variance, thereby achieving efficient solution and global optimization of the DG and energy storage joint optimization model based on the bi-level programming framework.

2. The optimization method for joint planning of distributed generation and energy storage in an active distribution network according to claim 1, characterized in that, The establishment of the two-layer robust programming model considering the uncertainty of new energy output includes: Based on the stochastic characteristics of wind and solar power output, a new energy output uncertainty model considering probability distribution is established to realize the modeling of new energy output uncertainty. The new energy output uncertainty model includes the Weibull distribution of wind power output and the Beta distribution of solar power output, providing a probabilistic basis for the subsequent application of sequence operation theory. By statistically modeling the randomness of wind speed using the Weibull distribution, and based on the wind speed probability density function and the relationship between wind power output and wind speed, the wind power output probability density function is derived; by statistically modeling the randomness of photovoltaic power using the Beta distribution, and based on the light intensity probability density function and the relationship between photovoltaic power output and solar irradiance, the photovoltaic power output probability density function is derived. The probability density function of the wind power output is derived as follows: （1） In the formula, , For wind power output, it represents the active power output of the wind turbine unit; This serves as a reference value, ensuring that when calculating wind speed from power, the cut-in wind speed can be correctly anchored. At this physical starting point; The probability density function of the photovoltaic output is: （2） In the formula, Contribute to photovoltaic power To maximize photovoltaic output.

3. The optimization method for joint planning of distributed generation and energy storage in an active distribution network according to claim 1, characterized in that, The desired output includes: The probability sequence of wind power output is The expected output is calculated as follows: （3） In the formula, Let be the probability sequence of wind power output during the t-th sampling period. This is the discretization step size; Let be the probability density function of wind power output. The index is a discrete state and is an integer variable. This represents the total length of the sequence, i.e., the maximum index value. The probability sequence of photovoltaic power output is The expected output is calculated as follows: （4） （5） In the formula, To contribute to the aspirations of wind power For wind power sequence length, For wind power sequence index, This is a probability sequence of wind power output. Contributing to the photovoltaic industry's aspirations The length of the photovoltaic sequence. For photovoltaic sequence indexing, The probability sequence for photovoltaic power output. This is the discretization step size; By planning 24-hour time intervals, the annual data is divided into seasons, and each season is represented by a typical day, resulting in 96 representative hours of expected output.

4. The optimization method for joint planning of distributed generation and energy storage in an active distribution network according to claim 1, characterized in that, The upper-level optimization of site selection and capacity allocation with the goal of minimizing total annual cost includes: The upper-level model aims to minimize the total annual cost and optimizes the site selection and capacity determination of distributed generation and energy storage. The upper-level model comprehensively considers equipment investment costs, operation and maintenance costs, and electricity purchase costs to form a complete framework for optimizing the total annual cost. The objective function of the upper-level model is: （6） In the formula, C1 is the equipment investment cost, C2 is the operation and maintenance cost, and C3 is the electricity purchase cost; （7） （8） （9） In the formula, The present value factor for the wind turbine (WT) is... Unit investment cost for wind turbines, unit: $ / kW For the total planned capacity of the wind turbines, The present value factor for photovoltaic (PV) power generation. The unit investment cost for photovoltaic power generation is expressed in $ / kW. For the total planned photovoltaic capacity, The present value factor for energy storage. Energy storage investment costs associated with rated power, in $ / kW. Energy storage investment costs associated with installed capacity, in units of $ / kWh This is the rated power of the energy storage. For energy storage installation capacity, This is a fixed maintenance cost factor, a maintenance factor related to the rated power of wind and solar power. For the number of days in each season, This is a variable operating cost factor, representing the cost associated with the actual power generation of wind and solar power ($ / kWh). To contribute to the wind power industry, the first season Expected value for the time period Contributing to the photovoltaic industry's aspirations For the annual operation and maintenance cost coefficient of energy storage, s represents seasonal index pairs, and h represents hourly index pairs. For time-of-use electricity pricing, For the system active load, For system active power loss, This refers to the energy storage discharge power; it is positive during discharge to reduce the amount of electricity purchased. This refers to the charging power of the energy storage system. It is positive during charging and increases the purchased capacity. The technical constraints of the upper-level model include: distributed generation capacity constraints and energy storage system capacity constraints.

5. The optimization method for joint planning of distributed generation and energy storage in an active distribution network according to claim 1, characterized in that, The lower layer optimizes energy storage scheduling with the goal of minimizing intraday operating costs, including: The lower-level model aims to minimize intraday operating costs and optimizes the charging and discharging strategy of the energy storage system, while also taking into account the uncertainty of distributed generation output. The objective function of the lower-level model is: （10） In the formula, for Time-of-use electricity pricing for different time periods for System active power loss during the time period for The charging and discharging power of energy storage during a given time period; The operational constraints of the lower-level model include: power balance equations, power flow equations, and energy storage system operational constraints.

6. The optimization method for joint planning of distributed generation and energy storage in an active distribution network according to claim 1, characterized in that, The coordination between planning and operation includes: The upper-level model optimizes the location and capacity of energy storage and distributed power sources to find the optimal annual economic objective function, and then passes the location and capacity of energy storage and distributed power sources to the lower-level model. The lower-level model optimizes the intraday scheduling of energy storage for each season to obtain the optimal annual fluctuating operating cost, and then returns the annual fluctuating operating cost to the upper-level model to generate the annual economic objective function. Achieve collaborative optimization between upper and lower level models and establish an effective connection mechanism between planning and operation.

7. The optimization method for joint planning of distributed generation and energy storage in an active distribution network according to claim 1, characterized in that, The improved binary particle swarm optimization algorithm based on chaos optimization includes: Based on the traditional binary particle swarm optimization algorithm, a chaotic optimization mechanism is introduced to enhance the global search capability and avoid premature convergence. The optimization search is performed by updating particle velocity and position, making it suitable for solving mixed-integer programming problems. The formula for updating particle velocity is: （11） In the formula, Let represent the current velocity of particle n in the k-th dimension. For inertial weights, and Here, `rand` is the acceleration coefficient, and `rand` is a random number in the range [0,1]. and These are the individual historical optimal solution and the global historical optimal solution, respectively. The position update algorithm for updating particle positions uses the Sigmoid function for binary conversion: （12） In the formula, For the Sigmoid function, The particle velocity; The new position is determined based on a random number: （13） In the formula, The particle position represents the nth The particle in the first The position value of a dimension can only be 0 or 1.

8. The optimization method for joint planning of distributed generation and energy storage in an active distribution network according to claim 1, characterized in that, The monitoring of population fitness variance dynamics includes: Premature convergence is identified by dynamically monitoring the population fitness variance, and chaotic optimization is triggered accordingly; the formula for calculating the dynamically monitored population fitness variance is as follows: （14） In the formula, Let m be the fitness value of particle m. The average fitness of the population. The optimal fitness of the population is Np, where Np is the population size. The standard deviation of population fitness; The premature convergence detection condition for identifying the premature convergence state is as follows: （15） in, and These are the PFV values ​​for the current iteration and the next iteration, respectively. and The threshold values ​​are set to 0.99 and 1.01 respectively. When the premature convergence detection condition for identifying premature convergence states is met, the chaos optimization process is automatically started.

9. The optimization method for joint planning of distributed generation and energy storage in an active distribution network according to claim 1, characterized in that, The introduced Tent mapping chaotic perturbation includes: To address the premature convergence problem of the algorithm, a Tent mapping is introduced to perform chaotic perturbation, leveraging the ergodicity and randomness of chaotic motion to enhance population diversity. The Tent mapping formula is as follows: （16） When periodic or fixed points appear in the iterative sequence, adding random perturbations causes the mapping to re-enter a chaotic state: （17） In the formula, For the chaotic variables mapped by Tent; Chaotic variables are used to modify particle positions. By perturbing the current solution by mapping it to the chaotic space, and then mapping it back to the solution space, global exploration is achieved.

10. The optimization method for joint planning of distributed generation and energy storage in an active distribution network according to claim 1, characterized in that, The efficient solution and global optimization of the DG and energy storage joint optimization model based on the two-level programming framework includes: Step C31: Initialize the particle swarm, set the population size Np=50, and the maximum number of iterations iter max =100, Inertia Weight Range And randomly generate initial position and velocity; Step C32: Calculate the fitness value of each particle, which is the objective function of the DG and energy storage joint optimization model based on the bi-level programming framework. In the formula, F1 is the objective function of the upper-level model, and F2 is the objective function of the lower-level model. Step C33: Update the individual's historical best solution and the global historical optimal solution ; Step C34: Update the particle velocity according to formula (11), and update the particle position according to formulas (12) and (13); Step C35: Calculate the population fitness variance Use formula (14) and check the premature convergence condition formula (15); if the condition is met, apply the Tent map chaotic perturbation formula (16) and formula (17); Step C36: Repeat steps C32-C35 until the convergence condition is met; The convergence condition is: Or it may reach the maximum number of iterations.

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