Feasible region evaluation method for mine virtual power plant under incomplete information

Abstract

The feasible region assessment (FRA) in industrial virtual power plants (VPPs) is driven by the demand for large-scale industrial load activation, which promotes the aggregation of flexible resources to cope with peak load regulation. However, in mine production lines, the large number of equipment and the need for privacy protection make the aggregation of differentiated resources challenging. The present invention discloses a feasible region assessment method for mine virtual power plants under incomplete information to solve the FRA problem of coal mine VPPs under incomplete information conditions. The data-driven inverse optimization feasible region estimation algorithm approximates equipment and FRA parameters based on historical energy scheduling data, effectively copes with the problem of incomplete information, and solves the imperfect information caused by unknown parameters and data privacy in mines. The tips of this article are summarized as follows. Section 2 briefly introduces the feasible region estimation problem of coal mine VPP.

Description

Technical Field

[0001] The present invention belongs to the technical field of energy scheduling, and specifically provides a feasible domain evaluation method for a mine virtual power plant under incomplete information. Background Art

[0002] The rise of renewable energy and the evolution of energy markets highlight the potential of virtual power plants (VPPs) for flexible energy management and trading. Unlike distributed energy resources, the industrial sector, with its significant conventional electricity demand, presents a significant opportunity for large-scale VPP aggregation. As China's primary energy-intensive industry, coal mining relies heavily on electricity to power its production processes, with annual electricity consumption reaching 95.1 billion kilowatts in 2022. Therefore, activating the potential flexibility resources within the Coal Mining Industry Energy System (CMIES) is crucial.

[0003] In this context, to enable VPPs to effectively participate in energy markets, it is necessary to establish accurate industrial energy system models to describe their energy consumption behavior and flexibility. Significant progress has been made in industrial energy system modeling. For example, the paper "A linear model of industrial production process for demand response" linearizes a complex nonlinear, nonconvex industrial demand response model and aggregates it into a virtual battery model, as proposed in the paper "Optimal virtual battery model for aggregating storage-like resources with network constraints." The paper "Aggregating additional flexibility from quick-start devices for multi-energy virtual power plants" proposes a multi-energy industrial park model that aggregates VPPs to participate in day-ahead energy and reserve markets, ensuring that all possible dispatch requests are met. Specifically for the coal mining industry, the paper "Two-stage robust stochastic scheduling for energy recovery in coal mine integrated energy systems" considers waste heat recovery in coal mines to improve operational economics. The paper "Distributionally robust energy-transportation coordination in coal mine integrated energy systems" integrates belt conveyors (BCs) and coal bunkers into demand response resources within an energy-transportation coordinated operation framework. In addition to economic costs, the paper "A multitask multiobjective operation optimization method for coalmine integrated energy system" uses a multitask, multiobjective algorithm to solve the CMIES multi-objective scheduling model. The paper "Blockchain-enabled carbon and energy trading for network-constrained coalmines with uncertainties" proposes a model for CMIES to participate in an integrated energy and carbon trading market, but treats coal mines as independent entities rather than aggregated VPPs. However, all of these models focus on coal mine energy scheduling, leaving significant gaps in the aggregation of CMIES flexibility.

[0004] Aggregation of flexibility has become a key research topic in the field of virtual public partnerships (VPPs). To effectively participate in energy markets, VPPs need to estimate a feasible region to define the boundaries of reliable management of aggregated resources. Existing methods, such as the convex hull approximation and the Minkowski sum estimation method, can address the FRA problem but still rely on complete information sharing among VPP participants, ignoring the practical need for privacy protection. The paper "Privacy-preserving feasibility assessment for p2p energy trading and storage integration" proposes a privacy-preserving FRA method for P2P trading of uncertain renewable energy generation. However, it relies on probability density functions, which are difficult to obtain through model-driven approaches. However, these methods have significant limitations when applied to CMIES due to incomplete information. The large number of devices and complex interactions between energy units in CMIES make it difficult to obtain complete parameters. This incomplete information makes it extremely challenging to aggregate coal mines into VPPs that can reliably participate in the market. Therefore, accurately determining the feasible region for CMIES aggregation remains an unresolved problem.

[0005] To overcome the incomplete information problem in FRA, data-driven methods have become an effective approach for estimating the feasible region of complex systems such as CMIES. Based on historical optimal scheduling data, the paper "Inverse optimization for the recovery of constraint parameters" proposes an inverse optimization method to infer the parameters and constraints that define the optimal operating state. The paper "Data-driven inverse optimization for modeling intertemporally responsive loads" combines a virtual battery model structure to propose an inverse optimization FRA algorithm based on the Newton method. The paper "Approximating energy-regulation feasible region of virtual power plants: a data-driven inverse optimization approach" develops a data-driven inverse optimization method to solve the VPP aggregation of electric vehicles. Despite progress in data-driven inverse optimization, existing methods struggle to cope with the unique complexity of CMIES (such as complex belt conveyor models, raw coal mining and transportation networks, and process coordination), and traditional methods still lack computational efficiency and accuracy under dynamic conditions. Summary of the Invention

[0006] In view of this, the purpose of the present invention is to provide a feasible region evaluation method for a mine virtual power plant under incomplete information, which is used to process the feasible region evaluation of a coal mine VPP under incomplete information conditions.

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

[0008] A feasible region assessment method for a mine virtual power plant under incomplete information includes the following steps:

[0009] Step 1: Define the feasible domain and subsystem model of the mine virtual power plant

[0010] The feasible region of the mine virtual power plant is defined as the subspace of energy scheduling variables, which represents the power exchange range with the distribution network operator and the belt conveyor load peak and valley regulation, denoted as Ω V :

[0011]

[0012] Where: Ω V represents the feasible region; Indicates that at all time intervals From Total power consumption of the indexed belt conveyor; represents the total power exchange between the coal mine VPP and the distribution network operator; and Ξ |I| are the decision variables and equipment external parameters of coal mine energy optimization scheduling; h(·) represents the set of all equality constraints; g(·) represents the set of all inequality constraints;

[0013] Since the parameter Ξ |I| Given the large number of unknown devices, it is not feasible to directly solve the NP-hard problem. Therefore, an approximate feasible region is estimated using historical data:

[0014]

[0015] in: Indicates that the parameter Ξ |I| The feasible region Ω obtained under unknown conditions is close to the real one V The agent feasible region; Represents parameter Ξ |I| Approximate value of For parameters Approximate value of represents the set of all equality constraints in the estimated feasible region; represents the set of all inequality constraints in the estimated feasible region;

[0016] Step 2: Constructing an energy-transportation coordinated coal mine optimization scheduling model

[0017] With the goal of minimizing the operating cost of coal mines, the objective function is constructed;

[0018] Based on the configuration of coal mine industrial energy system and coal transportation network, constraints are established according to coal transportation, energy units, belt conveyors, energy storage devices and energy balance; with the goal of minimizing coal mine operating costs, decision variables are used to determine the optimal operation mode. and Ξ |I| Reconstruct the constructed energy-transportation coordinated coal mine optimization scheduling model;

[0019] Step 3: Parameter identification based on inverse optimization

[0020] Based on historical data sets, the two-level optimization problem is converted into a single-level optimization problem through the KKT condition. With the goal of minimizing the loss function between the proxy region and the real region, a data-driven inverse optimization feasible region estimation model is constructed.

[0021] Step 4: Convert the data-driven inverse optimization feasible region estimation model into an inverse optimization problem, and use the learning-based FRA algorithm to optimize and solve the agent feasible region.

[0022] Furthermore, in step 2, with the goal of minimizing the coal mine operating cost, the objective function constructed is:

[0023]

[0024] Where: C Sys Represents the total cost of coal mine operation, including purchased electricity cost, fuel cost and operation and maintenance cost represents the time-varying price under energy transaction costs; represents the fuel cost coefficient for CHP power generation; Indicates the operating cost coefficient of photovoltaic power generation; Indicates the operating cost coefficient of wind turbine power generation; represents the operating cost coefficient of gas turbine power generation; represents the operating cost coefficient of the combined heat and power generation unit; It represents the operating cost coefficient of the ventilation oxidation thermal storage unit; Indicates the operating cost coefficient of the belt conveyor; represents the operating cost coefficient of pumped storage; The coefficient of the thermal storage tank operating cost coefficient is expressed as: Indicates the operating cost coefficient of the water source heat pump;

[0025] Indicates the power purchased from the distribution network operator; Indicates the power generation capacity of the cogeneration unit; Represents photovoltaic power generation power; Indicates the power generated by the wind turbine; Indicates the power generation capacity of the gas turbine; Indicates the power generation capacity of the wind-lack oxidation thermal storage unit; Represents the load power of the jth belt conveyor; N BC Indicates the number of belt conveyors; represents the pumped storage charging power; Indicates the discharge power of pumped storage; Indicates the heat storage power of the heat storage tank; Indicates the heat release power of the heat storage tank; Indicates the load power of the water source heat pump;

[0026] Furthermore, for coal transportation, the coal transportation network consists of coal working faces, belt conveyors, silos, and coal preparation plants; the coal transportation network is modeled as a graph:

[0027] G CTN ={σ L ,T N}

[0028] Where: L and T N represent coal transportation links and nodes respectively;

[0029] Node set T N Includes multiple hierarchical nodes, including the coal mining face supply node T CF , coal silo storage node T SS , transfer node T MS and coal preparation plant demand node T CPP , expressed as:

[0030] T N ={T CF ∪T SS ∪T MS ∪T CPP}

[0031] Each belt conveyor branch supports coal mass transfer as a flow between nodes at different levels, represented as:

[0032] σ L ={σ CF,SS ∪σ SS,MS ∪σ MS,CPP}

[0033] Where: CF,SS represents the link between the coal mining face node and the coal silo storage node; σ SS,MS represents the link between the coal silo storage node and the transfer node; σ MS,CPP Represents the link between the transfer node and the coal preparation plant demand node;

[0034] The coal flow flows from the coal mining face to the coal preparation plant, and the coal transportation network model is expressed as:

[0035]

[0036] in: are the coal quantity and coal feeding rate transported between the working face and the shaft respectively; and represent the minimum and maximum slope limits of coal mass transport, respectively; Indicates the maximum limit of coal quantity transported from the shaft silo to the main silo; is the coal demand in the coal preparation plant; since the coal flow only flows in one direction, l, m, n and p represent the coal transportation network nodes T CF 、T SS 、T MS and T CPP , the order is from coal mining face to coal preparation plant;

[0037] In order to describe the virtual energy storage characteristics in the coal transportation network, without considering the attenuation, the coal silo model is equivalent to the battery model, which is described as:

[0038]

[0039] in: represents the coal storage capacity of the kth coal bunker at time t; and They represent the amount of coal transported into and out of k silos at time t; M Silo,k and They represent the lower and upper limits of the coal storage capacity of the kth silo respectively; and They represent the coal storage capacity of the kth silo at time 1 and time 24 respectively; and Respectively represent the coal storage capacity limit value of the kth silo at the start time and the end time; N Silo Indicates the number of silos.

[0040] Furthermore, for the energy unit, the models of the exhaust air thermal storage oxidation unit, the cogeneration unit, the gas turbine unit and the water source heat pump are expressed as follows:

[0041]

[0042] X∈{RTO,CHP,GT,WSHP}

[0043] Of which: EHR X is the power generation to heat generation ratio of unit X; is the electric power of the wind-deficient thermal storage oxidation unit, cogeneration unit, gas turbine unit and water source heat pump at time t; is the thermal power of the wind-deficient thermal storage oxidation unit, cogeneration unit, gas turbine unit and water source heat pump at time t; h X 、 They are the lower and upper limits of thermal power for the wind-exhaust thermal storage oxidation unit, cogeneration unit, gas turbine unit and water source heat pump respectively.

[0044] Furthermore, for the belt conveyor, which transports the produced raw coal from the working face to the coal preparation plant by consuming electricity, the power consumption of the belt conveyor is represented by the general coal transportation model:

[0045]

[0046] in: Indicates the load electric power of the belt conveyor; cof BC Indicates the energy efficiency coefficient of the belt conveyor; V BC Indicates belt speed; represents the coal feeding rate of the belt conveyor; θ 2,j and θ 4,j They respectively represent the factory design parameters of the belt conveyor.

[0047] Furthermore, for energy storage devices, the pumped storage system established in the abandoned coal mine goaf provides a flexible option for storing and releasing electrical energy; the heat storage tank is used to reduce the peak heat load; the energy storage unit is represented as:

[0048]

[0049] in: and They represent the power storage capacity of pumped storage at time t+1 and time t respectively; E PHS and They represent the lower and upper limits of the electricity storage capacity of pumped storage, respectively; and Respectively represent the charging and discharging power of pumped storage; p PHSC 、 p PHSD and They represent the upper and lower limits of the charging and discharging power of pumped storage respectively; and They represent the electricity storage capacity of pumped storage at time 1 and 24 respectively; and are the power storage parameters of pumped storage at the start and end times respectively; γ PHS represents the attenuation coefficient of pumped storage power storage capacity; η PHS Indicates the charging and discharging efficiency of pumped storage;

[0050] and They represent the heat storage capacity of the heat storage tank at time t+1 and t respectively; E TST and They represent the lower and upper limits of the heat storage capacity of the heat storage tank respectively; and Respectively represent the charging and discharging power of the heat storage tank; h TSTC 、 h TSTD and Respectively represent the upper and lower limits of the charging and discharging heat power of the heat storage tank; and Respectively represent the heat storage capacity of the heat storage tank at time 1 and 24; and Represent the heat storage capacity parameters of the heat storage tank at the start and end time respectively; γ TST Represents the thermal storage capacity attenuation coefficient of the thermal storage tank; η TST Indicates the heat storage tank's charging and discharging efficiency;

[0051] Furthermore, for energy balance, the power and heat balance constraints of the coal mine are:

[0052]

[0053] in: Indicates the power purchased from the distribution network operator; Indicates the power generation capacity of the wind-lack oxidation thermal storage unit; Indicates the power generation capacity of the cogeneration unit; Indicates the power generation capacity of the gas turbine; Represents photovoltaic power generation power; Indicates the power generated by the wind turbine; Indicates the discharge power of pumped storage; represents the pumped storage charging power; Indicates the electrical load power; represents the load power of the j-th belt conveyor; Indicates the load power of the water source heat pump; is the thermal power of the wind-deficient thermal storage oxidation unit, cogeneration unit, gas turbine unit and water source heat pump at time t; and Respectively represent the charging and discharging power of the heat storage tank; Indicates heat load power; N BC Indicates the number of belt conveyors.

[0054] Furthermore, the reconstructed energy-transportation coordinated coal mine optimization scheduling model is:

[0055]

[0056] Where: p BC,j and They represent the lower and upper limits of the belt conveyor load power respectively; p g and Represent the lower and upper limits of the interaction power respectively; θ 2,j Indicates the factory design parameters of the belt conveyor; N BC Indicates the number of belt conveyors.

[0057] Furthermore, in step 3, the data-driven inverse optimization feasible region estimation model is expressed as:

[0058]

[0059] in: Indicates the historical data value of belt conveyor power; represents the historical data value of the power purchased by the power grid; μ represents the dual variable of the inequality constraint; μ T represents the transpose of the dual variable; represents the dual Lagrangian augmented function; λ represents the dual variable of the equality constraint; D is the historical data set, which is expressed as:

[0060]

[0061] in: Represents historical electricity price data.

[0062] Furthermore, the steps for optimizing the agent feasible region using the algorithm are as follows:

[0063] 31) Input iteration index ξ=1, penalty factor ρ, tolerance value ∈ and historical data set D; initialize

[0064] 32) Solve the inverse optimization feasible region estimation model;

[0065] 33) Determine whether If yes, then execute step 34); if no, then the iteration ends and the feasible region for the agent is obtained.

[0066] 34) Traverse |D| data samples starting from the current iteration number ξ and solve the inverse optimization problem to obtain represents the parameter value obtained in the ξth main iteration and the sth sub-iteration;

[0067] The inverse optimization problem is expressed as:

[0068]

[0069] in, represents the parameter estimation variable of the ξth iteration;

[0070] 35) Average the results of |D| sub-iterations and update the global parameters:

[0071]

[0072] 36) Let ξ = ξ + 1, and repeat step 32).

[0073] The beneficial effects of the present invention are:

[0074] The feasible region assessment (FRA) in industrial virtual power plants (VPPs) is driven by the demand for large-scale industrial load activation, which promotes the aggregation of flexible resources to cope with peak load regulation. However, in mine production lines, the large number of devices and the need for privacy protection make the aggregation of differentiated resources challenging. This paper proposes a feasible region assessment method for mine virtual power plants under incomplete information to solve the FRA problem of coal mine VPPs under incomplete information conditions. The data-driven inverse optimization feasible region estimation algorithm approximates equipment and FRA parameters based on historical energy scheduling data, effectively copes with the problem of incomplete information, and solves the imperfect information caused by unknown parameters and data privacy in mines. The tips of this article are summarized as follows. Section 2 briefly introduces the feasible region estimation problem of coal mine VPP. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] In order to make the purpose, technical solutions and beneficial effects of the present invention more clear, the present invention provides the following drawings for illustration:

[0076] Figure 1 This is a schematic diagram of the aggregation relationship of coal mine virtual power plants based on the coal mine industrial energy system;

[0077] Figure 2 System configuration diagrams for the power distribution network and coal transportation network;

[0078] Figure 3 Parameter identification results of 14 belt conveyors (BC);

[0079] Figure 4 is the FRA and error result. DETAILED DESCRIPTION

[0080] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0081] 1. Feasibility region assessment method of mine virtual power plant under incomplete information

[0082] The feasible region assessment method of a mine virtual power plant under incomplete information of this embodiment includes the following steps.

[0083] Step 1: Define the feasible domain and subsystem model of the mine virtual power plant

[0084] Consider a typical scenario: a mining industry virtual power plant (VPP) aggregates serval CMIES operating in the distribution network and is equipped with essential equipment such as generators, belt conveyors, and energy storage systems. This setup enables the CMIES to provide flexibility by dynamically managing its energy resources. This flexibility is crucial for enabling the distribution network to integrate renewable energy and implement peak load shifting and valley filling. To quantify the feasible region assessment (FRA) for this mining VPP, we rigorously define the following.

[0085] The feasible region of the mine virtual power plant is defined as the subspace of energy dispatch variables, which represents the power exchange range with the distribution network operator (DSO) and the peak and valley regulation of belt conveyor load, denoted as Ω V :

[0086]

[0087] Where: Ω V represents the feasible region; Indicates that at all time intervals From Total power consumption of the indexed belt conveyor; represents the total power exchange between the coal mine VPP and the distribution network operator; and Ξ |I| are the decision variables and equipment external parameters of coal mine energy optimization scheduling; h(·) represents the set of all equality constraints; g(·) represents the set of all inequality constraints.

[0088] Since the parameter Ξ |I| Unknown and huge number of equipment, in addition, a large number of equipment in the coal transportation network, making Ξ |I| For high-dimensional vectors, it is an NP-hard problem. An effective method is to use historical optimal scheduling data to learn the agent feasible region.

[0089] The feasible region is the projection of the exchange capacity and peak-valley regulation capacity on the original feasible set. It is not feasible to directly solve the NP-hard problem. Therefore, an estimated approximate feasible region is constructed using historical data:

[0090]

[0091] in: Indicates that the parameter Ξ |I| The feasible region Ω obtained under unknown conditions is close to the real one V The agent feasible region; Represents parameter Ξ |I| Approximate value of For parameters Approximate value of represents the set of all equality constraints in the estimated feasible region; represents the set of all inequality constraints in the estimated feasible region.

[0092] Therefore, without knowing |I| In the case of the true value, use the approximate To obtain a feasible region close to the real one Ω V of Therefore, the VPP FRA of coal mines can be expressed as:

[0093]

[0094] in: Yes and Ω V Therefore, historical data can be used to solve the above optimization problem.

[0095] Step 2: Constructing an energy-transportation coordinated coal mine optimization scheduling model

[0096] A. CMIES configuration

[0097] The configuration of CMIES and Coal Transportation Network (CTN) is as follows Figure 1 This coordinated energy transportation system includes wind turbines (WT), photovoltaic systems (PV), combined heat and power (CHP), microturbines (MT), regenerative thermal oxidizers (RTO), and water-source heat pumps (WSHP). Energy storage is provided by pumped hydro storage (PHS) and thermal storage tanks (TST). These components are integrated to provide both electricity and heat. To facilitate demand-responsive coal transportation, the CTN is equipped with belt conveyors (BCs) and silos at different levels. These BCs utilize electricity from the CMIES and are dispatched by the CTN to transport raw coal from the coal face to the coal preparation plant (CPP).

[0098] B. Objective Function

[0099] The goal is to minimize coal mine operating costs, including time-varying prices under energy transaction costs Power generation fuel cost and maintenance cost, and construct the objective function.

[0100] In this embodiment, the objective is to minimize the coal mine operating cost, and the objective function is constructed as follows:

[0101]

[0102] Where: C Sys Represents the total cost of coal mine operation, including purchased electricity cost, fuel cost and operation and maintenance cost represents the time-varying price under energy transaction costs; represents the fuel cost coefficient for CHP power generation; Indicates the operating cost coefficient of photovoltaic power generation; Indicates the operating cost coefficient of wind turbine power generation; represents the operating cost coefficient of gas turbine power generation; represents the operating cost coefficient of the combined heat and power generation unit; It represents the operating cost coefficient of the ventilation oxidation thermal storage unit; Indicates the operating cost coefficient of the belt conveyor; represents the operating cost coefficient of pumped storage; The coefficient of the thermal storage tank operating cost coefficient is expressed as: Represents the operating cost coefficient of the water source heat pump.

[0103] Indicates the power purchased from the distribution network operator; Indicates the power generation capacity of the cogeneration unit; Represents photovoltaic power generation power; Indicates the power generated by the wind turbine; Indicates the power generation capacity of the gas turbine; Indicates the power generation capacity of the wind-lack oxidation thermal storage unit; Represents the load power of the jth belt conveyor; N BC Indicates the number of belt conveyors; represents the pumped storage charging power; Indicates the discharge power of pumped storage; Indicates the heat storage power of the heat storage tank; Indicates the heat release power of the heat storage tank; Indicates the load power of the water source heat pump.

[0104] C. Constraints

[0105] Based on the configuration of coal mine industrial energy system and coal transportation network, constraints are established according to coal transportation, energy units, belt conveyors, energy storage devices and energy balance; with the goal of minimizing coal mine operating costs, decision variables are used to determine the optimal operation mode. and Ξ |I| The constructed energy-transportation coordinated coal mine optimization scheduling model is reconstructed.

[0106] (1) Coal transportation

[0107] For coal transportation, the coal transportation network consists of coal working faces, belt conveyors, silos, and coal preparation plants, arranged in a radial topology. The coal transportation network is modeled as a graph:

[0108] G CTN ={σ L,T N}

[0109] Where: L and T N Represent coal transportation links and nodes respectively.

[0110] Node set T N Includes multiple hierarchical nodes, including the coal mining face supply node T CF , coal silo storage node T SS , transfer node T MS and coal preparation plant demand node T CPP , expressed as:

[0111] T N ={T CF ∪T SS ∪T MS ∪T CPP}

[0112] Each belt conveyor branch supports coal mass transfer as a flow between nodes at different levels, represented as:

[0113] σ L ={σ CF,SS ∪σ SS,MS ∪σ MS,CPP}

[0114] Where: CF,SS represents the link between the coal mining face node and the coal silo storage node; σ SS,MS represents the link between the coal silo storage node and the transfer node; σ MS,CPP Represents the link between the transfer node and the coal preparation plant demand node.

[0115] The coal flow flows from the coal mining face to the coal preparation plant, and the coal transportation network model is expressed as:

[0116]

[0117] in: are the coal quantity and coal feeding rate transported between the working face and the shaft respectively; and represent the minimum and maximum slope limits of coal mass transport, respectively; Indicates the maximum limit of coal quantity transported from the shaft silo to the main silo; is the coal demand in the coal preparation plant; since the coal flow only flows in one direction, l, m, n and p represent the coal transportation network nodes T CF ,T SS ,c MS , and T CPP , the order is from coal mining face to coal preparation plant.

[0118] In order to describe the virtual energy storage characteristics in the coal transportation network, without considering the attenuation, the coal silo model is equivalent to the battery model, which is described as:

[0119]

[0120] in: represents the coal storage capacity of the kth coal bunker at time t; and They represent the amount of coal transported into and out of k silos at time t; M Silo,k and They represent the lower and upper limits of the coal storage capacity of the kth silo respectively; and They represent the coal storage capacity of the kth silo at time 1 and time 24 respectively; and Respectively represent the coal storage capacity limit value of the kth silo at the start time and the end time; N Silo Indicates the number of silos.

[0121] (2) Energy unit

[0122] For the energy unit, the models of the ventilation thermal storage oxidation unit, cogeneration unit, gas turbine unit and water source heat pump are expressed as follows:

[0123]

[0124] X∈{RTO,CHP,GT,WSHP}

[0125] Of which: EHR X is the power generation to heat generation ratio of unit X; is the electric power of the wind-deficient thermal storage oxidation unit, cogeneration unit, gas turbine unit and water source heat pump at time t; is the thermal power of the wind-deficient thermal storage oxidation unit, cogeneration unit, gas turbine unit and water source heat pump at time t; h X 、 They are the lower and upper limits of thermal power for the wind-exhaust thermal storage oxidation unit, cogeneration unit, gas turbine unit and water source heat pump respectively.

[0126] (3) Belt conveyor

[0127] The belt conveyor transports the raw coal from the working face to the coal preparation plant by consuming electricity. The power consumption of the belt conveyor is represented by the general coal transportation model:

[0128]

[0129] in: Indicates the load electric power of the belt conveyor; cof BC Indicates the energy efficiency coefficient of the belt conveyor; V BC Indicates belt speed; represents the coal feeding rate of the belt conveyor; θ 2,j and θ 4,j They respectively represent the factory design parameters of the belt conveyor.

[0130] (4) Energy storage device

[0131] For energy storage, a pumped hydroelectric storage system built in abandoned coal mine goaf provides a flexible option for storing and releasing electrical energy. Thermal storage tanks are used to mitigate peak heat loads. The energy storage unit is represented by:

[0132]

[0133] in: and They represent the power storage capacity of pumped storage at time t+1 and time t respectively; E PHS and They represent the lower and upper limits of the electricity storage capacity of pumped storage, respectively; and Respectively represent the charging and discharging power of pumped storage; p PHSC , p PHSD , They represent the upper and lower limits of the charging and discharging power of pumped storage respectively; and They represent the electricity storage capacity of pumped storage at time 1 and 24 respectively; and are the power storage parameters of pumped storage at the start and end times respectively; γ PHS represents the attenuation coefficient of pumped storage power storage capacity; η PHS Indicates the charging and discharging efficiency of pumped storage.

[0134] and They represent the heat storage capacity of the heat storage tank at time t+1 and t respectively; E TST and They represent the lower and upper limits of the heat storage capacity of the heat storage tank respectively; and Respectively represent the charging and discharging power of the heat storage tank; h TSTC , h TSTD , Respectively represent the upper and lower limits of the charging and discharging heat power of the heat storage tank; and Respectively represent the heat storage capacity of the heat storage tank at time 1 and 24; and Represent the heat storage capacity parameters of the heat storage tank at the start and end time respectively; γ TST Represents the thermal storage capacity attenuation coefficient of the thermal storage tank; η TST Indicates the charging and discharging efficiency of the heat storage tank.

[0135] (5) Energy balance

[0136] For energy balance, the power and heat balance constraints of the coal mine are:

[0137]

[0138] in: Indicates the power purchased from the distribution network operator; Indicates the power generation capacity of the wind-lack oxidation thermal storage unit; Indicates the power generation capacity of the cogeneration unit; Indicates the power generation capacity of the gas turbine; Represents photovoltaic power generation power; Indicates the power generated by the wind turbine; Indicates the discharge power of pumped storage; represents the pumped storage charging power; Indicates the electrical load power; represents the load power of the j-th belt conveyor; Indicates the load power of the water source heat pump; is the thermal power of the wind-deficient thermal storage oxidation unit, cogeneration unit, gas turbine unit and water source heat pump at time t; and Respectively represent the charging and discharging power of the heat storage tank; Indicates heat load power; N BC Indicates the number of belt conveyors.

[0139] D. Model reconstruction

[0140] The reconstructed energy-transportation coordinated coal mine optimization scheduling model is:

[0141]

[0142] Where: p BC,j and They represent the lower and upper limits of the belt conveyor load power respectively; p g and Represent the lower and upper limits of the interaction power respectively; θ 2,j Indicates the factory design parameters of the belt conveyor; N BC Indicates the number of belt conveyors.

[0143] Step 3: Parameter identification based on inverse optimization

[0144] Based on historical data sets, the two-level optimization problem is converted into a single-level optimization problem through the KKT condition. With the goal of minimizing the loss function between the proxy area and the real area, a data-driven inverse optimization feasible domain estimation model is constructed.

[0145] In this embodiment, the data-driven inverse optimization feasible region estimation model is expressed as:

[0146]

[0147] in: Indicates the historical data value of belt conveyor power; represents the historical data value of the power purchased by the power grid; μ represents the dual variable of the inequality constraint; μ T represents the transpose of the dual variable; represents the dual Lagrangian augmented function; λ represents the dual variable of the equality constraint; D is the historical data set, which is expressed as:

[0148]

[0149] in: Represents historical electricity price data.

[0150] where the constraints represent stationarity, primal feasibility, dual feasibility, complementary slackness, and strong duality conditions. By solving this problem with a finite number of data in D, Ω can be approximated efficiently. V .

[0151] Step 4: Convert the data-driven inverse optimization feasible region estimation model into an inverse optimization problem, and use the learning-based FRA algorithm to optimize and solve the agent feasible region.

[0152] In this embodiment, the method steps for optimizing and solving the agent feasible region using the algorithm are as follows:

[0153] 31) Input iteration index ξ=1, penalty factor ρ, tolerance value ∈ and historical data set D; initialize

[0154] 32) Solve the inverse optimization feasible region estimation model;

[0155] 33) Determine whether If yes, then execute step 34); if no, then the iteration ends and the feasible region for the agent is obtained.

[0156] 34) Traverse |D| data samples starting from the current iteration number ξ and solve the inverse optimization problem to obtain represents the parameter value obtained in the ξth main iteration and the sth sub-iteration;

[0157] The inverse optimization problem is expressed as:

[0158]

[0159] in, represents the parameter estimation variable of the ξth iteration;

[0160] 35) Average the results of |D| sub-iterations and update the global parameters:

[0161]

[0162] 36) Let ξ = ξ + 1, and repeat step 32).

[0163] 2. Case Study

[0164] The feasible domain evaluation method of a mine virtual power plant under incomplete information in this embodiment is described below with reference to a specific example.

[0165] 2.1 Test system settings

[0166] The numerical evaluation of the proposed LFRA method uses the data of coal mine in IEEE 33-bus distribution system, as Figure 2 The FRA was solved on a MATLAB R2023b platform using Guideline 11.0.0 and an Apple Silicon M1 CPU with 16GB of RAM.

[0167] 2.2 Parameter Identification

[0168] Figure 3 The results and percentage relative errors of the parameter θ2 for various BC devices during training are shown, revealing that the proposed LFRA can effectively approximate unknown parameters from historical data. It shows significant fluctuations at the beginning of training, which gradually decrease, indicating that the model is learning parameters to better fit the actual parameters. At the end of training, the best approximation of θ for different BCs maintains a low error rate of less than 1%, which is relatively acceptable in applications.

[0169] Table 1 Comparison of approximation error results

[0170]

[0171] 2.3 Feasible Region Assessment (FRA) Results

[0172] The maximum and minimum power values ​​predicted by the proposed method for power exchange within BC and VPP are Figure 4 to compare with the true value in .

[0173] The results show that the proposed LFRA method effectively approximates the maximum and minimum power bounds for the belt conveyor and power exchange, validating its accuracy and reliability. The low errors observed in the belt conveyor limits indicate that the method can accurately capture the stable operating characteristics of these components, likely due to the predictability of their power profiles. For the belt conveyor power approximation, the results show a final error below 1%, while the minimum power limit maintains an error below 0.3% across all data points. In the case of the power exchange, the approximation achieves an average error of approximately 3% for both the maximum and minimum power bounds. This demonstrates that the method can maintain accuracy compared to the historical data FRA.

[0174] Table 1 presents a comparative analysis of the approximation errors using two methods: LSTM and the proposed LFRA. The results show that LFRA consistently outperforms LSTM on all evaluated parameters, achieving significantly lower RMSE and MAE values. Specifically, for the maximum belt conveyor power, LFRA produces an RMSE of 2.95% and a MAE of 5.28%, which are significantly lower than the RMSE and MAE values ​​of LSTM, which are 25.35% and 25.02%, respectively. This indicates that LFRA has superior accuracy in capturing the peak-to-valley regulation potential of coal mine VPP. However, since the minimum BC power can reach 0, the RMSE and MAE of LSTM and LFRA are both NaN. It is worth noting that when approximating p g and When θ2 is used, LFRA maintains an accurate approximation, while LSTM shows higher RMSE and MAE. For parameter θ2, LFRA achieves 2.21% RMSE and 1.71% MAE, while LSTM has higher errors, further confirming LFRA's accuracy advantage. These results validate the effectiveness of LFRA for high-precision FRA in coal mine VPPs.

[0175] 3. Conclusion

[0176] To address the VPP problem in coal mines with incomplete information, this paper proposes a feasible region assessment method (LFRA) for mine virtual power plants under incomplete information. Compared with traditional methods, the proposed LFRA method demonstrates superior accuracy in approximating operational limits and achieves significantly lower RMSE and MAE on key parameters. Future work will focus on expanding the real-time application of LFRA and addressing the nonlinear characteristics of industrial FRA.

[0177] The above embodiments are merely preferred embodiments for the purpose of fully illustrating the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are within the scope of protection of the present invention. The scope of protection of the present invention shall be subject to the claims.

Claims

1. A feasible region assessment method for a mine virtual power plant under incomplete information, characterized by: The steps include: Step 1: Define the feasible domain and subsystem model of the mine virtual power plant The feasible region of the mine virtual power plant is defined as the subspace of energy scheduling variables, which represents the power exchange range with the distribution network operator and the belt conveyor load peak and valley regulation, denoted as Ω V : Where: Ω V represents the feasible region; Indicates that at all time intervals From Total power consumption of the indexed belt conveyor; represents the total power exchange between the coal mine VPP and the distribution network operator; and Ξ |I| are the decision variables and equipment external parameters of coal mine energy optimization scheduling; h(·) represents the set of all equality constraints; g(·) represents the set of all inequality constraints; Since the parameter Ξ |I| Given the large number of unknown devices, it is not feasible to directly solve the NP-hard problem. Therefore, an approximate feasible region is estimated using historical data: in: Indicates that the parameter Ξ |I| The feasible region Ω obtained under unknown conditions is close to the real one V The agent feasible region; Represents parameter Ξ |I| Approximate value of For parameters Approximate value of represents the set of all equality constraints in the estimated feasible region; represents the set of all inequality constraints in the estimated feasible region; Step 2: Constructing an energy-transportation coordinated coal mine optimization scheduling model With the goal of minimizing the operating cost of coal mines, the objective function is constructed; Based on the configuration of coal mine industrial energy system and coal transportation network, constraints are established according to coal transportation, energy units, belt conveyors, energy storage devices and energy balance; with the goal of minimizing coal mine operating costs, decision variables are used to determine the optimal operation mode. and Ξ |I| Reconstruct the constructed energy-transportation coordinated coal mine optimization scheduling model; Step 3: Parameter identification based on inverse optimization Based on historical data sets, the two-level optimization problem is converted into a single-level optimization problem through the KKT condition. With the goal of minimizing the loss function between the proxy region and the real region, a data-driven inverse optimization feasible region estimation model is constructed. Step 4: Convert the data-driven inverse optimization feasible region estimation model into an inverse optimization problem, and use the learning-based FRA algorithm to optimize and solve the agent feasible region.

2. The method for evaluating the feasible region of a mine virtual power plant under incomplete information according to claim 1 is characterized by: In step 2, the objective function is constructed with the goal of minimizing the coal mine operating cost as follows: Where: C Sys Represents the total cost of coal mine operation, including purchased electricity cost, fuel cost and operation and maintenance cost represents the time-varying price under energy transaction costs; represents the fuel cost coefficient for CHP power generation; Indicates the operating cost coefficient of photovoltaic power generation; Indicates the operating cost coefficient of wind turbine power generation; represents the operating cost coefficient of gas turbine power generation; represents the operating cost coefficient of the combined heat and power generation unit; It represents the operating cost coefficient of the ventilation oxidation thermal storage unit; Indicates the operating cost coefficient of the belt conveyor; represents the operating cost coefficient of pumped storage; The coefficient of the thermal storage tank operating cost coefficient is expressed as: Indicates the operating cost coefficient of the water source heat pump; Indicates the power purchased from the distribution network operator; Indicates the power generation capacity of the cogeneration unit; Represents photovoltaic power generation power; Indicates the power generated by the wind turbine; Indicates the power generation capacity of the gas turbine; Indicates the power generation capacity of the wind-lack oxidation thermal storage unit; Represents the load power of the jth belt conveyor; N BC Indicates the number of belt conveyors; represents the pumped storage charging power; Indicates the discharge power of pumped storage; Indicates the heat storage power of the heat storage tank; Indicates the heat release power of the heat storage tank; Indicates the load power of the water source heat pump.

3. The method for evaluating the feasible region of a mine virtual power plant under incomplete information according to claim 1 is characterized by: For coal transportation, the coal transportation network consists of coal working faces, belt conveyors, silos, and coal preparation plants; the coal transportation network is modeled as a graph: H CTN ={σ L ,T N } Where: L and T N represent coal transportation links and nodes respectively; Node set T N Includes multiple hierarchical nodes, including the coal mining face supply node T CF , coal silo storage node T SS , transfer node T MS and coal preparation plant demand node T CPP , expressed as: T N ={T CF ∪T SS ∪T MS ∪T CPP } Each belt conveyor branch supports coal mass transfer as a flow between nodes at different levels, represented as: s L ={σ CF,SS ∪σ SS,MS ∪σ MS,CPP } Where: CF,SS represents the link between the coal mining face node and the coal silo storage node; σ SS,MS represents the link between the coal silo storage node and the transfer node; σ MS,CPP Represents the link between the transfer node and the coal preparation plant demand node; The coal flow flows from the coal mining face to the coal preparation plant, and the coal transportation network model is expressed as: in: are the coal quantity and coal feeding rate transported between the working face and the shaft respectively; and represent the minimum and maximum slope limits of coal mass transport, respectively; Indicates the maximum limit of coal quantity transported from the shaft silo to the main silo; is the coal demand in the coal preparation plant; since the coal flow only flows in one direction, l, m, n and p represent the coal transportation network nodes T CF ,T SS ,T MS , and T CPP , the order is from coal mining face to coal preparation plant; In order to describe the virtual energy storage characteristics in the coal transportation network, without considering the attenuation, the coal silo model is equivalent to the battery model, which is described as: in: represents the coal storage capacity of the kth coal bunker at time t; and They represent the amount of coal transported into and out of k silos at time t; M Silo,k and They represent the lower and upper limits of the coal storage capacity of the kth silo respectively; and They represent the coal storage capacity of the kth silo at time 1 and time 24 respectively; and Respectively represent the coal storage capacity limit value of the kth silo at the start time and the end time; N Silo Indicates the number of silos.

4. The method for evaluating the feasible region of a mine virtual power plant under incomplete information according to claim 1 is characterized by: For the energy unit, the models of the ventilation thermal storage oxidation unit, cogeneration unit, gas turbine unit and water source heat pump are expressed as follows: X∈{RTO,CHP,GT,WSHP} Of which: EHR X is the power generation to heat generation ratio of unit X; is the electric power of the wind-deficient thermal storage oxidation unit, cogeneration unit, gas turbine unit and water source heat pump at time t; is the thermal power of the wind-deficient thermal storage oxidation unit, cogeneration unit, gas turbine unit and water source heat pump at time t; h X 、 They are the lower and upper limits of thermal power for the wind-exhaust thermal storage oxidation unit, cogeneration unit, gas turbine unit and water source heat pump respectively.

5. The method for evaluating the feasible region of a mine virtual power plant under incomplete information according to claim 1 is characterized by: The belt conveyor transports the raw coal from the working face to the coal preparation plant by consuming electricity. The power consumption of the belt conveyor is represented by the general coal transportation model: in: Indicates the load electric power of the belt conveyor; cof BC Indicates the energy efficiency coefficient of the belt conveyor; V BC Indicates belt speed; represents the coal feeding rate of the belt conveyor; θ 2,j and θ 4,j They respectively represent the factory design parameters of the belt conveyor.

6. The method for evaluating the feasible region of a mine virtual power plant under incomplete information according to claim 1 is characterized by: For energy storage, a pumped hydroelectric storage system built in abandoned coal mine goaf provides a flexible option for storing and releasing electrical energy. Thermal storage tanks are used to mitigate peak heat loads. The energy storage unit is represented by: in: and denote the power storage capacity of pumped storage at time t+1 and t respectively; E PHS and They represent the lower and upper limits of the electricity storage capacity of pumped storage, respectively; and They represent the charging and discharging power of pumped storage respectively; p PHSC 、 p PHSD and They represent the upper and lower limits of the charging and discharging power of pumped storage respectively; and They represent the electricity storage capacity of pumped storage at time 1 and 24 respectively; and are the power storage parameters of pumped storage at the start and end times respectively; γ PHS represents the attenuation coefficient of pumped storage power storage capacity; η PHS Indicates the charging and discharging efficiency of pumped storage; and represent the heat storage capacity of the heat storage tank at time t+1 and t respectively; E TST and They represent the lower and upper limits of the heat storage capacity of the heat storage tank respectively; and Respectively represent the charging and discharging power of the heat storage tank; h TStC 、 h TSTD and Respectively represent the upper and lower limits of the charging and discharging heat power of the heat storage tank; and Respectively represent the heat storage capacity of the heat storage tank at time 1 and 24; and Represent the heat storage capacity parameters of the heat storage tank at the start and end time respectively; γ TST Represents the thermal storage capacity attenuation coefficient of the thermal storage tank; η TST Indicates the charging and discharging efficiency of the heat storage tank.

7. The method for evaluating the feasible region of a mine virtual power plant under incomplete information according to claim 1 is characterized by: For energy balance, the power and heat balance constraints of the coal mine are: in: Indicates the power purchased from the distribution network operator; Indicates the power generation capacity of the wind-lack oxidation thermal storage unit; Indicates the power generation capacity of the cogeneration unit; Indicates the power generation capacity of the gas turbine; Represents photovoltaic power generation power; Indicates the power generated by the wind turbine; Indicates the discharge power of pumped storage; represents the pumped storage charging power; Indicates the electrical load power; represents the load power of the j-th belt conveyor; Indicates the load power of the water source heat pump; is the thermal power of the wind-deficient thermal storage oxidation unit, cogeneration unit, gas turbine unit and water source heat pump at time t; and Respectively represent the charging and discharging power of the heat storage tank; Indicates heat load power; N BC Indicates the number of belt conveyors.

8. The method for evaluating the feasible region of a mine virtual power plant under incomplete information according to claim 1 is characterized by: The reconstructed energy-transportation coordinated coal mine optimization scheduling model is: in: p BC,j and Respectively represent the lower limit and upper limit of belt conveyor load power; p g and Represent the lower and upper limits of the interaction power respectively; θ 2,j Indicates the factory design parameters of the belt conveyor; N BC Indicates the number of belt conveyors.

9. The method for evaluating the feasible region of a mine virtual power plant under incomplete information according to claim 1 is characterized by: In step 3, the data-driven inverse optimization feasible region estimation model is expressed as: in: Indicates the historical data value of belt conveyor power; represents the historical data value of the power purchased by the power grid; μ represents the dual variable of the inequality constraint; μ T represents the transpose of the dual variable; represents the dual Lagrangian augmented function; λ represents the dual variable of the equality constraint; D is the historical data set, which is expressed as: in: Represents historical electricity price data.

10. The method for evaluating the feasible region of a mine virtual power plant under incomplete information according to claim 9 is characterized in that: The steps for optimizing the agent's feasible region using the algorithm are as follows: 31) Input iteration index ξ=1, penalty factor ρ, tolerance value ∈ and historical data set D; initialize 32) Solve the inverse optimization feasible region estimation model; 33) Determine whether If yes, then execute step 34); if no, then the iteration ends and the feasible region for the agent is obtained. 34) Traverse |D| data samples starting from the current iteration number ξ and solve the inverse optimization problem to obtain represents the parameter value obtained in the ξth main iteration and the sth sub-iteration; The inverse optimization problem is expressed as: in, represents the parameter estimation variable of the ξth iteration; 35) Average the results of |D| sub-iterations and update the global parameters: 36) Let ξ = ξ + 1, and repeat step 32).

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