Robust Optimal Unit Dispatch Method for Transmission and Distribution Network Based on the Whole Process of Frequency Response

Abstract

The present invention discloses a method for robust optimization of unit scheduling of a transmission and distribution network based on the whole process of frequency response, and relates to the technical field of power systems. The method comprises: constructing a full-process frequency safety constraint around the three links of inertial response, primary frequency regulation and secondary frequency regulation, establishing a two-stage robust unit combination optimization model of a transmission and distribution network considering the whole process of frequency response with a min‑max‑min structure, and minimizing the start-stop cost, power generation cost and primary frequency regulation and secondary frequency regulation standby cost as the goal; using a column and constraint generation algorithm and a strong duality theory to convert the two-stage robust unit combination optimization model of the transmission and distribution network into a mixed integer second-order cone programming model and perform iterative solution. The method of the present invention can effectively improve the frequency regulation capability of the transmission and distribution network, reduce operating costs, improve the robustness and efficiency of the scheduling scheme, and ensure the safe, stable and economic operation of the transmission and distribution network under the conditions of uncertainty in the output of new energy sources such as wind and light.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular to a method for robustly optimizing unit dispatching of a transmission and distribution network based on the entire frequency response process. Background Art

[0002] With the rapid development of distributed generation technologies such as renewable energy generation, more and more distributed energy resources (DER) are participating in traditional distribution networks, which has promoted the gradual transformation of traditional distribution networks to active distribution networks (ADN), and the characteristics of multi-energy complementarity and bidirectional energy flow are becoming increasingly obvious. However, the current independent optimization method of transmission and distribution networks is prone to power imbalance on the boundary line and unnecessary grid congestion. It may also lead to insufficient utilization of grid resources and cannot guarantee the overall optimality of scheduling results. Therefore, how to tap ADN resources and achieve coordinated scheduling with the transmission network has become a key issue that needs to be solved urgently.

[0003] In recent years, a large number of renewable energy units, mainly wind and solar, have been connected to the power grid, and the installed capacity has increased year by year. Wind power and photovoltaic units are usually connected to the grid through power electronic devices. Compared with traditional units, they have the advantages of flexible regulation and fast response speed. However, since the active output of new energy units is almost decoupled from the grid frequency and does not have frequency response capabilities, their weak regulation characteristics have brought great challenges to the frequency security of the power grid. If the power grid has a long-term frequency deviation, it will seriously affect the safety and reliability of the power system.

[0004] In addition, affected by factors such as weather, time and geographical location, the output of new energy units such as wind power and photovoltaic power is highly uncertain. As an important part of system operation and regulation, unit combination can determine the start and stop status of the unit in the day before, which directly affects the system's dispatchable frequency regulation resource reserves the next day. Therefore, embedding frequency security constraints into the unit combination model (frequency constrained unit commitment, FCUC) has become an important measure to maintain system frequency security.

[0005] At present, there are two main optimization methods used for uncertain factors: stochastic optimization and robust optimization. Stochastic optimization uses random variables with a certain probability to describe the uncertainty of wind and solar output, but this method has the disadvantages of large amount of calculation, long calculation time, and difficulty in determining the prior probability distribution in practical applications. Robust optimization assumes that the uncertain data in the model belongs to a given uncertainty set, and obtains a robust solution that is feasible for any uncertain data in the uncertain set. It has the advantages of not requiring accurate probability distribution information of uncertain parameters and fast calculation. In order to avoid the actual effect of the optimal solution of robust optimization being poor due to excessive conservatism, an adaptive robust optimization model can be established to make some decision variables determined before the uncertain parameters, and other decision variables determined after the uncertain parameters, so as to gradually adjust the decision and improve the conservatism of the system. Summary of the invention

[0006] In order to solve the problem of how to reasonably dispatch distributed power sources and traditional power grid resources to ensure the stability and optimal operation of the power system, the present invention proposes a robust optimization unit dispatching method for the transmission and distribution network based on the whole process of frequency response. By comprehensively considering the frequency response of the power grid (including inertial response, primary and secondary frequency regulation), the start and stop and dispatching of the units in the transmission and distribution network are optimized to ensure the stability and economy of the power system under various circumstances.

[0007] In order to achieve the above object, the present invention is implemented by the following technical solutions:

[0008] A method for robust optimization of unit dispatching in a transmission and distribution network based on the entire frequency response process, the method comprising:

[0009] Establish the framework structure of the transmission and distribution network, take into account the start and stop status of thermal power units, analyze the whole process of dynamic frequency response of centralized new energy units, distributed energy and thermal power units for frequency support, and build the whole process frequency safety constraints around the three links of inertial response, primary frequency regulation and secondary frequency regulation;

[0010] The whole process frequency safety constraint includes primary frequency regulation safety constraint and secondary frequency regulation safety constraint;

[0011] The primary frequency regulation safety constraints include:

[0012] Frequency change rate constraint: When the system starts to have power shortage, the system frequency deviation , at this time, no unit in the system is in action, the system frequency change rate must meet the maximum allowable requirement, and the system inertia time constant is determined by the inertia time constants of all dispatchable frequency regulation resources in the system, expressed as:

[0013] ;

[0014] In the formula, is the frequency change rate; is the system frequency deviation after the power shortage occurs at time t; is the system reference frequency; is the system power shortage; is the inertia time constant of the system at time t; is the maximum allowable requirement for the frequency change rate;

[0015] Frequency minimum point constraint: Inertial response and primary frequency modulation work together to reduce the system frequency to the lowest frequency point In this process, each unit needs to reserve a frequency regulation reserve to participate in a frequency regulation to prevent the frequency deviation at time t from exceeding a given safety threshold, which is expressed as:

[0016] ;

[0017] In the formula, is the frequency deviation at time t; is the sum of the primary frequency regulation reserve capacity of the system at time t; is the system's primary frequency modulation response time; D is the load damping rate; is the system load; is the power shortage when the system enters inertial response at time t; is the frequency dead zone; is a given safety threshold;

[0018] Quasi-steady-state frequency constraint: When the primary frequency regulation reserve capacity of all generators in the system is fully released, the frequency will remain at the quasi-steady-state frequency At this time, the quasi-steady-state frequency deviation at time t must also be controlled within the maximum range allowed by the system. Within, it is expressed as:

[0019] ;

[0020] In the formula, is the quasi-steady-state frequency deviation at time t;

[0021] The secondary frequency regulation safety constraints include:

[0022] Secondary frequency regulation reserve capacity constraint: In order to restore the frequency to the nominal value at the end of secondary frequency regulation, the sum of the system's secondary frequency regulation reserve capacity and primary frequency regulation reserve capacity must not be less than the system power deficit, expressed as:

[0023] ;

[0024] In the formula, is the sum of the secondary frequency regulation reserve capacity of the system at time t;

[0025] Constraint on the cumulative amount of secondary frequency modulation frequency offset: The cumulative amount of secondary frequency modulation frequency offset of the system needs to be kept within a certain range to avoid excessive deviation of the frequency from the nominal value at the beginning of the secondary frequency modulation link, which is expressed as:

[0026] ;

[0027] In the formula, The end time of the secondary frequency modulation frequency deviation of the system; is the system frequency deviation coefficient; is the integral control parameter; and They are respectively the upper and lower limits of the accumulated frequency deviation of the system's secondary frequency modulation.

[0028] Considering the uncertainty of wind and solar output, the uncertainty set of wind and solar output is constructed in interval form, and a two-stage robust unit commitment optimization model of the transmission and distribution network considering the whole process of frequency response is established with a min-max-min structure, with the goal of minimizing the start-stop cost, power generation cost, and primary and secondary frequency regulation standby costs;

[0029] The column and constraint generation algorithm and strong duality theory are used to transform the two-stage robust unit combination optimization model of the transmission and distribution network into a mixed integer second-order cone programming model and iteratively solve it until the upper and lower bounds of the objective function converge, and the optimal unit scheduling plan under the worst wind and solar output scenarios is obtained.

[0030] A further improvement of the present invention is that in the framework structure of the transmission and distribution network, the dispatchable frequency regulation resources of the transmission network include thermal power units and wind power units taking into account the start and stop of the units, and the dispatchable frequency regulation resources of the active distribution network include distributed power generation units and photovoltaic units. The power between the transmission and distribution networks is transmitted bidirectionally to balance the overall load of the power grid and meet the system frequency safety requirements.

[0031] A further improvement of the present invention is that when a power shortage occurs in the system, the frequency shows a downward trend, and the system begins to enter a dynamic frequency response, and the whole process of the dynamic frequency response includes:

[0032] Inertial response: The frequency is adjusted by the kinetic energy provided by the inertia in the system. When the generator set is not working, the frequency change rate of the system RoCoF Reach the maximum value;

[0033] Primary frequency regulation: The generator sets in the system begin to change their mechanical power, and the inertial response and primary frequency regulation jointly adjust the power shortage. The thermal power units in the transmission network adjust the power generation and frequency regulation power based on the determined unit start and stop decisions. The wind turbines and the distributed generator sets and photovoltaic units in the active distribution network directly allocate output and frequency regulation resources until the unit output is equal to the disturbance and the frequency drops to the lowest frequency point. ;

[0034] Secondary frequency modulation: When the frequency stabilizes to the quasi-steady-state frequency , the primary frequency modulation process ends, and the system continues with secondary frequency modulation until the frequency returns to the nominal value.

[0035] A further improvement of the present invention is that the wind and solar output uncertainty set is expressed as:

[0036] ;

[0037] In the formula, represents the uncertainty set of wind and solar output; , are wind and light uncertainty sets, respectively; , They are the power after uncertain processing of wind and solar output respectively; , They are wind and solar predicted output respectively; , They are the maximum fluctuation ranges allowed for wind and solar output respectively; , are binary variables that represent the boundaries of the wind and solar output intervals at time t; , are the introduced wind and light uncertainties, respectively, representing the total number of times when wind power and photovoltaic outputs reach the boundaries of the interval; T is the total number of scheduling periods.

[0038] A further improvement of the present invention is that the objective function of the two-stage robust unit commitment optimization model of the transmission and distribution network is:

[0039] ;

[0040] In the formula, is the sum of the start-up and shutdown costs of thermal power units; is the sum of the power generation costs of thermal power units and distributed power generation units; is the sum of the primary frequency regulation and secondary frequency regulation reserve costs; T is the total number of dispatching time periods; , Thermal power units The start-up and shutdown costs; , They are the thermal power units at time t. On and off status; , Thermal power units , Distributed Generator Sets The cost of electricity generation; , Thermal power units , Distributed Generator Sets The meritorious contribution; , , , Thermal power units , wind turbines, distributed generators , the primary frequency regulation and backup cost of the photovoltaic unit p; , , , Thermal power units , wind turbines, distributed generators , secondary frequency regulation backup cost of PV unit p; , , , They are the thermal power units at time t. , wind turbines, distributed generators , the primary frequency regulation reserve capacity of the photovoltaic unit p; , , , They are the thermal power units at time t. , wind turbines, distributed generators , the secondary frequency regulation reserve capacity of photovoltaic unit p; TG, TW, DG, and DP are the collections of thermal power units, wind turbines, distributed generators, and photovoltaic units participating in the frequency regulation process.

[0041] A further improvement of the present invention is that the constraint conditions of the two-stage robust unit commitment optimization model of the transmission and distribution network, based on the frequency security constraint of the whole process, also include:

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[0068] In the formula, , Thermal power units , the active output of wind turbine w; for The transmission network load at the node, Forecast load of the transmission network at time t; is the transmission capacity of the tie line between the transmission and distribution networks at time t, and e represents The distribution network to which the node is connected; The terminal node The starting node set of Any starting node in; , For line , The transmission power of For line Susceptance; , , Node , the phase angle between node b and the equilibrium node at time t; For line Transmit power upper limit; , Thermal power units Minimum start and stop time; , , For thermal power units At the start / stop status at time t, time t-1, and time k, the value 1 indicates operation, and the value 0 indicates shutdown; , , Thermal power units Active power output, primary frequency regulation reserve capacity, and secondary frequency regulation reserve capacity at time t-1; , Thermal power units Upward and downward climbing rates; , Thermal power units Upper and lower limits of output; , They are the upper and lower limits of the wind turbine output w, respectively; The upper limit of the frequency regulation reserve capacity of thermal power units; The upper limit of the frequency regulation reserve capacity of wind turbines; , The active power injected into n nodes by distributed generators and photovoltaic units at time t respectively; , The reactive power injected into n nodes by distributed generators and photovoltaic units at time t respectively; , are the active and reactive power injected by node m to node n at time t respectively; , are the active and reactive power output from node n to node d at time t respectively; is the set of starting nodes when the end node is n; is the set of terminal nodes when the starting node is n, and d is any terminal node when the starting node is n; is the current flowing through line mn at time t; , are the resistance and reactance of line mn respectively; , The transmission network injects active and reactive power into the tie line between the transmission and distribution networks at node n at time t respectively; , Forecast load for n nodes at time t; , are the voltages of node m and node n at time t respectively; , The upper and lower limits of node n voltage respectively; , For distributed generators Upper and lower limits of output; is the active power output of the photovoltaic unit p; , They are the upper and lower limits of the photovoltaic unit p output respectively; The upper limit of frequency regulation reserve capacity for distributed generators; The upper limit of the frequency regulation reserve capacity of photovoltaic units; , They are the upper and lower limits of the transmission capacity of the interconnection lines between transmission and distribution networks, respectively.

[0069] A further improvement of the present invention is that: the two-stage robust unit commitment optimization model of the transmission and distribution network is converted into a mixed integer second-order cone programming model and iteratively solved, specifically including:

[0070] The objective function of the two-stage robust unit commitment optimization model of the transmission and distribution network is decomposed into a main problem and sub-problems. The transformed objective function and constraints are expressed in matrix form. The main problem is expressed as:

[0071] ;

[0072] In the formula, is the decision variable; is the variable in the objective function The coefficient vector of the correlation, is the transpose of the cost coefficient matrix of the main problem; η is the slack variable of the subproblem; is the transpose of the subproblem cost coefficient matrix; For the The solution of the subproblem after iterations; For the The worst scenario of wind and solar output after the iteration; is the variable coefficient matrix corresponding to the branch m with n as the terminal node in the second-order cone constraint; is the transpose of the constraint constant matrix corresponding to the branch m with n as the terminal node in the second-order cone constraint; A, B, E, F, G, H, K, O are the corresponding variable coefficient matrices; , , , , , is the corresponding constraint constant matrix;

[0073] The sub-problem is expressed as:

[0074] ;

[0075] In the formula, is the set of variables optimized in the second stage; U is the set of uncertainties of wind and solar output, The uncertain output of wind and light is gathered; To determine the optimization variables , back The feasible domain of For the The solution of the main problem after iterations; , , , , , are the dual variables corresponding to each constraint of the subproblem.

[0076] The max-min double-layer model in the subproblem cannot be solved directly by the solver. The inner min problem is transformed into a dual max problem by using the strong duality theory and the big M method. Combined with the outer layer, the following single-layer max model is obtained:

[0077] ;

[0078] In the formula, For wind and light forecast output collection; is the maximum fluctuation deviation allowed for wind and solar output; , are the dual variables on the left and right sides of the second-order cone constraint; A set of binary variables representing the interval boundaries of wind power and photovoltaic output at time t; Artificially introduce variables for the Big M method; is the introduced continuous auxiliary variable.

[0079] Compared with the prior art, the present invention has the following beneficial effects:

[0080] The present invention embeds the frequency safety constraint of the whole process into the unit combination, which can flexibly adjust the power generation and frequency modulation power of the thermal power unit. After considering the frequency support capacity of the active distribution network to the transmission network, it can reduce the start-stop state and start-stop cost of the thermal power unit, effectively alleviate the operating pressure of the thermal power unit, promote the coordinated operation of the transmission and distribution network, and improve the economy of the system operation.

[0081] The present invention takes into account the frequency safety constraints of the whole process, so that the frequency safety index is kept within the safety threshold after the first frequency regulation, and the system frequency is restored to the nominal value of 50Hz after the second frequency regulation, so as to ensure the frequency safety of the system. After considering the participation of distributed energy in frequency regulation, the total system operation cost and frequency regulation standby cost are reduced, so as to achieve the optimal economic operation of the transmission and distribution network.

[0082] The output uncertainty of wind turbines on the transmission network side and distributed photovoltaics on the active distribution network side of the present invention flexibly adjusts the conservatism of the system by changing the uncertainty of wind and light, so that the scheduling plan made by the system under the worst wind and light output scenarios has stronger robustness and stability, which is beneficial to improving the frequency regulation capability of the system under wind and light output fluctuations and realizing the optimal operation of the transmission and distribution network. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor. Among them:

[0084] Figure 1 is a flow chart of the method of the present invention;

[0085] Figure 2 is a diagram of the framework structure of a transmission and distribution network in an embodiment of the present invention;

[0086] Figure 3 A schematic diagram of a calculation example system in an embodiment of the present invention;

[0087] Figure 4 A system load prediction diagram in an embodiment of the present invention;

[0088] Figure 5 This is a comparison diagram of the lowest frequency points of scenario 1, scenario 2, and scenario 3 in an embodiment of the present invention;

[0089] Figure 6 1 is a comparison diagram of the frequency change rates of scenario 1, scenario 2 and scenario 3 in an embodiment of the present invention;

[0090] Figure 7 4 is a quasi-steady-state frequency comparison diagram of scenario 2 and scenario 3 in an embodiment of the present invention. DETAILED DESCRIPTION

[0091] In order to make the purpose, technical solution and advantages of the embodiment of the present invention clearer, the technical solution of the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings of the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the described embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field belong to the scope of protection of the present invention.

[0092] like Figure 1 As shown in FIG. 1 , an embodiment of the present invention is provided, which provides a method for robustly optimizing unit scheduling of a transmission and distribution network based on the entire frequency response process, comprising the following steps:

[0093] S1: Establish the framework structure of the transmission and distribution network, take into account the start and stop status of thermal power units, analyze the dynamic frequency response process of centralized new energy units (referring to large-scale centralized deployment of new energy power generation units, such as wind turbines, etc.), distributed energy (referring to small distributed power generation systems distributed in various regions, including small wind power, photovoltaic units, etc.) and thermal power units for frequency support, and build full-process frequency safety constraints around the three links of inertial response, primary frequency regulation and secondary frequency regulation.

[0094] In step S1, the framework structure of the transmission and distribution network refers to the general network structure of the transmission and distribution network (such as the connection method of nodes, lines, generator sets, substations, etc.). The construction method is a standard practice in power system design and will not be described here.

[0095] The transmission and distribution network framework structure of this embodiment is as follows Figure 2 The dispatchable frequency regulation resources of the transmission network include thermal power units and wind power units that take into account the start and stop of the units. The dispatchable frequency regulation resources of the active distribution network include conventional distributed generators (such as natural gas generators, diesel generators, etc.) and photovoltaic units. The power between the transmission and distribution networks is transmitted bidirectionally to balance the overall load of the power grid and meet the system frequency safety requirements, thereby achieving the optimal dispatch of unit output and frequency regulation reserves.

[0096] Specifically, when a power shortage occurs in the system, the frequency shows a downward trend and the system begins to enter dynamic frequency response. The whole process of dynamic frequency response includes:

[0097] Inertial response: The inertia in the system provides kinetic energy to adjust the frequency. The generator set is not working, and the system's rate of change of frequency (RoCoF) reaches its maximum value.

[0098] Primary frequency regulation: The generator sets in the system begin to change their mechanical power, and the inertial response and primary frequency regulation jointly adjust the power shortage. The thermal power units in the transmission network adjust the power generation and frequency regulation power based on the determined unit start and stop decisions. The wind turbines and conventional distributed generator sets and photovoltaic units in the active distribution network directly allocate output and frequency regulation resources until the unit output is equal to the disturbance and the frequency drops to the lowest frequency point. ;

[0099] Secondary frequency modulation: When the frequency stabilizes to the quasi-steady-state frequency , the primary frequency modulation process ends, and the system continues with secondary frequency modulation until the frequency returns to the nominal value.

[0100] In one of the preferred embodiments, the whole process frequency safety constraints are constructed around the three links of inertial response, primary frequency modulation and secondary frequency modulation, including primary frequency modulation safety constraints and secondary frequency modulation safety constraints;

[0101] Primary frequency regulation safety constraints include:

[0102] 1) Frequency change rate constraint: When the system starts to have power shortage, the system frequency deviation , at this time, no unit in the system is in action, the system frequency change rate must meet the maximum allowable requirement, and the system inertia time constant is determined by the inertia time constants of all dispatchable frequency regulation resources in the system, expressed as:

[0103] ;

[0104] In the formula, is the frequency change rate; is the system frequency deviation after the power shortage occurs at time t; is the system reference frequency; is the system power shortage; is the inertia time constant of the system at time t; is the maximum allowable requirement for the frequency change rate;

[0105] 2) Frequency minimum point constraint: The inertial response and primary frequency modulation work together to reduce the system frequency to the lowest frequency point During this process, each unit needs to reserve a frequency regulation reserve to participate in the frequency regulation to prevent t The frequency deviation at the moment exceeds the given safety threshold, which is expressed as:

[0106] ;

[0107] In the formula, is the frequency deviation at time t; is the sum of the primary frequency regulation reserve capacity of the system at time t; is the system's primary frequency modulation response time; D is the load damping rate; is the system load; is the power shortage when the system enters inertial response at time t; is the frequency dead zone; is a given safety threshold;

[0108] 3) Quasi-steady-state frequency constraint: When the primary frequency regulation reserve capacity of all generators in the system is fully released, the frequency will remain at the quasi-steady-state frequency At this time, the quasi-steady-state frequency deviation at time t must also be controlled within the maximum range allowed by the system. Within, it is expressed as:

[0109] ;

[0110] In the formula, is the quasi-steady-state frequency deviation at time t;

[0111] Secondary frequency regulation safety constraints include:

[0112] 1) Secondary frequency regulation reserve capacity constraint: In order to restore the frequency to the nominal value at the end of the secondary frequency regulation, the sum of the system's secondary frequency regulation reserve capacity and the primary frequency regulation reserve capacity must not be less than the system power deficit, expressed as:

[0113] ;

[0114] In the formula, is the sum of the secondary frequency regulation reserve capacity of the system at time t;

[0115] 2) Constraint on the cumulative amount of secondary frequency modulation frequency offset: The cumulative amount of secondary frequency modulation frequency offset of the system needs to be kept within a certain range to avoid excessive deviation of the frequency from the nominal value at the beginning of the secondary frequency modulation link, which is expressed as:

[0116] ;

[0117] In the formula, The end time of the secondary frequency modulation frequency deviation of the system; is the system frequency deviation coefficient; is the integral control parameter; and They are respectively the upper and lower limits of the accumulated frequency deviation of the system's secondary frequency modulation.

[0118] S2: Considering the uncertainty of wind and solar output, the uncertainty set of wind and solar output is constructed in interval form, and a two-stage robust unit commitment optimization model of the transmission and distribution network considering the whole process of frequency response is established with a min-max-min structure, with the goal of minimizing the start-stop cost, power generation cost, and primary frequency regulation and secondary frequency regulation reserve cost;

[0119] S21: The lower limit of the uncertainty set of wind and solar output represents the minimum value of wind and solar output power under the most unfavorable conditions, which satisfies the "worst output" sought by the model. The uncertainty set of wind and solar output is expressed as:

[0120] ;

[0121] In the formula, represents the uncertainty set of wind and solar output; , are wind and light uncertainty sets, respectively; , They are the power after uncertain processing of wind and solar output respectively; , They are wind and solar predicted output respectively; , They are the maximum fluctuation ranges allowed for wind and solar output respectively; , are binary variables that represent the boundaries of the wind and solar output intervals at time t; , are the introduced wind and light uncertainties, respectively, representing the total number of times when wind power and photovoltaic outputs obtain the interval boundaries; T is the total number of scheduling periods;

[0122] when When , the impact of wind and solar output uncertainty on the system is not considered, but it is somewhat risky; when At this time, the wind and solar outputs at all times take the boundary values ​​of the prediction interval, and the optimization results are too conservative.

[0123] S22: A two-stage robust unit commitment optimization model for transmission and distribution networks considering the whole process of frequency response is established with a min-max-min structure;

[0124] The min-max-min structure is a common optimization problem structure, which is often used to solve problems with multiple decision makers and multiple objectives. In this structure, there are multiple decision makers (also called players) and multiple objective functions, and each decision maker hopes to minimize its own objective function while maximizing the objective functions of other decision makers.

[0125] The two-stage robust optimization model is an optimization method applied to the min-max-min structure to deal with uncertainty and risk. It divides the problem into two stages, each of which has an optimization problem.

[0126] The first stage is a robust optimization problem, which takes uncertainty into account and seeks a robust solution, i.e. one with the minimum objective function value within the uncertainty range. The goal of this stage is to minimize the maximum objective function value of the second stage.

[0127] The second stage is a maximization problem, which seeks an optimal solution based on the solution of the first stage to maximize the objective function value. The goal of this stage is to maximize the objective function value of the second stage.

[0128] The mathematical representation of the two-stage robust optimization model is as follows:

[0129] Phase 1: minimize f1(x) subject to g1(x, w)≤0, x∈X;

[0130] Stage 2: maximize f2(x, y) subject to g2(x, y)≤0, y∈Y;

[0131] Among them, f1(x) and f2(x, y) are the objective functions of the first and second stages respectively, g1(x, w) and g2(x, y) are the constraints of the first and second stages respectively, x and y are decision variables, X and Y are the feasible domains of decision variables, and w is the uncertainty parameter.

[0132] The solution method of the two-stage robust optimization model usually involves the techniques of robust optimization and maximization problems, such as the concepts of robust optimization theory, optimal response and Nash equilibrium. By iteratively solving the optimization problems of the first and second stages, the solution of the min-max-min structure can be gradually approached, and uncertainty factors and risks can be considered.

[0133] In this embodiment, the objective function of the two-stage robust unit commitment optimization model of the transmission and distribution network is:

[0134] ;

[0135] In the formula, is the sum of the start-up and shutdown costs of thermal power units; is the sum of the power generation costs of thermal power units and distributed power generation units; is the sum of the primary frequency regulation and secondary frequency regulation reserve costs; T is the total number of dispatching time periods; , Thermal power units The start-up and shutdown costs; , They are the thermal power units at time t. On and off status; , Thermal power units , Distributed Generator Sets The cost of electricity generation; , Thermal power units , Distributed Generator Sets The meritorious contribution; , , , Thermal power units , wind turbines, distributed generators , the primary frequency regulation and backup cost of the photovoltaic unit p; , , , Thermal power units , wind turbines, distributed generators , secondary frequency regulation backup cost of PV unit p; , , , They are the thermal power units at time t. , wind turbines, distributed generators , the primary frequency regulation reserve capacity of the photovoltaic unit p; , , , They are the thermal power units at time t. , wind turbines, distributed generators , the secondary frequency regulation reserve capacity of photovoltaic unit p; TG, TW, DG, and DP are the collections of thermal power units, wind turbines, distributed generators, and photovoltaic units participating in the frequency regulation process.

[0136] Furthermore, the constraints of the two-stage robust unit commitment optimization model for the transmission and distribution network, based on the full-process frequency security constraints constructed in step S1, also include:

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[0161] ;

[0162] ;

[0163] In the formula, , Thermal power units , the active output of wind turbine w; for The transmission network load at the node, Forecast load of the transmission network at time t; is the transmission capacity of the tie line between the transmission and distribution networks at time t, and e represents The distribution network to which the node is connected; The terminal node The starting node set of Any starting node in; , For line , The transmission power of For line Susceptance; , , Node , the phase angle between node b and the equilibrium node at time t; For line Transmit power upper limit; , Thermal power units Minimum start and stop time; , , For thermal power units At the start / stop status at time t, time t-1, and time k, the value 1 indicates operation, and the value 0 indicates shutdown; , , Thermal power units Active power output, primary frequency regulation reserve capacity, and secondary frequency regulation reserve capacity at time t-1; , Thermal power units Upward and downward climbing rates; , Thermal power units Upper and lower limits of output; , They are the upper and lower limits of the wind turbine output w, respectively; The upper limit of the frequency regulation reserve capacity of thermal power units; The upper limit of the frequency regulation reserve capacity of wind turbines; , The active power injected into n nodes by distributed generators and photovoltaic units at time t respectively; , The reactive power injected into n nodes by distributed generators and photovoltaic units at time t respectively; , are the active and reactive power injected by node m to node n at time t respectively; , are the active and reactive power output from node n to node d at time t respectively; is the set of starting nodes when the end node is n; is the set of terminal nodes when the starting node is n, and d is any terminal node when the starting node is n; is the current flowing through line mn at time t; , are the resistance and reactance of line mn respectively; , The transmission network injects active and reactive power into the tie line between the transmission and distribution networks at node n at time t respectively; , Forecast load for n nodes at time t; , are the voltages of node m and node n at time t respectively; , The upper and lower limits of node n voltage respectively; , For distributed generators Upper and lower limits of output; is the active power output of the photovoltaic unit p; , They are the upper and lower limits of the photovoltaic unit p output respectively; The upper limit of frequency regulation reserve capacity for distributed generators; The upper limit of the frequency regulation reserve capacity of photovoltaic units; , They are the upper and lower limits of the transmission capacity of the interconnection lines between transmission and distribution networks, respectively.

[0164] S3: The two-stage robust unit commitment optimization model of the transmission and distribution network is transformed into a mixed-integer second-order cone programming model (MISOCP) by using the Column and Constraint Generation (C&CG) algorithm and strong duality theory, and it is solved iteratively until the upper and lower bounds of the objective function converge, and the optimal dispatching plan for the units under the worst wind and solar output scenarios is obtained;

[0165] The objective function of the two-stage robust unit commitment optimization model of the transmission and distribution network is decomposed into a master problem (MP) and a sub problem (SP). The transformed objective function and constraints are expressed in matrix form.

[0166] The main problem is expressed as:

[0167] ;

[0168] In the formula, x are decision variables (such as unit start and stop status, power allocation, etc.); is the transpose of the subproblem cost coefficient matrix; For the The solution of the subproblem after iterations; For the The worst scenario of wind and solar output after the iteration; Om is the second-order cone constraint n The branch of the terminal nodem The corresponding variable coefficient matrix at is the second-order cone constraint n The branch of the terminal node m The corresponding constraint constant matrix is ​​the transpose; A , B , E , F , G , H , K , O is the corresponding variable coefficient matrix; , , , , , is the corresponding constraint constant matrix;

[0169] The sub-problem is expressed as:

[0170] ;

[0171] In the formula, Optimize the set of variables for the second stage; U is the uncertainty set of wind and solar output, is the wind and solar power uncertain output set (the power after the wind and solar power output uncertainty processing, , ); To determine the optimization variables , back The feasible domain of For the The solution of the main problem after iterations; , , , , , are the dual variables corresponding to each constraint of the subproblem.

[0172] The max-min double-layer model in the subproblem cannot be solved directly by the solver. The inner min problem is transformed into a dual max problem by using the strong duality theory and the big M method. Combined with the outer layer, the following single-layer max model is obtained:

[0173] ;

[0174] In the formula, For wind and light forecast output collection; is the maximum fluctuation deviation allowed for wind and solar output; , are the dual variables on the left and right sides of the second-order cone constraint; , To characterize t A set of binary variables that represent the boundaries of the wind power and photovoltaic output intervals at each moment; Artificially introduce variables for the Big M method; is the introduced continuous auxiliary variable.

[0175] This method enables the MP to make preliminary decisions without considering uncertainties. The SP looks for harsh scenarios based on the decision results of the MP, so that the MP continuously introduces variables and constraints related to the SP, thereby obtaining more compact upper and lower bounds of the original objective function value until the algorithm converges.

[0176] In the following, in conjunction with a specific example, the robust optimization unit dispatching method for the transmission and distribution network based on the whole frequency response process proposed in the embodiment of the present invention is verified by coupling the IEEE 24-node transmission system with two IEEE 33-node distribution network systems to form a transmission and distribution network. The transmission and distribution network coupling system is as follows: Figure 3 As shown in Figure 2, the predicted load of the transmission and distribution network is as follows: Figure 4 shown.

[0177] This example sets up three groups of comparison scenarios to conduct comparative analysis on the example system:

[0178] Scenario 1: Without considering frequency safety constraints, adding unit spare capacity to assist the system in primary frequency regulation;

[0179] Scenario 2: Based on Scenario 1, the frequency security constraints of the entire process are considered, and the frequency is supported by thermal power units and wind power units;

[0180] Scenario 3: Based on Scenario 2, consider the participation of distributed energy in the whole process of frequency regulation of the system.

[0181] The lowest frequency point in scenario 1, scenario 2, and scenario 3 The comparison with the frequency change rate RoCoF is as follows Figure 5 and Figure 6 shown.

[0182] Depend on Figure 5 and Figure 6 It can be seen that the frequency of scene 1 is the lowest at 1-5 and 12-24. All of them exceed the safety range of 49.2Hz, and the frequency change rate RoCoF is greater than the maximum allowable RoCoF value of 0.125Hz / s at all times. This is because the frequency safety constraint is not considered in scenario 1, and only the primary frequency regulation constraint to maintain the basic stability of the system frequency is added on this basis. At this time, the system's primary frequency regulation reserve capacity cannot be guaranteed to be sufficient. Only the basic reserve capacity of each operating unit is used to adjust the frequency to a certain extent, which cannot ensure the stability of the system frequency under large interference conditions. When the frequency safety constraint is considered in scenarios 2 and 3, the lowest frequency point at each moment The frequency change rate RoCoF is kept within the set safety threshold, and the system frequency regulation performance in scenario 3 is close to that in scenario 2. The above analysis shows the important role of this method in improving the system frequency safety.

[0183] like Figure 7 As shown, after considering the secondary frequency regulation safety constraints, the quasi-steady-state frequencies corresponding to Scenario 2 and Scenario 3 are both greater than the set quasi-steady-state frequency safety threshold, and the secondary frequency regulation reserve capacity issued by the system at each moment is closely related to the quasi-steady-state frequency. The smaller the quasi-steady-state frequency, the larger the secondary frequency regulation reserve capacity issued by the system. Compared with Scenario 2, the quasi-steady-state frequency corresponding to Scenario 3 fluctuates more smoothly, proving that the invention is superior in ensuring safe and stable operation of the system. As shown in Table 1, this is a comparison of operating costs under each scenario:

[0184] Table 1 Comparison of costs among scenarios 1, 2, and 3

[0185]

[0186] In Table 1, since frequency safety constraints are not considered, the capacity of low-cost units in scenario 1 can meet the system load demand and frequency regulation demand. However, after considering frequency safety constraints in scenarios 2 and 3, some low-cost units in the system are used for frequency regulation, and high-cost units need to be called to participate in power generation. Therefore, compared with scenario 1, the power generation costs of scenarios 2 and 3 increased by 1.06×10 5 Yuan and 1.10×10 5 Since scenarios 2 and 3 consider economically efficient wind turbines and distributed energy to replace some thermal power units to participate in the system frequency regulation process, the frequency regulation reserve cost in scenario 2 is reduced by 4.70×10 compared with scenario 1. 4 The frequency regulation backup cost in scenario 3 is reduced by 1.60×10 compared with scenario 2. 4 At this time, because the distributed photovoltaic power generation capacity is reduced due to the frequency modulation, the thermal power units and conventional distributed power generation units need to generate additional power for power generation to compensate for the imbalance of system power at this time. Therefore, compared with scenario 2, the power generation cost of scenario 3 increases by 4×103 The above analysis proves that this method can improve the economic efficiency of the system.

[0187] In summary, the present invention can effectively reduce the fluctuation amplitude of the system frequency after suffering power disturbance through the full-process constraint design of inertial response, primary frequency regulation and secondary frequency regulation, ensure the frequency deviation within a safe range, and avoid frequency instability; the participation of new energy units and distributed energy shares the frequency regulation task of thermal power units, reduces the number of start-up and shutdown times of thermal power units and their operating burden; considering the joint participation of thermal power units, new energy units and distributed energy in frequency support, fully tap the advantages of various frequency regulation resources and improve the overall frequency regulation capability of the system.

[0188] The present invention rationally models and optimizes the output uncertainty of new energy units, which can reduce the risk of excessive frequency fluctuations caused by the access of new energy and ensure the stable operation of the system; the worst scenarios are analyzed and processed through robust optimization to ensure the feasibility and safety of the scheduling scheme under extreme conditions. Through the robust optimization model, it is possible to reduce the over-conservatism of the optimization results as much as possible on the basis of considering extreme situations, and improve the economic benefits of system operation. By optimizing the start and stop states of thermal power units, unnecessary start and stop operation costs are reduced. At the same time, when optimizing the allocation of power generation and frequency regulation reserves, the standby costs of primary and secondary frequency regulation are reduced, so that the overall operating cost of the system is minimized. Under the premise of frequency safety constraints, the configuration of power generation and standby resources is optimized, which not only ensures frequency stability but also achieves economic operation.

[0189] The column and constraint generation algorithm avoids directly solving complex full-space problems by gradually introducing the most relevant constraints, effectively improving the solution efficiency; the min-max-min model is transformed using strong duality theory, and the sub-problem solution results are gradually introduced into the main problem, making the optimization results more accurate, and the upper and lower bounds of the objective function eventually converge. By solving the unit dispatch plan under the worst wind and light scenarios, the stability and feasibility of the dispatch results under extreme conditions are ensured.

[0190] Therefore, the method of the present invention can effectively improve the frequency regulation capability of the transmission and distribution network, reduce operating costs, improve the robustness and efficiency of the scheduling scheme, and ensure the safe, stable and economical operation of the transmission and distribution network under the conditions of uncertainty in the output of new energy sources such as wind and light.

[0191] Those skilled in the art can understand that the accompanying drawing is only a schematic diagram of a preferred embodiment, and the serial numbers of the embodiments of the present invention are only for description and do not represent the advantages and disadvantages of the embodiments.

[0192] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of various changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A robust optimization unit dispatching method for a transmission and distribution network based on the whole frequency response process, characterized in that: The method comprises: Establish the framework structure of the transmission and distribution network, take into account the start and stop status of thermal power units, analyze the whole process of dynamic frequency response of centralized new energy units, distributed energy and thermal power units for frequency support, and build the whole process frequency safety constraints around the three links of inertial response, primary frequency regulation and secondary frequency regulation; The whole process frequency safety constraint includes primary frequency regulation safety constraint and secondary frequency regulation safety constraint; The primary frequency regulation safety constraints include: Frequency change rate constraint: When the system starts to have power shortage, the system frequency deviation , at this time, no unit in the system is in action, the system frequency change rate must meet the maximum allowable requirement, and the system inertia time constant is determined by the inertia time constants of all dispatchable frequency regulation resources in the system, expressed as: ; In the formula, is the frequency change rate; is the system frequency deviation after the power shortage occurs at time t; is the system reference frequency; is the system power shortage; is the inertia time constant of the system at time t; is the maximum allowable requirement for the frequency change rate; Frequency minimum point constraint: Inertial response and primary frequency modulation work together to reduce the system frequency to the lowest frequency point In this process, each unit needs to reserve a frequency regulation reserve to participate in a frequency regulation to prevent the frequency deviation at time t from exceeding a given safety threshold, which is expressed as: ； In the formula, is the frequency deviation at time t; is the sum of the primary frequency regulation reserve capacity of the system at time t; is the system's primary frequency modulation response time; D is the load damping rate; is the system load; is the power shortage when the system enters inertial response at time t; is the frequency dead zone; is a given safety threshold; Quasi-steady-state frequency constraint: When the primary frequency regulation reserve capacity of all generators in the system is fully released, the frequency will remain at the quasi-steady-state frequency At this time, the quasi-steady-state frequency deviation at time t must also be controlled within the maximum range allowed by the system. Within, it is expressed as: ； In the formula, is the quasi-steady-state frequency deviation at time t; The secondary frequency regulation safety constraints include: Secondary frequency regulation reserve capacity constraint: In order to restore the frequency to the nominal value at the end of secondary frequency regulation, the sum of the system's secondary frequency regulation reserve capacity and primary frequency regulation reserve capacity must not be less than the system power deficit, expressed as: ； In the formula, is the sum of the secondary frequency regulation reserve capacity of the system at time t; Constraint on the cumulative amount of secondary frequency modulation frequency offset: The cumulative amount of secondary frequency modulation frequency offset of the system needs to be kept within a certain range to avoid excessive deviation of the frequency from the nominal value at the beginning of the secondary frequency modulation link, which is expressed as: ； In the formula, The end time of the secondary frequency modulation frequency deviation of the system; is the system frequency deviation coefficient; is the integral control parameter; and They are the upper and lower limits of the accumulated frequency deviation of the secondary frequency modulation of the system respectively; Considering the uncertainty of wind and solar output, the uncertainty set of wind and solar output is constructed in interval form, and a two-stage robust unit commitment optimization model of the transmission and distribution network considering the whole process of frequency response is established with a min-max-min structure, with the goal of minimizing the start-stop cost, power generation cost, and primary and secondary frequency regulation standby costs; The column and constraint generation algorithm and strong duality theory are used to transform the two-stage robust unit combination optimization model of the transmission and distribution network into a mixed integer second-order cone programming model and iteratively solve it until the upper and lower bounds of the objective function converge, and the optimal unit scheduling plan under the worst wind and solar output scenarios is obtained.

2. The method for robust optimization of unit dispatching in a transmission and distribution network based on the whole frequency response process according to claim 1, characterized in that: In the framework structure of the transmission and distribution network, the dispatchable frequency regulation resources of the transmission network include thermal power units and wind power units taking into account the start and stop of the units, and the dispatchable frequency regulation resources of the active distribution network include distributed power generation units and photovoltaic units. The power between the transmission and distribution networks is transmitted bidirectionally to balance the overall load of the power grid and meet the system frequency safety requirements.

3. The method for robust optimization of unit dispatching in a transmission and distribution network based on the whole frequency response process according to claim 1, characterized in that: When the system has a power shortage, the frequency shows a downward trend and the system begins to enter a dynamic frequency response. The whole process of the dynamic frequency response includes: Inertial response: The frequency is adjusted by the kinetic energy provided by the inertia in the system. When the generator set is not working, the frequency change rate of the system RoCoF Reach the maximum value; Primary frequency regulation: The generator sets in the system begin to change their mechanical power, and the inertial response and primary frequency regulation jointly adjust the power shortage. The thermal power units in the transmission network adjust the power generation and frequency regulation power based on the determined unit start and stop decisions. The wind turbines and the distributed generator sets and photovoltaic units in the active distribution network directly allocate output and frequency regulation resources until the unit output is equal to the disturbance and the frequency drops to the lowest frequency point. ; Secondary frequency modulation: When the frequency stabilizes to the quasi-steady-state frequency , the primary frequency modulation process ends, and the system continues with secondary frequency modulation until the frequency returns to the nominal value.

4. The method for robust optimization of unit dispatching in a transmission and distribution network based on the whole frequency response process according to claim 1, characterized in that: The wind and solar output uncertainty set is expressed as: ； In the formula, represents the set of uncertainty of wind and solar output; , are wind and light uncertainty sets, respectively; , They are the power after uncertain processing of wind and solar output respectively; , They are wind and solar predicted output respectively; , They are the maximum fluctuation ranges allowed for wind and solar output respectively; , are binary variables that represent the boundaries of the wind and solar output intervals at time t; , are the introduced wind and light uncertainties, respectively, representing the total number of times when wind power and photovoltaic outputs reach the boundaries of the interval; T is the total number of scheduling periods.

5. The method for robust optimization of unit dispatching in a transmission and distribution network based on the whole frequency response process according to claim 1, characterized in that: The objective function of the two-stage robust unit commitment optimization model for the transmission and distribution network is: ； In the formula, is the sum of the start-up and shutdown costs of thermal power units; is the sum of the power generation costs of thermal power units and distributed power generation units; It is the sum of the primary frequency regulation and secondary frequency regulation reserve costs; T is the total number of scheduling time periods; , Thermal power units The start-up and shutdown costs; , They are the thermal power units at time t. On and off status; , Thermal power units , Distributed Generator Sets The cost of electricity generation; , Thermal power units , Distributed Generator Sets The meritorious contribution; , , , Thermal power units , wind turbines, distributed generators , the primary frequency regulation and backup cost of the photovoltaic unit p; , , , Thermal power units , wind turbines, distributed generators , secondary frequency regulation backup cost of PV unit p; , , , They are the thermal power units at time t. , wind turbines, distributed generators , the primary frequency regulation reserve capacity of the photovoltaic unit p; , , , They are the thermal power units at time t. , wind turbines, distributed generators , the secondary frequency regulation reserve capacity of photovoltaic unit p; TG, TW, DG, and DP are the collections of thermal power units, wind power units, distributed generators, and photovoltaic units participating in the frequency regulation process.

6. The method for robust optimization of unit dispatching in a transmission and distribution network based on the whole frequency response process as claimed in claim 5, characterized in that: The constraints of the two-stage robust unit commitment optimization model for the transmission and distribution network are based on the frequency security constraints of the whole process and also include: ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； In the formula, , Thermal power units , the active output of wind turbine w; for The transmission network load at the node, Forecast the load of the transmission network at time t; is the transmission capacity of the tie line between the transmission and distribution networks at time t, and e represents The distribution network to which the node is connected; The terminal node The starting node set of Any starting node in; , For line , The transmission power of For line Susceptance; , , Node , the phase angle between node b and the equilibrium node at time t; For line Transmit power upper limit; , Thermal power units Minimum start and stop time; , , For thermal power units At the start / stop status at time t, time t-1, and time k, the value 1 indicates operation, and the value 0 indicates shutdown; , , Thermal power units Active power output, primary frequency regulation reserve capacity, and secondary frequency regulation reserve capacity at time t-1; , Thermal power units Upward and downward climbing rates; , Thermal power units Upper and lower limits of output; , They are the upper and lower limits of the wind turbine output w, respectively; The upper limit of the frequency regulation reserve capacity of thermal power units; The upper limit of the frequency regulation reserve capacity of wind turbines; , The active power injected into n nodes by distributed generators and photovoltaic units at time t respectively; , The reactive power injected into n nodes by distributed generators and photovoltaic units at time t respectively; , are the active and reactive power injected by node m to node n at time t respectively; , are the active and reactive power output from node n to node d at time t respectively; is the set of starting nodes when the end node is n; is the set of terminal nodes when the starting node is n, and d is any terminal node when the starting node is n; is the current flowing through line mn at time t; , are the resistance and reactance of line mn respectively; , The transmission network injects active and reactive power into the tie line between the transmission and distribution networks at node n at time t respectively; , Forecast load for n nodes at time t; , are the voltages of node m and node n at time t respectively; , The upper and lower limits of node n voltage respectively; , For distributed generators Upper and lower limits of output; is the active power output of the photovoltaic unit p; , They are the upper and lower limits of the photovoltaic unit p output respectively; The upper limit of frequency regulation reserve capacity for distributed generators; The upper limit of the frequency regulation reserve capacity of photovoltaic units; , They are the upper and lower limits of the transmission capacity of the interconnection lines between transmission and distribution networks, respectively.

7. The method for robust optimization of unit dispatching in a transmission and distribution network based on the whole frequency response process as claimed in claim 6, characterized in that: The two-stage robust unit commitment optimization model of the transmission and distribution network is converted into a mixed integer second-order cone programming model and iteratively solved, specifically including: The objective function of the two-stage robust unit commitment optimization model of the transmission and distribution network is decomposed into a main problem and sub-problems. The transformed objective function and constraints are expressed in matrix form. The main problem is expressed as: ； In the formula, is the decision variable; is the variable in the objective function The coefficient vector of the correlation, is the transpose of the cost coefficient matrix of the main problem; η is the slack variable of the subproblem; is the transpose of the subproblem cost coefficient matrix; For the The solution of the subproblem after iterations; For the The worst scenario of wind and solar output after the iteration; is the variable coefficient matrix corresponding to the branch m with n as the terminal node in the second-order cone constraint; is the transpose of the constraint constant matrix corresponding to the branch m with n as the terminal node in the second-order cone constraint; A, B, E, F, G, H, K, O are the corresponding variable coefficient matrices; , , , , , is the corresponding constraint constant matrix; The sub-problem is expressed as: ； In the formula, is the set of variables optimized in the second stage; U is the set of uncertainties of wind and solar output, The uncertain output of wind and light is gathered; To determine the optimization variables , back The feasible domain of For the The solution of the main problem after iterations; ,γ, , , , are the dual variables corresponding to each constraint of the sub-problem; The max-min double-layer model in the subproblem cannot be solved directly by the solver. The inner min problem is transformed into a dual max problem by using the strong duality theory and the big M method. Combined with the outer layer, the following single-layer max model is obtained: ； In the formula, For wind and light forecast output collection; is the maximum fluctuation deviation allowed for wind and solar output; , are the dual variables on the left and right sides of the second-order cone constraint; A set of binary variables representing the interval boundaries of wind power and photovoltaic output at time t; Artificially introduce variables for the Big M method; is the introduced continuous auxiliary variable.

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