A dynamic optimization method for identifying key planning decision points of integrated energy systems

Abstract

The application discloses a dynamic optimization method for identifying a key planning decision point of a comprehensive energy system, and relates to the field of power system dispatching and control. First, based on the physical composition of the comprehensive energy system, a planning and operation joint optimization model considering equipment operation constraints is established. Second, a certain equipment capacity scheme is taken as an input parameter, and the operation state in a long operation period is taken as evaluation, so that the value of the current planning scheme is calculated to form a value function model of the planning decision. Then, a rolling time domain optimization model of the comprehensive energy system is constructed, the value function model is called by the system in a rolling manner, the value in the current state is calculated, and a continuous value curve is obtained through linear interpolation and reverse recursion. The application converts the one-time complex investment problem into a multi-stage dynamic planning scheme of the comprehensive energy system through a non-decreasing incremental planning mode.

Description

Technical Field

[0001] This invention relates to the field of power system dispatching and control, specifically a dynamic optimization method for identifying key planning and decision points in an integrated energy system. Background Technology

[0002] As a crucial component of energy transition and smart grid development, the current status and future trends of integrated energy systems in industrial parks have attracted significant attention. Currently, various heterogeneous energy flows, such as electricity, heat, cooling, and gas, are coupled and converted within the parks, forming a multi-energy network. Leveraging its mechanism of multi-energy complementarity and supply-demand interaction, integrated energy systems can optimize energy allocation while improving energy efficiency. Within the scope of the integrated energy system, it meets the energy needs of various users, gradually becoming an important vehicle for promoting low-carbon operation in industrial parks and increasing wind and solar power absorption rates. Current research and development trends in integrated energy systems for industrial parks mainly focus on two aspects: optimized scheduling and operation, and park planning and design methods. The optimized operation aspect includes refined modeling of the park's microgrid, economical operation scheduling, coordinated operation of main, distribution, and microgrids, and the participation of the park's microgrid in the electricity market. The planning and design aspect includes the configuration of multi-energy equipment within the park, the site selection and capacity determination of multi-energy equipment, production line process design and planning, and economic investment planning.

[0003] Industrial parks have diverse development stages and industrial structures in their integrated energy systems. Over long planning timeframes, load demand fluctuations and source-side uncertainties accumulate and amplify over time. The diversity and spatiotemporal heterogeneity of load demand place higher demands on the reliability and quality of energy supply. This necessitates that industrial park microgrids fully consider the impact of uncertain events during the planning phase and be able to adaptively and dynamically adjust planning schemes. Therefore, identifying key planning decision points and decomposing a comprehensive energy system planning scheme into multi-stage dynamic planning schemes over a long period is particularly important to avoid the risks associated with one-time investment planning.

[0004] Prior art 1 (CN120410105A) discloses a successive approximation stochastic dynamic programming method for integrated watershed hydro-wind-solar systems. This invention aims to solve the uncertainty optimization problem in multi-energy coupled complementary scheduling. Specific steps include: first, sampling discrete values ​​using theoretical probability distribution functions to describe the uncertainty of runoff, photovoltaic, and wind power output; then, constructing a transition probability matrix using Markov chains to characterize the time series continuity of input variables; next, establishing a complementary optimization scheduling model by combining the system objective function and constraints; then, using the successive approximation-stochastic dynamic programming (SDP-SA) method, deriving a scheduling decision table with initial reservoir capacity, runoff, and wind / solar output as multi-dimensional state variables and final reservoir capacity as the decision variable; finally, in actual operation, determining the optimal scheduling decision through table lookup and interpolation based on real-time reservoir capacity, inflow, and wind / solar forecast data. However, this method is based on a short-term scheduling strategy of approximation-stochastic dynamic programming and does not consider long-term planning and decision-making problems.

[0005] Existing technology 2 (CN120389434A) discloses a dynamic programming-based method for optimizing energy storage capacity in electric vehicle V2G microgrids. This invention belongs to the field of microgrid energy storage optimization technology and aims to address the shortcomings in energy storage capacity optimization caused by the spatial dynamic characteristics of electric vehicle mobility. The method first collects grid topology parameters and electric vehicle trajectory data, divides node locations using a geographic grid, and generates a spatiotemporal matrix using timestamps to identify high-frequency access nodes. Then, it constructs state transition equations based on the inter-node impedance matrix, setting node-level safety boundaries using the line capacity change rate as a dynamic constraint. Subsequently, it employs a phased inverse dynamic programming algorithm, prioritizing spatial dimension optimization for high-frequency access nodes to generate charging and discharging constraints that integrate voltage deviation and capacity over-limit penalties. Finally, it integrates the constraints, performs global optimization with the goal of minimizing total operating costs, outputs energy storage capacity configuration strategies for each time period, and generates an energy storage deployment scheme. However, it addresses the spatial optimization and operation issues of deploying electric vehicles, while focusing on short-term deployment and operation decisions and not involving long-term investment planning. Furthermore, it does not employ time-series rolling optimization, resulting in a significant increase in computational cost over long timescales.

[0006] Existing technologies typically focus on applying dynamic programming methods to short-term scheduling decisions, with less consideration given to investment planning problems on long-term timescales. Furthermore, current stochastic dynamic programming relies on the expected value of predictions, and the accuracy of these predictions affects the planning scheme. While dynamic programming methods have been applied in many fields, their in-depth application in the joint optimization and operation of integrated energy systems and industrial park planning is still not widespread. The two-layer architecture proposed in this invention, consisting of a time-series rolling optimization method and a value function model, achieves dimensionality reduction of the dynamic programming problem in the time dimension, ensuring the robustness of the planning scheme while avoiding the dimensionality curse of traditional dynamic programming. Summary of the Invention

[0007] The purpose of this invention is to address the problems in the prior art by providing a dynamic optimization method for identifying key planning decision points in an integrated energy system. Based on the physical structure of the integrated energy system, a joint planning and operation optimization model considering equipment operational constraints is established. A value function model for planning decisions is constructed to evaluate the value of the current planning scheme. A rolling time-domain optimization model for the integrated energy system is built, and the value function model is continuously invoked. A continuous value curve is obtained through linear interpolation and inverse recursion. Key planning decision points are identified using a peak value recognition algorithm. Finally, the complex one-time investment problem is transformed into a multi-stage dynamic planning scheme for the integrated energy system, reducing the planning risk of the park's integrated energy system and improving the system's operational benefits.

[0008] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0009] To achieve the above objectives, the present invention provides the following technical solution, including:

[0010] Step S1: Based on the energy supply structure and supply and demand equipment of the integrated energy system, construct an optimized operation model for the integrated energy system;

[0011] Step S2: Consider the operational status of a specific planning decision over a longer period of time to evaluate the value of the decision and construct a planning value function model for the integrated energy system;

[0012] Step S3: Construct a rolling time-domain optimization model for the integrated energy system and propose a method for identifying key decision points within the planning period;

[0013] Step S4: Based on a small number of high-planning-value decision points within a long planning period, propose a multi-stage dynamic planning scheme for the integrated energy system based on key decision points.

[0014] As a preferred embodiment of the dynamic optimization method for identifying key planning decision points in an integrated energy system according to the present invention, step S1 is analyzed, wherein:

[0015] Based on the energy supply structure and supply and demand equipment of the integrated energy system, an optimized operation model for the integrated energy system is constructed.

[0016] 1) Objective function

[0017] The optimization objective is to minimize the total cost of the system. Its annualized investment cost and cycle operating costs constitute.

[0018]

[0019] Annualized investment cost Determined by the capital recovery factor, it is the sum of the annualized investments of all equipment, satisfying the following formula:

[0020]

[0021] in, This indicates that the equipment belongs to the photovoltaic category. Wind power Energy storage ,gas turbine A set; For equipment The capacity; The unit investment cost of the equipment; The expected lifespan of the equipment; is the discount rate.

[0022] Cycle operating costs The total cost of electricity purchase, fuel, and operation and maintenance during the dispatch cycle is expressed by the following formula:

[0023]

[0024] in, , , These represent the electricity purchase and sales cost, gas purchase cost, and energy storage operation cost coefficients, respectively. , , , , These represent the integrated energy system's power purchase from the grid, power sales from the grid, power generation from the gas-fired power generation unit, charging power from the energy storage unit, and discharging power from the energy storage unit, respectively. T Indicates the total runtime period.

[0025] 2) Real-time power balance constraints

[0026] At every moment t The total power generation of the system must equal the total power consumption, and the system should satisfy the following constraints:

[0027]

[0028] in, Indicates time t User load.

[0029] 3) Renewable energy output constraints

[0030]

[0031]

[0032] in, , These represent the uncertainty coefficients for photovoltaic power output and wind power output, respectively. , They represent t The expected power generation of photovoltaic and wind power at any given time; , These represent the upper limits of installed capacity for photovoltaic and wind power, respectively; , These represent the power generation of photovoltaic and wind power at time t, respectively.

[0033] 4) Load response constraints

[0034]

[0035] in, The uncertainty factor representing the load; This represents the expected load at time t; This represents the load at time t.

[0036] 5) Output constraints of micro gas turbines

[0037]

[0038] in, express t The output power of the gas turbine at any given time; This indicates the upper limit of the gas turbine's output.

[0039] 6) Constraints of energy storage systems

[0040]

[0041] in, , This represents the state-of-charge capacity of the stored energy at the current time t and the time t-1 before. This represents the energy storage charging power at time t; This represents the energy storage discharge power at time t; , These represent the charge and discharge efficiencies, respectively.

[0042]

[0043] in, , These represent the minimum and maximum state-of-charge coefficients for energy storage, respectively. This indicates the upper limit of the energy storage state-of-charge capacity.

[0044]

[0045]

[0046] in, This represents the charge / discharge identifier at time t, where 0 indicates no charge / discharge and 1 indicates charge / discharge. This indicates the upper limit of the maximum charging and discharging power.

[0047]

[0048] Energy storage systems are expected to meet periodic power balance constraints during long-term operation.

[0049] 7) Interaction constraints between integrated energy system and power grid

[0050]

[0051]

[0052] in, , These represent the power purchased and sold at time t, respectively. This represents the electricity sales identifier at time t, where 0 indicates no electricity sales and 1 indicates electricity sales. This indicates the upper limit of the power that can be interacted with the power grid.

[0053]

[0054] in, , These represent the planned capacity and minimum planned capacity of device i, respectively.

[0055] As a preferred embodiment of the dynamic optimization method for identifying key planning decision points in an integrated energy system according to the present invention, step S2 is specifically analyzed, wherein:

[0056] Step S2 considers the operational status of a specific planning decision over a longer period to evaluate the value of the decision and constructs a planning value function model for the integrated energy system, specifically including:

[0057] 1) Functional model of the value assessment module

[0058]

[0059]

[0060] in, The value function represents the planning scheme, and the relative magnitude of its value indicates the applicability of the planning scheme. It is a functional relationship that takes the planning scheme value as input and the value function value as output; This represents the input set consisting of the planning scheme and external operating parameters; These represent the input sets containing the upper limits of planned energy storage capacity, planned photovoltaic power, planned wind power, and planned gas turbine output, respectively.

[0061] function The calculation results depend on a short-running optimization problem solved internally. We define the decision variables and objective function of this internal problem using the following formulas.

[0062]

[0063] in, Indicates the time window used for evaluation; Indicates time window Every moment; Indicates time The corresponding electricity purchase price; , Indicates time Purchase and sale power; This indicates the cost price of purchasing gas; Indicates the gas turbine at time The power; Indicates the time window for evaluation Penalty coefficient for internal system power imbalance; Indicates the time window for evaluation Unbalanced power within the system; Indicates the time window for evaluation The algebraic sum of the absolute values ​​of the unbalanced electrical quantities within the system; Indicates in The combined cost of operation and unbalanced power generation is considered within the time window.

[0064] 2) Value function calculation

[0065]

[0066] in, This indicates that the minimum has been obtained. The value; The scaling factor is used to adjust the result to a suitable order of magnitude.

[0067] As a preferred embodiment of the dynamic optimization method for identifying key planning decision points in an integrated energy system according to the present invention, step S3 is specifically analyzed, wherein:

[0068] Step S3 involves constructing a rolling time-domain optimization model for the integrated energy system and proposing a method for identifying key decision points within the planning period, specifically including:

[0069] S3.1. Through rolling optimization iteration, the system's operation throughout the year is simulated, and the current decision value function is calculated for each rolling step, forming a sequence of value functions;

[0070] S3.2 Based on the sequence of value functions obtained in S3.1, the value curves are iterated in reverse order from back to front to construct a continuous value curve that reflects long-term accumulated value within the long planning period.

[0071] S3.3 Automatically find the peak value on the final value curve to determine the key decision point and realize the identification and output of the key decision point.

[0072] Step S3.1 involves forming a value function sequence through rolling optimization iterations, specifically including:

[0073] 1) Initialization of rolling optimization iteration

[0074] The process begins at the first point in time. At this point, the system solves the joint optimization model for integrated energy system planning and operation based on step S1 to determine the initial baseline configuration of the system.

[0075]

[0076] in, This indicates the starting point of the rolling optimization; Indicates in Time optimization achieved The set of optimal decision quantities with minimum value.

[0077] Based on the value function calculation, the first time point is calculated. The decision-making value.

[0078]

[0079] in, Indicates the first time point The decision-making value.

[0080] 2) Rolling Iteration

[0081] For each subsequent rolling time point Repeat the solution process for the following sub-models. During the rolling iteration, it is necessary to set state update equations for the time-series variables; in this model, this specifically refers to the initial energy storage capacity. .

[0082]

[0083]

[0084]

[0085] in, This indicates the starting point and start time of subsequent rolling optimizations. difference k indivual S The time interval, S The sliding time window length, referred to as rolling optimization; initial energy storage capacity. express The initial energy storage capacity at any given time; Indicates in Time optimization achieved The set of optimal decision quantities for minimizing the value; express Initial energy storage capacity at any given time equal The optimized energy storage capacity at all times value , W The time window length is called the single-roll optimization; then it is determined by... The set of decision quantities optimized at each time step calculate The value of decision-making at any moment .

[0086] 3) Output of the value function sequence

[0087] After the rolling loop iterates through all the time points of the full cycle planning, the final output is a sparse sequence of state-value function points:

[0088]

[0089] Step S3.2 Constructs a value curve that is continuous over a long planning period and reflects long-term cumulative value, specifically including:

[0090] 1) Construction of continuous value curve interpolation

[0091] By connecting discrete value points, a continuous value curve is formed, defined for each hour within the entire planning cycle.

[0092]

[0093] in, This indicates that a continuous value function curve is formed after linear interpolation.

[0094] 2) Reverse iteration of the value curve

[0095] Based on the Bellman equation in dynamic programming, the total value at a given moment depends not only on the present but also on all possible future values. The value function, after reverse iteration, should satisfy the following formula.

[0096]

[0097]

[0098] in, The value functions at the critical point T of the planning cycle should be equal; This represents the immediate planning and decision-making value at time t. It is the future value discount factor, which represents the coefficient by which future value is discounted to the present moment; It represents the present value of the sum of all values ​​from time t+1 up to the future; It represents the cumulative value function of the potential of the system planning scheme from now until the future.

[0099] Step S3.3 Identification and output of key decision points, specifically including:

[0100] The goal is to select a set of time points from the value function curve using rigorous mathematical conditions. Each element in the set They are all defined as a key decision point.

[0101] 1) Local optimality condition

[0102] This condition ensures that the selected... Its value is higher than that of its two adjacent points to the left and right, and it is the optimal value within a local range.

[0103]

[0104] in, Indicates key decision points The value of a moment; It represents the logical AND.

[0105] 2) Significance condition

[0106] This condition ensures that the value function of the selected key decision points must be large enough to filter out insignificant minor fluctuations and guarantee that the identified decision points have significant value.

[0107]

[0108]

[0109] in, Indicates the minimum peak height threshold; It refers to the percentile threshold, meaning the minimum and peak values ​​should not exceed the percentile of the value curve. % It is an indicator function that takes the value 1 when the condition is true and 0 otherwise. This represents the minimum value that satisfies the condition, i.e., the infimum. This represents the minimum value selected after meeting the conditions.

[0110] 3) Sparsity condition

[0111] This condition ensures that there is a sufficient time interval between any two selected key decision points, avoiding excessive concentration of decision points and making multi-stage dynamic programming more practical.

[0112]

[0113] in, , These represent the selected number. i The, the j One decision point; Indicates the minimum time interval; This represents the set of key decision points.

[0114] As a preferred embodiment of the dynamic optimization method for identifying key planning decision points in an integrated energy system according to the present invention, step S4 is specifically analyzed, wherein:

[0115] Step S4 proposes a multi-stage dynamic planning scheme for the integrated energy system based on a small number of high-planning-value decision points within a long planning period. Specifically, this includes:

[0116] 1) Data Input

[0117] Based on the above step S3.3, obtain the set of key decision points. Minimum planned capacity of each device in the initial stage of initialization

[0118]

[0119] in, This represents the initial minimum planning capacity set; These represent the minimum planned capacity for energy storage, photovoltaic power, wind power, and gas turbines, respectively.

[0120] 2) Objective function

[0121]

[0122] in, , These represent the annualized investment cost and operating cost calculated within the planning window of the current stage k, respectively.

[0123] 3) Incremental programming constraints

[0124] Current stage k The planned capacity of each piece of equipment must be greater than or equal to that of the previous phase. k -1 represents the already determined optimal capacity.

[0125]

[0126] in, Indicates the first k Planning capacity values ​​within each planning phase express k The optimal planning value within the -1 stage.

[0127] Furthermore, the present invention also provides a computer device, including: a memory and a processor; the memory stores a computer program, and the processor executes the computer program to implement the steps of the above-described method.

[0128] Furthermore, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the method described.

[0129] The beneficial effects of this invention are as follows:

[0130] This invention establishes a joint optimization model for planning and operation, taking into account equipment operational constraints, based on the physical structure of an integrated energy system. Using a defined equipment capacity scheme as input parameters and the operational status over a relatively long operating period as an evaluation, it calculates and outputs the value of the current planning scheme, forming a value function model for planning decisions. A rolling time-domain optimization model for the integrated energy system is constructed, with the system continuously calling the value function model to calculate the value under the current state. A continuous value curve is obtained through linear interpolation and inverse recursion. Key planning decision points are identified based on a peak identification algorithm. Based on a small number of key decision points within a long planning period, and using these identified key decision points as decision stages, a non-decreasing incremental planning approach transforms a complex one-time investment problem into a multi-stage dynamic planning scheme for the integrated energy system. Attached Figure Description

[0131] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0132] Figure 1 This is an overall flowchart of a dynamic optimization method for identifying key planning decision points in an integrated energy system, according to Embodiment 1 of the present invention.

[0133] Figure 2 This is a schematic diagram of the value function curve and key decision points in Embodiment 2 of the present invention;

[0134] Figure 3 This is a diagram illustrating the evolution of the planning scheme in Embodiment 2 of the present invention;

[0135] Figure 4 This is a graph showing the change in energy storage capacity during the last scheduling cycle of the time-series rolling process in Embodiment 2 of the present invention.

[0136] Figure 5 This is a power balance analysis diagram for the last scheduling cycle of the timing rollout in Embodiment 2 of the present invention;

[0137] Figure 6 This is a distribution chart of annualized investment costs for Embodiment 2 of the present invention; Detailed Implementation

[0138] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0139] Example 1

[0140] Reference Figure 1 This is the first embodiment of the present invention, which provides a dynamic optimization method for identifying key planning decision points in an integrated energy system, comprising:

[0141] Step S1: Based on the energy supply structure and supply and demand equipment of the integrated energy system, construct an optimized operation model for the integrated energy system;

[0142] Step S2: Consider the operational status of a specific planning decision over a longer period of time to evaluate the value of the decision and construct a planning value function model for the integrated energy system;

[0143] Step S3: Construct a rolling time-domain optimization model for the integrated energy system and propose a method for identifying key decision points within the planning period;

[0144] Step S4: Based on a small number of high-planning-value decision points within a long planning period, propose a multi-stage dynamic planning scheme for the integrated energy system based on key decision points.

[0145] As a preferred embodiment of the dynamic optimization method for identifying key planning decision points in an integrated energy system according to the present invention, step S1 is analyzed, wherein:

[0146] Based on the energy supply structure and supply and demand equipment of the integrated energy system, an optimized operation model of the integrated energy system is constructed, characterized by:

[0147] 1) Objective function

[0148] The optimization objective is to minimize the total cost of the system. Its annualized investment cost and cycle operating costs constitute.

[0149]

[0150] Annualized investment cost Determined by the capital recovery factor, it is the sum of the annualized investments of all equipment, satisfying the following formula:

[0151]

[0152] in, This indicates that the equipment belongs to the photovoltaic category. Wind power Energy storage ,gas turbine A set; For equipment The capacity; The unit investment cost of the equipment; The expected lifespan of the equipment; is the discount rate.

[0153] Cycle operating costs The total cost of electricity purchase, fuel, and operation and maintenance during the dispatch cycle is expressed by the following formula:

[0154]

[0155] in, , , These represent the electricity purchase and sales cost, gas purchase cost, and energy storage operation cost coefficients, respectively. , , , , These represent the integrated energy system's power purchase from the grid, power sales from the grid, power generation from the gas-fired power generation unit, charging power from the energy storage unit, and discharging power from the energy storage unit, respectively. T Indicates the total runtime period.

[0156] 2) Real-time power balance constraints

[0157] At every moment t The total power generation of the system must equal the total power consumption, and the system should satisfy the following constraints:

[0158]

[0159] in, Indicates time t User load.

[0160] 3) Renewable energy output constraints

[0161]

[0162]

[0163] in, , These represent the uncertainty coefficients for photovoltaic power output and wind power output, respectively. , They represent tThe expected power generation of photovoltaic and wind power at any given time; , These represent the upper limits of installed capacity for photovoltaic and wind power, respectively; , These represent the power generation of photovoltaic and wind power at time t, respectively.

[0164] 4) Load response constraints

[0165]

[0166] in, The uncertainty factor representing the load; This represents the expected load at time t; This represents the load at time t.

[0167] 5) Output constraints of micro gas turbines

[0168]

[0169] in, express t The output power of the gas turbine at any given time; This indicates the upper limit of the gas turbine's output.

[0170] 6) Constraints of energy storage systems

[0171]

[0172] in, , This represents the state-of-charge capacity of the stored energy at the current time t and the time t-1 before. This represents the energy storage charging power at time t; This represents the energy storage discharge power at time t; , These represent the charge and discharge efficiencies, respectively.

[0173]

[0174] in, , These represent the minimum and maximum state-of-charge coefficients for energy storage, respectively. This indicates the upper limit of the energy storage state-of-charge capacity.

[0175]

[0176]

[0177] in, This represents the charge / discharge identifier at time t, where 0 indicates no charge / discharge and 1 indicates charge / discharge. This indicates the upper limit of the maximum charging and discharging power.

[0178]

[0179] Energy storage systems are expected to meet periodic power balance constraints during long-term operation.

[0180] 7) Interaction constraints between integrated energy system and power grid

[0181]

[0182]

[0183] in, , These represent the power purchased and sold at time t, respectively. This represents the electricity sales identifier at time t, where 0 indicates no electricity sales and 1 indicates electricity sales. This indicates the upper limit of the power that can be interacted with the power grid.

[0184]

[0185] in, , These represent the planned capacity and minimum planned capacity of device i, respectively.

[0186] As a preferred embodiment of the dynamic optimization method for identifying key planning decision points in an integrated energy system according to the present invention, step S2 is specifically analyzed, wherein:

[0187] Step S2 considers the operational status of a specific planning decision over a longer period to evaluate the value of the decision and constructs a planning value function model for the integrated energy system, specifically including:

[0188] 1) Functional model of the value assessment module

[0189]

[0190]

[0191] in, The value function represents the planning scheme, and the relative magnitude of its value indicates the applicability of the planning scheme. It is a functional relationship that takes the planning scheme value as input and the value function value as output; This represents the input set consisting of the planning scheme and external operating parameters; These represent the input sets containing the upper limits of planned energy storage capacity, planned photovoltaic power, planned wind power, and planned gas turbine output, respectively.

[0192] function The calculation results depend on a short-running optimization problem solved internally. We define the decision variables and objective function of this internal problem using the following formulas.

[0193]

[0194] in, Indicates the time window used for evaluation; Indicates time window Every moment; Indicates time The corresponding electricity purchase price; , Indicates time Purchase and sale power; This indicates the cost price of purchasing gas; Indicates the gas turbine at time The power; Indicates the time window for evaluation Penalty coefficient for internal system power imbalance; Indicates the time window for evaluation Unbalanced power within the system; Indicates the time window for evaluation The algebraic sum of the absolute values ​​of the unbalanced electrical quantities within the system; Indicates in The combined cost of operation and unbalanced power generation is considered within the time window.

[0195] 2) Value function calculation

[0196]

[0197] in, This indicates that the minimum has been obtained. The value; The scaling factor is used to adjust the result to a suitable order of magnitude.

[0198] As a preferred embodiment of the dynamic optimization method for identifying key planning decision points in an integrated energy system according to the present invention, step S3 is specifically analyzed, wherein:

[0199] Step S3 involves constructing a rolling time-domain optimization model for the integrated energy system and proposing a method for identifying key decision points within the planning period, specifically including:

[0200] S3.1. Through rolling optimization iteration, the system's operation throughout the year is simulated, and the current decision value function is calculated for each rolling step, forming a sequence of value functions;

[0201] S3.2 Based on the sequence of value functions obtained in S3.1, the value curves are iterated in reverse order from back to front to construct a continuous value curve that reflects long-term accumulated value within the long planning period.

[0202] S3.3 Automatically find the peak value on the final value curve to determine the key decision point and realize the identification and output of the key decision point.

[0203] Step S3.1 involves forming a value function sequence through rolling optimization iterations, specifically including:

[0204] 1) Initialization of rolling optimization iteration

[0205] The process begins at the first point in time. At this point, the system solves the joint optimization model for integrated energy system planning and operation based on step S1 to determine the initial baseline configuration of the system.

[0206]

[0207] in, This indicates the starting point of the rolling optimization; Indicates in Time optimization achieved The set of optimal decision quantities with minimum value.

[0208] Based on the value function calculation, the first time point is calculated. The decision-making value.

[0209]

[0210] in, Indicates the first time point The decision-making value.

[0211] 2) Rolling Iteration

[0212] For each subsequent rolling time point Repeat the solution process for the following sub-models. During the rolling iteration, it is necessary to set state update equations for the time-series variables; in this model, this specifically refers to the initial energy storage capacity. .

[0213]

[0214]

[0215]

[0216] in, This indicates the starting point and start time of subsequent rolling optimizations. difference k indivualS The time interval, S The sliding time window length, referred to as rolling optimization; initial energy storage capacity. express The initial energy storage capacity at any given time; Indicates in Time optimization achieved The set of optimal decision quantities for minimizing the value; express Initial energy storage capacity at any given time equal The optimized energy storage capacity at all times value , W The time window length is called the single-roll optimization; then it is determined by... The set of decision quantities optimized at each time step calculate The value of decision-making at any moment .

[0217] 3) Output of the value function sequence

[0218] After the rolling loop iterates through all the time points of the full cycle planning, the final output is a sparse sequence of state-value function points:

[0219]

[0220] Step S3.2 Constructs a value curve that is continuous over a long planning period and reflects long-term cumulative value, specifically including:

[0221] 1) Construction of continuous value curve interpolation

[0222] By connecting discrete value points, a continuous value curve is formed, defined for each hour within the entire planning cycle.

[0223]

[0224] in, This indicates that a continuous value function curve is formed after linear interpolation.

[0225] 2) Reverse iteration of the value curve

[0226] Based on the Bellman equation in dynamic programming, the total value at a given moment depends not only on the present but also on all possible future values. The value function, after reverse iteration, should satisfy the following formula.

[0227]

[0228]

[0229] in, The value functions at the critical point T of the planning cycle should be equal; This represents the immediate planning and decision-making value at time t. It is the future value discount factor, which represents the coefficient by which future value is discounted to the present moment; It represents the present value of the sum of all values ​​from time t+1 up to the future; It represents the cumulative value function of the potential of the system planning scheme from now until the future.

[0230] Step S3.3 Identification and output of key decision points, specifically including:

[0231] The goal is to select a set of time points from the value function curve using rigorous mathematical conditions. Each element in the set They are all defined as a key decision point.

[0232] 1) Local optimality condition

[0233] This condition ensures that the selected... Its value is higher than that of its two adjacent points to the left and right, and it is the optimal value within a local range.

[0234]

[0235] in, Indicates key decision points The value of a moment; It represents the logical AND.

[0236] 2) Significance condition

[0237] This condition ensures that the value function of the selected key decision points must be large enough to filter out insignificant minor fluctuations and guarantee that the identified decision points have significant value.

[0238]

[0239]

[0240] in, Indicates the minimum peak height threshold; It refers to the percentile threshold, meaning the minimum and peak values ​​should not exceed the percentile of the value curve. % It is an indicator function that takes the value 1 when the condition is true and 0 otherwise. This represents the minimum value that satisfies the condition, i.e., the infimum. This represents the minimum value selected after meeting the conditions.

[0241] 3) Sparsity condition

[0242] This condition ensures that there is a sufficient time interval between any two selected key decision points, avoiding excessive concentration of decision points and making multi-stage dynamic programming more practical.

[0243]

[0244] in, , These represent the selected number. i The, the j One decision point; Indicates the minimum time interval; This represents the set of key decision points.

[0245] As a preferred embodiment of the dynamic optimization method for identifying key planning decision points in an integrated energy system according to the present invention, step S4 is specifically analyzed, wherein:

[0246] Step S4 proposes a multi-stage dynamic planning scheme for the integrated energy system based on a small number of high-planning-value decision points within a long planning period. Specifically, this includes:

[0247] 1) Data Input

[0248] Based on the above step S3.3, obtain the set of key decision points. Minimum planned capacity of each device in the initial stage of initialization

[0249]

[0250] in, This represents the initial minimum planning capacity set; These represent the minimum planned capacity for energy storage, photovoltaic power, wind power, and gas turbines, respectively.

[0251] 2) Objective function

[0252]

[0253] in, , These represent the annualized investment cost and operating cost calculated within the planning window of the current stage k, respectively.

[0254] 3) Incremental programming constraints

[0255] Current stage k The planned capacity of each piece of equipment must be greater than or equal to that of the previous phase. k -1 represents the already determined optimal capacity.

[0256]

[0257] in, Indicates the first k Planning capacity values ​​within each planning phase express k The optimal planning value within the -1 stage.

[0258] Example 2

[0259] Reference Figure 2-6 As an embodiment of the present invention, a dynamic optimization method for identifying key planning decision points of an integrated energy system is provided. To verify the beneficial effects of the present invention, a comparative experiment is conducted for scientific demonstration.

[0260] The example demonstrates the planning of an integrated energy system for an industrial park, with the window width used for rolling optimization. W Set to 120 hours, rolling step S Set to 96 hours, the value function evaluation window is 2. W That is, 240 hours. Future value discount factor. γ Set to 0.1. Parameters such as equipment investment and operation and maintenance costs are all set in the model, as shown in Table 1.

[0261] Table 1. Park Equipment and Planned Operation Parameters

[0262] Table 1. Park equipment parameters

[0263]

[0264] First, the system's operation throughout the year is simulated using the S1-S3 process, generating an enhanced value curve that reflects long-term accumulated value. V ( t Then, using a peak identification algorithm, key decision points (KDPs) are automatically selected. The value function curve and key decision points are shown below. Figure 2 As shown.

[0265] Table 2 Key Decision Points and Value Functions

[0266] Table 2. Key decision points and value functions

[0267]

[0268] KDPs represent the peak values ​​of the system's "value function." A high value at a given point indicates the most acute supply-demand imbalance, the greatest operating cost pressure, or the most significant potential economic opportunities, making it a suitable time for planning. Based on the results in Table 2, the following analysis can be made:

[0269] The 865-hour period falls at the end of winter on a yearly timescale, one of the coldest periods of the year. Short days and weak sunlight result in photovoltaic output at its lowest point of the year, while winter heating demand keeps the total system load high. Under these extreme conditions, the system must rely heavily on expensive gas turbine power generation or purchase peak / off-peak electricity from the grid, causing operating costs to soar.

[0270] The periods 1537 and 1921 fall within a typical seasonal transition period, characterized by dramatic fluctuations in supply and demand. During periods of low load but abundant wind and solar power, the system faces the risk of significant wind and solar curtailment; conversely, during periods of sudden load increases but sharp drops in wind and solar power, it faces high reserve costs. The value function peaks at this point, indicating that the system has the highest potential benefit from configuring energy storage to mitigate fluctuations and perform energy time-shifting. This is a critical period for determining the power and capacity ratio of the energy storage system to cope with high-frequency fluctuations.

[0271] At 3649 hours, in early summer, cooling load begins to appear and gradually becomes dominant. Sunlight resources are abundant, and photovoltaic (PV) output enters its peak period. A seasonal shift occurs in the supply and demand structure, and the value function peaks here, assessing whether existing energy storage capacity is sufficient to transfer surplus daytime PV power to the new evening peak.

[0272] The 4897th hour falls during the height of summer, the hottest period of the year, when cooling loads peak and peak-valley electricity prices are most significant. During the day, solar power output is strongest, and off-peak electricity prices are lowest, making it the golden time for energy storage charging. In the evening, electricity load is highest, and peak-valley prices are most expensive, presenting the biggest window for profit from energy storage discharge. During the evening, the system faces its largest power shortage of the year, reaching its limit in its reliance on gas turbines, energy storage, and grid power purchases. This point in time represents the extreme balance between annual economic benefits and power supply costs. The peak of the value function typically occurs here, as it represents the maximum potential return from investing in an energy storage system.

[0273] At 6433 hours, which falls between summer and autumn, temperatures cool, cooling loads drop rapidly, and sunlight intensity and duration begin to weaken. During this shift in supply and demand, the value function peaks again, representing a "reverse evaluation"—a weighing of whether the large-capacity equipment invested in to capitalize on the summer peak will become an economic burden during the "off-season" of autumn. Decisions made here signify that the model must balance pursuing peak returns with ensuring average annual economic viability, avoiding over-investment.

[0274] Figure 3 shows the incremental changes in capacity after planning at the aforementioned KDPs. The capacity evolution of each device in this example demonstrates that in the initial planning stage, a certain scale of new energy output, such as wind and solar power, can be configured to fill the energy gap within the industrial park and reduce electricity purchase costs. As the capacity of new energy configuration continues to increase, the system's energy supply side gradually faces pressure to absorb the increased output due to the uncertainty of new energy sources. Therefore, subsequent planning needs to gradually increase energy storage configuration to enhance the system's absorption capacity. Simultaneously, the operation and scheduling of energy storage should be used to smooth out output and load fluctuations, and peak-valley arbitrage should be utilized to further reduce system operating costs.

[0275] Figure 4 , Figure 5 The changes in energy storage capacity and the system's power supply and demand balance within the final planning window are displayed, intuitively presenting the system's operational characteristics after the final implementation of this plan. The system purchases electricity from the grid during off-peak periods and sells electricity to the grid during peak periods to achieve peak-valley arbitrage. Simultaneously, energy storage is used for charging during peak photovoltaic output periods to absorb excess electricity, and then discharges during subsequent peak load periods to supply electricity to the load. Its capacity exhibits periodic fluctuations in accordance with electricity prices and changes in renewable energy output. Figure 6 The final overall plan's annualized investment cost breakdown is shown: photovoltaic and wind power investments account for 2.7% and 3.5% respectively, gas turbine investment accounts for 13.1%, and energy storage investment accounts for a high 80.7%, with a total investment of 6,721,730 yuan. The final planned scheme includes: energy storage capacity of 4,631 kWh, energy storage power of 972 kW, photovoltaic capacity of 2,540 kWh, wind power capacity of 942 kWh, and gas turbine capacity of 529 kWh.

[0276] Given that the energy consumption scale of the integrated energy system of the industrial park set in this example is relatively small, the investment scale of wind power and photovoltaic power is correspondingly small. The system mainly reduces subsequent operating costs by increasing investment in energy storage.

[0277] This invention is beneficial for improving the scientific nature of investment decisions in integrated energy systems, enhancing the economic efficiency and engineering feasibility of long-term planning schemes, and promoting the efficient absorption and utilization of renewable energy. It is significant in promoting the scientific planning and sustainable development of complex energy systems. The invention proposes a dynamic optimization method for identifying key planning decision points in integrated energy systems. By constructing an economic value function spanning the entire year, it identifies the key planning decision points that have the most significant impact on the system's overall planning cycle cost, generating a phased investment path that combines economic optimization with engineering feasibility.

[0278] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0279] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example, but not limited to, electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination thereof. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0280] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0281] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0282] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A dynamic optimization method for identifying key planning decision points in an integrated energy system, characterized in that, Includes the following steps: Step S1: Based on the energy supply structure and supply and demand equipment of the integrated energy system, construct an optimized operation model for the integrated energy system; Step S2: Consider the operational status of the planning decision over a longer period of time to evaluate the value of the decision and construct a planning value function model for the integrated energy system; Step S3: Construct a rolling time-domain optimization model for the integrated energy system and propose a method for identifying key decision points within the planning period; Step S4: Based on a small number of high-planning-value decision points within a long planning period, propose a multi-stage dynamic planning scheme for the integrated energy system based on key decision points; In step S2, the value of the planning decision is evaluated by considering its operation over a longer period of time. The planning value function model of the integrated energy system is constructed as follows: 1) Functional model of the value assessment module in, This represents the value function of a planning scheme, and the relative magnitude of its value indicates the applicability of the planning scheme. It is a functional relationship that takes the planning scheme value as input and the value function value as output; This represents the input set consisting of the planning scheme and external operating parameters; These represent the input sets containing the upper limits of planned energy storage capacity, planned photovoltaic power, planned wind power, and planned gas turbine output, respectively. function The calculation results depend on a short-running optimization problem solved internally, whose decision variables and objective function are defined by the following formulas: in, Indicates the time window used for evaluation; Indicates time window Every moment; Indicates time The corresponding electricity purchase price; , Indicates time Purchase and sale power; This indicates the cost price of purchasing gas; Indicates the gas turbine at time The power; Indicates the time window for evaluation Penalty coefficient for internal system power imbalance; Indicates the time window for evaluation Internal system imbalance power; Indicates the time window for evaluation The algebraic sum of the absolute values ​​of the unbalanced electrical quantities within the system; Indicates in The combined cost of operation and unbalanced power generation is considered within the time window; 2) Value function calculation in, This indicates that the minimum has been obtained. The value; The scaling factor is used to adjust the result to a suitable order of magnitude. The steps in step S3 for constructing a rolling time-domain optimization model for the integrated energy system and proposing a method for identifying key decision points within the planning period are as follows: S3.

1. Through rolling optimization iteration, the system's operation throughout the year is simulated, and the current decision value function is calculated for each rolling step, forming a sequence of value functions; S3.2 Based on the sequence of value functions obtained in S3.1, the value curves are iterated in reverse order from back to front to construct a continuous value curve that reflects long-term accumulated value within the long planning period. S3.3 Automatically find the peak value on the final value curve to determine the key decision point and realize the identification and output of the key decision point.

2. The dynamic optimization method for identifying key planning decision points in an integrated energy system according to claim 1, characterized in that, In step S1, based on the energy supply structure and supply and demand equipment of the integrated energy system, the optimized operation model of the integrated energy system is constructed as follows: 1) Objective function The optimization objective is to minimize the total cost of the system. Annualized investment cost and cycle operating costs constitute: Annualized investment cost Determined by the capital recovery factor, it is the sum of the annualized investments in all equipment, satisfying the following formula: in, This indicates that the equipment belongs to the photovoltaic category. Wind power Energy storage ,gas turbine A set; For equipment The capacity; The unit investment cost of the equipment; The expected lifespan of the equipment; The discount rate; Cycle operating costs The total cost of electricity purchase, fuel, and operation and maintenance during the dispatch cycle is expressed by the following formula: in, , , These represent the electricity purchase and sales cost, gas purchase cost, and energy storage operation cost coefficients, respectively. , , , , These represent the integrated energy system's power purchase from the grid, power sales from the grid, power generation from the gas-fired power generation unit, charging power from the energy storage unit, and discharging power from the energy storage unit, respectively. T Indicates the total runtime period; 2) Real-time power balance constraints At every moment t The total power generation of the system must equal the total power consumption, and the system should satisfy the following constraints: in, Indicates time t User load; 3) Renewable energy output constraints in, , These represent the uncertainty coefficients for photovoltaic power output and wind power output, respectively. , They represent t The expected power generation of photovoltaic and wind power at any given time; , These represent the upper limits of installed capacity for photovoltaic and wind power, respectively. , Let represent the power generation of photovoltaic and wind power at time t, respectively; 4) Load response constraints in, The uncertainty factor representing the load; This represents the expected load at time t; This represents the load at time t; 5) Output constraints of micro gas turbines in, express t The output power of the gas turbine at any given time; Indicates the upper limit of gas turbine output; 6) Constraints of energy storage systems in, , This represents the state-of-charge capacity of the stored energy at the current time t and the time t-1 before. This represents the energy storage charging power at time t; This represents the energy storage discharge power at time t; , These represent the charge and discharge efficiencies, respectively. in, , These represent the minimum and maximum state-of-charge coefficients for energy storage, respectively. Indicates the upper limit of the energy storage state-of-charge capacity; in, This represents the charge / discharge identifier at time t, where 0 indicates no charge / discharge and 1 indicates charge / discharge. Indicates the upper limit of maximum charging and discharging power; Energy storage systems are expected to meet periodic power balance constraints during long-term operation. 7) Interaction constraints between integrated energy system and power grid in, , These represent the power purchased and sold at time t, respectively. This represents the electricity sales identifier at time t, where 0 indicates no electricity sales and 1 indicates electricity sales. Indicates the upper limit of power interaction with the power grid; in, , These represent the planned capacity and minimum planned capacity of device i, respectively.

3. The dynamic optimization method for identifying key planning decision points in an integrated energy system according to claim 2, characterized in that, Step S3.1, which generates a value function sequence through rolling optimization iteration, specifically includes: 1) Initialization of rolling optimization iteration The process begins at the first point in time. At this point, the system solves the joint optimization model for integrated energy system planning and operation based on step S1 to determine the initial baseline configuration of the system: in, This indicates the starting point of the rolling optimization; Indicates in Time optimization achieved The set of optimal decision quantities for minimizing the value; Based on the value function calculation, the first time point is calculated. Decision value: in, Indicates the first time point The decision-making value; 2) Rolling Iteration For each subsequent rolling time point Repeat the solution of the following sub-models. During the rolling iteration process, it is necessary to set state update equations for the time series variables. In this model, the initial energy storage capacity is referred to as the initial energy storage capacity. : in, This indicates the starting point and start time of subsequent rolling optimizations. difference k indivual S The time interval, S The sliding time window length, referred to as rolling optimization; initial energy storage capacity. express The initial energy storage capacity at any given time; Indicates in Time optimization achieved The set of optimal decision quantities for minimizing the value; express Initial energy storage capacity at any given time equal The optimized energy storage capacity at all times value , W The time window length is called the single-roll optimization; then it is determined by... The set of decision quantities optimized at each time step calculate The value of decision-making at any moment ; 3) Output of the value function sequence After the rolling loop iterates through all the time points of the full cycle planning, the final output is a sparse sequence of state-value function points: 。 4. The dynamic optimization method for identifying key planning decision points in an integrated energy system according to claim 3, characterized in that, Step S3.2, which involves constructing a continuous value curve that reflects long-term cumulative value over a long planning period, specifically includes: 1) Construction of continuous value curve interpolation Connecting the discrete value points forms a continuous value curve defined for each hour throughout the entire planning period: in, This indicates the formation of a continuous value function curve after linear interpolation. 2) Reverse iteration of the value curve The value function, after reverse iteration, satisfies the following formula: in, The value functions at the critical point T of the planning cycle should be equal; This represents the immediate planning and decision-making value at time t. It is the future value discount factor, which represents the coefficient by which future value is discounted to the present moment; It represents the present value of the sum of all values ​​from time t+1 up to the future; It represents the cumulative value function of the potential of the system planning scheme from now until the future.

5. The dynamic optimization method for identifying key planning decision points in an integrated energy system according to claim 4, characterized in that, The identification and output of key decision points in step S3.3 specifically includes: The goal is to select a set of time points from the value function curve using rigorous mathematical conditions. Each element in the set Both are defined as a key decision point; 1) Local optimality condition in, Indicates key decision points The value of a moment; Represents the logical AND operator; 2) Significance condition in, Indicates the minimum peak height threshold; It refers to the percentile threshold, meaning the minimum and peak values ​​should not exceed the percentile of the value curve. % It is an indicator function that takes the value 1 when the condition is true and 0 otherwise. This represents the minimum value that satisfies the condition, i.e., the infimum. This represents the minimum value selected after meeting the conditions. 3) Sparsity condition in, , These represent the selected number. i The, the j One decision point; Indicates the minimum time interval; This represents the set of key decision points.

6. The dynamic optimization method for identifying key planning decision points in an integrated energy system according to claim 5, characterized in that, Step S4 proposes a multi-stage dynamic planning scheme for the integrated energy system based on a small number of high-planning-value decision points within a long planning period, specifically including: 1) Data Input Based on the above step S3.3, obtain the set of key decision points. Minimum planned capacity of each device in the initial stage of initialization in, This represents the initial minimum planning capacity set; These represent the minimum planned capacities for energy storage, photovoltaic power, wind power, and gas turbines, respectively. 2) Objective function in, , These represent the annualized investment cost and operating cost calculated within the planning window of the current stage k, respectively. 3) Incremental programming constraints Current stage k The planned capacity of each piece of equipment is greater than or equal to that of the previous phase. k -1 is the already determined optimal capacity: in, Indicates the first k Planning capacity values ​​within each planning phase express k The optimal planning value within the -1 stage.

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