Micro-grid economic dispatching method considering energy storage cycle life
By considering the energy storage cycle life in the microgrid economic scheduling model, calculating the energy storage discharge depth and linearizing it, and establishing a comprehensive cost optimization model, the problem of failure to effectively consider the impact of energy storage life in the existing technology is solved, and more efficient energy storage utilization and microgrid economic operation are achieved.
Patent Information
- Application Number
- CN202411656802.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-19
- Publication Date
- 2025-03-11
- Estimated Expiration
- 2044-11-19
AI Technical Summary
The existing microgrid economic scheduling model fails to effectively consider the impact of the number of energy storage charge and discharge times on the energy storage life, resulting in a large calculation result of the economic benefits in the actual configuration, and an economic scheduling method that reduces the loss value of the energy storage cycle life cannot be obtained.
A microgrid economic scheduling method considering the cycle life of energy storage is proposed. By reading electrical data, calculating the depth of energy storage discharge and linearizing it, a microgrid economic scheduling model aims at the minimum daily operating cost of the microgrid is established, including energy storage life loss cost, electricity purchase and sale cost, operation and maintenance cost and fuel cost, and solving the model to formulate energy storage charging and discharge strategies and power purchase strategies.
By considering the energy storage cycle life, the utilization efficiency of the energy storage life is improved, the operating cost of the microgrid is reduced, and the economic scheduling effect is achieved that is more realistic.
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Figure CN119602388A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of microgrid economic dispatching, and in particular to a microgrid economic dispatching method taking into account the cycle life of energy storage. Background Art
[0002] Microgrids have been increasingly widely used in power systems because they can effectively absorb clean energy. Energy storage technology, as a core element in the development of energy Internet, plays an important role in the balance of power and electricity, and can effectively cope with the challenges of randomness and volatility of new energy. However, the high investment cost of energy storage systems and their limited cycle life have become key factors restricting the realization of good economic effects in the energy storage planning process.
[0003] In this context, optimizing the coordinated scheduling of microgrid energy storage and source-load, and comprehensively considering factors such as the energy storage cycle life, can not only promote the efficient use of clean renewable power sources, but also effectively reduce peak loads, which is of far-reaching significance for ensuring the stable and safe operation of microgrids and improving the investment economy of energy storage.
[0004] In existing research, when studying the economic dispatch of microgrids, there is a lack of consideration from the perspective of source, load and storage, as well as the impact of the number of energy storage charge and discharge times on the energy storage life. However, with the continuous access to new energy and the increase in load demand, higher requirements are placed on the function of energy storage, but frequent charging and discharging will cause the energy storage cycle life to decrease. The existing energy storage planning model only considers the impact of the number of energy storage charge and discharge times on the energy storage life, and cannot quantify the life conversion cost of energy storage well, resulting in the economic benefit calculation results in the actual configuration of the microgrid being easily too large, which is not in line with reality, and it is impossible to obtain a microgrid economic dispatch method that reduces the energy storage cycle life depreciation value (Chen Mingyang, Liu Min, Yu Dengwu. Economic dispatch of microgrids considering energy storage life. Intelligent Computers and Applications, 2021, 11(10): 101-106.). Summary of the invention
[0005] The purpose of the present invention is to propose a microgrid economic dispatch method that takes into account the cycle life of energy storage, namely the impact of the number of energy storage charge and discharge times on the energy storage life, in view of the fact that the existing microgrid economic dispatch model lacks consideration of the impact of the number of energy storage charge and discharge times on the energy storage life, and to establish a microgrid economic dispatch model by combining new energy output data and load data to obtain a microgrid economic dispatch plan.
[0006] The purpose of the present invention is achieved by at least one of the following technical solutions.
[0007] A microgrid economic dispatch method considering energy storage cycle life includes the following steps:
[0008] S1. Read local electrical data;
[0009] S2. Calculate the energy storage discharge depth and linearize the function to obtain the energy storage life loss cost at different discharge depths;
[0010] S3. Establish a microgrid economic dispatch model with the goal of minimizing the daily operation cost of the microgrid. The daily operation cost of the microgrid includes the energy storage life loss cost, the cost of purchasing and selling electricity, the operation and maintenance cost of each unit, and the fuel cost;
[0011] S4. Solve the economic dispatch model of the microgrid, and formulate energy storage charging and discharging strategies and power purchasing strategies for the microgrid based on the obtained model decision variables.
[0012] Furthermore, in step S1, the electrical data includes: peak and valley electricity prices, wind turbine and photovoltaic output data, load data, gas turbine output upper limit P G.min , Gas turbine output lower limit P G.max 、Wind turbine operation and maintenance cost om.W , photovoltaic operation and maintenance cost c om.PV , gas turbine operation and maintenance cost c om.G , fuel unit cost c fuel 、Energy storage operation and maintenance cost om.bat , energy storage charging and discharging efficiency η, energy storage capacity upper limit SOC max , Energy storage capacity lower limit SOC min And the upper limit of the tie line P grid.max .
[0013] Furthermore, step S2 includes the following steps:
[0014] S2.1. Divide the 100% discharge depth into 5 sections on average, calculate the discharge depth at the energy storage time t, and determine the charge and discharge state coefficient, as follows:
[0015]
[0016] Among them, g d (t) is the charge-discharge state coefficient of the energy storage at the discharge depth of the dth segment. If the discharge depth of the energy storage at time t is in the dth segment, then the charge-discharge state coefficient of the energy storage at the discharge depth of the dth segment is g. d (t)=1, otherwise g d (t) = 0, 1 ≤ d ≤ 5; SOC(t) represents the state of charge of the energy storage at time t; dod d (t) represents the discharge depth of the dth segment at time t; come d are the upper and lower limits of the discharge depth of the dth segment respectively; g d (t) is the charge and discharge state coefficient of the energy storage at the discharge depth of the dth segment;
[0017] S2.2. According to the charge and discharge state coefficient, the exponential function formula is used to linearize the minimum value of different discharge depth intervals to determine the linearization coefficient K of the energy storage at the discharge depth of the dth segment. d , B d , as follows:
[0018] kp and kd are determined by the type of energy storage;
[0019] S2.3, the energy storage cycle count variable S at time t bat (t) Linearization, as follows:
[0020]
[0021] Among them, U bat When (t) is 0, it indicates energy storage discharge, U bat When (t) is 1, it indicates energy storage charging;
[0022] S2.4, according to the linearization coefficient K of the energy storage discharge depth in the dth section d , B d and the loop count variable S at time t bat (t), calculate the energy storage life loss cost C bat , as follows:
[0023]
[0024] Among them, M represents a very large number.
[0025] Furthermore, in step S3, the objective function of the microgrid economic dispatch model is expressed as follows:
[0026] minC=min{C ope} (1)
[0027] C ope =C grid +C om +C fuel +C bat (2)
[0028]
[0029] Where C is the comprehensive operation cost of the microgrid; C ope is the daily operating cost of the microgrid; ρ is the discount rate, r is the number of years of discount, C grid , C om and C fuel are the electricity purchase and sales cost, the operation and maintenance cost of each unit, and the fuel cost, respectively. grid (t) is the electricity price of the power grid at time t, c fuelis the unit cost of fuel; c om.W 、c om.PV 、c om.G 、c om,bat are the operation and maintenance cost coefficients of wind turbines, photovoltaics, gas turbines, and energy storage, respectively; P buy (t), P sell (t) are the power purchased and sold by the microgrid at time t; P G (t), P W (t) and P PV (t) are the output power of gas turbine, wind turbine and photovoltaic at time t respectively; P ch (t), P dis (t) are the energy storage charging and discharging power at time t; Δt is the time step.
[0030] Furthermore, in step S3, the constraints of the microgrid economic dispatch model include gas turbine constraints, distribution network power purchase constraints, energy storage power constraints and power balance constraints.
[0031] Furthermore, the gas turbine constraints are as follows:
[0032] P G.min ≤P G (t)≤P G.max (4)
[0033] Among them, P G.min , P G.max They are the upper and lower limits of the micro gas turbine output, which are limited by its minimum load factor and rated power respectively;
[0034] Microgrid power constraints are as follows:
[0035]
[0036] Among them, P buy (t), P sell (t) are the power purchased and sold by the microgrid at time t; P grid.max is the upper limit of the interaction power of the tie line between the microgrid and the distribution network; U grid (t) is the state variable of the microgrid power purchase and sale at time t, 1 represents power purchase and 0 represents power sale.
[0037] Furthermore, the energy storage power quantity constraints include energy storage charging and discharging power constraints and energy storage state of charge (State of Charge, SOC) constraints;
[0038] Energy storage charging and discharging power constraints are as follows:
[0039]
[0040] Pbat.max =μE bat.max (7)
[0041] Among them, P dis (t), P ch (t) are the energy storage discharge and charging power at time t; P bat.max is the upper limit of energy storage charging and discharging power, μ is the upper limit of energy storage power and rated capacity E bat.max A fixed proportionality factor;
[0042] Energy storage state of charge (SOC) constraints:
[0043]
[0044] Among them, Δt is the time step, which is 1h; E(0) is the initial energy storage capacity, SOC max , SOC min are the upper and lower limits of the state of charge of the energy storage, and η is the energy storage charging and discharging efficiency.
[0045] Furthermore, the power balance constraints are as follows:
[0046] P dis (t)-P ch (t)+P buy (t)-P sell (t)+P G (t)=0 (10).
[0047] Furthermore, in step S4, the model decision variables are solved by the commercial solver clpex, including: the energy storage system discharge and charging power P at time t dis (t) and P ch (t), and the power purchase and sale of the microgrid at time t P buy (t), P sell (t).
[0048] Compared with the prior art, the advantages of the present invention are:
[0049] 1. The microgrid operation dispatching model established by the present invention takes into account the new energy units, steam turbine units and energy storage, and can improve the economic dispatching benefits of the microgrid through good multi-energy complementarity;
[0050] 2. The present invention linearizes the energy storage life loss cost and cycle count variables, calculates the energy storage discharge depth and the cycle life loss cost of the energy storage, so that microgrid scheduling is conducive to improving the energy storage life and makes the results more practical. BRIEF DESCRIPTION OF THE DRAWINGS
[0051] Figure 1A flowchart of the steps of a microgrid economic dispatching method considering the energy storage cycle life in an embodiment of the present invention;
[0052] Figure 2 It is a schematic diagram of photovoltaic and wind turbine output and load parameters in an embodiment of the present invention;
[0053] Figure 3 This is a schematic diagram of the optimized operation results of the microgrid without considering the energy storage cycle life in the embodiment of the present invention;
[0054] Figure 4 This is a schematic diagram of the optimized operation results of a microgrid considering the energy storage cycle life in an embodiment of the present invention. DETAILED DESCRIPTION
[0055] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the specific implementation of the present invention is described in detail below with reference to the accompanying drawings and examples.
[0056] Example:
[0057] A microgrid economic dispatch method considering the energy storage cycle life, such as Figure 1 As shown, the following steps are included:
[0058] S1. Read local electrical data;
[0059] The electrical data include: peak and valley electricity prices, wind turbine and photovoltaic output data, load data, gas turbine output upper limit P G.min , Gas turbine output lower limit P G.max 、Wind turbine operation and maintenance cost om.W , photovoltaic operation and maintenance cost c om.PV , gas turbine operation and maintenance cost c om.G , fuel unit cost c fuel 、Energy storage operation and maintenance cost om.bat , energy storage charging and discharging efficiency η, energy storage capacity upper limit SOC max , Energy storage capacity lower limit SOC min And the upper limit of the tie line P grid.max .
[0060] S2. Calculate the energy storage discharge depth and linearize the function to obtain the energy storage life loss cost of different energy storage discharge depths, including the following steps:
[0061] S2.1. Divide the 100% discharge depth into 5 sections on average, calculate the discharge depth at the energy storage time t, and determine the charge and discharge state coefficient, as follows:
[0062]
[0063]
[0064] Among them, g d (t) is the charge-discharge state coefficient of the energy storage at the discharge depth of the dth segment. If the discharge depth of the energy storage at time t is in the dth segment, then the charge-discharge state coefficient of the energy storage at the discharge depth of the dth segment is g. d (t)=1, otherwise g d (t) = 0, 1 ≤ d ≤ 5; SOC(t) represents the state of charge of the energy storage at time t; dod d (t) represents the discharge depth of the dth segment at time t; come d are the upper and lower limits of the discharge depth of the dth segment respectively; g d (t) is the charge and discharge state coefficient of the energy storage at the discharge depth of the dth segment;
[0065] S2.2. According to the charge and discharge state coefficient, the exponential function formula is used to linearize the minimum value of different discharge depth intervals to determine the linearization coefficient K of the energy storage at the discharge depth of the dth segment. d , B d , as follows:
[0066] kp and kd are determined by the energy storage type. In one embodiment, kp and kd are 1.31 and 1.28 respectively;
[0067] S2.3, the energy storage cycle count variable S at time t bat (t) Linearization, as follows:
[0068]
[0069] Among them, U bat When (t) is 0, it indicates energy storage discharge, U bat When (t) is 1, it indicates energy storage charging;
[0070] S2.4, according to the linearization coefficient K of the energy storage discharge depth in the dth section d , B d and the loop count variable S at time t bat (t), calculate the energy storage life loss cost C bat , as follows:
[0071]
[0072] Wherein, M represents a very large number, and in one embodiment, the value is 10000.
[0073] S3. Establish a microgrid economic dispatch model with the goal of minimizing the daily operation cost of the microgrid. The daily operation cost of the microgrid includes the energy storage life loss cost, the cost of purchasing and selling electricity, the operation and maintenance cost of each unit, and the fuel cost;
[0074] The objective function of the microgrid economic dispatch model is expressed as follows:
[0075] minC=min{C ope} (1)
[0076] C ope =C grid +C om +C fuel +C bat (2)
[0077]
[0078] Where C is the comprehensive operation cost of the microgrid; C ope is the daily operating cost of the microgrid; ρ is the discount rate, r is the number of years of discount, C grid , C om and C fuel are the electricity purchase and sales cost, the operation and maintenance cost of each unit, and the fuel cost, respectively. grid (t) is the electricity price of the power grid at time t, c fuel is the unit cost of fuel; c om.W 、c om.PV 、c om.G 、c om,bat are the operation and maintenance cost coefficients of wind turbines, photovoltaics, gas turbines, and energy storage, respectively; P buy (t), P sell (t) are the power purchased and sold by the microgrid at time t; P G (t), P W (t) and P PV (t) are the output power of gas turbine, wind turbine and photovoltaic at time t respectively; P ch (t), P dis (t) are the energy storage charging and discharging power at time t; Δt is the time step.
[0079] Furthermore, in step S3, the constraints of the microgrid economic dispatch model include gas turbine constraints, distribution network power purchase constraints, energy storage power constraints and power balance constraints.
[0080] Furthermore, the gas turbine constraints are as follows:
[0081] P G.min ≤P G (t)≤P G.max (4)
[0082] Among them, P G.min , P G.max They are the upper and lower limits of the micro gas turbine output, which are limited by its minimum load factor and rated power respectively;
[0083] Microgrid power constraints are as follows:
[0084]
[0085] Among them, P buy (t), P sell (t) are the power purchased and sold by the microgrid at time t; P grid.max is the upper limit of the interaction power of the tie line between the microgrid and the distribution network; U grid (t) is the state variable of the microgrid power purchase and sale at time t, 1 represents power purchase and 0 represents power sale.
[0086] Energy storage power constraints include energy storage charging and discharging power constraints and energy storage state of charge (SOC) constraints;
[0087] Energy storage charging and discharging power constraints are as follows:
[0088]
[0089] P bat.max =μE bat.max (7)
[0090] Among them, P dis (t), P ch (t) are the energy storage discharge and charging power at time t; P bat.max is the upper limit of energy storage charging and discharging power, μ is the upper limit of energy storage power and rated capacity E bat.max A fixed proportionality factor;
[0091] Energy storage state of charge (SOC) constraints are as follows:
[0092]
[0093] Among them, Δt is the time step, which is 1h; E(0) is the initial energy storage capacity, SOC max , SOC min are the upper and lower limits of the state of charge of the energy storage, and η is the energy storage charging and discharging efficiency.
[0094] Power balance constraints are as follows:
[0095] P dis (t)-P ch (t)+P buy (t)-P sell (t)+P G (t)=0 (10).
[0096] S4. Solve the model using the commercial solver clpex to obtain the discharge and charging power P of the energy storage system at time t in the microgrid. dis (t) and P ch (t), and the power purchase and sale of the microgrid at time t P buy (t), P sell (t). Formulate energy storage charging and discharging strategy and power purchasing strategy for the microgrid at time t;
[0097] In one embodiment, taking a microgrid with energy storage, wind turbines, and photovoltaics as an example, the specific input data is shown in Table 1.
[0098] Table 1 Example setting data
[0099]
[0100] In this embodiment, the peak electricity price periods are 9:00-11:00 and 19:00-23:00, and the electricity price is 1.35 yuan / kWh. The off-peak electricity price periods are 24:00-8:00 and 12:00-18:00, and the electricity prices are 0.48 yuan / kWh and 0.9 yuan / kWh respectively.
[0101] In this embodiment, the photovoltaic and wind turbine output and load parameters are as follows: Figure 2 shown.
[0102] In this embodiment, Figure 3 , Figure 4 As shown in the figure, when the energy storage cycle life is taken into account, the energy storage discharge depth is significantly reduced from 0:00 to 5:00. During the peak period of electricity consumption from 12:00 to 18:00, the energy storage is discharged at the peak electricity price and not discharged at ordinary times, realizing the power transfer. The energy storage is charged during the low electricity consumption period from 19:00 to 24:00, which reduces the electricity purchase cost of the microgrid, reduces the number of energy storage charge and discharge, and reduces the cost of the microgrid from 4537 yuan to 43319 yuan / day, saving the total cost of the microgrid operation. In summary, in this embodiment, considering the energy storage cycle life, the energy storage system discharge and charging power P is obtained. dis (t) and P ch (t), and the power purchase and sale of the microgrid at time t P buy (t), P sell (t), formulating energy storage operation strategies and microgrid power purchase strategies can effectively reduce the life loss of energy storage, reduce the operation cost of microgrids, and realize the economic operation and dispatch of microgrids.
[0103] The preferred embodiments of the present application disclosed above are only used to help understand the present invention and its core ideas. For those skilled in the art, according to the ideas of the present invention, there will be changes in specific application scenarios and implementation operations, and this specification should not be interpreted as limiting the present invention. The present invention is only limited by the claims and their full scope and equivalents.
Claims
1. A microgrid economic dispatch method considering the energy storage cycle life, characterized in that: The following steps are involved: S1. Read local electrical data; S2. Calculate the energy storage discharge depth and linearize the function to obtain the energy storage life loss cost at different discharge depths; S3. Establish a microgrid economic dispatch model with the goal of minimizing the daily operation cost of the microgrid. The daily operation cost of the microgrid includes the energy storage life loss cost, the cost of purchasing and selling electricity, the operation and maintenance cost of each unit, and the fuel cost; S4. Solve the economic dispatch model of the microgrid, and formulate energy storage charging and discharging strategies and power purchasing strategies for the microgrid based on the obtained model decision variables.
2. A microgrid economic dispatch method considering energy storage cycle life according to claim 1, characterized in that: In step S1, the electrical data includes: peak and valley electricity prices, wind turbine and photovoltaic output data, load data, gas turbine output upper limit P G.min , Gas turbine output lower limit P G.max 、Wind turbine operation and maintenance cost om.W , photovoltaic operation and maintenance cost c om.PV , gas turbine operation and maintenance cost c om.G , fuel unit cost c fuel 、Energy storage operation and maintenance cost om.bat , energy storage charging and discharging efficiency η, energy storage capacity upper limit SOC max , Energy storage capacity lower limit SOC min And the upper limit of the tie line P grid.max .
3. A microgrid economic dispatching method considering energy storage cycle life according to claim 2, characterized in that: Step S2 includes the following steps: S2.
1. Divide the 100% discharge depth into 5 sections on average, calculate the discharge depth at the energy storage time t, and determine the charge and discharge state coefficient, as follows: Among them, g d (t) is the charge-discharge state coefficient of the energy storage at the discharge depth of the dth segment. If the discharge depth of the energy storage at time t is in the dth segment, then the charge-discharge state coefficient of the energy storage at the discharge depth of the dth segment is g. d (t)=1, otherwise g d (t) = 0, 1 ≤ d ≤ 5; SOC(t) represents the state of charge of the energy storage at time t; dod d (t) represents the discharge depth of the dth segment at time t; come d are the upper and lower limits of the discharge depth of the dth segment respectively; g d (t) is the charge and discharge state coefficient of the energy storage at the discharge depth of the dth segment; S2.
2. According to the charge and discharge state coefficient, the exponential function formula is used to linearize the minimum value of different discharge depth intervals to determine the linearization coefficient K of the energy storage at the discharge depth of the dth segment. d , B d , as follows: kp and kd are determined by the type of energy storage; S2.3, the energy storage cycle count variable S at time t bat (t) Linearization, as follows: Among them, U bat When (t) is 0, it indicates energy storage discharge, U bat When (t) is 1, it indicates energy storage charging; S2.4, according to the linearization coefficient K of the energy storage discharge depth in the dth section d , B d and the loop count variable S at time t bat (t), calculate the energy storage life loss cost C bat , as follows: Among them, M represents a very large number.
4. A microgrid economic dispatch method considering energy storage cycle life according to claim 3, characterized in that: In step S3, the objective function of the microgrid economic dispatch model is expressed as follows: minC=min{C ope }(1) C ope =C grid +C om +C fuel +C bat (2) Where C is the comprehensive operation cost of the microgrid; C ope is the daily operating cost of the microgrid; ρ is the discount rate, r is the number of years of discount, C grid , C om and C fuel are the electricity purchase and sales cost, the operation and maintenance cost of each unit, and the fuel cost, respectively. grid (t) is the electricity price of the power grid at time t, c fuel is the unit cost of fuel; c om.W 、c om.PV 、c om.G 、c om,bat are the operation and maintenance cost coefficients of wind turbines, photovoltaics, gas turbines, and energy storage, respectively; P buy (t), P sell (t) are the power purchased and sold by the microgrid at time t; P G (t), P W (t) and P PV (t) are the output power of gas turbine, wind turbine and photovoltaic at time t respectively; P ch (t), P dis (t) are the energy storage charging and discharging power at time t; Δt is the time step.
5. A microgrid economic dispatch method considering energy storage cycle life according to claim 3, characterized in that: In step S3, the constraints of the microgrid economic dispatch model include gas turbine constraints, distribution network power purchase constraints, energy storage power constraints and power balance constraints.
6. A microgrid economic dispatch method considering energy storage cycle life according to claim 5, characterized in that: Gas turbine constraints are as follows: P G.min ≤P G (t)≤P G.max (4) Among them, P G.min , P G.max They are the upper and lower limits of the micro gas turbine output, which are limited by its minimum load rate and rated power respectively.
7. A microgrid economic dispatch method considering energy storage cycle life according to claim 5, characterized in that: Microgrid power constraints are as follows: Among them, P buy (t), P sell (t) are the power purchased and sold by the microgrid at time t; P grid.max is the upper limit of the interaction power of the tie line between the microgrid and the distribution network; U grid (t) is the state variable of the microgrid power purchase and sale at time t, 1 represents power purchase and 0 represents power sale.
8. A microgrid economic dispatch method considering energy storage cycle life according to claim 5, characterized in that: Energy storage power constraints include energy storage charging and discharging power constraints and energy storage state of charge (SOC) constraints; Energy storage charging and discharging power constraints are as follows: P bat.max =μE bat.max (7) Among them, P dis (t), P ch (t) are the energy storage discharge and charging power at time t; P bat.max is the upper limit of energy storage charging and discharging power, μ is the upper limit of energy storage power and rated capacity E bat.max A fixed proportionality factor; Energy storage state of charge (SOC) constraints: Among them, Δt is the time step, which is 1h; E(0) is the initial energy storage capacity, SOC max , SOC min They are the upper and lower limits of the state of charge of the energy storage, and η is the energy storage charging and discharging efficiency.
9. A microgrid economic dispatch method considering energy storage cycle life according to any one of claims 6 to 8, characterized in that: Power balance constraints are as follows: P dis (t)-P ch (t)+P buy (t)-P sell (t)+P G (t)=0(10)。 10. A microgrid economic dispatch method considering energy storage cycle life according to claim 9, characterized in that: In step S4, the model decision variables are solved by the commercial solver clpex, including: the energy storage system discharge and charging power P at time t dis (t) and P ch (t), and the power purchase and sale of the microgrid at time t P buy (t), P sell (t).
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