A two-stage robust planning method for multi-energy microgrid in alpine region
Patent Information
- Application Number
- CN202610962357.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-06-30
- Publication Date
- 2026-09-22
AI Technical Summary
常规的规划方法无法适应可再生能源出力锐减或极寒致热负荷激增的极端工况
1、本发明针对高寒地区风电、光伏出力及电热负荷的强随机性与极端波动特性，采用多面体不确定性集分别建立了风电出力、光伏出力、电负荷与热负荷的数学描述，通过鲁棒控制参数灵活调节不确定性集的波动边界。相比传统确定性规划方法或简单的正态分布假设，本发明能够以解析形式涵盖极端低风速、极寒致热负荷激增等边缘工况，避免了因忽略极端场景而导致的规划方案在恶劣天气下失效的问题。同时，鲁棒控制参数为规划人员提供了保守度与经济性之间的可调节权衡工具，克服了传统鲁棒优化“最坏情况永远发生”的过度保守缺陷。
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Figure CN122801351A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of microgrid planning and new energy operation optimization technology, specifically involving a two-stage robust planning method for multi-element energy storage microgrids in high-altitude and cold regions. Background Technology
[0002] High-altitude and frigid regions experience harsh weather conditions, resulting in strong randomness and volatility in wind and solar power output and heating loads. Conventional planning methods are ill-suited to extreme conditions such as sharp declines in renewable energy output or surges in heating loads due to extreme cold. Existing microgrid planning models often assume constant equipment operating parameters, neglecting the nonlinear degradation of energy storage equipment's physical characteristics in high-altitude and frigid environments. Furthermore, for multi-element energy storage microgrids, few planning methods consider the impact of high-altitude and frigid environments on compressed air energy storage systems. Summary of the Invention
[0003] The purpose of this invention is to overcome the above-mentioned defects in the prior art and provide a two-stage robust planning method for multi-element energy storage microgrids in high-altitude and cold regions, so as to achieve synergistic optimization of the economy and reliability of microgrids in high-altitude and cold regions, and solve the problems of dual uncertainty of source and load, low temperature energy storage attenuation, and difficulty in balancing economy and reliability in the planning of existing microgrids in high-altitude and cold regions.
[0004] This invention provides a two-stage robust planning method for multi-element energy storage microgrids in high-altitude and cold regions, which includes the following steps: S1: Construct a dual uncertainty set of source and load, and use a polyhedral uncertainty set to characterize the fluctuation boundaries of wind power output, photovoltaic power output, electrical load and heat load respectively; S2: Establish a multi-dimensional energy storage constraint model that takes into account the characteristics of high cold, introduce a continuous environmental temperature penalty mechanism to characterize the energy storage efficiency decay under extreme cold conditions, extract multi-stage compression and expansion heat transfer constraints for compressed air energy storage, and establish a correlation thermal balance coupling equation. S3: Construct a two-stage robust optimization objective function with a "minimum-maximum-minimum" structure, where the first stage is capacity configuration decision and the second stage is multi-timescale scheduling operation verification; S4: Based on the column and constraint generation algorithm, the original robust optimization model is decoupled into the main problem and sub-problems for alternating iterative solution. According to the solution status of the sub-problems, the newly identified severe scenarios and their corresponding new operating variables and operating balance constraints are fed back to the main problem until the convergence tolerance accuracy is met, and the optimal microgrid configuration scheme that takes into account both the extreme toughness of high cold and the economic efficiency of the whole life cycle is output.
[0005] The two-stage robust planning method for multi-energy storage microgrids in high-altitude and cold regions quantifies the dual uncertainties of source and load, as well as the low-temperature penalty effect, avoiding accidents caused by neglecting extreme operating conditions in traditional deterministic planning. The two-stage robust optimization architecture balances investment economy with operational reliability under extreme scenarios, and the column and constraint generation algorithm (C&CG) ensures the convergence and computational efficiency of the solution.
[0006] Furthermore, in step S1, constructing the source-load dual uncertainty set includes the wind power output uncertainty set. Uncertainty in photovoltaic power output Uncertainty set of electrical load and heat load uncertainty set ; The uncertainty set of wind power output The expression is:
[0007] in, To predict the output, The maximum deviation, To assist in fluctuation variables, These are robust control parameters used to precisely control the conservatism of the planning scheme; The photovoltaic output uncertainty set The expression is:
[0008] in, To contribute to actual photovoltaic power, Contribute to photovoltaic forecasting, The maximum prediction bias, As an auxiliary scaling variable for photovoltaic fluctuations, Robust space parameters for controlling the conservatism of photovoltaic output; The set of electrical load uncertainties The expression:
[0009] in, and These represent the actual and predicted electrical loads of the microgrid. This represents the maximum positive deviation of the electrical load. For robust control parameters of electrical load; The heat load uncertainty set The expression:
[0010] in, and These are the actual and predicted heat loads, respectively. This represents the maximum deviation in heat load that may surge under extreme cold weather conditions. These are the robust control parameters for thermal load.
[0011] The above four types of uncertainty sets together constitute the source-load joint polyhedral uncertainty set. The second-stage robust scheduling searches for the source-load combination scenario that results in the highest system operating cost within this uncertainty set.
[0012] The above technical solution adopts a polyhedral uncertainty set A mathematical model is constructed to address the dual uncertainties of source and load. Centering on the predicted value and with the maximum deviation as the radius, auxiliary fluctuation variables and robust control parameters are introduced to adjust the fluctuation boundary of the uncertainty set. The robust control parameters control the upper limit of the sum of the absolute values of fluctuation variables at each time segment, thus providing an adjustable trade-off between conservatism and economy, effectively describing the extreme fluctuation characteristics of wind and solar power output and electrical and thermal loads in high-altitude and cold regions. By adjusting the robust control parameters, planners can flexibly control the conservatism of the scheme according to their risk preferences, avoiding the over-conservatism problem of traditional robust optimization where "the worst case always occurs."
[0013] Furthermore, in step S2, a continuous environmental temperature penalty mechanism is introduced to characterize the energy storage efficiency decay under extremely cold conditions. The low-temperature performance parameters of electrochemical energy storage are obtained by fitting test curves from battery manufacturers, historical operating data, or low-temperature experimental data. Ambient temperature affects the charging efficiency, discharging efficiency, and usable capacity of electrochemical energy storage, as expressed by:
[0014]
[0015]
[0016] in, , , This is a low-temperature correction function; To improve the charging efficiency of electrochemical energy storage, For electrochemical energy storage discharge efficiency, Available capacity for electrochemical energy storage;
[0017]
[0018] in, The state of charge of the electrochemically stored energy at time t+1; The state of charge of the electrochemically stored energy at time t; The charging power for electrochemical energy storage; This is the rated capacity of the electrochemical energy storage. This refers to the available capacity for electrochemical energy storage.
[0019] The operating status of a CAES (Compressed Air Storage System) is jointly described by its gas storage status and thermal storage status. The gas storage status reflects the amount of compressed air stored, while the thermal storage status reflects the available heat of compression. Ambient temperature affects the heat loss, heat exchange efficiency, and expansion power generation efficiency of the thermal storage unit.
[0020]
[0021]
[0022]
[0023] in, The gas storage state quantity of the compressed air energy storage system at time t+1; This refers to the gas storage state quantity of a compressed air energy storage system. The energy conversion efficiency of the compressed air energy storage system during the compressed air energy storage process; This refers to the compressor's compression power. Power generation for the expander; The energy conversion efficiency of the expansion and energy release process in a compressed air energy storage system; The available heat in the thermal storage unit during time period t+1; The available heat in the thermal storage unit during time period t; The heat recovered during the compression stage and enters the thermal storage unit; The internal heat recovery required for expansion-based power generation; To supply heat to external heat loads; This refers to the heat loss of the thermal storage unit. This is the equivalent heat loss coefficient of the thermal storage unit; Temperature of the thermal storage unit; The ambient temperature.
[0024] Furthermore, in step S2, the multi-stage compression and expansion heat transfer constraints of compressed air energy storage are extracted, and the water outlet node of the air-water cooling heat exchanger between compressor stages is used as the input end of the heat source topology matrix and connected in parallel to the heating structure to establish a correlational heat balance coupling equation: The microgrid thermal energy structure is mainly used to describe the compression heat recovery, heat storage, and expansion reheat processes within a CAES system. During the compression energy storage stage, CAES recovers compression heat through multi-stage compressor interstage coolers and stores the recovered heat in the heat storage unit. During the expansion power generation stage, the heat storage unit provides reheat to the expander inlet air to meet the heat requirements of the CAES power generation process.
[0025] The heat recovered during the compression stage is represented as:
[0026] in, The total heat power recovered during the CAES compression phase in time period t; Let t be the heat power recovered by the interstage cooler of the i-th stage compressor.
[0027] The heat power recovered by the interstage cooler of the i-th stage compressor is expressed as:
[0028] in, Let t be the mass flow rate of the i-th stage compressed air. The specific heat capacity of air at constant pressure; and These are the air-side inlet and outlet temperatures of the i-th stage cooler, respectively.
[0029] The thermal state balance of the thermal storage unit is expressed as:
[0030] in, The available heat in the thermal storage unit during time period t+1; The available heat in the thermal storage unit during time period t; The heat recovered during the compression stage and enters the thermal storage unit; The internal heat recovery required for expansion-based power generation; To supply heat to external heat loads; This represents the heat loss of the thermal storage unit.
[0031] The heat loss of the thermal storage unit is expressed as:
[0032] in, This refers to the heat loss power of the thermal storage unit; This is the equivalent heat loss coefficient of the thermal storage unit; Temperature of the thermal storage unit; Let t be the ambient temperature during time period t.
[0033] For nonlinear functions such as the energy storage efficiency function and the CAES heat transfer efficiency function under the influence of ambient temperature, the SOS2 piecewise linearization method is used for processing: The nonlinear function is expressed as:
[0034] in, Let be a nonlinear function to be piecewise linearized. For the first Each segment node As weight variables, Let be the weight variable for the k-th segment node.
[0035] Furthermore, in step S3, the two-stage robust optimization objective function with a "minimum-maximum-minimum" structure is: ; Where X is the set of decision variables for capacity allocation in the first stage, c is the vector of investment cost coefficients, and u is the set of source load uncertainty variables. The uncertainty set of the joint polyhedron of wind power, photovoltaic, electrical load and heat load constructed in step S1; This is the set of variables for the second phase of multi-timescale scheduling. For a given capacity configuration and uncertainty, the operational feasible domain is... The operating and load shedding penalty cost coefficient; T is the transpose symbol.
[0036] The above technical solution constructs a typical two-stage robust optimization mathematical model. The outermost min corresponds to the capacity allocation decision in the first stage, seeking to minimize the investment cost. The sum of the operating costs under the worst-case scenario and the maximum operating costs. The intermediate layer max searches within the uncertainty set U for the "worst-case" source-load scenario u that results in the highest operating cost. The inner layer min seeks the optimal multi-timescale scheduling strategy y given x and u to minimize the operating cost and load shedding penalty. .
[0037] Furthermore, in step S4, the original robust optimization model is decoupled into a main problem and sub-problems, which are then solved iteratively and alternately. The main problem model is as follows:
[0038]
[0039]
[0040]
[0041] in, As variables for the first stage of investment decisions, X Configure the set of decision variables for the first phase of capacity; As an auxiliary variable characterizing the operating costs of the second phase; In the first The worst known scenario The second stage of the decision-making process, K These are the decision variables for the second stage of operation; , For the corresponding coefficient vector; , , The lower bound is the constraint coefficient matrix, which is updated after each solution to the main problem. ;T is the transpose symbol.
[0042] Furthermore, in step S4, the sub-problem is the capacity configuration setting value obtained from the main problem. As a known constant, it is used to search within the polyhedral uncertainty set U in the most severe scenario that results in the highest system operating cost. Its mathematical model is:
[0043] ; By utilizing the strong duality theory of linear programming, and introducing the dual variable vector π corresponding to the inner minimization problem constraints, the inner "maximum-minimum" logic is transformed into a completely equivalent single-layer maximization bilinear model:
[0044] ; The first-stage optimal capacity configuration setting is obtained; U is the source-load joint polyhedral uncertainty set; y is the set of multi-timescale scheduling and operation decision variables for the second stage; Ω(x*,u) is the second-stage operational feasible region given the capacity configuration x* and the uncertainty variable `u`; d is the second-stage operation cost and load shedding penalty cost coefficient vector; T is the transpose symbol; G is the constraint coefficient matrix corresponding to the second-stage operation decision variable y; h is the constraint right-hand constant vector; E is the constraint coefficient matrix; M is the constraint coefficient matrix corresponding to the uncertainty variable u; π is the dual variable vector corresponding to the inner minimization problem constraint; u(π) represents the value of the uncertainty variable associated with the dual variable π. For the bilinear terms generated in the objective function The Big M method is used to introduce Boolean variables for equivalent linearization; the most severe scenarios that currently cause the system to operate at the highest cost are identified. Then, update the global upper bound. UB :
[0045] Where c is the investment cost system vector, and T is the transpose symbol. The optimal configuration capacity setting value obtained from the main problem is... The objective function value for the subproblem.
[0046] The above technical solution provides a mathematical model of the subproblem and its dual transformation process. The inner layer of the subproblem is a given... The objective function of the dual problem of the linear programming problem under u is: Since u is an uncertain variable, the objective function contains a bilinear term. By dualizing the inner-level min problem, the original "max-min" structure is transformed into a single-level "max" problem. The application of strong duality theory is a key mathematical technique for solving two-stage robust optimization problems. It transforms the complex two-level optimization problem into an equivalent single-level optimization problem, laying the foundation for subsequent linearization and the Big M method.
[0047] Furthermore, in step S4, based on the solution status of the sub-problems, the newly identified severe scenarios are... and their corresponding newly added runtime variables The operational balance constraint is fed back to the main problem, i.e., a dynamic feasibility cut is fed back to handle power deficit, or an optimality cut is fed back to handle economic deviation; the difference between the upper and lower bounds is compared to determine whether the algorithm meets the preset convergence tolerance accuracy. : ; If the convergence condition is not met, repeat the iteration process; if the convergence condition is met, terminate the iteration and output the optimal microgrid configuration scheme.
[0048] Furthermore, the optimal microgrid configuration scheme output in step S4 includes: wind power installed capacity, photovoltaic installed capacity, volume and power of compressed air energy storage system, and electrochemical energy storage capacity.
[0049] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention addresses the strong randomness and extreme fluctuations in wind power, photovoltaic power output, and electrical and thermal loads in high-altitude and cold regions. It employs a polyhedral uncertainty set to establish mathematical descriptions of wind power output, photovoltaic power output, electrical load, and thermal load, respectively. Robust control parameters flexibly adjust the fluctuation boundaries of the uncertainty set. Compared to traditional deterministic programming methods or simple normal distribution assumptions, this invention analytically encompasses edge cases such as extreme low wind speeds and surges in thermal load due to extreme cold, avoiding the failure of planning schemes under severe weather conditions due to neglecting extreme scenarios. Simultaneously, the robust control parameters provide planners with an adjustable trade-off between conservatism and economy, overcoming the overly conservative flaw of traditional robust optimization that assumes "the worst case always happens."
[0050] 2. This invention, for the first time, incorporates the nonlinear degradation effect of high-altitude and cold-climate environmental temperatures on the performance of energy storage devices into the planning model in analytical form. It establishes an electrochemical energy storage charge-discharge model that includes a temperature penalty factor. Through piecewise linearization, the nonlinear efficiency function is transformed into a mixed-integer linear constraint (MILP), enabling the planning model to adaptively increase the energy storage capacity to compensate for efficiency losses under extremely cold conditions. Compared to existing technologies that assume constant equipment operating parameters, this invention effectively solves practical engineering problems such as limited depth of discharge and usable capacity degradation of electrochemical batteries in high-altitude and cold-climate regions, ensuring the power supply reliability of microgrids under extreme low-temperature conditions.
[0051] 3. This invention targets compressed air energy storage systems (CAES), extracting detailed heat transfer constraints during multi-stage compression and expansion processes. It uses the outlet water node of the air-water cooling heat exchanger between compressor stages as the input end of the heat source topology matrix, connecting it in parallel to the underlying heating water network structure of the microgrid, and establishing a correlated thermal balance coupling equation. Compared to existing planning methods that simply equate CAES to electrical energy storage devices or ignore its thermodynamic processes, this invention fully explores the combined heat and cold generation potential of CAES during compression and expansion. It directly uses low-grade compression heat for heating in high-altitude and cold regions and uses expansion cold for auxiliary cooling, significantly improving the system's overall energy utilization efficiency. It is particularly suitable for high-altitude and remote scenarios with both power and heating needs.
[0052] 4. This invention constructs The structure employs a two-stage robust optimization objective function. The outer layer, min, corresponds to the first-stage capacity configuration decision, minimizing the sum of investment cost and operating cost under the worst-case scenario. The middle layer, max, searches within the uncertainty set U for the "worst-case" source-load scenario that results in the highest operating cost. The inner layer, min, seeks the optimal multi-timescale scheduling strategy given the configuration and uncertainties. This structure ensures the feasibility of the planning scheme under any possible uncertainty (especially in extreme scenarios), while optimizing the scheme's lifecycle economics, fundamentally resolving the contradiction between "high redundant investment costs" and "large-scale load shedding during extreme cold weather" mentioned in the background technology.
[0053] In summary, this invention effectively solves core technical challenges in microgrid planning in high-altitude and cold regions, such as dual uncertainties between source and load, low-temperature energy storage attenuation, and the difficulty in balancing economy and resilience, through the comprehensive integration of techniques including polyhedral uncertainty set construction, continuous environmental temperature penalty mechanism, multi-stage heat transfer constraint extraction for compressed air energy storage, a two-stage robust optimization architecture of "min-maximum-min," and iterative solution using the C&CG algorithm. Compared with existing technologies, this invention achieves significant technical advancements in uncertainty characterization accuracy, equipment modeling detail, optimization solution efficiency, and engineering practicality. Attached Figure Description
[0054] Figure 1 This is a flowchart of a two-stage robust planning method for multi-element energy storage microgrids in high-altitude and cold regions according to the present invention. Detailed Implementation
[0055] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.
[0056] This embodiment uses a typical microgrid planning project in a high-altitude, remote area as an example to illustrate in detail the specific implementation process of the two-stage robust planning method for a multi-element energy storage microgrid in high-altitude, remote areas described in this invention. The multi-element energy storage microgrid in high-altitude, remote areas described in this invention includes wind power units, photovoltaic units, an advanced adiabatic compressed air energy storage system, an electrochemical energy storage system, an electrical bus, a thermal storage unit, a hot water supply network, electrical loads, and thermal loads. The advanced adiabatic compressed air energy storage system recovers compression heat during the compression energy storage stage and stores it in the thermal storage unit. During the expansion energy release stage, it prioritizes using the heat from the thermal storage unit for air reheating. After meeting its own heat requirements for power generation, the excess heat is supplied to the hot water supply network through a heat exchange interface. The electrochemical energy storage system is used to smooth wind and solar power fluctuations and provide short-term power support, while the advanced adiabatic compressed air energy storage system is used for long-term energy storage and thermoelectric coupling regulation. Microgrid system operating variables include actual wind power absorption, actual photovoltaic power absorption, wind and solar curtailment power, CAES compression power, expansion power generation, gas storage status, thermal storage status, expansion heat recovery, external heat supply, electrochemical energy storage charge and discharge power, electrochemical energy storage SOC, power shedding load, and heat shedding load, etc. like Figure 1 As shown, the two-stage robust planning method for multi-element energy storage microgrids in high-altitude and cold regions includes the following steps: Step S1: Construct a source-load dual uncertainty set, and use a polyhedral uncertainty set to characterize the fluctuation boundaries of wind power output, photovoltaic power output, electrical load and heat load respectively; Constructing a source-load dual uncertainty set includes a wind power output uncertainty set. Uncertainty in photovoltaic power output Uncertainty set of electrical load and heat load uncertainty set The microgrid in this embodiment is located in a county on the Qinghai-Tibet Plateau at an altitude of 3,800 meters, where the extreme low temperature in winter can reach -35°C. The planning period is 1 year, and the time resolution is 1 hour (T=8760). Based on local historical meteorological data (past 10 years) and historical load data, the predicted curves of wind power and photovoltaic output and their prediction error distribution, as well as the predicted curves of electrical load and heat load and their fluctuation characteristics, are obtained.
[0057] The uncertainty set of wind power output The expression is:
[0058] in, The predicted output is obtained based on numerical weather prediction. The maximum deviation is set at 20% of the predicted output. As an auxiliary fluctuation variable; This is a robust control parameter used to precisely control the conservatism of the planning scheme; its value is 12. The photovoltaic output uncertainty set The expression is:
[0059] in, To contribute to actual photovoltaic power; The photovoltaic prediction output is obtained based on a solar radiation model. The maximum prediction deviation is set at 25% of the predicted photovoltaic output. As an auxiliary scaling variable for photovoltaic fluctuations, Robust space parameters for controlling the conservatism of photovoltaic output; The set of electrical load uncertainties The expression:
[0060] in, and These are the actual and predicted electrical loads of the microgrid, obtained based on historical data from the same period. This represents the maximum positive deviation of the electrical load, and is taken as 15% of the predicted electrical load. The parameter for robust control of electrical load is set to 8. The heat load uncertainty set The expression:
[0061] in, and These are the actual and predicted heat loads, obtained based on an outdoor temperature model. This represents the maximum deviation of heat load that may surge under extreme cold weather conditions, and is taken as 40% of the predicted heat load. The value is 6, which is the robust control parameter for heat load.
[0062] S2: A multi-element energy storage constraint model considering extreme cold characteristics is established, and a continuous environmental temperature penalty mechanism is introduced to characterize the energy storage efficiency decay under extreme cold conditions; the low-temperature performance parameters of electrochemical energy storage are obtained by fitting battery manufacturer test curves, historical operating data, or low-temperature experimental data; environmental temperature affects the charging efficiency, discharging efficiency, and usable capacity of electrochemical energy storage, and its expression is:
[0063]
[0064]
[0065] in, , , This is a low-temperature correction function; To improve the charging efficiency of electrochemical energy storage, For electrochemical energy storage discharge efficiency, Available capacity for electrochemical energy storage;
[0066]
[0067] in, The state of charge of the electrochemically stored energy at time t+1; The state of charge of the electrochemically stored energy at time t; The charging power for electrochemical energy storage; This is the rated capacity of the electrochemical energy storage. This refers to the available capacity for electrochemical energy storage.
[0068] The operating status of CAES is described by both the gas storage status and the thermal storage status; the gas storage status reflects the amount of compressed air stored, and the thermal storage status reflects the amount of compressed heat available; the ambient temperature affects the heat loss, heat exchange efficiency and expansion power generation efficiency of the thermal storage unit.
[0069]
[0070]
[0071] in, The gas storage state quantity of the compressed air energy storage system at time t+1; This refers to the gas storage state quantity of a compressed air energy storage system. The energy conversion efficiency of the compressed air energy storage system during the compressed air energy storage process; This refers to the compressor's compression power. Power generation for the expander; The energy conversion efficiency of the expansion and energy release process in a compressed air energy storage system; The available heat in the thermal storage unit during time period t+1; The available heat in the thermal storage unit during time period t; The heat recovered during the compression stage and enters the thermal storage unit; The internal heat recovery required for expansion-based power generation; To supply heat to external heat loads; This refers to the heat loss of the thermal storage unit. This is the equivalent heat loss coefficient of the thermal storage unit; Temperature of the thermal storage unit; The ambient temperature.
[0072] This embodiment configures a compressed air energy storage system (CAES) with 3 compression stages and 3 expansion stages. The multi-stage compression and expansion heat exchange constraints of the compressed air energy storage system are extracted. The outlet water node of the air-water cooling heat exchanger between compressor stages is used as the input terminal of the heat source topology matrix and connected in parallel to the underlying heating water network structure of the microgrid, establishing a correlational heat balance coupling equation. The microgrid thermal energy structure is mainly used to describe the compression heat recovery, heat storage, and expansion reheat processes within the CAES system. In the compression energy storage stage, CAES recovers compression heat through multi-stage compressor interstage coolers and stores the recovered heat in the heat storage unit. In the expansion power generation stage, the heat storage unit provides reheat to the expander inlet air to meet the heat required for the CAES power generation process. The heat recovered during the compression stage is represented as:
[0073] in, The total heat power recovered during the CAES compression phase in time period t; The heat power recovered by the interstage cooler of the i-th stage compressor during time period t; The heat power recovered by the interstage cooler of the i-th stage compressor is expressed as:
[0074] in, Let t be the mass flow rate of the i-th stage compressed air. The specific heat capacity of air at constant pressure; and These are the air-side inlet and outlet temperatures of the i-th stage cooler, respectively. The thermal state balance of the thermal storage unit is expressed as:
[0075] in, The available heat in the thermal storage unit during time period t+1; The available heat in the thermal storage unit during time period t; The heat recovered during the compression stage and enters the thermal storage unit; The internal heat recovery required for expansion-based power generation; To supply heat to external heat loads; This refers to the heat loss of the thermal storage unit. The heat loss of the thermal storage unit is expressed as:
[0076] in, This refers to the heat loss power of the thermal storage unit; This is the equivalent heat loss coefficient of the thermal storage unit; Temperature of the thermal storage unit; The ambient temperature during time period t; For nonlinear functions such as the energy storage efficiency function and the CAES heat transfer efficiency function under the influence of ambient temperature, the SOS2 piecewise linearization method is used for processing: The nonlinear function is expressed as:
[0077] in, Let be a nonlinear function to be piecewise linearized. For the first Each segment node As weight variables, Let be the weight variable for the k-th segment node.
[0078] Step S3: Construct a two-stage robust optimization objective function with a "min-maximum-min" structure, where the first stage is capacity configuration decision and the second stage is multi-timescale scheduling operation verification; specifically, the two-stage robust optimization objective function with the "min-maximum-min" structure is: ; Where X is the set of decision variables for capacity allocation in the first stage, c is the vector of investment cost coefficients, and u is the set of source load uncertainty variables. It is a polyhedral uncertainty set; This is the set of variables for the second phase of multi-timescale scheduling. For a given capacity configuration and uncertainty, the operational feasible domain is... The operating and load shedding penalty cost coefficient; T is the transpose symbol.
[0079] The first-stage capacity configuration decision variable set X includes: wind power installed capacity, photovoltaic installed capacity, AA-CAES gas chamber volume, AA-CAES turbine power, and electrochemical energy storage capacity.
[0080] The second-stage operating variables y include: actual wind power absorption capacity, actual photovoltaic power absorption capacity, wind and solar curtailment power, CAES compression power, expansion power generation capacity, gas storage status, thermal storage status, expansion heat recovery capacity, external heat supply capacity, electrochemical energy storage charging and discharging power, electrochemical energy storage SOC, power shedding load, and heat shedding load.
[0081] Step S4: Based on the column and constraint generation algorithm, the original robust optimization model is decoupled into the main problem and sub-problems and solved iteratively. According to the solution status of the sub-problems, the newly identified severe scenarios and their corresponding new operating variables and operating balance constraints are fed back to the main problem until the convergence tolerance accuracy is met, and the optimal microgrid configuration scheme that takes into account both the extreme toughness of high cold and the economic efficiency of the whole life cycle is output.
[0082] Specifically, this includes step S4.1: Based on the column and constraint generation algorithm, the original robust optimization model is decoupled into a main problem and sub-problems, and then iteratively solved. The main problem model is:
[0083]
[0084]
[0085]
[0086] in, As variables for the first stage of investment decisions, X Configure the set of decision variables for the first phase of capacity; As an auxiliary variable characterizing the operating costs of the second phase; In the first The worst known scenario The second stage of the decision-making process, K These are the decision variables for the second stage of operation; , For the corresponding coefficient vector; , , The lower bound is the constraint coefficient matrix, which is updated after each solution to the main problem. ;T is the transpose symbol.
[0087] Step S4.2: The subproblem is to obtain the capacity configuration setting value from the main problem. As a known constant, it is used to search within the polyhedral uncertainty set U in the most severe scenario that results in the highest system operating cost. Its mathematical model is:
[0088] ; By utilizing the strong duality theory of linear programming, and introducing the dual variable vector π corresponding to the inner minimization problem constraints, the inner "maximum-minimum" logic is transformed into a completely equivalent single-layer maximization bilinear model:
[0089] ; Q(x*) is the objective function value of the subproblem given the first-stage capacity configuration x*`; x* is the first-stage optimal capacity configuration setting obtained from the main problem; U is the source-load joint polyhedral uncertainty set; y is the set of decision variables for the second-stage multi-timescale scheduling operation; Ω(x*,u) is the second-stage operational feasible region given the capacity configuration x* and the uncertainty variable `u`; d is the second-stage operating cost and load shedding penalty cost coefficient vector; T is the transpose sign; G is the constraint coefficient matrix corresponding to the second-stage operational decision variable y; h is the constraint right-hand constant vector; E is the constraint coefficient matrix; M is the constraint coefficient matrix corresponding to the uncertainty variable u; π is the dual variable vector corresponding to the inner minimization problem constraint; u(π) represents the value of the uncertainty variable associated with the dual variable π. For the bilinear terms generated in the objective function The Big M method is used to introduce Boolean variables for equivalent linearization; the most severe scenarios that currently cause the system to operate at the highest cost are identified. Then, update the global upper bound. UB :
[0090] Where c is the investment cost system vector, and T is the transpose symbol. The optimal configuration capacity setting value obtained from the main problem is... The objective function value for the subproblem.
[0091] Step S4.3: Based on the solution status of the sub-problems, classify the newly identified severe scenarios... and their corresponding newly added runtime variables The operational balance constraint is fed back to the main problem, i.e., a dynamic feasibility cut is fed back to handle power deficit, or an optimality cut is fed back to handle economic deviation; the difference between the upper and lower bounds is compared to determine whether the algorithm meets the preset convergence tolerance accuracy. (Value 1%) ; If the conditions are not met, the newly identified severe scenarios will be... and their corresponding runtime variables Add constraints to the main problem and set... Return to step 4.1 to continue iterating; if the convergence condition is met, terminate the iteration and output the optimal microgrid configuration scheme.
[0092] The two-stage robust planning method for multi-element energy storage microgrids in high-altitude and cold regions proposed in this invention can effectively quantify the dual uncertainties of source and load and the low-temperature penalty effect, achieving optimal investment economy while ensuring power supply reliability under extreme weather conditions. Compared with conventional planning that does not consider temperature penalties, the load shedding rate of the configuration scheme in this embodiment is reduced from 12.7% to 0.5% under extreme cold wave conditions, and the system's total life cycle cost increases by only 8.3%, verifying the effectiveness and economy of the invention. In summary, this invention effectively solves the core technical challenges in microgrid planning in high-altitude and cold regions, such as dual uncertainties of source and load, low-temperature energy storage attenuation, and the difficulty in balancing economy and resilience, through the comprehensive integration of techniques such as polyhedral uncertainty set construction, continuous environmental temperature penalty mechanism, multi-stage heat transfer constraint extraction of compressed air energy storage, "min-maximum-min" two-stage robust optimization architecture, and C&CG algorithm iterative solution. Compared with existing technologies, this invention has achieved significant technical progress in terms of uncertainty characterization accuracy, equipment modeling detail, optimization solution efficiency, and engineering practicality.
Claims
1. A two-stage robust planning method for multi-element energy storage microgrids in high-altitude and cold regions, characterized in that, Includes the following steps: S1: Construct a dual uncertainty set of source and load, and use a polyhedral uncertainty set to characterize the fluctuation boundaries of wind power output, photovoltaic power output, electrical load and heat load respectively; S2: Establish a multi-dimensional energy storage constraint model that takes into account the characteristics of high cold, introduce a continuous environmental temperature penalty mechanism to characterize the energy storage efficiency decay under extreme cold conditions, extract multi-stage compression and expansion heat transfer constraints for compressed air energy storage, and establish a correlation thermal balance coupling equation. S3: Construct a two-stage robust optimization objective function with a "minimum-maximum-minimum" structure, where the first stage is capacity configuration decision and the second stage is multi-timescale scheduling operation verification; S4: Based on the column and constraint generation algorithm, the original robust optimization model is decoupled into the main problem and sub-problems for alternating iterative solution. According to the solution status of the sub-problems, the newly identified severe scenarios and their corresponding new operating variables and operating balance constraints are fed back to the main problem until the convergence tolerance accuracy is met, and the optimal microgrid configuration scheme that takes into account both the extreme toughness of high cold and the economic efficiency of the whole life cycle is output.
2. The two-stage robust planning method for multi-element energy storage microgrids in high-altitude and cold regions according to claim 1, characterized in that, In step S1, the source-load dual uncertainty set is constructed, including the wind power output uncertainty set. Uncertainty in photovoltaic power output Uncertainty set of electrical load and heat load uncertainty set ; The uncertainty set of wind power output The expression is: in, To contribute to actual wind power, To predict the output, The maximum deviation, To assist in fluctuation variables, These are robust control parameters used to precisely control the conservatism of the planning scheme; The photovoltaic output uncertainty set The expression is: in, To contribute to actual photovoltaic power, Contribute to photovoltaic forecasting, The maximum prediction bias, As an auxiliary scaling variable for photovoltaic fluctuations, Robust space parameters for controlling the conservatism of photovoltaic output; The set of electrical load uncertainties The expression: in, and These represent the actual and predicted electrical loads of the microgrid. This represents the maximum positive deviation of the electrical load. As an auxiliary scaling variable for electrical load fluctuations, For robust control parameters of electrical load; The heat load uncertainty set The expression: in, and These are the actual and predicted heat loads, respectively. This represents the maximum deviation in heat load that may surge under extreme cold weather conditions. As an auxiliary scaling variable for heat load fluctuations, These are the robust control parameters for thermal load.
3. The two-stage robust planning method for multi-element energy storage microgrids in high-altitude and cold regions according to claim 1, characterized in that, In step S2, a continuous environmental temperature penalty mechanism is introduced to characterize the energy storage efficiency degradation under extremely cold conditions; the low-temperature performance parameters of electrochemical energy storage are obtained by fitting battery manufacturer test curves, historical operating data, or low-temperature experimental data; environmental temperature affects the charging efficiency, discharging efficiency, and usable capacity of electrochemical energy storage, and its expression is: in, , , This is a low-temperature correction function; To improve the charging efficiency of electrochemical energy storage, For electrochemical energy storage discharge efficiency, Available capacity for electrochemical energy storage; in, The state of charge of the electrochemically stored energy at time t+1; The state of charge of the electrochemically stored energy at time t; The charging power for electrochemical energy storage; This is the rated capacity of the electrochemical energy storage. This refers to the available capacity for electrochemical energy storage. The operating status of CAES is described by both the gas storage status and the thermal storage status; the gas storage status reflects the amount of compressed air stored, and the thermal storage status reflects the amount of compressed heat available; the ambient temperature affects the heat loss, heat exchange efficiency and expansion power generation efficiency of the thermal storage unit. in, The gas storage state quantity of the compressed air energy storage system at time t+1; This refers to the gas storage state quantity of a compressed air energy storage system. The energy conversion efficiency of the compressed air energy storage system during the compressed air energy storage process; This refers to the compressor's compression power. Power generation for the expander; The energy conversion efficiency of the expansion and energy release process in a compressed air energy storage system; The available heat in the thermal storage unit during time period t+1; The available heat in the thermal storage unit during time period t; The heat recovered during the compression stage and enters the thermal storage unit; The internal heat recovery required for expansion-based power generation; To supply heat to external heat loads; This refers to the heat loss of the thermal storage unit. This is the equivalent heat loss coefficient of the thermal storage unit; Temperature of the thermal storage unit; The ambient temperature.
4. The two-stage robust planning method for multi-element energy storage microgrids in high-altitude and cold regions according to claim 1, characterized in that, In step S2, the multi-stage compression and expansion heat exchange constraints of compressed air energy storage are extracted, and the water outlet node of the air-water cooling heat exchanger between compressor stages is used as the input end of the heat source topology matrix and connected in parallel to the bottom layer heating water network structure of the microgrid to establish the correlation heat balance coupling equation. The microgrid thermal energy structure is mainly used to describe the compression heat recovery, heat storage, and expansion reheat processes within the CAES system. In the compression energy storage stage, CAES recovers compression heat through multi-stage compressor interstage coolers and stores the recovered heat in the heat storage unit. In the expansion power generation stage, the heat storage unit provides reheat to the expander inlet air to meet the heat required for the CAES power generation process. The heat recovered during the compression stage is represented as: in, The total heat power recovered during the CAES compression phase in time period t; The heat power recovered by the interstage cooler of the i-th stage compressor during time period t; The heat power recovered by the interstage cooler of the i-th stage compressor is expressed as: in, Let t be the mass flow rate of the i-th stage compressed air. The specific heat capacity of air at constant pressure; and These are the air-side inlet and outlet temperatures of the i-th stage cooler, respectively. The thermal state balance of the thermal storage unit is expressed as: in, The available heat in the thermal storage unit during time period t+1; The available heat in the thermal storage unit during time period t; The heat recovered during the compression stage and enters the thermal storage unit; The internal heat recovery required for expansion-based power generation; To supply heat to external heat loads; This refers to the heat loss of the thermal storage unit. The heat loss of the thermal storage unit is expressed as: in, This refers to the heat loss power of the thermal storage unit; This is the equivalent heat loss coefficient of the thermal storage unit; Temperature of the thermal storage unit; The ambient temperature during time period t; For nonlinear functions such as the energy storage efficiency function and the CAES heat transfer efficiency function under the influence of ambient temperature, the SOS2 piecewise linearization method is used for processing: The nonlinear function is expressed as: in, Let be a nonlinear function to be piecewise linearized. For the first Each segment node As weight variables, Let be the weight variable for the k-th segment node.
5. The two-stage robust planning method for multi-element energy storage microgrids in high-altitude and cold regions according to claim 1, characterized in that, In step S3, the two-stage robust optimization objective function with a "minimum-maximum-minimum" structure is: Where X is the set of decision variables for capacity allocation in the first stage, and c is the vector of investment cost coefficients; The uncertainty set of the joint polyhedron of wind power, photovoltaic, electrical load and heat load constructed in step S1; y is the set of multi-timescale scheduling operation variables for the second stage; Let b be the operational feasible region under given capacity configuration and uncertainty, and T be the operation and load shedding penalty cost coefficient.
6. The two-stage robust planning method for multi-element energy storage microgrids in high-altitude and cold regions according to claim 1, characterized in that, In step S4, the original robust optimization model is decoupled into a main problem and sub-problems based on the column and constraint generation algorithm, and then iteratively solved. The main problem model is as follows: Where x is the investment decision variable in the first stage, and X is the set of capacity allocation decision variables in the first stage; As an auxiliary variable characterizing the operating costs of the second phase; For the k-th known worst-case scenario The second-stage operational decision variables are defined below; K is the second-stage operational decision variable; c and d are the corresponding coefficient vectors; E, G, and M are the constraint coefficient matrices, and the lower bound is updated after each solution to the main problem. ;T is the transpose symbol.
7. The two-stage robust planning method for multi-element energy storage microgrids in high-altitude and cold regions according to claim 1, characterized in that, In step S4, the sub-problem is the capacity configuration setting value obtained from the main problem. As a known constant, the mathematical model for searching the extremely severe scenario u that results in the highest system operating cost within the polyhedral uncertainty set U is as follows: ； By utilizing the strong duality theory of linear programming, and introducing the dual variable vector π corresponding to the inner minimization problem constraints, the inner "maximum-minimum" logic is transformed into a completely equivalent single-layer maximization bilinear model: ； `Q(x*)` represents the objective function value of the subproblem given the first-stage capacity configuration `x*`; x* is the first-stage optimal capacity configuration setting obtained from the main problem; U is the source-load joint polyhedral uncertainty set; y is the set of decision variables for multi-timescale scheduling and operation in the second stage; Ω(x*,u) is the second-stage operational feasible region given the capacity configuration x* and the uncertainty variable `u`; d is the second-stage operating cost and load shedding penalty cost coefficient vector; T is the transpose sign; G is the constraint coefficient matrix corresponding to the second-stage operational decision variable y; h is the constraint right-hand constant vector; E is the constraint coefficient matrix; `M` is the constraint coefficient matrix corresponding to the uncertainty variable `u`; π is the dual variable vector corresponding to the inner minimization problem constraint; u(π) represents the value of the uncertainty variable associated with the dual variable π. For the bilinear terms generated in the objective function The solution is obtained by introducing Boolean variables through the Big M method to achieve equivalent linearization. Identify the most severe scenarios that currently cause the system to operate at the highest cost. Then, update the global upper bound. UB : Where c is the investment cost system vector, and T is the transpose symbol. The optimal configuration capacity setting value obtained from the main problem is... The objective function value for the subproblem.
8. The two-stage robust planning method for multi-element energy storage microgrids in high-altitude and cold regions according to claim 7, characterized in that, In step S4, based on the solution status of the sub-problems, the newly identified severe scenarios are... and their corresponding newly added runtime variables The operational balance constraint is fed back to the main problem, i.e., a dynamic feasibility cut is fed back to handle power deficit, or an optimality cut is fed back to handle economic deviation; the difference between the upper and lower bounds is compared to determine whether the algorithm meets the preset convergence tolerance accuracy. : ； If the convergence condition is not met, repeat the iteration process; if the convergence condition is met, terminate the iteration and output the optimal microgrid configuration scheme.
9. The two-stage robust planning method for multi-element energy storage microgrids in high-altitude and cold regions according to claim 1, characterized in that, The optimal microgrid configuration scheme output in step S4 includes: wind power installed capacity, photovoltaic installed capacity, air chamber volume and turbine power of advanced adiabatic compressed air energy storage system, electrochemical energy storage capacity, and spatial layout coordinates and grid connection topology of each device.