An interval optimization scheduling method considering new energy uncertainty and grid flexibility demand

Abstract

The application discloses an interval optimization scheduling method considering new energy uncertainty and power grid flexibility demand, and comprises the following steps: constructing a new energy output uncertainty model, the new energy output uncertainty model considering wind power and photovoltaic output values and wind power and photovoltaic output prediction error probability density curves in each period to obtain wind power and photovoltaic output intervals; establishing a multi-objective interval optimization scheduling model with the minimum power system comprehensive operation cost, the minimum voltage offset, the maximum power supply margin of the whole network and the maximum consumption margin of the whole network as targets; solving the multi-objective interval optimization scheduling model by using an NSGA-11 multi-objective genetic algorithm to obtain multiple sets of optimal objective functions and corresponding Pareto solution sets; and realizing interval optimization scheduling according to the obtained interval scheduling plan scheme corresponding to the Pareto optimal solution set.

Description

Technical Field

[0001] This invention belongs to the field of power grid optimization scheduling technology, specifically relating to an interval optimization scheduling method that considers the uncertainty of new energy sources and the flexibility requirements of the power grid. Background Technology

[0002] With the continuous development of new power systems, the proportion of new energy sources such as wind power and photovoltaics in my country's power system is constantly increasing. New energy sources like wind and photovoltaics have intermittent, fluctuating, and random output characteristics. Large-scale grid connection of wind and photovoltaics exacerbates the uncertainty on the power system's source side, making traditional deterministic dispatching models potentially inapplicable in actual power system operation. In severe cases, this can even lead to power curtailment, wind curtailment, and solar curtailment, thus affecting unit output plans. Therefore, considering the uncertainty of new energy output is of great significance for the dispatching of new power systems.

[0003] Currently, extensive research has been conducted both domestically and internationally on power system dispatching problems involving uncertain renewable energy output. Optimization methods based on uncertainty modeling mainly fall into four categories: scenario generation, stochastic optimization, robust optimization, and interval optimization. Scenario generation represents uncertainty by generating numerous scenarios. This method relies on known probability distributions of variables and involves significant computational costs, making it generally difficult to implement in large-scale power systems. Stochastic optimization describes uncertainty through random scenarios, but the computational burden increases with the number of input models, and the reduced number of scenarios cannot guarantee the feasibility of the optimal solution under stochastic conditions. Robust optimization seeks the optimal solution for the worst-case scenario within the range of uncertain parameters, but the results are often overly conservative. Interval optimization describes random variables in the form of interval numbers, requiring less information about the distribution of uncertain variables and incurring less computational costs, thus avoiding the conservatism of robust optimization when considering worst-case scenarios. However, if the range of values ​​for the interval variables is too large, the results will also tend towards conservatism. Therefore, the interval values ​​of the variables are crucial for interval optimization. However, research on the optimal scheduling problem of power system intervals has largely focused on the efficiency of model solving and the comprehensiveness of the model's objective, while modeling the optimal scheduling problem under the background of power system flexibility requirements and considering the values ​​of interval variables are relatively lacking. Regarding the modeling of new energy power output prediction errors, existing studies mostly describe the probability density distribution of new energy power output prediction errors through single or combined probability distribution models. However, due to the influence of uncertainties such as weather forecast errors and terrain differences, the prediction errors of new energy power output often exhibit different distribution characteristics in different time periods. Single or combined probability distribution models are insufficient to describe the data characteristics of the probability density distribution of new energy power output prediction errors, such as peaks, heavy tails, asymmetry, and multiple peaks. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides an interval optimization scheduling method that considers the uncertainty of new energy sources and the flexibility requirements of the power grid. The method describes the output fluctuation range of new energy sources in the form of interval numbers to characterize the uncertainty of new energy output. Based on this, a power system scheduling model that considers the uncertainty of new energy sources and the flexibility requirements of the power grid is constructed. The objective function is solved by interval arithmetic to achieve the optimal objective in the form of intervals, thereby improving the flexibility of power system operation while ensuring the safe and stable operation of the power system.

[0005] The technical solution of the present invention is as follows:

[0006] This invention provides an interval optimization scheduling method that considers the uncertainty of new energy sources and the flexibility requirements of the power grid, comprising the following steps:

[0007] Input power system line parameters and new energy information to construct a new energy output uncertainty model. The new energy output uncertainty model considers the wind power and photovoltaic output values ​​and the probability density curves of wind power and photovoltaic output prediction errors in each time period to obtain the wind power and photovoltaic output ranges.

[0008] A multi-objective interval optimization scheduling model is established with the objectives of minimizing the overall operating cost of the power system, minimizing voltage deviation, maximizing the power supply margin of the entire network, and maximizing the absorption margin of the entire network.

[0009] The NSGA-11 multi-objective genetic algorithm is used to solve the multi-objective interval optimization scheduling model, obtain multiple sets of optimal objective functions and corresponding Pareto solutions, and realize interval optimization scheduling based on the interval scheduling plan scheme corresponding to the obtained Pareto optimal solution set.

[0010] Preferably, the specific calculation steps for the wind power and photovoltaic output range are as follows:

[0011] Wind power and solar power output at different times t: The wind power and solar power output at each time period are considered as the predicted output value and the predicted output error value, and the expression is as follows:

[0012]

[0013] In equation (1), P w (t), P v (t) represents the power output of wind and solar power at time t, P wP (t), P vP (t) represents the predicted output of wind power and photovoltaic power at time t, ΔP w (t), ΔP v (t) represents the power output prediction error value of wind power and photovoltaic at time t;

[0014] A nonparametric kernel density estimation method is used to establish a distribution model of the prediction error values ​​for wind power and photovoltaic power output. Assume ΔP w (t)1,ΔP w (t)2,…,ΔP w (t) q ,…,ΔP w (t) n Let ΔP be n samples of the wind power output prediction error value at time t. v (t)1,ΔP v (t)2,…,ΔP v (t) q ,…,ΔP v (t) n Given n samples representing the photovoltaic power output prediction error values ​​at time t, the kernel density expressions for the wind power and photovoltaic power output prediction error values ​​are as follows:

[0015]

[0016] In equation (2), ΔP represents the probability distribution function of the prediction error value for wind power and solar power output. w (t), ΔP v (t) represents any sample of wind power and solar power output prediction error values, the kernel function K(·) is the weighting function, and h is the bandwidth;

[0017] The kernel density expression for the prediction error values ​​of wind power and photovoltaic power generation uses the standard Gaussian kernel function, as shown in the following expression:

[0018]

[0019] Substituting the standard Gaussian kernel function into equation (2) yields the kernel density expression for the prediction error values ​​of wind power and photovoltaic power output. And on Integrating, we get Integral function;

[0020] The integral functions are the probability distribution functions F of the wind power and solar power output prediction error values, respectively. w (x), F v (x), based on the kernel density expression curves of wind power and photovoltaic output prediction error values, find the α of the prediction error. w,t ,α v,t and β w,t ,β v,t Corresponding points, substitute In the integral function, the output range of wind power and photovoltaic power is calculated according to the following formula:

[0021]

[0022] In equation (4), For predicted wind and solar power output, μ w μ v The confidence levels for wind power and solar power are respectively, with parameter α. w,t ,α v,t ∈(0,0.5], β w,t ,β v,t ∈(0.5,1],β w,t -α w,t =μ w ,β v,t -α v,t =μ v , t=1,2,…,24, These are the probability distribution functions F w (x), F v The inverse function of (x).

[0023] Preferably, the comprehensive operating cost consists of the operating costs of the diesel generator set and the energy storage system, as expressed below:

[0024]

[0025] In equation (4), C DE (t),C ESS (t) represent the power generation cost of the diesel generator set and the operating cost of the energy storage system at time t, respectively. f,DE ,g o,DE P represents the fuel cost coefficient and operation and maintenance cost coefficient per kWh of diesel generator, respectively. k,DE (t) represents the power of the diesel generator set at the k-th node at time t, g o,ESS Let α represent the operating cost coefficient per kW·h of the energy storage device, and let β represent the charging and discharging amounts of the energy storage unit at the g-th node at time t, respectively. α and β are 0-1 variables, representing the charging and discharging states of the energy storage, respectively.

[0026] Preferably, the voltage offset is calculated using a voltage offset objective function, and the calculation method is as follows:

[0027] The voltage fluctuation function is used as a criterion for voltage quality evaluation. The expression for the voltage fluctuation function is as follows:

[0028]

[0029]

[0030] In the formula, U s(i) ΔU represents the voltage fluctuation value at the i-th node. i =|U i -1|,ΔU min ,ΔU maxThese represent the unacceptable and acceptable voltage fluctuation values, respectively, where n is the number of system nodes, and ΔU as This represents the total voltage offset value.

[0031] Based on the wind power and photovoltaic power output ranges at each time point, the power flow of the grid intervals is calculated to obtain the node voltage ranges. Then, the voltage offset ranges at each time point are calculated according to equations (5) and (6). The voltage offset objective function is transformed according to the δ-sequence relationship of the interval as follows:

[0032]

[0033] Preferably, the expression for the overall network power supply margin is as follows:

[0034]

[0035] In equation (8), L represents the maximum power generation capacity of the entire power grid. g,e For the entire network's power load, P c,o For power transmission via the connecting line, This represents the maximum generating capacity of the DE unit. This represents the maximum discharge power of the energy storage device. Let be the upper bound of the output range of the i-th wind power at time t. M is the upper bound of the output range of the i-th photovoltaic cell at time t. w M represents the total number of wind power units. v This represents the total number of photovoltaic (PV) displays.

[0036] Preferably, the expression for the overall network absorption margin is as follows:

[0037]

[0038] In equation (9), L is the minimum power generation capacity of the entire grid. g,e For the entire network's power load, P c,o For power transmission via the connecting line, This represents the minimum generating capacity of the DE unit. This is the minimum discharge power of the energy storage device. Let be the lower bound of the output range of the i-th wind power at time t. M is the lower bound of the output range of the i-th photovoltaic cell at time t. w M represents the total number of wind power units. v This represents the total number of photovoltaic (PV) displays.

[0039] Preferably, when using the NSGA-II multi-objective genetic algorithm to analyze and solve the multi-objective interval optimization scheduling model, it is necessary to calculate the objective functions of the comprehensive operating cost, voltage offset, power supply margin of the whole network, and absorption margin of the whole network within the population, and transform the interval model according to the interval order relationship.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] 1. This invention proposes an interval optimization scheduling method that considers the uncertainty of new energy sources and the flexibility requirements of the power grid. It describes the output fluctuation range of new energy sources such as wind power and photovoltaic power in the form of interval numbers to characterize the uncertainty of new energy output. On this basis, a power system scheduling model that considers the uncertainty of new energy sources and the flexibility requirements of the power grid is constructed, and the objective function is solved by interval arithmetic to achieve the optimal objective in the form of interval, thereby improving the flexibility of power system operation while ensuring the safe and stable operation of the power system.

[0042] 2. This invention uses interval numbers to describe the power output fluctuation range of new energy sources such as wind power and photovoltaics, which can effectively quantify the uncertainty of new energy power output and meet the reliability requirements of decision-makers. It uses a non-parametric kernel density estimation method to establish a distribution model of wind power and photovoltaic power output prediction error values. It does not need to assume in advance that the wind power and photovoltaic power output prediction error values ​​follow a certain mathematical model. It can directly use known samples to estimate the probability density. Compared with parametric estimation, it can better reflect the true distribution of new energy power output data and has a better fitting effect.

[0043] 3. This invention considers the flexibility requirements of power grid operation. Based on flexible resources such as diesel generator sets and energy storage systems, a multi-objective optimization scheduling model is established with the objectives of minimizing the comprehensive operating cost C of the power system, minimizing the voltage deviation V, maximizing the power supply margin GPM of the entire network, and maximizing the absorption margin GAM of the entire network. The power grid flexibility requirements, such as the power supply margin and the absorption margin of the entire network, are incorporated into the objective function of interval optimization, providing more comprehensive information for power system scheduling and ensuring the safe and stable operation of the power system while meeting the flexibility requirements of the power system.

[0044] 4. To address the issue of excessive subjectivity in the selection of weight factors in multi-objective optimization problems, the scheduling method of this invention is based on the output range of new energy sources such as wind power and photovoltaics. It optimizes the objective function range by comparing the merits of different ranges according to the interval order relationship, and uses a fast non-dominated sorting genetic algorithm to solve the optimal solution set of the multi-objective interval optimization scheduling model. It can provide multiple sets of mutually non-dominated optimal solutions and provide decision-makers with selection space according to the actual operation needs of the power system. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the interval optimization scheduling method of the present invention. Detailed Implementation

[0046] The present invention will be further described below with reference to the accompanying drawings and preferred embodiments.

[0047] like Figure 1 As shown, this invention provides an interval optimization scheduling method that considers the uncertainty of new energy sources and the flexibility requirements of the power grid, including the following steps:

[0048] S1. Input the power system line parameters and new energy information to construct a new energy output uncertainty model. The new energy output uncertainty model considers the wind power and photovoltaic output values ​​and the probability density curves of wind power and photovoltaic output prediction errors in each time period to obtain the wind power and photovoltaic output ranges.

[0049] Among them, the wind power and photovoltaic power output values ​​for each time period can be regarded as the power output prediction value and the power output prediction error value, as expressed below:

[0050]

[0051] In equation (1), P w (t), P v (t) represents the power output of wind and solar power at time t, P wP (t), P vP (t) represents the predicted output of wind power and photovoltaic power at time t, ΔP w (t), ΔP v (t) represents the power output prediction error value of wind power and photovoltaic at time t;

[0052] A nonparametric kernel density estimation method is used to establish a distribution model for the prediction error values ​​of wind power and photovoltaic power output. Nonparametric kernel density estimation is a type of nonparametric estimation method that can well describe continuous density functions. This method studies the distribution characteristics based on the inherent features of the data, without requiring prior assumptions about the data distribution. In this embodiment, ΔP is assumed. w (t)1,ΔP w (t)2,…,ΔP w (t) q ,…,ΔP w (t) n Let ΔP be n samples of the wind power output prediction error value at time t. v (t)1,ΔP v (t)2,…,ΔP v (t) q ,…,ΔP v (t) n Given n samples representing the photovoltaic power output prediction error values ​​at time t, the kernel density expressions for the wind power and photovoltaic power output prediction error values ​​are as follows:

[0053]

[0054] The specific calculation steps for the wind power and photovoltaic power output ranges are as follows:

[0055] Wind power and solar power output at different times t: The wind power and solar power output at each time period are considered as the predicted output value and the predicted output error value, and the expression is as follows:

[0056]

[0057] In equation (1), P w (t), P v (t) represents the power output of wind and solar power at time t, P wP (t), P vP (t) represents the predicted output of wind power and photovoltaic power at time t, ΔP w (t), ΔP v (t) represents the power output prediction error value of wind power and photovoltaic at time t;

[0058] A nonparametric kernel density estimation method is used to establish a distribution model of the prediction error values ​​for wind power and photovoltaic power output. Assume ΔP w (t)1,ΔP w (t)2,…,ΔP w (t) q ,…,ΔP w (t) n Let ΔP be n samples of the wind power output prediction error value at time t. v (t)1,ΔP v (t)2,…,ΔP v (t) q ,…,ΔP v (t) n Given n samples representing the photovoltaic power output prediction error values ​​at time t, the kernel density expressions for the wind power and photovoltaic power output prediction error values ​​are as follows:

[0059]

[0060] In equation (2), ΔP represents the probability distribution function of the prediction error value for wind power and solar power output. w (t), ΔP v (t) represents any sample of wind power and solar power output prediction error values, the kernel function K(·) is the weighting function, and h is the bandwidth;

[0061] The kernel density expression for the prediction error values ​​of wind power and photovoltaic power generation uses the standard Gaussian kernel function, as shown in the following expression:

[0062]

[0063] Substituting the standard Gaussian kernel function (3) into equation (2) yields the kernel density expression for the prediction error values ​​of wind power and photovoltaic power output. And on Integrating, we get Integral function;

[0064] The integral functions are the probability distribution functions F of the wind power and solar power output prediction error values, respectively. w (x), F v (x), based on the kernel density expression curves of wind power and photovoltaic output prediction error values, find the α of the prediction error. w,t ,α v,t and β w,t ,β v,t Corresponding points, substitute In the integral function, the output range of wind power and photovoltaic power is calculated according to the following formula:

[0065]

[0066] In equation (4), For predicted wind and solar power output, μ w μ v The confidence levels for wind power and solar power are respectively, with parameter α. w,t ,α v,t ∈(0,0.5], β w,t ,β v,t ∈(0.5,1],β w,t -α w,t =μ w ,β v,t -α v,t =μ v , t=1,2,…,24, These are the probability distribution functions F w (x), F v The inverse function of (x).

[0067] S2. A multi-objective interval optimization scheduling model is established with the objectives of minimizing the comprehensive operating cost C of the power system, minimizing the voltage deviation V, maximizing the power supply margin GPM of the entire network, and maximizing the absorption margin GAM of the entire network.

[0068] Since the cost of generating electricity from new energy sources such as wind power and photovoltaics is relatively lower than that of fuel power generation, the generation costs of wind power and photovoltaics are ignored in this embodiment. The comprehensive operating cost mainly consists of the operating costs of the diesel generator set and the energy storage system, as shown in the following expression:

[0069]

[0070] In equation (5), C DE (t),CESS (t) represent the power generation cost of the diesel generator set and the operating cost of the energy storage system at time t, respectively. f,DE ,g o,DE P represents the fuel cost coefficient and operation and maintenance cost coefficient per kWh of diesel generator, respectively. k,DE (t) represents the power of the diesel generator set at the k-th node at time t, g o,ESS α represents the operating cost coefficient per kW·h of the energy storage device, β represents the charging and discharging amount of the energy storage unit at the g-th node at time t, respectively, and α and β are 0-1 variables, representing the charging and discharging states of the energy storage, respectively.

[0071] Voltage offset is calculated using a voltage offset objective function, and a voltage fluctuation function is used as the voltage quality evaluation criterion. The expression for the voltage fluctuation function is as follows:

[0072]

[0073]

[0074] In the formula, U s(i) ΔU represents the voltage fluctuation value at the i-th node. i =|U i -1|,ΔU min ,ΔU max These represent the unacceptable and acceptable voltage fluctuation values, respectively, where n is the number of system nodes, and ΔU as This represents the total voltage offset value.

[0075] Based on the wind and solar power output intervals at each time point in the above steps, the power flow between grid intervals is calculated to obtain the node voltage intervals. Then, the voltage offset interval [ΔU] at each time point is calculated according to equations (6) and (7). a m s in(t),ΔU a m s Based on the δ-sequence relationship within the interval, the voltage offset objective function is transformed as follows:

[0076]

[0077] The expression for the overall power supply margin is as follows:

[0078]

[0079] In equation (9), L represents the maximum power generation capacity of the entire power grid. g,e For the entire network's power load, P c,o For power transmission via the connecting line, This represents the maximum generating capacity of the DE unit. This represents the maximum discharge power of the energy storage device. Let be the upper bound of the output range of the i-th wind power at time t. M is the upper bound of the output range of the i-th photovoltaic cell at time t. w M represents the total number of wind power units. v The total number of photovoltaic units;

[0080] The expression for the overall network absorption margin is as follows:

[0081]

[0082] In equation (10), L is the minimum power generation capacity of the entire grid. g,e For the entire network's power load, P c,o For power transmission via the connecting line, This represents the minimum generating capacity of the DE unit. This is the minimum discharge power of the energy storage device. Let be the lower bound of the output range of the i-th wind power at time t. M is the lower bound of the output range of the i-th photovoltaic cell at time t. w M represents the total number of wind power units. v This represents the total number of photovoltaic (PV) displays.

[0083] The constraints of the multi-objective interval optimization scheduling model include power flow equality constraints, diesel generator set constraints, and the voltage intervals of each node calculated by ES power flow. Therefore, the power flow equality constraints are:

[0084]

[0085] In equation (11), [P G,i (t)] and [Q G,i [(t)] represents the injected active power and reactive power at node i at time t, respectively; [P D,i (t)] and [Q D,i [(t)] represents the active power and reactive power of the load at node i at time t, respectively; [U i [θ(t)] represents the node voltage range at node i at time t, where [θ] ij [(t)] represents the voltage phase angle between node i and node j, G ij and B ij These represent the conductance and susceptance between the lines, respectively.

[0086] Diesel generator set constraints:

[0087]

[0088]

[0089]

[0090] In the formula, These represent the upper and lower limits of the diesel engine unit's output, respectively. γ represents the maximum climbing rate of the diesel generator set. g,t T represents the 0-1 state variable indicating the start-up and shutdown of the diesel generator unit at the g-th node at time t. on,k,t ,T off,k,t T represents the continuous start-up time and continuous shutdown time of the diesel generator set, respectively. on,k ,T off,k These represent the minimum start-up time and minimum downtime of the diesel generator set, respectively.

[0091] ESS state-of-charge constraints:

[0092]

[0093]

[0094] S soc (0)=S soc (T) (17)

[0095] In the formula, S soc (t) represents the state of charge of ESS at time t; These represent the lower and upper limits of the ESS's charged power, respectively; These represent the maximum discharge power and charging power per hour of energy storage, respectively; S soc (0),S soc (T) represent the state of charge of the stored energy at the initial and final times, respectively.

[0096] S3. Use the NSGA-11 multi-objective genetic algorithm to solve the multi-objective interval optimization scheduling model, obtain multiple sets of optimal objective functions and corresponding Pareto solution sets, and formulate the interval scheduling plan based on the obtained Pareto optimal solution set.

[0097] The steps for solving the problem using the NSGA-11 multi-objective genetic algorithm are as follows:

[0098] (1) Set the NSGA-II algorithm parameters, randomly generate the initial population, and set the number of generations Gen=1;

[0099] (2) Calculate the objective function values ​​within the population and convert the interval model according to the interval order relationship;

[0100] (3) Perform a quick non-dominated sort:

[0101] Each individual x in the population i Both have two parameters N i and S i N i Represents the dominant individual x in the population.i The number of individuals, S i is the individual dominated by x i For the set of individuals, calculate the four objective function values corresponding to individual x i C(x i ), V(x i ), GPM(x i ), GAM(x i ); Calculate the four objective function values C(x j ), V(x j ), GPM(x j ), GAM(x j ) corresponding to other individuals x in the population, and judge whether individual x j is an individual with N i =0, that is, there is no individual in the population that dominates x i . If so, assign individual x i a non-dominated rank of 1 and put this individual into the non-dominated set rank1. Traverse all individuals in the population to find all individuals that satisfy N i =0 and put them into the non-dominated set rank1; Among them, the "dominance" principle is: The four objective functions of comprehensive operating cost, voltage deviation, power supply margin of the whole network, and consumption margin of the whole network are denoted as C(x), V(x), GPM(x), and GAM(x) respectively. If individuals x1 and x2 satisfy C(x1)<C(x2), V(x1)<V(x2), GPM(x1)<GPM(x2), and GAM(x1)<GAM(x2) at the same time, then it is said that individual x1 dominates individual x2; If C(x1)≤C(x2), V(x1)≤V(x2), GPM(x1)<GPM(x2), and GAM(x1)<GAM(x2) hold for all four objective functions and at least one of C(x1)<C(x2), V(x1)<V(x2), GPM(x1)<GPM(x2), and GAM(x1)≤GAM(x2) holds for the four objective functions, then it is said that individual x1 weakly dominates individual x2; Among the four objective functions, if one of C(x1)≤C(x2), V(x1)≤V(x2), GPM(x1)≤GPM(x2), and GAM(x1)≤GAM(x2) holds, and at the same time there is one of C(x1)>C(x2), V(x1)>V(x2), GPM(x1)>GPM(x2), and GAM(x1)>GAM(x2) holds, then it is said that individual x1 and individual x2 do not dominate each other;

[0102] For each individual in the set rank1, subtract 1 from N of each individual in the set of individuals it dominates. If N j ​​​j If -1 = 0, then individual j is placed in set rank2 and assigned a non-dominant rank of 2.

[0103] Repeat the above operation for individuals in rank2 until all individuals are assigned a non-dominated rank. The non-dominated rank is also called the Pareto rank. Individuals with a Pareto rank of 1 are not dominated by other individuals and are called non-dominated solutions, also known as Pareto optimal solutions, which are the optimal solutions that satisfy the four objective functions. The curve formed by the solution set is called the Pareto front.

[0104] (4) Calculate the crowding distance:

[0105] When calculating the crowding distance for individuals at a certain level, let's assume there are m individuals in that level, and each individual is represented by x. i Let i = 1, 2, ..., m; x i-1 ,x i+1 Let i represent the individuals before and after the individual when i = 2, 3, ..., m-1; let i be the crowding distance of the i-th individual under the multi-objective function. d ;

[0106] For the objective function C(x), the objective function values ​​C(x) of m individuals are... i Let the minimum and maximum values ​​of ) be C. min (x i ),C max (x i If the crowding distance Dis of individual i in the objective function C(x) is... i,C The expression is as follows:

[0107]

[0108] For the objective function V(x), the objective function values ​​V(x) of m individuals are... i Let the minimum and maximum values ​​of ) be V. min (x i ),V max (x i If the crowding distance Dis of individual i in the objective function V(x) is... i,V The expression is as follows:

[0109]

[0110] For the objective function GPM(x), the objective function values ​​GPM(x) of m individuals are... i The minimum and maximum values ​​of GPM are set as follows: min (x i ), GPM max (x iIf the crowding distance Dis of individual i in the objective function GPM(x) is... i,GPM The expression is as follows:

[0111]

[0112] For the objective function GAM(x), the objective function values ​​GAM(x) of m individuals are... i The minimum and maximum values ​​of GAM are set as follows: min (x i ), GAM max (x i If the crowding distance Dis of individual i in the objective function GAM(x) is... i,GAM The expression is as follows:

[0113]

[0114] Define the crowding distance i of individual i under four objective functions. d The expression is as follows:

[0115] i d =Dis i,C +Dis i,V +Dis i,GPM +Dis i,GAM (twenty two)

[0116] (5) Tournament Selection

[0117] After the fast non-dominated sorting in step (3) and the crowding calculation in step (4), each individual i in the population has two attributes: non-dominated order i rank and the distance i of congestion d Compare individual i and individual j. If any of the following conditions are met, individual i wins:

[0118] The non-dominated layer of individual i is superior to the non-dominated layer of individual j, i.e. rank <j rank ;

[0119] Individuals i and j have the same non-dominated hierarchy level, and the crowding distance of individual i is greater than that of individual j, i. rank =j rank And i d >j d ;

[0120] The fractional tournament involves selecting a few individuals from the population at once, and then choosing the winning individuals from these individuals to be retained in the next generation of the population. The specific steps are as follows:

[0121] Determine the number of individuals N selected each time;

[0122] Randomly select N individuals from the population (each individual has an equal probability of being selected), and select the winning individual to enter the next generation of the population based on the non-dominated order and crowding distance of each individual;

[0123] Repeat the above steps multiple times (the number of repetitions equals the population size) until the new population size reaches the original population size; repeat this operation until the new population size reaches the original population size.

[0124] (6) Perform population crossover and mutation to generate offspring population Q0. Use an elite strategy to mix the parent and offspring populations. The specific steps of the elite strategy are as follows:

[0125] The parent and offspring populations are merged into a new population, and a non-dominated sort is performed on the new population.

[0126] To generate new parents, first place non-dominant individuals with Pareto level 1 into the new parent set, then place individuals with Pareto level 2 into the new parent set, and so on.

[0127] If the number of individuals in the new parent set is less than n after all individuals of level k are placed into the new parent set, and the number of individuals in the set is greater than n after all individuals of level k+1 are placed into the new parent set, then the crowding distance is calculated for all individuals of level k+1 and all individuals are sorted in descending order according to the crowding distance. Then, all individuals of level greater than k+1 are eliminated.

[0128] (7) Calculate four objective functions for the mixed population, and perform fast non-dominated sorting on the individuals in the mixed population, selecting the top N individuals as the parent population.

[0129] (8) Determine whether the specified number of iterations has been reached. If the specified number of iterations has not been reached, repeat steps (2) to (7). If the specified number of iterations has been reached, the Pareto optimal solution set is obtained, which is the optimal solution of the interval scheduling model.

[0130] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention specification, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. An interval optimization scheduling method considering the uncertainty of new energy sources and the flexibility requirements of the power grid, characterized in that, Includes the following steps: Input power system line parameters and new energy information to construct a new energy output uncertainty model. The new energy output uncertainty model considers the wind power and photovoltaic output values ​​and the probability density curves of wind power and photovoltaic output prediction errors in each time period to obtain the wind power and photovoltaic output ranges. A multi-objective interval optimization scheduling model is established with the objectives of minimizing the overall operating cost of the power system, minimizing voltage deviation, maximizing the power supply margin of the entire network, and maximizing the absorption margin of the entire network. The total operating cost consists of the operating costs of the diesel generator set and the energy storage system. The expression for the total operating cost C is as follows: （5） In equation (5), They represent t The power generation cost of the diesel generator set and the operating cost of the energy storage system are constantly being considered. These represent the fuel cost coefficient and operation and maintenance cost coefficient per kWh of diesel generator, respectively. express t Time of the first k The power of the diesel generator set at each node This represents the operating cost coefficient per kW·h of energy storage devices. , They represent t Time of the first g The charging and discharging amounts of the energy storage units at each node. The variables are 0-1, where α represents the charging state of the energy storage, β represents the discharging state of the energy storage, and Δt represents the scheduling time interval. The voltage offset is calculated using a voltage offset objective function, and the calculation method is as follows: The voltage fluctuation function is used as a criterion for voltage quality evaluation. The expression for the voltage fluctuation function is as follows: （6） （7） In the above formula, Indicates the first i Voltage fluctuation values ​​at each node, , These represent unacceptable and acceptable voltage fluctuation values, respectively. n The number of system nodes. This represents the total voltage offset value. Based on the wind power and photovoltaic power output intervals at each time point, the power flow of the grid intervals is calculated to obtain the node voltage intervals. Then, the voltage offset intervals at each time point are calculated according to equations (6) and (7). According to the order relation of the intervals The voltage offset objective function is transformed as follows: （8） Where V represents the voltage offset objective function; , These represent the minimum and maximum values ​​of the voltage offset at time t, respectively. The expression for the overall power supply margin is as follows: （9） In equation (9), This represents the maximum power generation capacity of the entire power grid. For the entire network's power load, For power transmission via the connecting line, This represents the maximum power output of the diesel generator set. This represents the maximum discharge power of the energy storage device. For the first i A wind power plant t The upper bound of the output range at any given moment. For the first i A photovoltaic in t The upper bound of the output range at any given moment. For the total number of wind power, The total number of photovoltaic units; The expression for the overall network absorption margin is as follows: （10） In equation (10), This represents the minimum power generation capacity of the entire power grid. This is the minimum power output of the diesel generator set. This is the minimum discharge power of the energy storage device. For the first i A wind power plant t The lower bound of the output range at any given time. For the first i A photovoltaic in t The lower bound of the output range at any given moment; The NSGA-II multi-objective genetic algorithm is used to solve the multi-objective interval optimization scheduling model, obtain multiple sets of optimal objective functions and corresponding Pareto solutions, and realize interval optimization scheduling based on the interval scheduling plan corresponding to the obtained Pareto optimal solution set.

2. The interval optimization scheduling method considering the uncertainty of new energy sources and the flexibility requirements of the power grid according to claim 1, characterized in that, The specific calculation steps for the wind power and photovoltaic power output ranges are as follows: different times t The wind power and solar power output values: The wind power and solar power output values ​​for each time period are considered as the predicted output value and the predicted output error value, as expressed below: (1) In equation (1), Indicating wind power and solar power in t Output value at any given moment Indicating wind power and solar power in t The predicted output value at any given time. Indicating wind power and solar power in t The output prediction error value at any given time; A nonparametric kernel density estimation method is used to establish a distribution model of the prediction error values ​​for wind power and photovoltaic power output. Assume... for t Wind power output prediction error value at any time n One sample, for t The time is the photovoltaic output prediction error value n For each sample, the kernel density of the wind power and solar power output prediction error values ​​is expressed as follows: （2） In equation (2), This represents the probability distribution function of the predicted error values ​​for wind power and solar power output. Let be the predicted error value of wind power and photovoltaic output at any time t, and the kernel function be... For the weight function, h For bandwidth; The kernel density expression for the prediction error values ​​of wind power and photovoltaic power generation uses the standard Gaussian kernel function, as shown in the following expression: （3） Substituting the standard Gaussian kernel function into equation (2) yields the kernel density expression for the prediction error values ​​of wind power and photovoltaic power output. and to Integrating, we get Integral function; The integral functions are the probability distribution functions of the prediction error values ​​for wind power and photovoltaic power output, respectively. Based on the kernel density expression curves of wind power and solar power output prediction errors, the prediction error can be found. and Corresponding points, substitute In the integral function, the output range of wind power and photovoltaic power is calculated according to the following formula: （4） In equation (4), Forecast values ​​for wind power and solar power output. Confidence levels for wind power and solar power, respectively, parameters , , , , , These are the probability distribution functions. The inverse function of .

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