Integrated Energy Multi-Market Trading Risk-Return Efficiency Quantification Method

Abstract

This invention belongs to the field of computer technology, specifically relating to a method for quantifying the risk-return efficiency of integrated energy multi-market transactions; analyzing multi-market risk transmission mechanisms and constructing risk sets for multiple market types, revealing the coupling relationship and risk transmission driving factors among the electricity-gas-heat-carbon multi-markets, and constructing a standardized risk set; using extreme value theory to fit the tail distribution of risk factors, characterizing the nonlinear dependency structure of multiple risk factors, and combining Sobol global sensitivity analysis and Granger causality tests to identify key risk factors and transmission paths; establishing a four-dimensional efficiency factor system, and constructing a comprehensive efficiency quantification model based on the entropy weight method for objective weighting; improving the moth-flame optimization and the alternating direction multiplier method for hybrid solution, achieving distributed and efficient solution through the alternating direction multiplier method. This invention can achieve accurate quantification and evaluation of multi-market transaction efficiency, providing a reliable quantitative tool for multi-market transaction decisions of integrated energy system operators.

Description

Technical Field

[0001] This invention belongs to the field of computer technology, specifically relating to a method for quantifying the risk-return efficiency of integrated energy multi-market transactions. Background Technology

[0002] Integrated energy systems, through the coupling and complementarity of multiple energy categories such as electricity, gas, heat, and cooling, achieve tiered utilization and efficient allocation of energy, and have become the core carrier for the construction of new power systems. With the continuous deepening of power market reform, integrated energy system operators can simultaneously participate in multiple types of market transactions, including the electricity spot market, ancillary services market, natural gas market, heat market, and carbon trading market, thereby improving operational revenue through the synergistic optimization of multiple markets.

[0003] Among them, the quantification of risk-return efficiency in multi-market transactions is a key technical link in the operation and decision-making of integrated energy systems. It aims to build a scientific quantitative evaluation system to comprehensively reflect the overall performance of multi-market trading strategies and provide accurate quantitative support for operators' trading decisions.

[0004] Existing technologies have significant limitations in quantifying the risk-return effectiveness of multi-market transactions. Current research often focuses only on price or demand risk in a single market, neglecting the risk transmission mechanisms formed through energy coupling between multiple markets. This fails to comprehensively identify all-dimensional risk sources in multi-market transactions, leading to significant discrepancies between risk quantification results and actual outcomes. Existing transaction effectiveness quantification methods often use only a simple ratio of return to risk as an evaluation indicator, neglecting the mitigation effects of risk transmission and the robustness of trading strategies. This fails to comprehensively reflect the overall effectiveness of multi-market trading strategies, resulting in distorted effectiveness assessments and an inability to provide accurate support for operators' trading decisions. For high-dimensional, nonlinear multi-market transaction effectiveness quantification models, existing solution algorithms often suffer from problems such as getting trapped in local optima, slow convergence speed, and insufficient solution accuracy, making it difficult to meet the needs of practical engineering applications. These technical problems severely restrict the scientific rigor and reliability of multi-market transaction decisions in integrated energy systems, urgently requiring solutions through technological innovation. Summary of the Invention

[0005] To achieve the above objectives, this application provides the following technical solution: A method for quantifying the risk-return efficiency of integrated energy multi-market transactions includes the following steps: Step 1: Analysis of multi-market risk transmission mechanisms and construction of multi-type market risk sets, clarifying the boundaries and coupling relationships of multi-market transactions in the integrated energy system, revealing the risk transmission mechanism, and constructing standardized multi-type market risk sets; Step 2: Quantification of multi-dimensional risk factors and identification of key risk transmission paths. Extreme value theory is used to fit the marginal distribution of risk factors, the nonlinear dependence structure of multiple risk factors is characterized by the Pair-Copula function, Monte Carlo simulation is combined to generate full-scenario risk samples, Sobol global sensitivity analysis is used to identify key risk factors, and Granger causality test and directed acyclic graph are used to identify key risk transmission paths. Step 3: Consider the construction of a risk-adjusted multi-market trading efficiency quantification model. Based on the multi-market trading return model and with conditional value at risk as the core risk measurement indicator, construct a trading efficiency factor system, determine objective weights based on the entropy weight method, and construct a comprehensive trading efficiency quantification model. Step 4: Improve the hybrid solution of moth flame optimization and alternating direction multiplier method. Introduce chaotic mapping to initialize the population, adaptive weight factor and elite back learning strategy to improve the moth flame optimization algorithm. Decompose the original model into four sub-problems for distributed solution by alternating direction multiplier method.

[0006] Furthermore, the coupling relationships between the multiple markets in step 1 include: There are multiple types of coupling channels. The first type is the electro-gas coupling channel, which realizes the bidirectional conversion of electricity and natural gas through gas turbines and electro-gas conversion equipment. The second type is the electro-thermal coupling channel, which realizes the bidirectional conversion of electricity and heat through cogeneration units and electric boilers; The third category is the electricity-carbon coupling channel, which forms a coupling relationship through carbon emissions generated from fossil energy consumption; The fourth category is the cross-timescale electricity market coupling channel, which covers the interaction between the day-ahead market, intraday market and real-time market.

[0007] Furthermore, the driving factors of the risk transmission mechanism in step 1 include: Market coupling strength, correlation of trading positions, impact intensity of risk events, and market liquidity are all factors that influence risk transmission efficiency across multiple markets. Higher market coupling strength, stronger correlation of trading positions, greater impact intensity of risk events, weaker market liquidity, and higher efficiency of risk transmission across multiple markets are all factors that influence market coupling strength.

[0008] Furthermore, the multi-type market risk set in step 1 includes: The four primary subsets contain multiple specific risk factors. Among them, the market price risk subset includes seven risk factors: day-ahead electricity market price risk, intraday electricity market price risk, real-time electricity market price risk, ancillary services market price risk, natural gas market price risk, heat market price risk, and carbon trading market price risk. The market demand risk subset includes three risk factors: electricity demand fluctuation risk, heat demand fluctuation risk, and gas demand fluctuation risk. The risk subset of the coupling link includes the risk of energy conversion equipment failure and the risk of energy transmission network congestion; The policy and rule risk subset includes the risk of adjustments to market trading rules, the risk of changes in carbon quota allocation policies, and the risk of adjustments to energy price control policies.

[0009] Furthermore, step 2 also includes: The tail distribution of risk factors is fitted using the over-threshold model in extreme value theory. A loss sequence is constructed for any risk factor, defined as the negative logarithmic return of the risk factor. An excess loss sequence is constructed after setting a preset threshold for excess loss. The excess loss sequence follows a generalized Pareto distribution. The parameters of the generalized Pareto distribution are estimated by the maximum likelihood estimation method, and the fitting effect is verified by the Kolmogorov-Smirnov test.

[0010] Furthermore, in step 2, the Pair-Copula function decomposes the high-dimensional joint distribution into the product of multiple pairwise Copula functions based on the vine structure. The optimal Copula function type is selected through the Akaike Information Criterion. Among them, GumbelCopula can accurately characterize the upper tail correlation and is suitable for capturing risk transmission under extreme upward market conditions, while Clayton Copula characterizes the lower tail correlation and is suitable for capturing risk transmission under extreme downward market conditions.

[0011] Furthermore, in step 2, Sobol global sensitivity analysis calculates the first-order sensitivity index and the total sensitivity index of each risk factor on the total return of the integrated energy system transaction. The first-order sensitivity index reflects the degree of independent contribution of the risk factor itself to the variance of the total return, while the total sensitivity index reflects the degree of contribution of the risk factor itself and its interaction with other risk factors to the variance of the total return. Based on the ranking results of the total sensitivity index, the risk factors with the highest ranking are selected as key risk factors. The Granger causality test is used to verify the temporal causal relationship between two risk factors. If the lagged value of risk factor X improves the prediction accuracy of risk factor Y, then X is called a Granger cause of Y. Based on the results of the Granger causality test, a risk transmission network in the form of a directed acyclic graph is constructed. The nodes in the directed acyclic graph correspond to key risk factors, and the directed edges correspond to the direction and intensity of risk transmission.

[0012] Furthermore, in step 3, the conditional value of risk, as a core risk metric, reflects the average level of extreme losses faced by the trading strategy. The calculation of the conditional value of risk is transformed into a convex optimization problem using the auxiliary function method. Among the four dimensions of trading efficiency factors, the basic return efficiency factor is quantified by the ratio of the expected total return of the trading strategy to the expected total return of the benchmark strategy. The benchmark strategy is the integrated energy system's trading strategy that only participates in the day-ahead electricity market. The risk control effectiveness factor is quantified by the ratio of the conditional value at risk of the benchmark strategy to the conditional value at risk of the trading strategy. The risk transmission mitigation effectiveness factor is quantified by the attenuation ratio of the risk transmission intensity along key risk transmission paths before and after the implementation of a trading strategy. The strategy robustness effectiveness factor is the inverse of the coefficient of variation of the trading strategy returns.

[0013] Furthermore, the constraints of the comprehensive transaction efficiency quantification model in step 3 include: The first category is the physical operation constraints of the integrated energy system, including power balance constraints, thermal balance constraints, natural gas balance constraints, upper and lower limits of equipment output constraints, equipment ramping constraints, energy storage equipment charging and discharging constraints, and state of charge constraints. The second category is multi-market trading rule constraints, including upper and lower limits on trading volume in each market, price range constraints, delivery time constraints, and deviation assessment constraints. The third category is total carbon emission constraints; The fourth category is the constraint on the intensity of risk transmission; The fifth category is non-negativity constraints on variables.

[0014] Furthermore, the improved moth flame optimization algorithm in step 4 is improved in three aspects: first, chaotic mapping is introduced to initialize the population, thereby increasing the diversity of initial solutions and expanding the search range of the algorithm; Secondly, an adaptive weighting factor is introduced, which uses a larger weight in the early stage of iteration to enhance the global search capability, and a smaller weight in the later stage of iteration to enhance the local development capability. Third, an elite reverse learning strategy is introduced, which performs reverse learning on the elite individuals in each iteration to generate new high-quality individuals; The position of the moth corresponds to the decision variable of the comprehensive transaction efficiency quantification model, the fitness value of the moth corresponds to the comprehensive transaction efficiency index, and the number of flames is adaptively updated according to the number of iterations. The alternating direction multiplier method decomposes the original optimization problem into four subproblems: the revenue optimization subproblem, the risk quantification subproblem, the efficiency evaluation subproblem, and the risk transmission constraint subproblem. The augmented Lagrangian function of the original problem includes the decision variables, objective function, Lagrangian multiplier vector, and penalty factor of the four subproblems.

[0015] Compared with the prior art, the present invention has the following beneficial effects: This invention addresses the problem of incomplete risk identification in existing technologies by adding a risk transmission mechanism analysis module covering the coupling relationships between multiple markets (electricity, gas, heat, and carbon) and a standardized multi-type market risk set. By clarifying the risk transmission logic of multiple core coupling channels between markets, it quantifies the impact of core factors such as market coupling strength, trading position correlation, and the impact intensity of risk events on risk transmission efficiency. The constructed standardized risk set, comprising four primary subsets—market price, market demand, coupling links, and policy rules—achieves comprehensive coverage of all-dimensional risk sources in multi-market transactions, improving the fit and accuracy of efficiency quantification results with real-world scenarios from the very beginning of model construction.

[0016] This invention addresses the problem of distorted extreme risk quantification in existing technologies by adding a multi-dimensional risk joint distribution fitting unit based on extreme value theory and the Pair-Copula function, and a key risk transmission path identification unit based on Granger causality tests and directed acyclic graphs. It accurately characterizes the extreme tail volatility features of risk factors through generalized Pareto distribution fitting, fully restores the nonlinear dependency structure between multiple risk factors through the high-dimensional joint distribution constructed using the Pair-Copula function, and achieves precise location of key risk transmission paths and quantitative calculation of transmission strength by combining the risk transmission network constructed with the directed acyclic graph. This provides a direct quantitative basis for constructing risk transmission mitigation constraints in trading efficiency quantification models.

[0017] This invention overcomes the inherent limitations of existing single-risk-reward ratio assessment frameworks by adding a trading performance factor system encompassing four dimensions: basic return performance, risk control performance, risk transmission mitigation performance, and strategy robustness performance. It also includes a comprehensive trading performance quantification model based on entropy weighting with objective weighting, which adjusts for risk. The risk transmission mitigation performance factor directly quantifies the risk attenuation effect of the trading strategy on key risk transmission paths. The strategy robustness performance factor comprehensively characterizes the strategy's ability to stabilize returns under different risk scenarios. The objective weighting method of entropy weighting avoids evaluation biases caused by subjective weighting. The constructed comprehensive performance quantification model achieves a multi-dimensional quantitative evaluation of trading strategies.

[0018] This invention addresses the problems of existing algorithms, such as getting trapped in local optima, slow convergence, and insufficient accuracy, by adding a hybrid solution algorithm module that combines the improved moth flame optimization with the alternating direction multiplier method. Through chaotic mapping population initialization, adaptive weighting factors, and elite back-learning strategies, the global search capability and convergence accuracy of the moth flame optimization algorithm are significantly improved. The alternating direction multiplier method decomposes the high-dimensional original model into four low-dimensional subproblems for distributed solution, greatly reducing the solution dimensionality and improving computational efficiency. The hybrid solution algorithm can significantly shorten the solution time while ensuring a globally optimal solution, making it suitable for the real-time and high-precision requirements of multi-market transaction decisions in practical engineering scenarios.

[0019] This invention, through the aforementioned newly added core components, forms a complete technical closed loop from risk identification, risk quantification, and transmission path identification to comprehensive efficiency quantification and efficient solution. The newly added components form a close logical connection and technical support. The construction of the risk set provides the basic object for risk quantification, the identification of risk transmission paths provides the core constraints for the efficiency quantification model, and the construction of the efficiency quantification model provides the target framework for the solution algorithm. The synergistic effect of each module realizes the accurate quantification and evaluation of multi-market transaction efficiency, and can provide a reliable quantitative tool for multi-market transaction decisions of integrated energy system operators. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the process of a method for quantifying the risk-return efficiency of integrated energy multi-market transactions, as claimed in an embodiment of the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0022] The terms "first," "second," and "third" in this application are for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first," "second," or "third" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified. All directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of this application are only used to explain the relative positional relationships and movements between components in a specific orientation (as shown in the figures). If the specific orientation changes, the directional indications also change accordingly. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices.

[0023] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0024] According to the first embodiment of the present invention, referring to Figure 1 This invention claims protection for a method for quantifying the risk-return efficiency of integrated energy multi-market transactions, comprising the following steps: Step 1: Analysis of multi-market risk transmission mechanisms and construction of multi-type market risk sets, clarifying the boundaries and coupling relationships of multi-market transactions in the integrated energy system, revealing the risk transmission mechanism, and constructing standardized multi-type market risk sets; Step 2: Quantification of multi-dimensional risk factors and identification of key risk transmission paths. Extreme value theory is used to fit the marginal distribution of risk factors, the nonlinear dependence structure of multiple risk factors is characterized by the Pair-Copula function, Monte Carlo simulation is combined to generate full-scenario risk samples, Sobol global sensitivity analysis is used to identify key risk factors, and Granger causality test and directed acyclic graph are used to identify key risk transmission paths. Step 3: Consider the construction of a risk-adjusted multi-market trading efficiency quantification model. Based on the multi-market trading return model and with conditional value at risk as the core risk measurement indicator, construct a trading efficiency factor system, determine objective weights based on the entropy weight method, and construct a comprehensive trading efficiency quantification model. Step 4: Improve the hybrid solution of moth flame optimization and alternating direction multiplier method. Introduce chaotic mapping to initialize the population, adaptive weight factor and elite back learning strategy to improve the moth flame optimization algorithm. Decompose the original model into four sub-problems for distributed solution by alternating direction multiplier method.

[0025] Furthermore, the coupling relationships between the multiple markets in step 1 include: There are multiple types of coupling channels. The first type is the electro-gas coupling channel, which realizes the bidirectional conversion of electricity and natural gas through gas turbines and electro-gas conversion equipment. The second type is the electro-thermal coupling channel, which realizes the bidirectional conversion of electricity and heat through cogeneration units and electric boilers; The third category is the electricity-carbon coupling channel, which forms a coupling relationship through carbon emissions generated from fossil energy consumption; The fourth category is the cross-timescale electricity market coupling channel, which covers the interaction between the day-ahead market, intraday market and real-time market.

[0026] Furthermore, the driving factors of the risk transmission mechanism in step 1 include: Market coupling strength, correlation of trading positions, impact intensity of risk events, and market liquidity are all factors that influence risk transmission efficiency across multiple markets. Higher market coupling strength, stronger correlation of trading positions, greater impact intensity of risk events, weaker market liquidity, and higher efficiency of risk transmission across multiple markets are all factors that influence market coupling strength.

[0027] Furthermore, the multi-type market risk set in step 1 includes: The four primary subsets contain multiple specific risk factors. Among them, the market price risk subset includes seven risk factors: day-ahead electricity market price risk, intraday electricity market price risk, real-time electricity market price risk, ancillary services market price risk, natural gas market price risk, heat market price risk, and carbon trading market price risk. The market demand risk subset includes three risk factors: electricity demand fluctuation risk, heat demand fluctuation risk, and gas demand fluctuation risk. The risk subset of the coupling link includes the risk of energy conversion equipment failure and the risk of energy transmission network congestion; The policy and rule risk subset includes the risk of adjustments to market trading rules, the risk of changes in carbon quota allocation policies, and the risk of adjustments to energy price control policies.

[0028] In this embodiment, the boundaries and coupling relationships of multi-market transactions in the integrated energy system are first clarified, and the risk transmission mechanism is revealed based on this, thereby constructing a multi-dimensional set of market risks.

[0029] Integrated energy system operators participate in multiple market types, including the electricity spot market, ancillary services market, natural gas trading market, heat trading market, and carbon trading market. The electricity spot market comprises trading instruments across three time scales: day-ahead market, intraday market, and real-time market. The coupling relationships between these markets are formed through energy conversion equipment and trading activities, specifically including four coupling channels. The first is the electricity-gas coupling channel, which achieves bidirectional conversion between electricity and natural gas through gas turbines and electricity-to-gas conversion equipment. The power output of the gas turbine determines the scale of natural gas procurement, and fluctuations in natural gas prices directly affect the marginal cost of gas-fired power generation, thus influencing the pricing strategy in the electricity market. The second is the electricity-heat coupling channel, which achieves bidirectional conversion between electricity and heat through combined heat and power (CHP) units and electric boilers. The CHP output ratio of CHP units directly links the trading positions in the electricity and heat markets. The third is the electricity-carbon coupling channel, which forms a coupling relationship through carbon emissions generated from fossil fuel consumption. Price fluctuations in the carbon trading market directly change the power generation costs of fossil fuel units, thus affecting the clearing results and trading revenue of the electricity market. The fourth category is the cross-timescale electricity market coupling channel. The winning bid volume in the day-ahead market constrains the trading space in the intraday and real-time markets, and the price fluctuations in the real-time market in turn affect the bidding strategy and profit level of the day-ahead market.

[0030] Based on multi-market coupling relationships, this invention reveals the risk transmission mechanism among multiple markets. The essence of risk transmission is that risk disturbances in a single market spread, amplify, or attenuate through coupling channels between markets within a multi-market network, ultimately affecting the overall trading returns and risk levels of the integrated energy system. Driving factors of risk transmission include market coupling strength, the correlation of trading positions, the impact intensity of risk events, and market liquidity. Higher market coupling strength, stronger correlation of trading positions, greater impact intensity of risk events, and weaker market liquidity result in higher efficiency of risk transmission among multiple markets and a greater likelihood of amplifying the risk effect.

[0031] Based on the analysis of risk transmission mechanisms, this invention comprehensively identifies potential risk sources in multi-market transactions and constructs a standardized multi-type market risk set. The risk set is divided into four primary subsets: market price risk subset, market demand risk subset, coupling link risk subset, and policy and rule risk subset.

[0032] The market price risk subset covers price fluctuation risks in all participating markets, specifically including day-ahead electricity market price risk, intraday electricity market price risk, real-time electricity market price risk, ancillary services market price risk, natural gas market price risk, heat market price risk, and carbon trading market price risk.

[0033] The market demand risk subset covers the volatility risk of end-use energy demand, specifically including the volatility risk of electricity load demand, the volatility risk of heat load demand, and the volatility risk of gas load demand.

[0034] The risk subset of the coupling link covers the operational risks of energy conversion and transmission links, specifically including the risk of energy conversion equipment failure and the risk of energy transmission network congestion.

[0035] The policy and rule risk subset covers policy adjustment risks related to market transactions and the energy industry, specifically including risks of adjustments to market transaction rules, risks of changes in carbon quota allocation policies, and risks of adjustments to energy price control policies.

[0036] This invention normalizes the set of multiple types of market risks into a set R, which contains four first-level subsets, specifically in the form of...

[0037] In formula (1), Represents a subset of market price risk. This represents a subset of market demand risk. This represents a subset of risks in the coupling process. express.

[0038] Furthermore, step 2 also includes: The tail distribution of risk factors is fitted using the over-threshold model in extreme value theory. A loss sequence is constructed for any risk factor, defined as the negative logarithmic return of the risk factor. An excess loss sequence is constructed after setting a preset threshold for excess loss. The excess loss sequence follows a generalized Pareto distribution. The parameters of the generalized Pareto distribution are estimated by the maximum likelihood estimation method, and the fitting effect is verified by the Kolmogorov-Smirnov test.

[0039] Furthermore, in step 2, the Pair-Copula function decomposes the high-dimensional joint distribution into the product of multiple pairwise Copula functions based on the vine structure. The optimal Copula function type is selected through the Akaike Information Criterion. Among them, GumbelCopula can accurately characterize the upper tail correlation and is suitable for capturing risk transmission under extreme upward market conditions, while Clayton Copula characterizes the lower tail correlation and is suitable for capturing risk transmission under extreme downward market conditions.

[0040] Furthermore, in step 2, Sobol global sensitivity analysis calculates the first-order sensitivity index and the total sensitivity index of each risk factor on the total return of the integrated energy system transaction. The first-order sensitivity index reflects the degree of independent contribution of the risk factor itself to the variance of the total return, while the total sensitivity index reflects the degree of contribution of the risk factor itself and its interaction with other risk factors to the variance of the total return. Based on the ranking results of the total sensitivity index, the risk factors with the highest ranking are selected as key risk factors. The Granger causality test is used to verify the temporal causal relationship between two risk factors. If the lagged value of risk factor X improves the prediction accuracy of risk factor Y, then X is called a Granger cause of Y. Based on the results of the Granger causality test, a risk transmission network in the form of a directed acyclic graph is constructed. The nodes in the directed acyclic graph correspond to key risk factors, and the directed edges correspond to the direction and intensity of risk transmission.

[0041] In this embodiment, for the multi-dimensional risk factors in the risk set, the marginal distribution of the risk factors is fitted by extreme value theory, the nonlinear dependence structure of the multiple risk factors is characterized by the Pair-Copula function, the full-scenario risk samples are generated by Monte Carlo simulation, key risk factors are identified by global sensitivity analysis, and finally key risk transmission paths are identified by Granger causality test and directed acyclic graph.

[0042] The price and demand sequences in the energy market exhibit significant leptokurtosis and heavy tails, making it difficult for traditional normal distributions to accurately depict the distribution patterns of extreme risk events. This invention employs a super-threshold model from extreme value theory to fit the tail distribution of risk factors, thereby achieving precise quantification of extreme risks.

[0043] First, for any risk factor X, construct the corresponding loss sequence. The loss sequence is defined as the negative logarithmic return of the risk factor, specifically in the form of...

[0044] In formula (2), This represents the loss value of risk factor X at time t. This represents the actual value of risk factor X at time t. This represents the actual value of risk factor X at time t-1.

[0045] Next, a threshold u for excess loss is set. For samples in the loss sequence that exceed the threshold u, an excess loss sequence Y is constructed. The definition of the excess loss sequence is...

[0046] In formula (3), Y represents the excess loss sequence, L represents the loss sequence of the risk factor, and u represents the threshold of excess loss. The threshold u is determined by the average remaining lifetime map method to ensure that the excess loss sequence meets the fitting requirements of the generalized Pareto distribution.

[0047] The excess loss sequence follows a generalized Pareto distribution, and the distribution function of the generalized Pareto distribution is:

[0048] In formula (4), Let represent the distribution function of the generalized Pareto distribution, and y represent the values ​​of the excess loss sequence. This represents the shape parameter of the generalized Pareto distribution. The scale parameter represents the generalized Pareto distribution. The shape parameter... The tail characteristics that determine the distribution When the value is greater than 0, the distribution exhibits a heavy-tailed distribution, consistent with the tail characteristics of energy market risk factors. Scale parameter It determines the degree of dispersion of the distribution.

[0049] The shape parameter of the generalized Pareto distribution is estimated using the maximum likelihood estimation method. With scale parameters The Kolmogorov-Smirnov test was used to verify the fit, ensuring that the fitted distribution accurately characterizes the tail features of the risk factors. Marginal distributions were fitted sequentially to all risk factors in the risk set to obtain the marginal distribution function for each risk factor.

[0050] Risk factors across multiple markets exhibit significant nonlinear and asymmetric tail correlations, which traditional linear correlation coefficients cannot accurately characterize. This invention employs a Pair-Copula function to construct a high-dimensional joint distribution of multiple risk factors, precisely characterizing the nonlinear dependence structure among them.

[0051] The Pair-Copula function, based on a vine structure, decomposes a high-dimensional joint distribution into the product of multiple pairwise Copula functions, enabling flexible characterization of the dependency structure between different risk factors. For an n-dimensional risk factor vector... Its joint distribution function is decomposed into the following by the Pair-Copula function:

[0052] In formula (5), This represents the joint distribution function of n-dimensional risk factors. Represents an n-dimensional Pair-Copula function. Let i represent the marginal distribution function of the i-th risk factor. This represents the value of the i-th risk factor.

[0053] The optimal Copula function type is selected using the Akaike Information Criterion. Available Copula function types include Gaussian Copula, t-Copula, Gumbel Copula, and Clayton Copula. Gumbel Copula accurately characterizes upper-tail correlation, making it suitable for capturing risk transmission during extreme upward trends; Clayton Copula accurately characterizes lower-tail correlation, making it suitable for capturing risk transmission during extreme downward trends. By fitting the optimal Copula function, a high-dimensional joint distribution function of multiple risk factors is obtained.

[0054] Based on the fitted high-dimensional joint distribution function of multiple risk factors, this invention uses Monte Carlo simulation to generate a large number of risk scenarios. Each risk scenario contains the time-series values ​​of all risk factors within the scheduling period, covering normal operation scenarios and extreme risk scenarios, providing a full-scenario sample for subsequent return and risk quantification.

[0055] Based on the generated risk scenario samples, this invention employs the Sobol global sensitivity analysis method to calculate the sensitivity index of each risk factor to the total return of the integrated energy system transaction, thereby identifying key risk factors. Sobol global sensitivity analysis can decompose the total variance of the model output into the variance contribution of each risk factor, quantifying the degree of influence of each risk factor on the model output.

[0056] The formula for calculating the first-order sensitivity index of a risk factor is as follows:

[0057] In formula (6), Let represent the first-order sensitivity index of the i-th risk factor, reflecting the degree of independent contribution of that risk factor to the total return variance. V represents the variance calculation operator, E represents the expectation calculation operator, and Y represents the total return of the integrated energy system transaction. Represents the i-th risk factor. This represents all risk factors except for the i-th risk factor.

[0058] The formula for calculating the overall sensitivity index of risk factors is as follows:

[0059] In formula (7), This represents the total sensitivity index of the i-th risk factor, reflecting the total contribution of the risk factor itself and its interaction with other risk factors to the total return variance.

[0060] Based on the ranking of the overall sensitivity index, the top-ranked risk factors are selected as key risk factors, providing core objects for subsequent risk transmission path identification and effectiveness quantification model construction.

[0061] This invention identifies key risk factors, uses Granger causality tests to determine the causal relationships between these factors, and constructs a multi-market risk transmission network using directed acyclic graphs to identify key risk transmission paths.

[0062] The Granger causality test is used to verify the temporal causal relationship between two risk factors. If the lagged value of risk factor X significantly improves the prediction accuracy of risk factor Y, then X is said to be a Granger cause of Y, corresponding to the risk being transmitted from X to Y.

[0063] Based on the results of the Granger causality test, a directed acyclic graph (DAG) is constructed. Nodes in the DAG correspond to key risk factors, and directed edges correspond to the direction and intensity of risk transmission. The intensity of risk transmission is quantified by the rate of change of conditional value of risk, reflecting the degree to which the volatility of upstream risk factors affects the extreme losses of downstream risk factors.

[0064] By constructing a risk transmission network using a directed acyclic graph, we can clearly identify the direction, path, and intensity of risk transmission across multiple markets. The path with the highest transmission intensity can be selected as the key risk transmission path, providing a basis for risk transmission mitigation constraints in subsequent effect quantification models.

[0065] Furthermore, in step 3, the conditional value of risk, as a core risk metric, reflects the average level of extreme losses faced by the trading strategy. The calculation of the conditional value of risk is transformed into a convex optimization problem using the auxiliary function method. Among the four dimensions of trading efficiency factors, the basic return efficiency factor is quantified by the ratio of the expected total return of the trading strategy to the expected total return of the benchmark strategy. The benchmark strategy is the integrated energy system's trading strategy that only participates in the day-ahead electricity market. The risk control effectiveness factor is quantified by the ratio of the conditional value at risk of the benchmark strategy to the conditional value at risk of the trading strategy. The risk transmission mitigation effectiveness factor is quantified by the attenuation ratio of the risk transmission intensity along key risk transmission paths before and after the implementation of a trading strategy. The strategy robustness effectiveness factor is the inverse of the coefficient of variation of the trading strategy returns.

[0066] Furthermore, the constraints of the comprehensive transaction efficiency quantification model in step 3 include: The first category is the physical operation constraints of the integrated energy system, including power balance constraints, thermal balance constraints, natural gas balance constraints, upper and lower limits of equipment output constraints, equipment ramping constraints, energy storage equipment charging and discharging constraints, and state of charge constraints. The second category is multi-market trading rule constraints, including upper and lower limits on trading volume in each market, price range constraints, delivery time constraints, and deviation assessment constraints. The third category is total carbon emission constraints; The fourth category is the constraint on the intensity of risk transmission; The fifth category is non-negativity constraints on variables.

[0067] In this embodiment, a multi-market trading profit model is used as the basis, with conditional value at risk as the core risk metric. Multi-dimensional performance factors are introduced to construct a multi-market trading performance quantification model that considers risk adjustment, thereby achieving a comprehensive quantitative evaluation of trading strategies.

[0068] This invention sets the scheduling period as T, with each time step being 1 hour, and the total time step within the scheduling period is T. The integrated energy system operator participates in multiple types of market transactions simultaneously within the scheduling period, and the total revenue is the sum of the net revenues from each market transaction.

[0069] The formula for calculating the total revenue from multi-market transactions in an integrated energy system is as follows:

[0070] In formula (8), This represents the total revenue from multi-market transactions within the integrated energy system during the scheduling period. This indicates the net proceeds from transactions in the electricity market and ancillary services market. This indicates the net trading revenue in the natural gas market. This indicates the net proceeds from transactions in the heat market. This indicates the net trading revenue of the carbon trading market. This indicates the equipment operation and maintenance costs of an integrated energy system.

[0071] The formula for calculating the net proceeds from transactions in the electricity market and ancillary services market is as follows:

[0072] In formula (9), This represents the day-ahead clearing price of the electricity market at time t. This represents the total electricity sold by the integrated energy system in the day-ahead market at time t. A positive value indicates electricity sold, and a negative value indicates electricity purchased. This represents the clearing price of the electricity market at time t within the day. This represents the trading volume of the integrated energy system in the intraday market at time t. This represents the clearing price of electricity in the real-time electricity market at time t. This represents the deviation of the integrated energy system's trading volume in the real-time market at time t. This represents the clearing price of the ancillary services market at time t. This represents the winning bid capacity of the integrated energy system in the ancillary services market at time t. This represents the transmission and distribution price of the power grid at time t. This represents the amount of electricity exchanged between the integrated energy system and the power grid at time t. This represents the unit time step, with a value of 1 hour.

[0073] The formula for calculating net trading revenue in the natural gas market is as follows:

[0074] In formula (10), This represents the trading price of natural gas in the market at time t. This represents the amount of natural gas procured by the integrated energy system at time t. This represents the pipeline transportation price of natural gas at time t. This represents the natural gas pipeline transport volume of the integrated energy system at time t.

[0075] The formula for calculating net trading income in the heat market is as follows:

[0076] In formula (11), This represents the transaction price in the heat market at time t. This represents the amount of heat sold by the integrated energy system to the heat market at time t.

[0077] The formula for calculating net trading revenue in the carbon trading market is as follows:

[0078] In formula (12), This indicates the transaction price in the carbon trading market. This represents the total carbon allowance allocated to the integrated energy system during the scheduling cycle. This indicates the total actual carbon emissions of the integrated energy system during the scheduling cycle.

[0079] The formula for calculating equipment operation and maintenance costs is as follows:

[0080] In formula (13), This represents the unit operating and maintenance cost of the i-th device. Let t represent the output of the i-th device at time t, and N represent the total number of devices in the integrated energy system.

[0081] This invention uses conditional value at risk as the core risk measurement indicator. Conditional value at risk is a consistent risk measurement indicator that can accurately depict the average level of extreme losses and is more reasonable than value at risk.

[0082] First, we define the loss function for multi-market transactions in an integrated energy system. The loss function is the negative of the total revenue, and its specific form is:

[0083] In formula (14), Let X represent the loss function corresponding to the trading strategy, X represent the decision variable vector of the multi-market trading strategy, and S represent the risk scenario vector. This represents the total return corresponding to trading strategy X under risk scenario S.

[0084] At confidence level α, the value at risk is defined as the maximum probability that the loss function will not exceed a certain threshold, specifically in the form of:

[0085] In formula (15), P represents the value at risk of trading strategy X at a confidence level of α, m represents the loss threshold, and α represents the confidence level, which is usually 0.95 or 0.99.

[0086] Conditional value at risk is defined as the conditional expectation that a loss exceeds the value at risk, specifically in the form of:

[0087] In formula (16), Value at risk (VaR) represents the conditional value of risk for trading strategy X at confidence level α, reflecting the average level of extreme losses faced by the trading strategy.

[0088] To simplify the calculation, this invention employs an auxiliary function method to transform the calculation of conditional risk value into a convex optimization problem. The auxiliary function takes the form of:

[0089] In formula (17), The auxiliary function represents the conditional value at risk, where m represents an auxiliary variable corresponding to a value of risk. The value at risk is m when the auxiliary function reaches its minimum value; the minimum value of the auxiliary function is the conditional value at risk.

[0090] This invention breaks through the limitations of the traditional single risk-reward ratio and constructs a four-dimensional trading performance factor to comprehensively reflect the overall performance of the trading strategy.

[0091] The first dimension is the basic return efficiency factor, which reflects the absolute return-generating capability of the trading strategy. It is quantified by the ratio of the expected total return of the trading strategy to the expected return of the benchmark strategy. The benchmark strategy is a trading strategy for integrated energy systems that only participates in the day-ahead electricity market, used to measure the return improvement effect of multi-market collaborative trading. The formula for calculating the basic return efficiency factor is as follows:

[0092] In formula (18), Indicates the basic return efficiency factor. This represents the expected total return of the trading strategy. This represents the expected total return of the benchmark strategy.

[0093] The second dimension is the risk control effectiveness factor, which reflects the risk control capability of the trading strategy. It is quantified by the ratio of the conditional value at risk of the benchmark strategy to the conditional value at risk of the trading strategy, measuring the risk diversification effect of multi-market collaborative trading. The formula for calculating the risk control effectiveness factor is as follows:

[0094] In formula (19), Indicates the risk control effectiveness factor. This represents the conditional value of risk of the benchmark strategy at confidence level α. This represents the conditional value of risk for trading strategy X at confidence level α.

[0095] The third dimension is the risk transmission mitigation effectiveness factor, which reflects the trading strategy's ability to mitigate risk transmission across multiple markets. It is quantified by the attenuation ratio of risk transmission intensity along key risk transmission paths before and after the implementation of the trading strategy, and is one of the core innovations of this invention. The calculation formula for the risk transmission mitigation effectiveness factor is as follows:

[0096] In formula (20), Indicates the risk transmission and slow-release efficacy factor. This indicates the initial risk transmission strength along a key risk transmission path without trading strategy constraints. This indicates the actual risk transmission intensity of the key risk transmission path after the implementation of trading strategy X.

[0097] The fourth dimension is the strategy robustness effectiveness factor, which reflects the stability of a trading strategy's returns under different risk scenarios. It is calculated by taking the inverse of the coefficient of variation of the strategy's returns. The smaller the coefficient of variation, the stronger the strategy's return stability and the better its robustness. The formula for calculating the strategy robustness effectiveness factor is as follows:

[0098] In formula (21), This represents the strategy robustness performance factor. The standard deviation of the total return of a trading strategy reflects the volatility of the returns.

[0099] This invention determines the objective weights of four performance factors based on the entropy weight method, avoiding the bias caused by subjective weighting, and thus constructs a comprehensive transaction performance quantification model.

[0100] First, construct the performance factor decision matrix. For M groups of candidate trading strategies, each strategy corresponds to the values ​​of four performance factors, and the decision matrix takes the form of:

[0101] In formula (22), A represents the efficiency factor decision matrix. represents the value of the j-th performance factor of the i-th trading strategy, M represents the total number of alternative trading strategies, and 4 represents the number of performance factors.

[0102] The decision matrix is ​​standardized to eliminate the influence of dimensions. The standardized matrix is ​​as follows:

[0103] In formula (23), B represents the standardized decision matrix. This represents the value of the j-th performance factor of the i-th trading strategy after standardization.

[0104] The information entropy of the j-th efficiency factor is calculated using the following formula:

[0105] In formula (24), This represents the information entropy of the j-th performance factor. This represents the proportion of the j-th performance factor value of the i-th trading strategy to the total value of that factor, calculated using the following formula: .

[0106] The weight of the j-th performance factor is calculated using the following formula:

[0107] In formula (25), Let the weight of the j-th performance factor be denoted as , satisfying And all weights are non-negative.

[0108] The final comprehensive transaction efficiency quantification model is as follows:

[0109] In formula (26), The comprehensive transaction efficiency index is the core output of this invention. , , , The weights correspond to the basic return efficiency factor, risk control efficiency factor, risk transmission and mitigation efficiency factor, and strategy robustness efficiency factor, respectively.

[0110] The constraints of the comprehensive trading efficiency quantification model include five categories: physical operation constraints of the comprehensive energy system, multi-market trading rule constraints, total carbon emission constraints, risk transmission intensity constraints, and variable non-negativity constraints.

[0111] The physical operation constraints of an integrated energy system include power balance constraints, thermal balance constraints, natural gas balance constraints, upper and lower limits of equipment output constraints, equipment ramp-up constraints, energy storage equipment charge and discharge constraints, and state of charge constraints.

[0112] Multi-market trading rules include upper and lower limits on trading volume in each market, price range constraints, delivery time constraints, and deviation assessment constraints.

[0113] The total carbon emission constraint is that the actual total carbon emissions of the integrated energy system during the scheduling cycle shall not exceed the sum of the total carbon quota and the carbon market purchase volume.

[0114] The risk transmission strength constraint ensures that, after the implementation of the trading strategy, the risk transmission strength on the key risk transmission path does not exceed the set upper limit, thus avoiding the amplification of risk across multiple markets.

[0115] The non-negativity constraint ensures that all decision variables take non-negative values, which aligns with the physical meaning of actual transactions and operations.

[0116] Furthermore, the improved moth flame optimization algorithm in step 4 is improved in three aspects: first, chaotic mapping is introduced to initialize the population, thereby increasing the diversity of initial solutions and expanding the search range of the algorithm; Secondly, an adaptive weighting factor is introduced, which uses a larger weight in the early stage of iteration to enhance the global search capability, and a smaller weight in the later stage of iteration to enhance the local development capability. Third, an elite reverse learning strategy is introduced, which performs reverse learning on the elite individuals in each iteration to generate new high-quality individuals; The position of the moth corresponds to the decision variable of the comprehensive transaction efficiency quantification model, the fitness value of the moth corresponds to the comprehensive transaction efficiency index, and the number of flames is adaptively updated according to the number of iterations. The alternating direction multiplier method decomposes the original optimization problem into four subproblems: the revenue optimization subproblem, the risk quantification subproblem, the efficiency evaluation subproblem, and the risk transmission constraint subproblem. The augmented Lagrangian function of the original problem includes the decision variables, objective function, Lagrangian multiplier vector, and penalty factor of the four subproblems.

[0117] In this embodiment, for the high-dimensional nonlinear constrained comprehensive transaction efficiency quantification model constructed by this invention, traditional solution algorithms suffer from problems such as being prone to getting trapped in local optima, slow convergence speed, and insufficient solution accuracy. This invention proposes a hybrid solution algorithm combining the improved moth-flame optimization and the alternating direction multiplier method. By combining the global search capability of the metaheuristic algorithm with the distributed solution advantage of the alternating direction multiplier method, the model can be solved efficiently and accurately.

[0118] The moth-flame optimization algorithm is a metaheuristic intelligent optimization algorithm based on the moth's lateral positioning and navigation mechanism. It achieves global search through the moth's spiral position update around the flame, characterized by its simple structure and strong search capability. However, traditional moth-flame optimization algorithms are prone to getting trapped in local optima in the later stages of iteration, resulting in insufficient convergence accuracy. This invention improves upon the traditional algorithm in three aspects: First, it introduces a chaotic mapping to initialize the population, increasing the diversity of initial solutions and expanding the algorithm's search range. Second, it introduces an adaptive weighting factor to balance the algorithm's global search and local exploitation capabilities. Larger weights are used in the early stages of iteration to strengthen the global search capability, while smaller weights are used in the later stages to strengthen the local exploitation capability. Third, it introduces an elite back-learning strategy, performing back-learning on the elite individuals in each iteration to generate new high-quality individuals, thus avoiding the algorithm getting trapped in local optima.

[0119] The alternating direction multiplier method is a distributed optimization algorithm that decomposes a high-dimensional original optimization problem into multiple low-dimensional subproblems. These subproblems are solved separately and then converged iteratively through a coordination factor, significantly reducing the dimensionality of the solution and improving the solution speed. This invention decomposes the original comprehensive transaction efficiency quantification model into four subproblems: a profit optimization subproblem, a risk quantification subproblem, an efficiency evaluation subproblem, and a risk transmission constraint subproblem. The alternating direction multiplier method is used to achieve distributed solving and iterative coordination of these subproblems.

[0120] The moth's position corresponds to the decision variable in the comprehensive transaction efficiency quantification model, and the moth's fitness value corresponds to the comprehensive transaction efficiency index. The improved moth position update formula is as follows:

[0121] In formula (27), Let represent the updated position of the i-th moth. Indicates the adaptive weighting factor. Let represent the distance between the i-th moth and the j-th flame, b represent a constant defining the spiral shape, and l represent a random number between [-1, 1]. This indicates the position of the j-th flame.

[0122] The formula for calculating the adaptive weighting factor is as follows:

[0123] In formula (28), This represents the maximum value of the adaptive weights. This represents the minimum value of the adaptive weights, and k represents the current iteration number. This indicates the maximum number of iterations.

[0124] The adaptive update formula for the number of flames is:

[0125] In formula (29), This represents the number of flames corresponding to the current iteration number, N represents the initial size of the moth population, and round represents the rounding operator.

[0126] This invention decomposes the objective function of the original optimization problem into four sub-objective functions, each corresponding to one of the four sub-problems. The augmented Lagrangian function of the original problem is:

[0127] In formula (30), This represents the augmented Lagrange function. , , , These represent the decision variables for the four sub-problems. , , , Let each represent the objective function of the four subproblems. Denotes the Lagrange multiplier vector. Let A, B, C, and D represent the coefficient matrices of the subproblems, and c represent the right-hand side of the equality constraint. This represents the L2 norm computation operator.

[0128] The iterative formula for the alternating direction multiplier method is:

[0129] In formulas (31) to (35), k represents the current iteration number, the superscript k represents the calculation result of the kth iteration, and the superscript k+1 represents the calculation result of the (k+1)th iteration.

[0130] The execution steps of the hybrid solution algorithm are divided into seven stages.

[0131] The first stage is the initialization of algorithm parameters. This involves setting the moth population size, maximum number of iterations, maximum and minimum values ​​of adaptive weights, spiral shape constant, penalty factor, convergence accuracy threshold, and initializing the position of the moth population and the Lagrange multiplier vector.

[0132] The second stage is the decomposition of the original problem. The original comprehensive transaction efficiency quantification model is decomposed into a profit optimization sub-problem, a risk quantification sub-problem, an efficiency evaluation sub-problem, and a risk transmission constraint sub-problem, and the decision variables, objective function, and constraints for each sub-problem are determined.

[0133] The third stage involves solving the subproblems. An improved moth-flame optimization algorithm is used to solve the four subproblems, obtaining the optimal solution and corresponding objective function value for each subproblem.

[0134] The fourth stage is the Lagrange multiplier update. Based on the solutions to the four subproblems, the Lagrange multiplier vectors and penalty factors are updated according to the iterative formula.

[0135] The fifth stage is the convergence test. The equality constraint residuals of the original problem are calculated, and it is determined whether the residuals are less than the set convergence accuracy threshold. If the convergence condition is met, the process proceeds to the sixth stage. If the convergence condition is not met, the process returns to the third stage to continue iterating.

[0136] The sixth stage is the output of the optimal solution. The output includes the optimal decision variables that satisfy the convergence conditions, along with the corresponding comprehensive trading efficiency index, expected total return, conditional value at risk, risk transmission strength, and robustness index.

[0137] The seventh stage is model validation. The optimal strategy obtained by solving the problem is compared with the traditional strategy to verify the superiority of the model and algorithm of this invention.

[0138] The following is a specific embodiment. This implementation plan takes a regional integrated energy system in northern my country as the implementation object. Combining actual operation data and market transaction rules, the technical solution proposed in this invention is specifically implemented to verify the feasibility and superiority of this invention.

[0139] The regional integrated energy system selected in this implementation plan serves the industrial park and surrounding residential communities, with a total peak power supply load of 80MW and a total peak heating load of 60MW. The energy production and conversion equipment included in the system includes one 40MW gas turbine combined heat and power unit, two 20MW gas boilers, two 15MW electric boilers, a 30MW photovoltaic power station, a 20MW wind farm, a 20MW lithium battery energy storage system, and a 30MW / 120MWh thermal storage tank.

[0140] Integrated energy system operators participate in six types of market transactions, including the day-ahead electricity market, intraday electricity market, real-time electricity market, AGC ancillary services market, natural gas pipeline trading market, regional heating market, and national carbon trading market.

[0141] The electricity market adopts a three-tiered trading model: day-ahead, intraday, and real-time. The day-ahead market submits electricity and price curves for the following 24 hours one day in advance; the intraday market adjusts electricity volumes four hours in advance; and the real-time market settles deviations within 15 minutes. The ancillary services market uses a centralized bidding clearing method, with winning units providing AGC frequency regulation services and receiving corresponding revenue. The natural gas market uses a monthly long-term contract + daily spot market trading model, with fixed monthly long-term contract prices and market-driven daily spot prices. The heat market uses a two-part pricing model, including fixed capacity fees and variable flow fees. The carbon trading market uses a quota trading model, with quota allocation based on a baseline method. Excess emissions must be compensated by purchasing additional quotas in the carbon market, while remaining quotas can be sold.

[0142] The scheduling cycle for this implementation plan is 24 hours per typical heating day, with a time step of 1 hour and a total time step of 24. The confidence level is set at 95%, and the number of risk scenarios generated by the Monte Carlo simulation is 10,000.

[0143] This implementation plan strictly follows the core logic of the technical solution and is divided into four core implementation phases. The specific implementation steps are as follows.

[0144] Phase 1: Analysis of Multi-Market Risk Transmission Mechanisms and Construction of Multi-Type Market Risk Sets Step 1: Quantifying Multi-Market Coupling Relationships This step first quantifies the coupling strength among multiple markets, using a coupling degree model to calculate the coupling degree values ​​between each market. The calculated coupling degree for the electricity-gas market is 0.78, indicating a strong coupling level. The calculated coupling degree for the electricity-heat market is 0.85, also indicating a strong coupling level. The calculated coupling degree for the electricity-carbon market is 0.62, indicating a moderately strong coupling level. The calculated coupling degree for the cross-timescale electricity market is 0.91, indicating an extremely strong coupling level. The quantified coupling results verify the existence of significant coupling relationships among multiple markets, providing a channel for risk transmission.

[0145] Step 2: Risk Source Identification and Data Collection This step comprehensively identifies potential risk sources in multi-market transactions and collects historical operational data for the corresponding risk factors. The data collection period is from January 2022 to December 2024, with a time resolution of 1 hour. The collected data includes historical electricity price data for day-ahead, intraday, and real-time electricity markets; historical price data for the AGC ancillary services market; historical price data for monthly long-term contracts and daily spot prices of natural gas; historical price data for the heat market; historical transaction price data for the carbon trading market; historical operational data for the electricity, heat, and gas loads of industrial parks; historical data on equipment failures; and historical documents related to market trading rules and policy adjustments.

[0146] Step 3: Construction of Multi-Type Market Risk Sets This step constructs a standardized multi-type market risk set based on the identified risk sources. The risk set contains four primary subsets, totaling 16 specific risk factors.

[0147] The market price risk subset includes seven risk factors: day-ahead electricity market price risk, intraday electricity market price risk, real-time electricity market price risk, AGC ancillary service market price risk, natural gas market price risk, heat market price risk, and carbon trading market price risk.

[0148] The market demand risk subset includes three risk factors: electricity demand fluctuation risk, heat demand fluctuation risk, and gas demand fluctuation risk.

[0149] The risk subset of the coupling link includes three risk factors: gas turbine failure risk, energy storage equipment failure risk, and thermal pipeline blockage risk.

[0150] The policy and rule risk subset includes three risk factors: the risk of adjustments to electricity market trading rules, the risk of changes in carbon quota allocation policies, and the risk of adjustments to natural gas price control policies.

[0151] The final risk set conforms to the standardized expression of formula (1), providing a complete risk factor system for subsequent risk quantification.

[0152] Phase Two: Quantification of Multi-Dimensional Risk Factors and Identification of Key Risk Transmission Paths Step 1: Risk Factor Data Preprocessing This step preprocesses the collected historical data. First, the 3σ criterion is used to remove outliers to ensure data validity. Second, the augmented Dickey-Fuller test is used to test the stationarity of all risk factor sequences. The test results show that all sequences reject the null hypothesis of a unit root at the 1% significance level, indicating that all sequences are stationary. Finally, the Jacques-Bella test is used to test the normality of the sequences. The test results show that all sequences reject the null hypothesis of a normal distribution at the 1% significance level, indicating that the sequences have significant leptokurtic and heavy-tailed characteristics, making them suitable for fitting using extreme value theory.

[0153] Step 2: Fitting the marginal distribution of risk factors based on the POT-GPD model For each risk factor, this step constructs a loss sequence according to formula (2), uses the average remaining lifetime map method to determine the threshold u of excess loss, estimates the shape parameter ξ and scale parameter β of the generalized Pareto distribution by the maximum likelihood estimation method, and verifies the fitting effect by the Kolmogorov-Smirnov test.

[0154] Taking the real-time electricity market price risk factor as an example, the determined threshold u is 0.032, the estimated shape parameter ξ is 0.216, the scaling parameter β is 0.018, and the Kolmogorov-Smirnov test p-value is 0.372, which is greater than the significance level of 0.05, indicating a good fit. The shape parameter ξ being greater than 0 verifies that the sequence has a heavy-tailed characteristic, consistent with the pattern of energy market price fluctuations.

[0155] Marginal distributions were fitted sequentially to the 16 risk factors in the risk set to obtain the optimal generalized Pareto distribution parameters for each risk factor. All fitting results passed the significance test, ensuring the fitting accuracy of the marginal distributions.

[0156] Step 3: Constructing the joint distribution of multiple risk factors based on the Pair-Copula function This step, based on the fitted marginal distributions of risk factors, constructs a joint distribution of 16-dimensional risk factors using a Pair-Copula function with a C-vine structure. The optimal type of each pairwise Copula function is selected using the Akaike Information Criterion, with Gumbel Copula accounting for 42%, Clayton Copula for 35%, and t-Copula for 23%, verifying the significant nonlinear tail correlation among the risk factors. By fitting the joint distribution function of the 16-dimensional risk factors, the dependency structure among multiple risk factors is accurately characterized.

[0157] Step 4: Monte Carlo simulation risk scenario generation This step, based on the fitted joint distribution function of 16 risk factors, uses Monte Carlo simulation to generate 10,000 risk scenarios. Each scenario includes the time-series values ​​of 16 risk factors over a 24-hour scheduling period. The generated risk scenarios cover both normal operation and extreme risk scenarios, with extreme risk scenarios accounting for approximately 5%, meeting the 95% confidence level risk measurement requirement and providing a full-scenario sample for subsequent return and risk quantification.

[0158] Step 5: Identification of Key Risk Factors Based on the 10,000 risk scenarios generated, this step uses the Sobol global sensitivity analysis method to calculate the first-order sensitivity index and the total sensitivity index of each risk factor to the total return. The calculation results are shown in Table 1 (only the top 5 risk factors are shown).

[0159] Table 1. Calculation Results of Sensitivity Index for Key Risk Factors

[0160] Based on the ranking of the overall sensitivity index, the top 5 risk factors were selected as key risk factors to provide core targets for subsequent risk transmission path identification.

[0161] Step 6: Identification of Key Risk Transmission Paths This step, based on the five identified key risk factors, uses Granger causality tests to determine the causal relationships between the risk factors. The test results show that natural gas market price risk is a Granger cause of day-ahead electricity market price risk, day-ahead electricity market price risk is a Granger cause of real-time electricity market price risk, carbon trading market price risk is a Granger cause of day-ahead electricity market price risk, and electricity load demand fluctuation risk is a Granger cause of real-time electricity market price risk.

[0162] Based on the results of the Granger causality test, a risk transmission network in the form of a directed acyclic graph was constructed, the risk transmission intensity of each transmission path was calculated, and three key risk transmission paths were finally identified.

[0163] The first key risk transmission path is natural gas market price risk → day-ahead electricity market price risk → real-time electricity market price risk, with a transmission strength of 0.68.

[0164] The second key risk transmission path is carbon trading market price risk → day-ahead electricity market price risk → real-time electricity market price risk, with a transmission strength of 0.52.

[0165] The third key risk transmission path is the risk of fluctuations in electricity load demand → the risk of real-time electricity market prices, with a transmission strength of 0.47.

[0166] The identification results of key risk transmission paths provide a clear basis for risk transmission mitigation constraints in subsequent effect quantification models.

[0167] Phase 3: Construction of a risk-adjusted multi-market trading efficiency quantification model Step 1: Building a Multi-Market Trading Profit Model Based on the equipment parameters and market transaction rules of the implementation object, this step constructs a multi-market transaction revenue model according to formulas (8) to (13), and clarifies the input parameters and decision variables of the model.

[0168] The model's input parameters include the equipment's rated capacity, power generation efficiency, heating efficiency, unit operation and maintenance cost, historical price data for each market, load forecast data, wind and solar power output forecast data, and total carbon quota allocation.

[0169] The decision variables of the model include the electricity traded in the day-ahead, intraday, and real-time electricity markets at each time point, the winning bid capacity in the ancillary services market at each time point, the natural gas purchase volume at each time point, the heat sold at each time point, the output plan of each device at each time point, the charging and discharging plan of the energy storage device, and the charging and discharging plan of the thermal storage tank.

[0170] Based on the constructed profit model, the expected total return of the benchmark strategy is calculated. The benchmark strategy is a trading strategy in which the integrated energy system only participates in the day-ahead electricity market, and the expected total return of the benchmark strategy is calculated to be 386,200 yuan.

[0171] Step 2: Building a Risk Measurement Model This step constructs a risk measurement model based on conditional value of risk according to formulas (14) to (17), with a confidence level set at 95%. Based on 10,000 risk scenarios generated by Monte Carlo simulation, the conditional value of risk of the benchmark strategy is calculated. The conditional value of risk of the benchmark strategy at a 95% confidence level is RMB 128,500, reflecting that the average level of extreme losses faced by the benchmark strategy is RMB 128,500.

[0172] Step 3: Calculation of multi-dimensional trading performance factors This step constructs four-dimensional trading efficiency factors according to formulas (18) to (21), and clarifies the calculation method of each factor.

[0173] The basic return efficiency factor is the ratio of the expected total return of the trading strategy to the expected total return of the benchmark strategy, reflecting the return improvement effect of multi-market trading.

[0174] The risk control effectiveness factor is the ratio of the conditional value at risk of the benchmark strategy to the conditional value at risk of the trading strategy, reflecting the risk diversification effect of multi-market trading.

[0175] The risk transmission mitigation effectiveness factor is the percentage decrease in the intensity of risk transmission along key risk transmission paths before and after the implementation of a trading strategy, reflecting the strategy's ability to mitigate risk transmission. In this step, without trading strategy constraints, the initial risk transmission intensity of the key risk transmission paths is set at 0.68, corresponding to the transmission intensity of the first key transmission path.

[0176] The strategy robustness performance factor is the ratio of the expected total return of a trading strategy to the standard deviation of its returns, reflecting the stability of the strategy's returns under different risk scenarios.

[0177] Step 4: Determining the weights of performance factors This step determines the objective weights of the four performance factors based on the entropy weight method. First, 20 candidate trading strategies are selected, and the values ​​of the four performance factors corresponding to each strategy are calculated to construct a performance factor decision matrix. The matrix is ​​then standardized. The information entropy of each performance factor is calculated according to formula (24). The information entropy of the basic return performance factor is 0.862, the information entropy of the risk control performance factor is 0.825, the information entropy of the risk transmission and mitigation performance factor is 0.914, and the information entropy of the strategy robustness performance factor is 0.887.

[0178] The weights of each performance factor are calculated according to formula (25). The weights of the basic return performance factor are 0.28, the risk control performance factor is 0.35, the risk transmission and mitigation performance factor is 0.17, and the strategy robustness performance factor is 0.20. The sum of the four weights is 1, which meets the normalization requirement of the weights.

[0179] Step 5: Construction of a comprehensive transaction efficiency quantification model This step constructs a comprehensive transaction efficiency quantitative model according to formula (26). The objective function of the model is to maximize the comprehensive transaction efficiency index \(\eta_{total}\).

[0180] The model has five types of constraints, as detailed below.

[0181] The first category is the physical operation constraints of the integrated energy system, including power balance constraints, thermal balance constraints, natural gas balance constraints, upper and lower limits of equipment output constraints, equipment ramp-up constraints, and charging / discharging constraints and state of charge constraints of the energy storage system. Among them, the state of charge constraint of the energy storage system is 0.1 to 0.9, and the upper and lower limits of charging / discharging power are -20MW to 20MW, with the negative sign indicating charging.

[0182] The second category is multi-market trading rule constraints, including upper and lower limits for trading volume in each market. The upper and lower limits for day-ahead market trading volume are -80MW to 80MW, with a negative sign indicating power purchase. The upper and lower limits for real-time market deviation trading volume are -20MW to 20MW.

[0183] The third category is the total carbon emission constraint, where the actual total carbon emissions during the scheduling period do not exceed the sum of the allocated total carbon quota and the carbon market purchase volume.

[0184] The fourth category is the risk transmission strength constraint. After the trading strategy is implemented, the risk transmission strength on the key risk transmission path shall not exceed 0.4 to avoid the amplification of risk.

[0185] The fifth category is non-negativity constraints, where all decision variables such as equipment output, transaction volume, and procurement volume satisfy non-negativity constraints.

[0186] The final comprehensive trading effectiveness quantification model fully covers four dimensions: returns, risks, risk transmission and mitigation, and robustness, enabling comprehensive quantitative evaluation of multi-market trading strategies.

[0187] Phase 4: Solving with Hybrid Algorithms and Result Analysis Step 1: Algorithm parameter initialization This step initializes the parameters of the hybrid solution algorithm combining the improved moth flame optimization and the alternating direction multiplier method. The moth population size is set to 50, the maximum number of iterations to 200, the maximum adaptive weight to 0.9, the minimum to 0.2, the spiral shape constant b to 1, the penalty factor ρ to 1.5, and the convergence accuracy threshold to 1e-6. The positions of the moth population are initialized, corresponding to the model's decision variables, and the Lagrange multiplier vectors are initialized to zero.

[0188] Step 2: Decomposition of the original problem and solution of subproblems This step decomposes the original comprehensive transaction efficiency quantification model into four sub-problems: profit optimization, risk quantification, efficiency evaluation, and risk transmission constraint. An improved moth-flame optimization algorithm is then used to solve each of the four sub-problems, yielding the optimal solution for each.

[0189] Step 3: Iterative Update and Convergence Judgment This step updates the Lagrange multiplier vectors according to formulas (31) to (35) based on the solution results of the subproblems, and calculates the equality constraint residuals. When the number of iterations reaches 126, the constraint residuals are less than the convergence accuracy threshold of 1e-6, the algorithm converges, and the iteration stops.

[0190] Step 4: Output the optimal result This step outputs the optimal result after the algorithm converges, including the optimal multi-market trading strategy, comprehensive trading performance index, expected total return, conditional value at risk, risk transmission strength, and robustness index.

[0191] The optimal strategy has a comprehensive trading performance index of 1.86 and an expected total return of 548,400 yuan, representing a 42.0% improvement over the benchmark strategy. The conditional value of risk at a 95% confidence level is 75,800 yuan, a 41.0% decrease compared to the benchmark strategy. The risk transmission strength of the key risk transmission path is 0.32, a 52.9% decrease compared to the initial value, meeting the risk transmission strength constraint requirements. The strategy robustness performance factor is 4.82, a 61.2% improvement compared to the benchmark strategy's 2.99.

[0192] Step 5: Model Validation and Comparative Analysis This step compares the model proposed in this invention with the traditional profit maximization model and the traditional Sharpe ratio efficiency quantification model. The comparison results are shown in Table 2.

[0193] Table 2 Comparison of Calculation Results for Different Models

[0194] The comparative results show that the traditional return maximization model has the highest expected total return, but it also faces the greatest extreme risk, the strongest risk transmission, and the lowest overall trading efficiency. While the traditional Sharpe ratio model improves risk control compared to the return maximization model, it does not consider the mitigation effect of risk transmission, and its overall trading efficiency is still lower than that of the model proposed in this invention. The model proposed in this invention, while ensuring increased returns, significantly reduces extreme risk and the intensity of risk transmission, and its overall trading efficiency is significantly better than the traditional model, verifying the superiority of this invention.

[0195] This implementation plan, based on a real-world regional integrated energy system, fully implements the technical solution proposed in this invention. It successfully constructs a quantitative model of multi-market trading efficiency considering both revenue and risk, and achieves efficient model solving through an improved hybrid solution algorithm. The results show that the model proposed in this invention can accurately quantify the comprehensive efficiency of multi-market trading. While improving trading returns, it effectively controls extreme risks and risk transmission between multiple markets. The comprehensive trading efficiency is significantly better than traditional models, providing accurate and reliable technical support for multi-market trading decisions by integrated energy system operators.

[0196] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces, or indirect coupling or communication connection between apparatuses or units, and may be electrical, mechanical, or other forms.

[0197] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated units described above can be implemented in hardware or as software functional units. The above are merely embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made based on the description and drawings of this application, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

[0198] The specific embodiments of the invention have been described in detail above, but they are only examples, and this application is not limited to the specific embodiments described above. For those skilled in the art, any equivalent modifications or substitutions to the invention are also within the scope of this application. Therefore, all equivalent changes, modifications, and improvements made without departing from the spirit and principles of this application should be covered within the scope of this application.

Claims

1. A method for quantifying the risk-return efficiency of integrated energy multi-market transactions, characterized in that, Includes the following steps: Step 1: Analysis of multi-market risk transmission mechanisms and construction of multi-type market risk sets, clarifying the boundaries and coupling relationships of multi-market transactions in the integrated energy system, revealing the risk transmission mechanism, and constructing standardized multi-type market risk sets; Step 2: Quantification of multi-dimensional risk factors and identification of key risk transmission paths. Extreme value theory is used to fit the marginal distribution of risk factors, the nonlinear dependence structure of multiple risk factors is characterized by the Pair-Copula function, Monte Carlo simulation is combined to generate full-scenario risk samples, Sobol global sensitivity analysis is used to identify key risk factors, and Granger causality test and directed acyclic graph are used to identify key risk transmission paths. Step 3: Consider the construction of a risk-adjusted multi-market trading efficiency quantification model. Based on the multi-market trading return model and with conditional value at risk as the core risk measurement indicator, construct a trading efficiency factor system, determine objective weights based on the entropy weight method, and construct a comprehensive trading efficiency quantification model. Step 4: Improve the hybrid solution of moth flame optimization and alternating direction multiplier method. Introduce chaotic mapping to initialize the population, adaptive weight factor and elite back learning strategy to improve the moth flame optimization algorithm. Decompose the original model into four sub-problems for distributed solution by alternating direction multiplier method.

2. The method for quantifying the risk-return efficiency of integrated energy multi-market transactions according to claim 1, characterized in that, The coupling relationships among the multiple markets in step 1 include: There are multiple types of coupling channels. The first type is the electro-gas coupling channel, which realizes the bidirectional conversion of electricity and natural gas through gas turbines and electro-gas conversion equipment. The second type is the electro-thermal coupling channel, which realizes the bidirectional conversion of electricity and heat through cogeneration units and electric boilers; The third category is the electricity-carbon coupling channel, which forms a coupling relationship through carbon emissions generated from fossil energy consumption; The fourth category is the cross-timescale electricity market coupling channel, which covers the interaction between the day-ahead market, intraday market and real-time market.

3. The method for quantifying the risk-return efficiency of integrated energy multi-market transactions according to claim 1, characterized in that, The driving factors of the risk transmission mechanism in step 1 include: Market coupling strength, correlation of trading positions, impact intensity of risk events, and market liquidity are all factors that influence risk transmission efficiency across multiple markets. Higher market coupling strength, stronger correlation of trading positions, greater impact intensity of risk events, weaker market liquidity, and higher efficiency of risk transmission across multiple markets are all factors that influence market coupling strength.

4. The method for quantifying the risk-return efficiency of integrated energy multi-market transactions according to claim 1, characterized in that, The multi-type market risk set in step 1 includes: The four primary subsets contain multiple specific risk factors. Among them, the market price risk subset includes seven risk factors: day-ahead electricity market price risk, intraday electricity market price risk, real-time electricity market price risk, ancillary services market price risk, natural gas market price risk, heat market price risk, and carbon trading market price risk. The market demand risk subset includes three risk factors: electricity demand fluctuation risk, heat demand fluctuation risk, and gas demand fluctuation risk. The risk subset of the coupling link includes the risk of energy conversion equipment failure and the risk of energy transmission network congestion; The policy and rule risk subset includes the risk of adjustments to market trading rules, the risk of changes in carbon quota allocation policies, and the risk of adjustments to energy price control policies.

5. The method for quantifying the risk-return efficiency of integrated energy multi-market transactions according to claim 1, characterized in that, Step 2 also includes: The tail distribution of risk factors is fitted using the over-threshold model in extreme value theory. A loss sequence is constructed for any risk factor, defined as the negative logarithmic return of the risk factor. An excess loss sequence is constructed after setting a preset threshold for excess loss. The excess loss sequence follows a generalized Pareto distribution. The parameters of the generalized Pareto distribution are estimated by the maximum likelihood estimation method, and the fitting effect is verified by the Kolmogorov-Smirnov test.

6. The method for quantifying the risk-return efficiency of integrated energy multi-market transactions according to claim 1, characterized in that, In step 2, the Pair-Copula function decomposes the high-dimensional joint distribution into the product of multiple pairwise Copula functions based on the vine structure. The optimal Copula function type is selected by the Akaike Information Criterion. Among them, Gumbel Copula can accurately characterize the upper tail correlation and is suitable for capturing the risk transmission under extreme upward market conditions, while Clayton Copula characterizes the lower tail correlation and is suitable for capturing the risk transmission under extreme downward market conditions.

7. The method for quantifying the risk-return efficiency of integrated energy multi-market transactions according to claim 1, characterized in that, In step 2, Sobol global sensitivity analysis calculates the first-order sensitivity index and the total sensitivity index of each risk factor on the total return of the integrated energy system transaction. The first-order sensitivity index reflects the degree of independent contribution of the risk factor itself to the variance of the total return, while the total sensitivity index reflects the degree of contribution of the risk factor itself and its interaction with other risk factors to the variance of the total return. Based on the ranking results of the total sensitivity index, the risk factors with the highest ranking are selected as key risk factors. The Granger causality test is used to verify the temporal causal relationship between two risk factors. If the lagged value of risk factor X improves the prediction accuracy of risk factor Y, then X is called a Granger cause of Y. Based on the results of the Granger causality test, a risk transmission network in the form of a directed acyclic graph is constructed. The nodes in the directed acyclic graph correspond to key risk factors, and the directed edges correspond to the direction and intensity of risk transmission.

8. The method for quantifying the risk-return efficiency of integrated energy multi-market transactions according to claim 1, characterized in that, In step 3, conditional value of risk, as a core risk metric, reflects the average level of extreme losses faced by the trading strategy. The calculation of conditional value of risk is transformed into a convex optimization problem using the auxiliary function method. Among the four dimensions of trading efficiency factors, the basic return efficiency factor is quantified by the ratio of the expected total return of the trading strategy to the expected total return of the benchmark strategy. The benchmark strategy is the integrated energy system's trading strategy that only participates in the day-ahead electricity market. The risk control effectiveness factor is quantified by the ratio of the conditional value at risk of the benchmark strategy to the conditional value at risk of the trading strategy. The risk transmission mitigation effectiveness factor is quantified by the attenuation ratio of the risk transmission intensity along key risk transmission paths before and after the implementation of a trading strategy. The strategy robustness effectiveness factor is the inverse of the coefficient of variation of the trading strategy returns.

9. The method for quantifying the risk-return efficiency of integrated energy multi-market transactions according to claim 1, characterized in that, The constraints of the comprehensive transaction efficiency quantification model in step 3 include: The first category is the physical operation constraints of the integrated energy system, including power balance constraints, thermal balance constraints, natural gas balance constraints, upper and lower limits of equipment output constraints, equipment ramping constraints, energy storage equipment charging and discharging constraints, and state of charge constraints. The second category is multi-market trading rule constraints, including upper and lower limits on trading volume in each market, price range constraints, delivery time constraints, and deviation assessment constraints. The third category is total carbon emission constraints; The fourth category is the constraint on the intensity of risk transmission; The fifth category is non-negativity constraints on variables.

10. The method for quantifying the risk-return efficiency of integrated energy multi-market transactions according to claim 1, characterized in that, The improved moth flame optimization algorithm in step 4 is improved in three aspects: first, chaotic mapping is introduced to initialize the population, which increases the diversity of initial solutions and expands the search range of the algorithm; Secondly, an adaptive weighting factor is introduced, which uses a larger weight in the early stage of iteration to enhance the global search capability, and a smaller weight in the later stage of iteration to enhance the local development capability. Third, an elite reverse learning strategy is introduced, which performs reverse learning on the elite individuals in each iteration to generate new high-quality individuals; The position of the moth corresponds to the decision variable of the comprehensive transaction efficiency quantification model, the fitness value of the moth corresponds to the comprehensive transaction efficiency index, and the number of flames is adaptively updated according to the number of iterations. The alternating direction multiplier method decomposes the original optimization problem into four subproblems: the revenue optimization subproblem, the risk quantification subproblem, the efficiency evaluation subproblem, and the risk transmission constraint subproblem. The augmented Lagrangian function of the original problem includes the decision variables, objective function, Lagrangian multiplier vector, and penalty factor of the four subproblems.

Images