Micro-grid robust optimization scheduling method considering segmented multi-interval uncertainty set

Abstract

The invention provides a micro-grid robust optimization scheduling method considering a segmented multi-interval uncertainty set, and the method comprises the steps: carrying out the segmentation fitting of the source load prediction power and error data of wind, light and loads based on a Gaussian mixture model, and combining with a box-type interval uncertainty set to build a multi-interval uncertainty set of power segmentation segments; the uncertainties are used for describing wind, light and load uncertainties; constructing a microgrid robust optimization scheduling model considering the segmented multi-interval uncertainty set and the carbon emission by taking the minimization of the operating cost and the carbon emission cost of the microgrid as a target; and solving the micro-grid robust optimization scheduling model by adopting a column sum constraint generation algorithm. According to the method, the problems of uncertainty modeling and carbon emission of the micro-grid can be solved, the conservative property of a robust optimization scheduling strategy is reduced, and the economical efficiency of micro-grid scheduling is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of microgrid planning, and in particular to a robust optimization scheduling method for a microgrid considering segmented multi-interval uncertainty sets. Background Art

[0002] Microgrid MG is composed of renewable energy RE, energy storage system and load, and plays an important role in the transformation of power grid to low-carbon, green and intelligent. MG has created huge economic benefits for the power grid. However, the uncertainty of RE output power and load demand has brought great challenges to the reliable operation of MG. How to solve the uncertainty of MG source and load and realize the economic and safe operation of MG is a direction worthy of research.

[0003] At present, domestic and foreign scholars have conducted in-depth research on MG optimization scheduling considering the influence of uncertainty factors, with the goals of operating economy, RE absorption capacity and reducing carbon emissions. The current methods for dealing with uncertainty factors include scenario analysis, stochastic optimization SO, robust optimization RO and distributed robust optimization DRO. Among them, scenario analysis and SO methods both rely on the probability distribution information of uncertain variables, require a large amount of sample data, increase the complexity of the problem, and may ignore some extreme scenarios. RO does not rely on the probability distribution of uncertain variables, and represents the uncertainty of variables in the form of uncertainty sets. It can solve the optimal scheduling scheme of the system under extreme scenarios, so it has been widely used in MG optimization scheduling. Existing literature constructs a two-stage robust MG energy management model, using polyhedron sets to describe the uncertainty of source and load. There are also literatures based on the polyhedron set of periodic budgets to develop a two-stage RO model with binary pursuit variables. However, the above literatures all use simple uncertainty sets to describe the uncertainty of the system, resulting in many scenarios that are impossible to occur in reality, making the scheduling results too conservative and reducing the operating efficiency of the system.

[0004] In order to overcome the particularity of SO and the conservative defects of RO, DRO extracts probability information from historical data and constructs fuzzy sets containing probability distributions of uncertain variable factors, thereby solving the minimum expected cost in the worst case. According to the different methods of establishing fuzzy sets, DRO can be divided into two types: based on moment information and based on distance measurement. The DRO method based on moment information derives the probability distribution parameters of uncertain parameters from historical data. The distance-based DRO method establishes the confidence set of the fuzzy set by introducing a statistical distance between two probability distributions. However, these methods convert the DRO model into a semidefinite programming or second-order cone programming problem to improve numerical tractability, which is prone to suboptimal solutions.

[0005] Although the above literature has achieved rich results in reducing the conservatism of RO, most studies have ignored the direct relationship between the uncertainty parameter data set and the prediction error. How to mine the prediction error information contained in the source-load data set and combine it with the uncertainty set modeling to improve the quality of the robust scheduling results is still a challenge. Existing literature combines the least squares fitting straight line with the polyhedral uncertainty set to construct an uncertainty set containing the spatiotemporal correlation of photovoltaic power generation. There are also literatures that use multi-interval uncertainty sets to solve the adaptive RO scheduling problem in MG, which to a certain extent avoids the worst scenario always being at the boundary of the prediction interval. There are also literatures that use the Dirichlet process mixture model and the Bayesian non-parametric method to fit the uncertainty set, thereby eliminating the difference between the traditional polyhedral set and the historical scenario. Existing literature selects some extreme scenarios in historical data and combines them with the traditional convex uncertainty set to describe the spatiotemporal correlation of the uncertainty set and prove its applicability. Summary of the invention

[0006] The purpose of the present invention is to provide a robust optimization scheduling method for a microgrid considering segmented multi-interval uncertainty sets, which can solve the uncertainty modeling and carbon emission problems of the microgrid, reduce the conservatism of the robust optimization scheduling strategy and improve the economy of microgrid scheduling.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is: a robust optimization scheduling method for microgrid considering segmented multi-interval uncertainty sets, comprising the following steps: Step 1: Based on the Gaussian mixture model, the source-load prediction power and error data of wind, light and load are segmented and fitted, and combined with the box-type interval uncertainty set to establish a multi-interval uncertainty set of power segmentation to describe the uncertainty of wind, light and load; Step 2: Taking the minimization of microgrid operation cost and carbon emission cost as the goal, a robust optimization scheduling model of microgrid considering segmented multi-interval uncertainty set and carbon emission is constructed; Step 3: Using the column and constraint generation algorithm to solve the microgrid robust optimization scheduling model, including the following steps: Step 31, dividing the microgrid robust optimization scheduling model into a main problem and a sub-problem; Step 32: The subproblem max-min is transformed into a single-layer max problem by Lagrangian duality method, and the dual problem of the subproblem is transformed into a mixed integer linear programming problem by using the big M method: the product of binary variables and continuous variables is linearized by introducing auxiliary variables and related constraints; Step 33, alternately iterate and solve the main and sub-problems. After the derivation and transformation in step 32, the proposed two-stage robust optimization scheduling model has been transformed into the form of a mixed integer linear programming problem. The main problem and the sub-problems are solved iteratively through the column and constraint generation algorithm until the difference between the upper bound LB and the lower bound UB is reduced to the convergence threshold ξ, and the final optimized daily stage scheduling decision is obtained.

[0008] Preferably, the actual values ​​of wind, light and load power in step 1 are represented by the sum of their power prediction values ​​and prediction errors, and the power prediction error is: e ψ,t =P ψ,t -P ψ,t In the formula: unit ψ includes wind turbine WT, photovoltaic PV and load Load; e ψ,t is the power prediction error of unit ψ during period t; P ψ,t is the actual power of unit ψ during period t; P ψ,t is the power prediction value of unit ψ in period t; The source-load power prediction value is divided into three intervals, and a Gaussian mixture model is used to fit the power prediction error in each interval.

[0009] Preferably, establishing a multi-interval uncertainty set for power partitions in step 1 includes the following steps: Step 11, obtaining the probability distribution of the corresponding prediction error according to the source load prediction power partition section situation; Step 12, combining the multi-interval partitioning of the power segmentation uncertainty set to analyze the construction method of the multi-interval uncertainty set of the power segmentation error; Step 13: According to the size and probability of prediction error, combined with the uncertain budget parameter Γ ψ The error single interval Divided into NAS intervals, satisfying the following formula: Where: NSP is the number of power prediction value segments; and is the predicted upper and lower deviation values ​​of the unit ψ in the power section s error interval j during the time period t; Γ ψ,j,s is the uncertain time budget parameter of unit ψ in the error interval j of power segment s, and the degree of uncertainty can be changed by adjusting its size; and is the predicted upper and lower deviation values ​​of unit ψ in a single interval during time period t; Γ ψ is the single-interval uncertain time budget parameter; ρ ψ,j is the occurrence probability of unit ψ in interval j, and its value can be obtained according to the fitting result of the corresponding probability distribution, ρ ψ is the occurrence probability of unit ψ in a single interval; Step 14: According to the constructed data driven segmented multi-interval source-load uncertainty set, the wind-solar and load uncertainties in the MG are as follows: Where: U ψ The piecewise multi-interval uncertainty set representing the unit ψ; It is a Boolean variable, indicating that the predicted deviation variable is located in the upper or lower half of the jth interval.

[0010] Preferably, the microgrid includes a traditional distributed power source, a renewable distributed power source, an energy storage system and a load.

[0011] Preferably, in step 2, a two-stage robust optimization scheduling model is established with the goal of minimizing the microgrid operating cost and environmental cost. The constraints that need to be met include power generation constraints, energy storage system constraints, demand response load constraints, and interactive power constraints with the power grid. The objective function is as follows:

[0012] Preferably, the microgrid robust optimization scheduling model constructed in step 2 considering segmented multi-interval uncertainty sets and carbon emissions is as shown in the following formula: Corresponding to the power generation constraint, energy storage system constraint, demand response load constraint, and interactive power constraint with the power grid, the inner layer 'max' is to find the worst scenario with uncertainty concentration, and 'min' is to minimize the microgrid operation cost under the worst scenario; the outer layer "min" is to optimize the day-ahead scheduling decision by the corresponding scheduling power under the worst scenario; c represents the coefficient column vector corresponding to the objective function (28); B and I represent the equality constraint coefficient matrix of the day-ahead deterministic scenario; e represents the constant column vector of the equality constraint of the day-ahead deterministic scenario; A, C, D and F represent the inequality constraint coefficient moments of the day-ahead deterministic scenario; d, f and h represent the constant column vector of the inequality constraint of the day-ahead deterministic scheduling scheme; x and y represent the optimization variables of the day-ahead scenario, and the specific expressions are as follows:

[0013] Preferably, the main problem in step 31 is written in the following form: Where: Uw is the set of all worst cases searched; for each worst case us in Uw, the corresponding hourly variable yk and its constraints are generated, and the mean umeean of the uncertainty range is selected as the initial worst uncertainty scenario u0*; The sub-problem is expressed as:

[0014] Preferably, in step 32, the subproblem max-min is converted into a single-layer max problem by Lagrangian duality method, and Ω(x,u) represents the feasible domain of the optimization variable y when a set (x,u) is given, and the specific expression is as follows: Where: σ, ω, τ, θ and ρ are the dual variables corresponding to each inner constraint; When (x,u) is given, the inner layer of the subproblem is a linear problem. The dual problem of the subproblem can be obtained according to the corresponding relationship of the following formula:

[0015] Preferably, in step 32, the dual problem of the subproblem is transformed into a mixed integer linear programming problem using the big M method: Where: Δu j+ , Δu j- is the power prediction deviation; is the introduced continuous auxiliary variable; π j+ , π j- is a binary variable; M is the upper bound of the dual variable, which is a sufficiently large positive integer.

[0016] Preferably, the alternating iterative solution between the main and sub-problems in step 33 includes the following steps: Step 331: Given a set of uncertain variable values ​​u meean , as the initial worst scenario, the upper bound UB = +∞, the lower bound LB = -∞, the number of iterations k = 1, and the convergence gap is set to ξ = 0.01; Step 332: u meean Substitute into the main problem and get the optimal solution (x k ,y k ,λ k ), update the objective function value of the main problem as the new lower bound LB = λ k ; Step 333: k Substitute into the subproblem and get the optimal solution f of the subproblem k (x k ) and the corresponding worst scenario u k+1 , update the sub-problem objective function value as the new upper bound UB = min{UB,f k (x k )}; Step 334: If UB–LB≤0.01, stop the iteration and return the optimal solution (x k ,y k), otherwise, increase the variable y k+l and the following constraints: Let k=k+1, and return to step 332 until the algorithm converges.

[0017] The beneficial effects of the present invention are:

[0018] This scheme aims at the uncertainty of source and load in microgrid, considers the direct relationship between uncertainty parameter data set and prediction error, and establishes a robust optimization scheduling method for microgrid considering segmented multi-interval uncertainty set. The following conclusions are drawn through example analysis:

[0019] 1) Comprehensively considering demand response, carbon emission costs and source-load uncertainty can fully tap the dispatching potential on the source-load side, effectively smooth out wind, solar and load fluctuations in the worst scenarios, and reduce system operating costs.

[0020] 2) By describing the uncertainty of wind, solar and load by segmented multi-interval uncertainty sets, the conservatism of microgrid scheduling schemes can be effectively reduced, and the total cost of system scheduling can be reduced.

[0021] 3) When the determined budget parameter is set small, the system scheduling cost is low, but the robustness is weak; when the uncertain parameter is set large, the robustness of the system scheduling result is strong, but the scheduling cost is high. Therefore, in the actual process of formulating the scheduling plan, the appropriate uncertain budget parameter can be selected according to the system requirements to flexibly adjust the robustness and economy of the scheduling plan.

[0022] This paper focuses on the uncertainty set model of wind, solar and load uncertainties in traditional microgrids, and solves the robust optimization scheduling model of microgrids based on the uncertainty set. In the future, we will explore and analyze the various complex uncertain factors in integrated energy microgrids and multi-microgrids, and conduct in-depth research on the robust optimization scheduling of integrated energy microgrids and multi-microgrids.

[0023] The main contributions of this solution are summarized as follows:

[0024] 1) A new power segmentation multi-interval uncertainty set modeling method is proposed. In order to reduce the conservatism of the robust optimization scheduling strategy and improve the economy of MG scheduling, the Gaussian mixture model is used to fit the prediction error within the source-load power interval based on the historical predicted power and error data of uncertain parameters. Then, according to the error distribution fitting results corresponding to different power intervals, a new power segmentation multi-interval uncertainty set modeling method is proposed.

[0025] 2) A two-stage robust optimization scheduling model for microgrids that takes into account source-load uncertainty and environmental costs is established. The model takes into account the economic efficiency, environmental protection and conservatism of the microgrid's operation results.

[0026] 3) The proposed model is linearized by the big M method and Lagrangian duality theory, and the improved CCG algorithm is used to solve the MILP. Four cases are designed for comparative analysis, which verifies that the proposed model balances the economic and environmental benefits of MG operation while ensuring the robustness of the dispatch strategy and the absorption of renewable energy. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0028] Figure 1 It is a schematic diagram of the structure of the microgrid system of the present invention.

[0029] Figure 2 It is a scatter diagram of the wind power prediction value and its prediction error of the present invention.

[0030] Figure 3 It is a probability density fitting curve diagram of wind power prediction error of the present invention.

[0031] Figure 4 Schematic diagram of multi-interval uncertainty sets in existing literature.

[0032] Figure 5 It is a multi-interval partitioning diagram of the power segment uncertainty set of the present invention.

[0033] Figure 6 It is a schematic diagram of the segmented multi-interval uncertainty set of the present invention.

[0034] Figure 7 This is a curve diagram of source-load power prediction of the microgrid of the present invention.

[0035] Figure 8 This is the micro-grid electricity sales plan diagram of the present invention.

[0036] Fig. 9 This is the day-ahead scheduling plan diagram of the DG and ESS of the present invention.

[0037] Fig.10 This is the actual power consumption plan diagram of the DR of the present invention. DETAILED DESCRIPTION

[0038] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0039] The present invention discloses a robust optimization scheduling method for a microgrid considering segmented multi-interval uncertainty sets. The embodiment includes the following steps: Step 1: Based on the Gaussian mixture model, the source-load prediction power and error data of wind, light and load are segmented and fitted, and combined with the box-type interval uncertainty set to establish a multi-interval uncertainty set of power segmentation to describe the uncertainty of wind, light and load; Step 2: Taking the minimization of microgrid operation cost and carbon emission cost as the goal, a robust optimization scheduling model of microgrid considering segmented multi-interval uncertainty set and carbon emission is constructed; Step 3: Using the column and constraint generation algorithm to solve the microgrid robust optimization scheduling model, including the following steps: Step 31, dividing the microgrid robust optimization scheduling model into a main problem and a sub-problem; Step 32: The subproblem max-min is transformed into a single-layer max problem by Lagrangian duality method, and the dual problem of the subproblem is transformed into a mixed integer linear programming problem by using the big M method: the product of binary variables and continuous variables is linearized by introducing auxiliary variables and related constraints; Step 33, alternately iterate and solve the main and sub-problems. After the derivation and transformation in step 32, the proposed two-stage robust optimization scheduling model has been transformed into the form of a mixed integer linear programming problem. The main problem and the sub-problems are solved iteratively through the column and constraint generation algorithm until the difference between the upper bound LB and the lower bound UB is reduced to the convergence threshold ξ, and the final optimized daily stage scheduling decision is obtained.

[0040] like Figure 1 The figure shows a typical system of a grid-connected microgrid. The system includes traditional distributed power micro-turbine MT, renewable distributed power PV, WT, energy storage system and load. MG interacts with the upper distribution network through centralized power lines. Under the premise of considering the economy and environmental protection of the microgrid, the control center optimizes the scheduling of each flexible unit in the system to improve the economy and reliability of operation.

[0041] At present, MG robust scheduling ignores the important parameter characteristics of source-load historical data, thus breaking the connection between day-ahead prediction and scheduling. Therefore, in order to improve the disadvantage of RO being too conservative, firstly, the prediction errors in different power intervals are fitted using the probability characteristic information of wind and solar output and load itself, which proves that the power segment fitting method can more accurately reflect the true distribution of source-load prediction errors. Then, according to the error distribution fitting results corresponding to different power intervals, the traditional single-interval uncertainty set is divided into multiple intervals. Finally, the uncertain budget parameters are allocated according to the distribution of prediction errors in each power interval, so that the defined multi-interval uncertainty set is more in line with the actual situation, effectively reducing the conservatism of the scheduling scheme.

[0042] The actual values ​​of wind, light and load power in step 1 are represented by the sum of their power prediction values ​​and prediction errors. The power prediction error is: In the formula: unit ψ includes wind turbine WT, photovoltaic PV and load Load; e ψ,t is the power prediction error of unit ψ during period t; P ψ,t is the actual power of unit ψ during period t; is the power prediction value of unit ψ in period t.

[0043] Some literature points out that there are differences in the error probability distribution corresponding to the power forecast values ​​in different sections. Taking wind power as an example, the wind power output and error data of Elia power grid in 2022 are selected for analysis, and the data are normalized by wind power installed capacity. The scatter plot of wind power forecast value and its forecast error is shown in Figure 2 As shown, from Figure 2 It can be seen that the prediction error corresponding to the low power prediction value is more concentrated and has a smaller value, while the prediction error corresponding to the high power prediction value is more dispersed and has a larger value. This shows that the distribution characteristics of the power prediction error are correlated with the size of the power prediction value, and these characteristics need to be mined to better describe the source load uncertainty.

[0044] The Gaussian mixture model has the advantage of high applicability in describing distributions of different characteristics and can effectively handle the probability distribution fitting problem of wind and solar power and load forecasting errors with strong uncertainty, as shown in formula (2).

[0045] Where: f i (ΔP) represents the probability density function of the power prediction error ΔP of the i-th power section; ω k is the weight coefficient of the kth normal distribution; is the probability density function of the kth normal distribution; μ k and are the expectation and variance respectively; m is the number of normal distributions in the Gaussian mixture model.

[0046] In this embodiment, the source load power prediction value is divided into three intervals, specifically [0, 0.3], [0.3, 0.6] and [0.6, 1], and the Gaussian mixture model is used to fit the power prediction error in each interval. The probability distribution of the prediction error in each interval and the probability distribution of the overall error when no segmentation is performed are as follows: Figure 3 As shown. Figure 3 It can be seen that the probability distribution of prediction errors in different intervals is significantly different: when When it is less than 0.3, the fitting curve shows a peak characteristic; when When it is between 0.3 and 0.6, the fitting curve is symmetrical; When it is greater than 0.6, the fitting curve is right-skewed. Therefore, the method of fitting the prediction error by prediction power partition can more realistically reflect the distribution of prediction error.

[0047] Robust optimization scheduling models often use a single interval uncertainty set to describe source-load uncertainty, but the optimization results are conservative. To this end, some literature has proposed multiple interval uncertainty sets, such as Figure 4 As shown. Figure 4 It can be seen that although the multi-interval source-load uncertainty set can reduce the conservatism of robust optimization to a certain extent, it ignores the relationship between the source-load predicted power and the prediction error, resulting in the uncertainty set covering many extreme scenarios that are impossible to occur in practice.

[0048] In order to effectively eliminate extreme scenarios that are impossible to occur in the uncertainty interval, a more realistic multi-interval uncertainty set of power segments is constructed by considering the relationship between historical predicted power and prediction error. The establishment of a multi-interval uncertainty set of power segments in step 1 includes the following steps: Step 11, obtaining the probability distribution of the corresponding prediction error according to the source load prediction power partition section situation; Step 12: Taking the prediction error probability distribution of the power prediction standard value in the interval [0.6,1] as an example, combined with Figure 5 The construction method of multi-interval uncertainty set of power segmentation error is further analyzed; Step 13: According to the prediction error size and probability in the figure, combined with the uncertain budget parameter Γ ψ The error single interval Divided into NAS intervals, satisfying formula (3) Where: NSP is the number of power prediction value segments; and is the predicted upper and lower deviation values ​​of the unit ψ in the power section s error interval j during the time period t; Γ ψ,j,s is the uncertain time budget parameter of unit ψ in the error interval j of power segment s, and the degree of uncertainty can be changed by adjusting its size; and is the predicted upper and lower deviation values ​​of unit ψ in a single interval during time period t; Γ ψ is the single-interval uncertain time budget parameter; ρ ψ,j is the occurrence probability of unit ψ in interval j, and its value can be obtained according to the fitting result of the corresponding probability distribution, ρ ψ is the occurrence probability of unit ψ in a single interval; Step 14: According to the constructed data driven segmented multi-interval source-load uncertainty set, the wind and solar power and load uncertainties in the MG are shown in formula (4). The uncertainty scenario is as follows: Figure 6 As shown: Where: U ψ The piecewise multi-interval uncertainty set representing the unit ψ; It is a Boolean variable, indicating that the predicted deviation variable is located in the upper or lower half of the jth interval.

[0049] Compared with the uncertainty set proposed in the existing literature, the prediction error corresponding to the power value in different sections of the uncertainty set proposed in this embodiment is determined according to the fitted probability distribution parameters, making it closer to reality, thereby reducing the conservatism of the robust optimization result. This is because this embodiment not only considers the time correlation of the source and load, but also considers the distribution characteristics of the prediction error corresponding to its day-ahead prediction value.

[0050] Traditional distributed power generation: The cost of traditional distributed power generation in microgrid is shown in formula (5), which includes operation and maintenance cost and fuel consumption cost.

[0051] Where: CMT(t) is the power generation cost of the MT machine in period t; bMT is the operation and maintenance cost coefficient; PMT(t) is the output power of the MT in period t; cMT is the unit price of fuel; ηMT is the operating efficiency of the MT, which is 40%; Δt is the scheduling step, which is 1h; T is the scheduling period, which is 24h.

[0052] Since the power response speed of MT is faster than that of hourly scheduling, its ramp rate constraint is not considered, and only the power generation constraint is considered: P MT,min ≤P MT (t)≤P MT,max (6)

[0053] Where: PMT,min and PMT,max are the upper and lower limits of the MT output power, which are limited by its rated power and minimum load rate.

[0054] Renewable distributed generation: Operation and maintenance costs can be defined as:

[0055] Where: Cj(t) is the operation and maintenance cost of WT and PV in period t; bj is the operation and maintenance cost coefficient; Pj(t) is the output power of wind and solar power in period t.

[0056] Energy storage system: Constraints on the charge and discharge state of ESS: O ch(t)+O dis (t)≤1 (8)

[0057] Where: Och(t) represents the charging state of ESS in period t (“1” represents charging, “0” represents no charging), and Odis(t) represents the discharging state of ESS in period t (“1” represents discharging, “0” represents no discharging).

[0058] ESS charging and discharging constraints: 0≤P dis (t)≤O dis (t)P dis,max (9) 0≤P ch (t)≤O ch (t)P ch,max (10) P ESS (t) = P dis (t)-P ch (t) (11)

[0059] Where: PESS(t) is the output power of ESS in period t; Pdis(t) and Pch(t) are the charge and discharge powers of ESS in period t respectively.

[0060] ESS state of charge (SOC) constraints: SOC(t=0)=SOC(t=T) (13) SOC min ≤SOC(t)≤SOC max (14)

[0061] Where: Formula (12) represents the energy constraint of ESS; ηch and ηdis are the charge and discharge efficiencies of ESS respectively; Pr is the rated capacity of ESS; SOCmin and SOCmax are the lower and upper limits of ESS charge state respectively. Formula (13) ensures that the capacity of energy storage is equal at the beginning and end of the dispatch, which is conducive to the cyclic dispatch of energy storage.

[0062] Lead-acid batteries and lithium batteries are commonly used in ESS in MG. The battery life depends on the depth of charge / discharge. When the depth of charge / discharge increases, the battery life decreases. The aging cost of ESS can be expressed as:

[0063] Where: CESS(t) is the aging cost of ESS in period t; cESS is the aging cost.

[0064] Demand response load: The implementation of demand response DR is to encourage users to transfer non-essential loads to obtain benefits. P DR (t) = P up (t)-P down (t) (16) 0≤P up (t)≤O up (t)P up,max (17) 0≤P down (t)≤O down (t)P down,max (18) O up (t)+O down (t)≤1 (19)

[0065] Where: PDR(t) is the actual dispatch power of DR in period t, that is, the amount of power load transferred; Pup(t) and Pdown(t) are the upward / downward adjustment power of DR in period t, respectively. The power limits for upward and downward adjustment are given by equations (17) and (18). Equation (19) ensures that the power load cannot be adjusted downward and upward at the same time. Oup(t) represents the upward adjustment state of the power load in period t, and Odown(t) represents the downward adjustment state of the power load in period t. Equation (20) ensures that the total power consumption of the load remains unchanged during the dispatch period.

[0066] The scheduling cost of implementing DR can be expressed as:

[0067] Where: CDR(t) is the implementation cost of DR in period t; cDR is the scheduling cost coefficient of DR.

[0068] Interaction power with the grid: When there is a shortage or surplus of energy supply in the MG system, it is necessary to interact with the grid to adjust the power balance and realize the local consumption of renewable energy.

[0069] In order to avoid the situation where the microgrid simultaneously purchases and sells electricity from the grid, the constraints are set as: O buy (t)+O sell (t)≤1 (22) 0≤P buy (t)≤O buy (t)P buy,max (twenty three) 0≤P sell (t)≤O sell (t)P sell,max (twenty four)

[0070] Where: Obuy(t) represents the state of MG purchasing electricity from the grid during period t, Osell(t) represents the state of MG selling electricity to the grid during period t; Pbuy(t) and Psell(t) are the power purchased and sold from the grid during period t, respectively.

[0071] The power balance constraint is: P buy (t)-P sell (t)+P ESS (t)+P PV (t)+P WT (t)+P MT (t) = P DR (t)+P RL (t)+P EV (t) (25)

[0072] Where: PRL(t) is the non-dispatchable load in the power grid during period t.

[0073] The cost of interacting with the main grid to buy and sell electricity is:

[0074] Pollutant treatment costs: The cost of microgrids to treat environmental pollution, including the environmental compensation cost of MT and the environmental compensation cost of fossil energy combustion in the distribution network. The pollutants considered in this embodiment mainly include CO2, SO2, and NOX, and their costs are described as follows:

[0075] Where: Cemi(t) is the pollutant treatment cost of the microgrid in period t; qMT,p is the emission coefficient of the p-th type of pollutant generated by the traditional distributed power source; bp is the treatment cost of the p-th type of pollutant; qG,p is the emission coefficient of the p-th type of pollutant generated by the distribution network.

[0076] In step 2, a two-stage robust optimization scheduling model is established with the goal of minimizing the microgrid operation cost and environmental cost. The constraints that need to be met include equations (6), (8-14), (16-20), and (22-25). The objective function is shown in equation (28):

[0077] The scheduling results of the deterministic optimization model depend to a large extent on the accuracy of the forecast data, but the uncertainty of the MG has a great impact on the accuracy of the scheduling results. Therefore, uncertainty should be considered when formulating the day-ahead scheduling plan. The two-stage "min-max-min" robust optimization model constructed in this embodiment is shown in formula (29). Formula (29) corresponds to constraints (6), (8-14), (16-20), and (22-25).

[0078] Where: the inner layer 'max' is to find the worst scenario in the uncertainty concentration, and 'min' is to minimize the microgrid operating cost in the worst scenario. The outer layer "min" is to optimize the day-ahead scheduling decision by the corresponding scheduling power in the worst scenario. c represents the coefficient column vector corresponding to the objective function (28); B and I represent the equality constraint coefficient matrix of the day-ahead deterministic scenario; e represents the constant column vector of the equality constraint of the day-ahead deterministic scenario; A, C, D and F represent the inequality constraint coefficient moments of the day-ahead deterministic scenario; d, f and h represent the constant column vector of the inequality constraint of the day-ahead deterministic scheduling scheme.

[0079] x and y represent the optimization variables of the day-ahead scenario, and the specific expressions are as follows:

[0080] The two-stage robust optimization problem cannot be solved directly, so this embodiment uses the column and constraint generation C&CG algorithm to solve the MG robust optimization problem. First, the proposed two-stage RO model (29) needs to be divided into a main problem (31) and a sub-problem (32), and then the main and sub-problems are solved alternately and iteratively. The main problem is written as follows:

[0081] Where: Uw is the set of all worst cases searched. For each worst case us in Uw, the corresponding hourly phase variable yk and its constraints are generated. The mean umeean of the uncertainty range is selected as the initial worst uncertainty scenario u0*.

[0082] The sub-problem can be expressed as:

[0083] The inner layer of the subproblem contains only continuous variables. The present invention transforms the subproblem max-min into a single-layer max problem through the Lagrangian duality method. Ω(x,u) represents the feasible domain of the optimization variable y when a set (x,u) is given. The specific expression is as follows:

[0084] Where: σ, ω, τ, θ and ρ are the dual variables corresponding to the inner constraints respectively.

[0085] When (x,u) is given, the inner layer of the subproblem is a linear problem. According to the corresponding relationship of formula (33), the dual problem of the subproblem can be obtained:

[0086] However, the bilinear term uTρ in the subproblem poses a challenge to the solution of the inner problem. Considering that the optimization result of u must be the vertex of each subinterval of the uncertainty set, the deviation variable is 0 or 1, and then the big M method is used to transform equation (34) into a mixed integer linear programming MILP problem: the product of binary variables and continuous variables will appear, and it will be linearized by introducing auxiliary variables and related constraints.

[0087] Where: Δuj+, Δuj- are power prediction deviations; φj+, φj- are introduced continuous auxiliary variables; πj+, πj- are binary variables; M is the upper bound of the dual variable, which is a sufficiently large positive integer.

[0088] After the above derivation and transformation, the proposed two-stage RO model has been transformed into the form of a mixed integer linear programming problem. The main problem and sub-problems can be solved iteratively through the C&CG algorithm until the difference between LB and UB is reduced to the convergence threshold ξ, and the final optimized daily stage scheduling decision is obtained. The solution process is as follows: Step 331: Given a set of uncertain variable values ​​u meean , as the initial worst scenario, the upper bound UB = +∞, the lower bound LB = -∞, the number of iterations k = 1, and the convergence gap is set to ξ = 0.01; Step 332: u meean Substitute into the main problem and get the optimal solution (x k ,y k ,λ k ), update the objective function value of the main problem as the new lower bound LB = λ k ; Step 333: x k Substitute into the subproblem and get the optimal solution f of the subproblem k (x k ) and the corresponding worst scenario u k+1 , update the sub-problem objective function value as the new upper bound UB = min{UB,f k (x k )}; Step 334: If UB–LB≤0.01, stop the iteration and return the optimal solution (x k ,y k), otherwise, increase the variable y k+l and the following constraints: Let k=k+1, and return to step 332 until the algorithm converges.

[0089] The case study and analysis were carried out, and all simulation experiments were run on a personal computer equipped with an Intel Core i7-6700 CPU and 16GRAM. The established robust optimization scheduling model was modeled by using MATLAB 2018a and YALMIP, and the CPLEX solver was called to solve the optimization problem.

[0090] Simulation parameter setting: In order to verify the effectiveness of the proposed microgrid robust optimization scheduling model and method, based on Figure 1 The microgrid framework described in the paper is simulated. The simulation parameters are shown in Table 1. The emission coefficients and treatment costs of pollutants are shown in Table 2. The day-ahead transaction electricity price for power exchange between the distribution network and the microgrid is based on the residential electricity tiered price, as shown in Table 3. The price of electricity sold to the main grid is set to 40% of the purchase price. Table 1 Parameter settings Table 2 Pollutant emission coefficients and treatment costs Table 3. Grid day-ahead transaction time-of-use electricity prices

[0091] According to the analysis, the specific distribution parameters of the source-load segment power prediction error are shown in Tables 3 to 5. According to the specific distribution parameters corresponding to the source-load prediction power error in different sections, the wind-solar power uncertainty set is divided into three intervals with deviations of μ±σ, μ±2σ and μ±3σ, and the load uncertainty set is divided into two intervals with deviations of μ±1.5σ and μ±3σ. ψ Divide, can be set as: (Γ pv,1 ,Γ pv,2 ,Γ pv,3 )=(4,1,1),(Γ wt,1 ,Γ wt,2 ,Γ wt,3 )=(8,3,1) and (Γ L,1 ,Γ L,2 )=(9,3). The number and size of intervals depend on the amount of historical data obtained from actual projects. If more information about the dominant uncertainty is obtained, the uncertainty set can be divided into finer intervals, which not only conforms to the actual situation but also significantly reduces the conservatism of robust optimization. Figure 7Predicted source-load power curve for the microgrid, the shaded area indicates the range of uncertainty sets considered. Table 3 Probability distribution parameters of wind power prediction error Table 4. Probability distribution parameters of photovoltaic power prediction error Table 5 Load power forecast error probability distribution parameters

[0092] Results and analysis: The microgrid is optimized and dispatched according to the two-stage robust optimization method for microgrids proposed in this embodiment. The interactive power distribution between the system and the main grid under the worst scenario obtained by optimization is as follows: Figure 8 As shown in Figure 2, the charging and discharging power of energy storage is as follows: Fig. 9 The demand response results are shown in Fig.10 As shown in the figure, the ESS discharges to the microgrid, the power is positive, and the charging power is negative; the microgrid purchases electricity from the upper grid, the power is positive, and the selling power is negative.

[0093] Depend on Figure 8-Figure 9 It can be seen that wind power and photovoltaic energy generation are fully absorbed, realizing the maximum utilization of clean energy. However, when the photovoltaic power generation is zero at night, renewable energy generation cannot meet the energy balance demand. To ensure the stable operation of the microgrid system, the system adopts measures such as purchasing electricity from the grid, micro gas turbine power generation, and ESS power generation. At this time, the MT power generation cost is higher than the grid electricity price, MG mainly purchases electricity from the main grid, and MT outputs minimum power operation (24-7h the next day). In the rest of the time period, MT operates at maximum power to increase the amount of electricity sold to the distribution network, thereby effectively increasing the electricity sales revenue, enhancing the energy interaction between MG and the grid, and reducing the operating cost of MG. The participation of DG effectively ensures that the microgrid sells electricity to the grid at maximum power in the high electricity price range, which can effectively reduce the operating cost. At the same time, ESS charges during low electricity price periods and low load demand, and discharges during high electricity price periods and high load demand to achieve the peak shaving and valley filling effect of the grid. The participation of ESS effectively increases the absorption of renewable power generation, reduces the operating cost of MG, and fully reflects the flexibility of ESS in participating in optimal scheduling. The power grid plays a very important role in ensuring the stable operation of the microgrid. MG purchases electricity from the power grid and charges the ESS in the low power price range. MG sells electricity to the power grid at maximum power in the high power price range.

[0094] After implementing demand response, electricity load demand has changed. Fig.10The power load demand before and after the implementation of demand response. It can be seen that under the conditions of meeting the total power demand and power consumption constraints, the power load demand in the high power price period is transferred to the low power price period (1-7h), which is conducive to reducing the cost of purchasing electricity from the main power grid. In the high power price period, MG will increase the power output of the MT unit to reduce the cost of purchasing electricity, further optimizing the operating efficiency of the system.

[0095] Comparison with different robust optimization models: Considering the uncertainty of source load, a two-stage robust optimization model of MG is established. In order to intuitively describe the accuracy of the proposed uncertain model, this embodiment constructs 4 models for comparative experiments. The corresponding models are as follows:

[0096] Model 1 (benchmark): Ignore the uncertainty caused by source and load power in the day-ahead scheduling, and use the day-ahead forecast data. This model is also called a deterministic scheduling model; Model 2: The uncertainty set is captured by a normal distribution, and the corresponding mean and variance are obtained through 1000 historical sampling data. This model can be called a two-stage chance-constrained optimization model; Model 3: Uncertainty is represented by a multi-interval uncertainty set; Model 4 (proposed): The uncertainty set is described by a data-driven piecewise multi-interval uncertainty set. Table 6 Cost comparison of different models

[0097] The optimization results of the four models are shown in Table 6. As can be seen from Table 6, Model 1 has the lowest scheduling cost because it does not consider the influence of uncertain factors. However, due to the influence of uncertain factors in the actual operation of the system, the scheduling results obtained are less robust. Compared with Model 2, the total system scheduling cost of Model 3 increased by 224.2 yuan. This is because the two-stage opportunity constraint optimization model further considers the prediction of uncertain parameters compared with the multi-interval uncertainty set, which can better cope with the changes in uncertainty and reduce the scheduling cost of the model. Compared with Model 3, Model 4 considers the historical data distribution characteristics of uncertainty parameters and describes the uncertainty parameters more accurately, making it more in line with the actual situation. Therefore, the total cost is reduced by 126.4 yuan. It is proved that the proposed model reduces the conservatism of the model while ensuring the robustness of the day-ahead scheduling results. Although the strategy of Model 4 has a higher total cost than Model 2 and Model 1, the model can ensure that the dispatchable units in the MG operate in a safe area and ensure the safe operation of the system. When uncertainty is revealed in Models 1 and 2, the dispatchable units may exceed the safe operation range, resulting in the collapse of the MG system. Therefore, in order to ensure the balance between economy and risk, the proposed model 4 is more suitable for actual engineering.

[0098] Comparison of microgrid operation costs with different uncertain budget parameters: In order to analyze the impact of uncertain budget parameters on the operation cost of microgrids, four uncertain budget parameters are set for comparison. The four uncertain budget parameters are: 0, 25%, 50% and 100%. The system dispatch costs under different uncertain budget parameters are shown in Table 7. Table 7 Influence of uncertain adjustment parameters on optimization results

[0099] It can be seen from Table 7 that when the uncertain budget parameters are all 0, the robust optimization model is transformed into a deterministic optimization model, and the total system scheduling cost is the lowest. As the uncertain budget parameters continue to increase, the total system scheduling cost also continues to increase, and the scheduling plan gradually tends to be conservative. ψ,j The larger the value, the more time periods when the load power reaches the maximum value of the prediction interval and the photovoltaic output reaches the boundary value of the prediction interval. Therefore, the uncertainty faced by the power balance of the microgrid is also higher, resulting in a more conservative MG scheduling plan. Therefore, in the actual process of formulating the scheduling plan, appropriate uncertainty budget parameters can be set as needed to flexibly adjust the economy and robustness of the scheduling plan.

[0100] It should be noted that the parts not described in detail in the above embodiments are all prior art.

[0101] The above description is only a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention should be covered within the protection scope of the present invention.

Claims

1. A robust optimization scheduling method for microgrid considering segmented multi-interval uncertainty sets, characterized by: The following steps are involved: Step 1: Based on the Gaussian mixture model, the source-load prediction power and error data of wind, light and load are segmented and fitted, and combined with the box-type interval uncertainty set to establish a multi-interval uncertainty set of power segmentation to describe the uncertainty of wind, light and load; Step 2: Taking the minimization of microgrid operation cost and carbon emission cost as the goal, a robust optimization scheduling model of microgrid considering segmented multi-interval uncertainty set and carbon emission is constructed; Step 3: Using the column and constraint generation algorithm to solve the microgrid robust optimization scheduling model, including the following steps: Step 31, dividing the microgrid robust optimization scheduling model into a main problem and a sub-problem; Step 32: The subproblem max-min is transformed into a single-layer max problem by Lagrangian duality method, and the dual problem of the subproblem is transformed into a mixed integer linear programming problem by using the big M method: the product of binary variables and continuous variables is linearized by introducing auxiliary variables and related constraints; Step 33, alternately iterate and solve the main and sub-problems. After the derivation and transformation in step 32, the proposed two-stage robust optimization scheduling model has been transformed into the form of a mixed integer linear programming problem. The main problem and the sub-problems are solved iteratively through the column and constraint generation algorithm until the difference between the upper bound LB and the lower bound UB is reduced to the convergence threshold ξ, and the final optimized daily stage scheduling decision is obtained.

2. According to claim 1, a robust optimization scheduling method for microgrid considering segmented multi-interval uncertainty sets is characterized by: The actual values ​​of wind, light and load power in step 1 are represented by the sum of their power prediction values ​​and prediction errors. The power prediction error is: In the formula: unit ψ includes wind turbine WT, photovoltaic PV and load Load; e ψ,t is the power prediction error of unit ψ during period t; P ψ,t is the actual power of unit ψ during period t; is the power prediction value of unit ψ in period t; The source-load power prediction value is divided into three intervals, and a Gaussian mixture model is used to fit the power prediction error in each interval.

3. A robust optimization scheduling method for microgrid considering segmented multi-interval uncertainty sets according to claim 2, characterized in that: The step 1 of establishing a multi-interval uncertainty set for power partitions includes the following steps: Step 11, obtaining the probability distribution of the corresponding prediction error according to the source load prediction power partition section situation; Step 12, combining the multi-interval partitioning of the power segmentation uncertainty set to analyze the construction method of the multi-interval uncertainty set of the power segmentation error; Step 13: According to the size and probability of prediction error, combined with the uncertain budget parameter Γ ψ The error single interval Divided into NAS intervals, satisfying the following formula: Where: NSP is the number of power prediction value segments; and is the predicted upper and lower deviation values ​​of the unit ψ in the power section s error interval j during the time period t; Γ ψ,j,s is the uncertain time budget parameter of unit ψ in the error interval j of power segment s, and the degree of uncertainty can be changed by adjusting its size; and is the predicted upper and lower deviation values ​​of unit ψ in a single interval during time period t; Γ ψ is the single-interval uncertain time budget parameter; ρ ψ,j is the probability of occurrence of unit ψ in interval j, and its value can be obtained according to the fitting result of the corresponding probability distribution, ρ ψ is the occurrence probability of unit ψ in a single interval; Step 14: According to the constructed data driven segmented multi-interval source-load uncertainty set, the wind-solar and load uncertainties in the MG are as follows: Where: U ψ The piecewise multi-interval uncertainty set representing the unit ψ; It is a Boolean variable, indicating that the predicted deviation variable is located in the upper or lower half of the jth interval.

4. The robust optimization scheduling method for microgrid considering segmented multi-interval uncertainty sets according to claim 1 is characterized by: The microgrid includes traditional distributed power sources, renewable distributed power sources, an energy storage system and loads.

5. A robust optimization scheduling method for microgrid considering segmented multi-interval uncertainty sets according to claim 4, characterized in that: In step 2, a two-stage robust optimization scheduling model is established with the goal of minimizing the microgrid operation cost and environmental cost. The constraints that need to be met include power generation constraints, energy storage system constraints, demand response load constraints, and interactive power constraints with the power grid. The objective function is as follows:

6. A robust optimization scheduling method for microgrid considering segmented multi-interval uncertainty sets according to claim 5, characterized in that: The microgrid robust optimization scheduling model constructed in step 2 considering the segmented multi-interval uncertainty set and carbon emissions is shown as follows: Corresponding to the power generation constraint, energy storage system constraint, demand response load constraint, and interactive power constraint with the power grid, the inner layer 'max' is to find the worst scenario with uncertainty concentration, and 'min' is to minimize the microgrid operation cost under the worst scenario; the outer layer "min" is to optimize the day-ahead scheduling decision by the corresponding scheduling power under the worst scenario; c represents the coefficient column vector corresponding to the objective function (28); B and I represent the equality constraint coefficient matrix of the day-ahead deterministic scenario; e represents the constant column vector of the equality constraint of the day-ahead deterministic scenario; A, C, D and F represent the inequality constraint coefficient moments of the day-ahead deterministic scenario; d, f and h represent the constant column vector of the inequality constraint of the day-ahead deterministic scheduling scheme; x and y represent the optimization variables of the day-ahead scenario, and the specific expressions are as follows:

7. The robust optimization scheduling method for microgrid considering segmented multi-interval uncertainty sets according to claim 1 is characterized by: The main problem in step 31 is written as follows: Where: Uw is the set of all worst cases searched; for each worst case us in Uw, the corresponding hourly variable yk and its constraints are generated, and the mean umeean of the uncertainty range is selected as the initial worst uncertainty scenario u0*; The sub-problem is expressed as:

8. The robust optimization scheduling method for microgrid considering segmented multi-interval uncertainty sets according to claim 7 is characterized by: In step 32, the subproblem max-min is transformed into a single-layer max problem by using the strong Lagrangian duality method. Ω(x,u) represents the feasible domain of the optimization variable y when a set (x,u) is given. The specific expression is as follows: Where: σ, ω, τ, θ and ρ are the dual variables corresponding to each inner constraint; When (x,u) is given, the inner layer of the subproblem is a linear problem. The dual problem of the subproblem can be obtained according to the corresponding relationship of the following formula:

9. A robust optimization scheduling method for microgrid considering segmented multi-interval uncertainty sets according to claim 8, characterized in that: In step 32, the dual problem of the subproblem is transformed into a mixed integer linear programming problem using the big M method: Where: Δu j+ , Δu j- is the power prediction deviation; is the introduced continuous auxiliary variable; π j+ , π j- is a binary variable; M is the upper bound of the dual variable, which is a sufficiently large positive integer.

10. A robust optimization scheduling method for microgrid considering segmented multi-interval uncertainty sets according to claim 9, characterized in that: The alternating iterative solution between the main and sub-problems in step 33 includes the following steps: Step 331: Given a set of uncertain variable values ​​u meean , as the initial worst scenario, the upper bound UB = +∞, the lower bound LB = -∞, the number of iterations k = 1, and the convergence gap is set to ξ = 0.01; Step 332: u meean Substitute into the main problem and get the optimal solution (x k ,y k ,λ k ), update the objective function value of the main problem as the new lower bound LB = λ k ; Step 333: k Substitute into the subproblem and get the optimal solution f of the subproblem k (x k ) and the corresponding worst scenario u k+1 , update the sub-problem objective function value as the new upper bound UB = min{UB,f k (x k )}; Step 334: If UB–LB≤0.01, stop the iteration and return the optimal solution (x k ,y k ), otherwise, increase the variable y k+l And the following constraints: Let k=k+1, and return to step 332 until the algorithm converges.

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