Output Uncertainty Research Articles

Stochastic Flexible Resource Operations in Coordinated Green-Seaport Energy-Logistics Systems Using Constraint Generation Approach

The increasing penetration of renewable energy sources (RESs) in modern green seaports calls for more flexible management approaches that can minimize the daily seaport operation costs and RES curtailments. This paper establishes an optimal strategy in two-time intervals for flexible operations of energy storage systems and combined electric-thermal power demands of reefer containers in the coordinated green-seaport energy-logistics systems (ELS). For the day-ahead operation, a multi-stage stochastic optimization model is established to minimize the expected ELS operation cost according to the 24-hour-ahead forecasts. Uncertainties of RES power outputs, load demands, electricity prices, and ambient temperatures are considered in the optimization of day-ahead operation. For the intra-day operation, hydrogen, battery, and thermal storage systems as well as reefer containers operations are optimized based on the short-lead-time forecasts. Numerical simulations are carried out based on the Jurong seaport operation in Singapore to verify the effectiveness of the proposed optimal operation strategy for the coordinated green-seaport ELS. Simulation results reveal that the proposed strategy can achieve the lowest operation cost and the lowest RES curtailment in a green-seaport.

Probabilistic Voltage Optimization Considering Load Static Voltage Characteristics

In the conventional power flow calculation, the load is mostly treated as a constant power node. When the voltage deviation occurs, the static voltage characteristics of the load will change, resulting in the change of the power flow calculation. This situation is more likely to occur in the distribution network with distributed power supply. Therefore, it is very important to consider the static voltage response characteristics of the load in the power flow calculation. In the existing literature, when evaluating and optimizing voltage stability, deterministic indicators are usually used to evaluate the voltage level of the system. In the active distribution network with uncertain new energy output, this method has its limitations. Based on the above analysis, this paper uses the power flow calculation method considering the static voltage characteristics of the load to solve the node voltage distribution of the distribution network system. Considering the uncertainty of new energy output and load, the semi-invariant method is used to analyze the probabilistic power flow. An evaluation index considering the digital characteristics of voltage deviation distribution is proposed. The voltage optimization model is established according to the proposed index, and the genetic algorithm is used to solve the problem. The IEEE33 node standard example is simulated to verify the correctness and feasibility of the proposed method.

Prediction of Non-Stationary Multi-Head Cloud Motion Vectors for Intra-Hourly Satellite-Derived Solar Power Forecasting

Solar photovoltaic (PV) power has become one of the major renewable energy sources in modern power systems. Hence, solar forecasting is indispensable for addressing the uncertainties of PV power outputs. Since PV power generation mainly depends on solar radiation conditions, satellite-derived methods have been proven effective in large-scale short-term solar forecasting. These methods utilize satellite optical images to track cloud motion and do not require supplemental ground cameras. However, cloud motion between two consecutive satellite images is highly non-stationary, as the motion includes both displacement and shape variation. Conventional motion estimation methods may miss the detailed cloud variation information, increasing the errors in solar forecasting. In this study, a multi-head cloud motion vector prediction method is proposed to address this challenge. The method models cloud variation as the probabilistic sum of pixels moving under multiple optical flow vectors. Time-varying solar intensity is also considered in the method. In order to estimate these optical flow vectors, a learning-based intelligent model with a self-attention structure is established. The proposed method of multi-step-ahead satellite-derived solar forecasting is superior to conventional methods, as the results of case studies indicate that the proposed method improves the precision of intra-hourly PV power prediction.

Impacts of Permeability Uncertainty in a Coupled Surface‐Subsurface Flow Model Under Perturbed Recharge Scenarios

AbstractCoupled simulations of surface and variably saturated subsurface flow, termed integrated hydrologic models (IHMs), can provide powerful insights into the complex dynamics of watersheds. The system of governing equations solved by an IHM is non‐linear, making them a significant computational burden and challenging to accurately parameterize. Consequently, a large fraction of the IHM studies to date have been “numerical hypothesis testing” studies, but, as parallel computing continues to improve, IHMs are approaching the point where they might also be useful as predictive tools. For this to become reality, the predictive uncertainty of such highly parameterized simulations must be considered. However, uncertainty is seldom considered in the IHM literature, likely due to the long runtimes of the complex simulations. The questions considered herein are how much uncertainty is there in an IHM for a common watershed simulation scenario, and how likely is it that any one realization of a system will give the same relative change as any other due to a perturbation in recharge? A stochastic ensemble of 250 permeability field realizations was used to show that uncertainty in a high‐mountain headwaters systems is dominated by the subsurface. Recharge perturbation scenarios echo these results, but the uncertainty of changes in streamflow or groundwater pressure heads were significantly smaller than the uncertainty in their base‐case values. The main finding is that IHMs do provide confident, predictive estimates of relative changes in watersheds, even when uncertainty in specific simulation outputs may be high.

Risk assessment of distribution network operation with scale distributed photovoltaics

In the context of large-scale photovoltaic integration into the distribution network, it is of great significance to comprehensively consider the uncertainty of photovoltaic output and load and scientifically and effectively evaluate the operational risks of the distribution network, in order to ensure the reliable and economic operation of the distribution network. At the same time, with the increase of distributed photovoltaic installed capacity, the small interference stability caused by it has an increasing impact on the operation of the distribution network. In this paper, we first establish a probabilistic model of photovoltaic output and load. Then, we propose a risk calculation method based on the non-sequential Monte Carlo method and probabilistic power flow calculation. Then, a risk analysis of large-scale photovoltaic access to the distribution network was carried out. A new small interference stability risk index was constructed to evaluate the risk of system oscillation caused by photovoltaic access. On this basis, the comprehensive risk value is calculated, and the risk levels are divided based on the voltage over-limit risk and power flow over-limit risk. Finally, the feasibility and effectiveness of the risk assessment model are verified through case analysis.

Optimal allocation method for MIES-based shared energy storage using cooperative game theory and CSP

To further promote the efficient use of energy storage and the local consumption of renewable energy in a multi-integrated energy system (MIES), a MIES model is developed based on the operational characteristics and profitability mechanism of a shared energy storage station (SESS), considering concentrating solar power (CSP), integrated demand response, and renewable energy output uncertainty. We propose a corresponding MIES model based on co-operative game theory and the CSP and an optimal allocation method for MIES shared energy storage. The model considers the maximum operating benefit of the SESS as the upper objective function and the minimum operating cost of the MIES as the lower objective function. First, the Karush–Kuhn–Tucker conditions of the lower-layer model are transformed into constraints of the upper-layer model, and the Big-M method is used to linearize the nonlinear problem and convert the two-layer nonlinear model into a single-layer linear model. Second, based on the Nash negotiation theory, the benefits of each IES in the MIES are allocated. Finally, the fuzzy chance constraints are used to relax the power balance constraints, and the trapezoidal fuzzy numbers are transformed into a deterministic equivalence class to assess the impact of renewable energy output uncertainty on system operation. The validity and rationality of the proposed two-layer model are verified through simulation, and the results demonstrate that the proposed shared storage capacity leasing model can effectively reduce the total operation cost, increase the profitability of the shared storage operator, and increase the utilization rate of the SESS.

Adaptive temperature scaling for Robust calibration of deep neural networks

In this paper, we study the post-hoc calibration of modern neural networks, a problem that has drawn a lot of attention in recent years. Despite the plethora of calibration methods proposed, there is no consensus yet on the inherent complexity of the task and, while some authors claim that simple functions solve the problem, others suggest that more expressive models are needed to capture misscalibration. As a first approach, we focus on the task of confidence scaling, specifically on post-hoc methods that generalize Temperature Scaling, which we refer to as the Adaptive Temperature Scaling family. We begin by demonstrating that while complex models like neural networks provide an advantage when there is ample data, they fail in scenarios where it is limited, notably common in fields like medical diagnosis. We then show how under this ideal data conditions the more expressive methods learn a relationship between the entropy of a prediction and its level of overconfidence, and based on this observation, we propose Entropy-based Temperature Scaling, a simple method that scales the confidence of a prediction according to this relationship. Results show that our method obtains state-of-the-art performance and is robust against data scarcity. Moreover, our proposed model enables a deeper understanding of the calibration process by the interpretation of the entropy as a measure of uncertainty in the network outputs.

Sensitivity of long-term productivity estimations in mixed forests to uncertain parameters related to fine roots

Forest growth models are increasingly being used in forestry and ecology research as predictive tools to help developing practical guidelines and to improve understanding of the drivers of forest ecosystem functioning. Models are usually calibrated using parameters directly obtained or estimated from empirical field observation, and hence are subject to uncertainty. Thus, output accuracy depends on input parameters precision and on how influential is each parameter on model behaviour. Hence, it is important to analyse parameter-related uncertainty and its effects on model outputs. This can be done by performing sensitivity analyses, which allow to explore the influence of one or several calibration parameters on model outputs. As studies on tree root parameters are particularly scarce, the aim of the present work was to evaluate the influence of parameters related to fine roots on estimations of long-term forest growth patterns in pure and mixed forests, using FORECAST (a hybrid forest growth model) as a virtual lab. The fine root parameters assessed were biomass, turnover rate, and nitrogen content. The analysis was performed by simulating monospecific stands of two contrasting species (Pinus sylvestris L. and Fagus sylvatica L.), and mixed stands formed by both species. In all cases, FORECAST showed good capability to contain uncertainty propagation during the first and middle stages of stand development (<40 years). After that moment, model output uncertainty steadily increased, but it reached different maximum uncertainty levels depending on stand type. Simulations of the less nutrient demanding P. sylvestris manifested very little sensitivity when growing in monospecific stands. However, F. sylvatica monospecific stands showed intermediate sensitivity, but significant species interactions occurred in mixed stands that determined the biggest impact detected of uncertainty related to fine root parameters over model outputs. All things considered, FORECAST displayed an interesting capability to capture some of the interspecific interactions that are key in mixed forests functioning. Our results suggest an acceptable model performance under uncertain parameterization but also caution against expecting accurate quantitative estimations of forest growth, especially when considering long-term scenarios in complex mixed stands.

Two-stage low-carbon optimal dispatch of the power system considering demand response to defend large uncertainties and risks

Introduction: In order to promote the consumption of renewable energy, reduce carbon emissions, and take into account the uncertainty of renewable energy output and load fluctuations in the new power system that can affect the normal operation of market mechanism, a two-stage low-carbon optimization scheduling method for power system that considers demand response under multiple uncertainties is proposed in this paper.Methods: Uncertain scene sets are generated through Latin hypercube sampling and heuristic synchronous backpropagation method is used to reduce scenes to obtain typical scenes and their probabilities. Then, a one-stage optimization model is established with the goal of maximizing energy efficiency and corresponding demand response strategies are obtained. Green certificate carbon trading joint mechanism model consisting of tiered green certificate trading and time-sharing tiered carbon trading are established, and the output of two-stage units are optimized with the goal of minimizing comprehensive operating costs.Result: The simulation results show that the carbon emissions are decreased by 251.57 tons, the consumption rate of renewable energy is increased by 8.64%, and the total costs are decreased by 124.0612 million yuan.Discussion: From this, it can be seen that the dual layer low-carbon optimization scheduling strategy for power system considering demand response under multiple uncertainties can effectively reduce the operating costs and carbon emissions of the system, while balancing the economic and environmental aspects of power system operation.

Optimal Coordination of Energy Coupling System Considering Uncertainty of Renewable Energy Sources

To advance carbon neutrality policies, many countries are increasingly integrating Renewable Energy Sources (RESs) into their energy mix. However, for harnessing natural energy in power generation, RESs present challenges in output control, potentially leading to power imbalances. Such imbalances, when coupled with an excessive reliance on unpredictable RES, may necessitate the curtailment of grid-integrated renewable generation, halting production despite available capacity. This paper proposes strategies to mitigate the economic and operational efficiency impacts of increased RESs on the power grid. It focuses on the optimal operation of Battery Energy Storage Systems (BESSs) and Power to Gas (P2G) technology, which flexibly converts surplus electricity into hydrogen. By employing Mixed Integer Linear Programming (MILP) for optimization and Stochastic Programming (SP) for the management of the uncertainty of renewable energy output, this paper evaluates the anticipated benefits of BESS and P2G applications.

Multi-Indicator Fused Resilience Assessment of Power Grids Considering Wind-Photovoltaic Output Uncertainty during Typhoon Disasters

Extreme weather events such as typhoons pose a serious threat to the safe operation of power grids. In the field of power system resilience assessment during typhoon disasters, a parametric typhoon wind field model combined with actual historical meteorological data has not been well adopted, and the conventional renewable energy uncertainty modeling methods are not suitable for typhoon disaster periods. In this paper, a multi-indicator fused resilience assessment strategy considering wind-photovoltaic uncertainty and component failure during typhoon disasters is proposed. Firstly, based on the actual historical meteorological data of typhoons, an uncertainty model of typhoon wind speed is established by a rolling non-parametric Dirichlet process Gaussian mixture model. Then, a spatial–temporal contingency set is constructed by considering the best-fit wind field model and stress–strength interference model for failure probability of transmission lines. On this basis, a holistic resilience assessment framework is established from the perspectives of priority, robustness, rapidity, and sustainability, and the entropy weight method combined with the technology for order preference by similarity to an ideal solution is leveraged to obtain the comprehensive resilience indicator. Finally, numerical studies are performed on the IEEE-30 bus test system to identify vulnerable lines and improve system resilience during typhoon disasters.

Integrated energy system scheduling optimization considering vertical-axis wind turbines and thermal inertia in oilfield management areas

Traditional horizontal-axis wind turbines (HAWTs) have limited efficiency in low-wind speed regions. In this paper, an integrated energy system (IES) incorporating vertical-axis wind turbines (VAWTs) is proposed; this IES is located in an oilfield management area, which can utilize the low-wind speed resources more efficiently and improve renewable energy consumption, and it also introduces a demand response model based on thermal inertia (TI), thus smoothing out the volatility caused by the VAWT. Typical output scenarios are obtained through stochastic optimization to deal with wind turbine and photovoltaic output uncertainties, and an optimal scheduling model is proposed to minimize the system operating cost. Finally, a simulation study was conducted in a micro-oilfield management area in Shandong Province, China, to demonstrate the performance of the proposed system. The results show that the IES using a VAWT and TI can increase the renewable energy consumption capacity by 87% over the conventional HAWT system, change the user behavior, increase the economic efficiency by 12%, and achieve the smoothing of load-side fluctuation of electric and thermal loads, peak shaving, and valley filling. This paper provides a feasible solution for an IES in low-wind speed areas.

Optimal Allocation Stochastic Model of Distributed Generation Considering Demand Response

Demand response (DR) can improve the accommodation of renewable energy and further affect the distributed generation (DG) allocation strategy. In this context, this paper proposes a stochastic optimal allocation model of DG, considering DR. Firstly, to address the uncertainty of wind and solar power outputs, a large number of scenarios of wind and solar power are generated based on the scenario method, which are then clustered into 10 typical scenarios by the k-means method. Secondly, with the goal of maximizing the total cost, the DR cost and corresponding constraints are introduced. Then, the stochastic planning model for DG is established, where the planning level aims to minimize the investment cost while the operation level minimizes the total operation expectation cost. For the non-linear term in the DR cost and power flow constraint, the Taylor expansion method and second-order conic relaxation method are both adopted to transform the original mixed-integer non-linear model to the mixed-integer second-order conic planning model. Finally, the whole planning model for DG is solved by CPLEX 12.6.0. The results show that DR can reduce the total cost and improve the accommodation of renewable energy in the DG planning process, which should be paid more attention to in the DG planning model.

Enhanced decentralised fractional-order control using tree seed optimisation and singular value analysis

Higher-order multi-input multi-output systems pose challenges in terms of stability and control performance due to increased complexity and interactions between multiple subsystems. Hence, this research work proposes a novel comprehensive approach to design a decentralised fractional order control strategy for higher-order systems using tree seed algorithm. The design focuses on enhancing control performance by imposing constraints on performance indices – the integral of absolute error and closed-loop amplitude ratio. Further, this work incorporates stability analysis through the singular values of the sensitivity function. The proposed decentralised fractional-order proportional-integral-derivative (FOPID) controller parameters are optimised using the tree seed algorithm. Besides, the stability is examined using the singular values of the sensitivity function. The tree seed algorithm explores the parameter space and converges to optimal controller settings that satisfy the imposed constraints by ensuring system stability. Simulation studies are conducted on various higher-order systems to analyse the proposed approach. The findings demonstrate that the decentralised control with tree seed algorithm-based FOPID controller achieves improved control performance by reducing the loop interactions among subsystems with enhanced stability. Furthermore, robustness is ensured by considering output uncertainty and parameter variations.

Stochastic optimal allocation for a battery energy storage system in high renewable-penetrated distribution networks

As the penetration of renewable distributed generation (RDG) continues to grow, the stochastic and intermittent nature of its output imposes significant challenges on distribution networks (DNs), such as source–load mismatch and voltage fluctuations, which seriously affects the safety and reliability of the system. Thus, this paper presents a stochastic optimal allocation method for a battery energy storage system (BESS) in the DN, with the consideration of annual load growth, BESS degradation, and DN operation, aiming to minimize the overall cost of DNs and harvest more renewable energy. Based on the rainflow-counting concept, BESS degradation is efficiently modeled and linearized to improve solvability. Additionally, to address the uncertainties of RDG outputs and loads, a stochastic optimization (SO) method is adopted. Furthermore, considering that a large number of integer variables of the BESS allocation model may cause a heavy computational burden, a feasibility pump-based solution algorithm is introduced to accelerate the solving speed. Finally, the effectiveness of the proposed BESS allocation method and the solution algorithm is verified on a 33-bus DN system through comparative analyses, showing high efficiency and performance.

A coordinated green hydrogen and blue hydrogen trading strategy between virtual hydrogen plant and electro‐hydrogen energy system

AbstractIn the hydrogen‐based integrated energy system (HIES), there exists a hydrogen trading market where hydrogen producers and consumers are distinct stakeholders. Current research in hydrogen trading predominantly focuses on high‐cost green hydrogen (GH), which is not aligned with the current trend of utilizing hydrogen from multiple sources. To address this, this paper proposes a hydrogen trading strategy between the virtual hydrogen plant (VHP) and electro‐hydrogen energy system (EHES) based on a bi‐level model, considering the synergy of GH produced from electrolyzers and blue hydrogen (BH) derived from natural gas in the HIES. In the VHP level, the objective is to maximize profit from hydrogen sales, allowing for the determination of hydrogen prices. In the EHES level, the goal is to minimize the cost of energy supply, leading to the formulation of GH and BH purchasing plans based on hydrogen prices. Additionally, this paper incorporates a risk‐averse model from the information gap decision theory (IGDT) to account for the impact of wind power output uncertainties in the VHP level. Subsequently, leveraging the Karush–Kuhn–Tucker (KKT) conditions of the EHES level, the bi‐level problem is transformed into a solvable single‐level mathematical program with equilibrium constraints (MPEC), with the non‐linear equilibrium constraints linearized. The proposed bi‐level optimization model is validated through case studies encompassing industrial and residential hydrogen utilization within the HIES. The outcomes confirm the rationality of the proposed model, demonstrating that, in comparison to exclusively trading GH, the coordinated GH and BH trading can increase the profit of the VHP by 2.7% and reduce the costs of the EHES by 8.5%.

Statistical Machine Learning Model for Distributed Energy Planning in Industrial Park

With the advancement of industrial modernization, industrial parks have become the main body of new energy production and consumption. However, due to the large demand for energy in industrial agglomeration, the way of energy utilization is changing to sustainable. The direct connection of distributed energy resources in industrial parks, including photovoltaic power generation systems, has an important impact on its planning and operation. Furthermore, weather scenarios can have an impact on distributed photovoltaic generation, and the uncertainty in photovoltaic power output will, in turn, affect the uncertainty in industrial park planning. Therefore, this paper aims to address the issues of inaccurate prediction of distributed electricity generation during the planning period and the non-uniform distribution of energy resources such as electricity, heating, and cooling. This is achieved through the application of statistical machine learning. The paper intends to incorporate the ideas of statistical machine learning into the model for industrial park distributed energy random opportunity-constrained planning, aiming to resolve the problems of non-uniform distribution of distributed energy sources within the park, along with uncertainty in their outputs and high overall investment costs. The model takes the planning, construction and operating costs of the industrial park as the objective function, uses the lost load cost to ensure the safety of the industrial park, and uses the Chebyshev inequality probability to limit the output characteristics of distributed energy equipment. In terms of operation, the planning period is subdivided into heating period, cooling period and transition period, and the balance of electricity, heat and cold is considered. Finally, an actual example of an industrial park is used to verify the effectiveness of this method. Experimental validation shows that this approach can ensure safety requirements in industrial parks during the heating season, cooling season, and transitional periods by flexibly adjusting the confidence threshold. Simultaneously, it delivers significant economic benefits.

Robust Collaborative Scheduling Strategy for Multi-Microgrids of Renewable Energy Based on a Non-Cooperative Game and Profit Allocation Mechanism

The Multiple Microgrid System (MMG) facilitates synergistic complementarity among various energy sources, reduces carbon emissions, and promotes the integration of renewable energy generation. In this context, we propose a two-stage robust cooperative scheduling model for MMGs based on non-cooperative game theory and a benefit allocation mechanism. In the first stage, considering electricity price fluctuations and uncertainties in wind and solar power outputs, a robust optimization approach is applied to establish an electric energy management model for MMGs. This model enables point-to-point energy sharing among microgrids. In the second stage, addressing the benefit allocation problem for shared electric energy, we introduce a Cost Reduction Ratio Distribution (CRRD) model based on non-cooperative game theory. The generalized Nash equilibrium is utilized to determine the benefit distribution for shared electric energy. Finally, through case studies, the proposed model is validated, ensuring fair returns for each microgrid. The results indicate that the proposed model optimizes the operational states of individual microgrids, reduces operational costs for each microgrid, and lowers the overall total operational costs of the MMG system. Additionally, an investigation is conducted into the impact of electricity price uncertainty coefficients and confidence levels of wind and solar uncertainties on the operational costs of microgrids.

Groundwater delineation for sustainable improvement and development aided by GIS, AHP, and MIF techniques

Exploration of groundwater is an integral part of viable resource growth for society, economy, and irrigation. However, uncontrolled utilization is mainly reported in urban and industries due to the increasing demand for water in semi-arid and arid regions of the world. In the background, groundwater demarcation for potential areas is vital in meeting necessary demand. The current study applied an integrated method comprising the analytical hierarchy process (AHP), multiple influence factors (MIF), combined with a linear regression curve and observatory well data for groundwater prospects mapping. Thematic maps such as flow direction, flow accumulation, elevation map, land use land cover, slope, soil texture, hill shade, geomorphology, normalized vegetation index, and groundwater depth map were generated utilizing remote sensing techniques. The relative weight of each parameter was estimated and then assigned to major and minor parameters. Potential zones for groundwater were classified into five classes, namely very good, good, moderate, poor, and very poor, based on AHP and MIF methods. A spatially explicit sensitivity and uncertainty analysis method to a GIS-based multi-criteria groundwater potential zone model is presented in this research. The study addressed a flaw in the way groundwater potential mapping results are typically presented in GIS-based multi-criteria decision analysis studies, where discrete class outputs are used without any assessment of their certainty with respect to variations in criteria weighting, which is one of the main contributors to output uncertainty. The study region is categorized based on inferred results as very poor, poor, marginal, and very good in potential ground quality 3.04 km2 is considered extremely poor, 3.33 km2 is considered poor, 64.42 km2 is considered very good, and 85.84 km2 is considered marginal zones, which shows reliable and potential implementation. The outcomes of AHP and MIF were validated by linear regression curve and actual water table in a study area. The study results help to formulate the potential demarcation of groundwater zones for future sustainable planning and development of groundwater sources. This study may be helpful to provide a cost-effective solution to water resources crises. The current study finding may be helpful for decision-makers and administrative professionals for sustainable management of groundwater resources for present and future demands.

Master–slave game operation scheduling strategy of an integrated energy system considering the uncertainty of wind and solar output

Introduction: With the development of the energy market and the gradual rise of emerging market players, the linkage of interests between energy sources and loads in the Integrated Energy System (IES) has become increasingly complex. Additionally, the reliability of the system has been impacted by the growing proportion of renewable energy output.Methods: To address the challenges posed by the above issues. This paper first proposes an operational strategy for an integrated energy system that incorporates the uncertainty of wind and solar output using a master-slave game approach. To enhance system robustness and cost-effectiveness, the paper introduces the information gap decision theory (IGDT). Second, building on this foundation, the system operator is considered as the leader, adding a tiered carbon trading mechanism and cloud energy storage system, and building a system revenue maximization model. Then, the user is regarded as the follower, and an optimization model is developed based on integrated demand response (IDR). Finally, the two-layer model is converted into a mixed-integer linear programming problem (MILP) to be solved by the Karush-Kuhn-Tucker conditions (KKT) combined with the big M method.Results: The analysis of the example shows that according to the difference of the decision maker’s attitude towards risk, different scheduling schemes can be obtained through the two perspectives of risk-seeking and risk-avoiding, which can provide guidance for the dynamic operation of the system, and at the same time, the users can be guided by the energy differentials to reasonably use the energy under this strategy.Discussion: Therefore, the proposed strategy in this paper can balance the economy and robustness of the system.