Robust Optimal Dispatch Research Articles

Robust optimal dispatch strategy of integrated energy system considering CHP-P2G-CCS

Integrated energy systems (IESs) can improve energy efficiency and reduce carbon emissions, essential for achieving peak carbon emissions and carbon neutrality. This study investigated the characteristics of the CHP model considering P2G and carbon capture systems, and a two-stage robust optimization model of the electricity-heat-gas- cold integrated energy system was developed. First, a CHP model considering the P2G and carbon capture system was established, and the electric-thermal coupling characteristics and P2G capacity constraints of the model were derived, which proved that the model could weaken the electric-thermal coupling characteristics, increase the electric power regulation range, and reduce carbon emissions. Subsequently, a two-stage robust optimal scheduling model of an IES was constructed, in which the objective function in the day-ahead scheduling stage was to minimize the start-up and shutdown costs. The objective function in the real-time scheduling stage was to minimize the equipment operating costs, carbon emission costs, wind curtailment, and solar curtailment costs, considering multiple uncertainties. Finally, after the objective function is linearized with a ψ-piecewise method, the model is solved based on the C&CG algorithm. Simulation results show that the proposed model can effectively absorb renewable energy and reduce the total cost of the system.

Distributed Robust Optimal Dispatch of Regional Integrated Energy Systems Based on ADMM Algorithm with Adaptive Step Size

Distributed Robust Optimal Dispatch of Regional Integrated Energy Systems Based on ADMM Algorithm with Adaptive Step Size

Robust Optimal Scheduling of Microgrid with Electric Vehicles Based on Stackelberg Game

With increasing penetration of distributed generators (DG), the uncertainty and intermittence of renewable energy has brought new challenges to the economic dispatch and promotion of environment sustainability of microgrids. Active loads, especially in electric vehicles (EVs), are thought to be an efficient way to deal with the uncertainty and intermittence of renewable energy. One of the most important features of EVs is that their demand will vary in response to the electricity price. How to determine the real-time charging price to guide the orderly charging of EVs and operate with an uncertain renewable energy output represents an important topic for the microgrid operator (MGO). To this end, this paper formulates the optimal pricing and robust dispatch problem of the MGO as a Stackelberg game, in which the upper level minimizes the MGO’s cost, while the lower level minimizes the charging cost of each EV. In the problem, the approximate linear relationship between the node voltage and equivalent load is modeled, and the approximate linear expression of the node voltage security constraint is derived. Using dual optimization theory, the robust optimal dispatch model is transformed into a linear programming model without uncertain variables. Then, the Stackelberg game model is transformed into a mixed integer linear program by using the duality theorem of linear programming. Finally, the effectiveness of the proposed method is proved by simulation within the modified IEEE33-bus system.

Risk-based distributionally robust optimal dispatch for multiple cascading failures in regional integrated energy system using surrogate modeling

Regional integrated energy system (RIES) with the close coupling of multiple energies faces various cascading failure risks in its operation, and formulating the risk-based optimal dispatch scheme is important to ensure the secure and economic operation of the RIES. Considering that the occurrence probability of each subsequent failure path caused by the initial failure in the cascading failure chain varies with the change of dispatch scheme, the cooling/heating and gas pipeline dynamics and the uncertainty of renewable energy, a risk-based distributionally robust optimal dispatch model for multiple cascading failures in a RIES is proposed. A kernel ambiguity set is constructed by using the maximum mean discrepancy between the real and reference probability distributions and the kernel mean embedding technology, which can obtain the more accurate worst-case probability distribution. Moreover, a surrogate modeling method based on piecewise convex quadratic functions is proposed to learn the mapping between the cascading failure risks and the decision variables, and the original large-scale mixed integer nonlinear programming model is transformed into a small-scale mixed integer quadratic constrained programming model for efficient solution. Finally, case study on an actual RIES demonstrates the effectiveness and advantages of the proposed method. Compared to optimal dispatch without considering the cascading failure risks, the proposed method can reduce the total failure risk cost by nearly 60%.

Multi-objective confidence gap decision based robust optimal dispatch of integrated energy system using entropy expectation maximization GMM

To cope with the uncertainty of renewable energy output and achieve robust optimal dispatch of the integrated energy system, the confidence gap decision theory with Gaussian mixed probability distribution is introduced into the dispatch model. The entropy expectation maximization Gaussian mixture model (GMM), which is developed by adding an entropy factor to the expectation maximization algorithm, is proposed to reduce the initial value sensitivity in the GMM hidden variables solution process. Considering the comprehensive optimization objectives of maximizing exergy efficiency and minimizing operating cost, a multi-objective robust optimal dispatch model based on the confidence gap decision is established. And the model is transformed into a deterministic model according to the uncertainty theory for the sake of convenient calculation. Further, an efficient non-dominated sorting mechanism is combined with an improved differential evolution algorithm to efficiently solve the model. Finally, the effectiveness and superiority of the proposed method are verified by example analysis.

Distributionally Robust Collaborative Dispatch of Integrated Energy Systems with DNE Limits Considering Renewable and Contingency Uncertainties

Collaborative optimisation of system reserves and utilisation of renewable energy is an efficient approach to achieving robust optimal dispatch of integrated energy systems (IES). However, conventional robust dispatch methods are often too conservative and lack the ability to consider uncertainties such as renewable energy and contingency probabilities. To address these limitations, this paper proposes a distributionally robust dispatch model that co-optimises reserves and do-not-exceed (DNE) limits while considering these uncertainties. First, a deterministic optimisation model of IES is established with a minimum operational cost objective and security constraints. Next, a two-stage robust collaborative optimisation framework of IES is built, based on the Wasserstein measure, with random equipment faults represented by an adjustable ambiguity set. Finally, to overcome the computational challenges associated with robust approaches, duality theory and Karush-Kuhn-Tucker (KKT) conditions are used to convert the formulation into a mixed integer linear programming (MILP) model. The Simulation results on the modified IEEE 33-bus system demonstrate the effectiveness of the proposed model and solution methodology.

Distributionally Robust Optimal Dispatch of Offshore Wind Farm Cluster Connected by VSC-MTDC Considering Wind Speed Correlation

Distributionally Robust Optimal Dispatch of Offshore Wind Farm Cluster Connected by VSC-MTDC Considering Wind Speed Correlation

Distributed Robust Optimal Dispatch for the Microgrid Considering Output Correlation between Wind and Photovoltaic

As an effective carrier of integrated clean energy, the microgrid has attracted wide attention. The randomness of renewable energies such as wind and solar power output brings a significant cost and impact on the economics and reliability of microgrids. This paper proposes an optimization scheme based on the distributionally robust optimization (DRO) model for a microgrid considering solar-wind correlation. Firstly, scenarios of wind and solar power output scenarios are generated based on non-parametric kernel density estimation and the Frank-Copula function; then the generated scenario results are reduced by K-means clustering; finally, the probability confidence interval of scenario distribution is constrained by 1-norm and ∞-norm. The model is solved by a column-and-constraint generation algorithm. Experimental studies are conducted on a microgrid system in Jiangsu, China and the obtained scheduling solution turned out to be superior under wind and solar power uncertainties, which verifies the effectiveness of the proposed DRO model.

Decentralized robust optimal dispatch of user-level integrated electricity-gas-heat systems considering two-level integrated demand response

With the change of users’ energy consumption concept, the users are no longer rigid as the traditional inelasticity but can be flexible to carry out integrated demand response (IDR). The load has also been transformed from a traditional purely consumptive load to a new type of load that combines production and consumption with the improvement and popularization of renewable energy production technologies such as wind power and photovoltaic. In this paper, considering the IDR of loads and the uncertainty of renewable energy output, a decentralized robust optimal dispatch study is conducted on user-level integrated electricity-gas-heat systems (IEGHSs) composed of energy hubs (EHs) and some users. This paper firstly developed the comprehensive model of the user-level IEGHS, including the detailed mathematical model of EH, IDR, and users. Then, based on the established model, an optimal dispatching model is established with the goal of the lowest operating cost for the system. In order to cope with the uncertainty of the output of renewable energy equipment while protecting the security and privacy of different participants in the integrated energy system (IES), a decentralized robust algorithm is used to solve the model. Finally, the proposed model is analyzed and verified by an IES example composed of one EH and three users with the ability of IDRs, and the feasibility of the proposed model and algorithm is verified.

Robust optimal dispatch of distribution system considering carbon capture and demand response

Participation of carbon capture power plants and demand response in power system dispatch is an important mean to achieve the carbon-neutral goal. In order to take into account uncertainty of wind power and low-carbon economic operation of the distribution system, a two-stage robust optimal dispatch model of the distribution system considering carbon capture and demand response is proposed in this paper. In the day-ahead stage, the unit commitment plan and the price demand response (PDR) schedule are established. In the intra-day stage, the carbon related cost is included in the optimization objective. The strategies for the generators and the incentive demand response (IDR) are optimized under the worst-case output of wind power based on the results of the day-ahead stage. Karush-Kuhn-Tucker (KKT) conditions and the column-and-constraint generation (C&CG) algorithm are used to solve the proposed two-stage model. A revised IEEE 33-bus distribution system is used to verify the feasibility and effectiveness of the proposed model.

Distributionally robust optimal dispatch in the power system with high penetration of wind power based on net load fluctuation data

The power system with high penetration of wind power faces a great challenge for system dispatch due to the high volatility and intermittency of the wind power. This work proposes a day-ahead optimal dispatch model which is formulated for a power system with thermal power, hydropower, and controllable load as dispatchable resources. According to the anti-peak regulation, the system dynamic power regulation margin model considering adjacent time periods is established to address the uncertainty in the fluctuation rate of net load power, and to sufficiently use the dispatchable resources to reduce wind curtailment. However, in some circumstances, curtailing wind has to be considered to ensure secure operation of the system and maintain the economic goal from the total cost point of view. The risk of curtailing wind is formulated using conditional value at risk (CVaR), and is minimized as part of the total operating cost. Another objective function of the proposed dispatch model is to maximize the power regulation margin. Uncertainty in the fluctuation rate of net load power is modelled for different weather conditions using moment-based ambiguity set. The moment information is obtained from large amount of historical data using clustering methodologies. The proposed optimal dispatch model with uncertainty and CVaR formulation is reformulated and solved under the distributionally robust conditional value at risk (DRCVaR) framework. The model is transformed into a semi-definite programming problem through the duality theory and can be solved efficiently by commercial solvers. Simulation results show that the proposed dispatch model can effectively strengthen wind power absorption, ensure secure operation, and improve the robustness of the dispatch strategy facing the uncertainty from the wind power.

Day-ahead robust optimal dispatch of integrated energy station considering battery exchange service

In order to improve the energy utilization efficiency and decrease the environmental pollution, multiple energy production, conversion and storage devices are integrated as a whole, called an integrated energy station (IES), which can meet various energy demands. In this paper, a day-ahead robust optimal scheduling strategy of IES for electricity, cold energy and heat energy supply is proposed, where the battery exchange service is incorporated by introducing the electric vehicle exchange station (EVES). Distinguished from the prevalent detailed modeling of each battery, an integrated model of EVES based on the state of charge (SOC) interval of batteries is established to reduce the number of variables, by which the charging priority of batteries is embedded into the optimal dispatch of IES. Considering the uncertainties of renewable energy resources and load demands, a two-stage robust optimization model of day-ahead dispatch of IES is formulated to minimize the total operation cost under the worst case, which can be solved efficiently by the column-and-constraint generation (C&CG) algorithm. The effectiveness of the proposed method is demonstrated in the case study. The results show that the total operation cost of IES decreases by 9.2%, indicating the role played by the flexibility of EVES. Moreover, the worst-case cost is reduced compared with the deterministic approach.

Robust optimal dispatch of integrated energy system considering with coupled wind and hydrogen system

Hydrogen production from renewable energy will become one of the important features of the integrated energy system in the future. By considering the coupled wind and hydrogen system, it can not only take the advantages of fast power regulation of hydrogen energy, but improve the economy of wind and hydrogen system. In view of the high volatility of the wind power, this paper proposes a robust optimal scheduling model for integrated energy system considering with coupled wind and hydrogen system. Firstly, it establishes a comprehensive energy system model with wind and hydrogen system, forming an efficient electric-gas-electric energy closed-loop flow model with fuel cells. Then, based on improved multi-interval uncertainty sets, the model of wind turbines, electrical load and hydrogen load are described respectively, which can reduce the conservatism compared with the traditional robust optimization. And the two-stage robust optimal scheduling model is established and it can be solved by adopting Column and Constraint Generation method (C&CG). Finally, an example is given to verify the advantages of the proposed method.

Distributionally Robust Optimal Dispatch of Virtual Power Plant Based on Moment of Renewable Energy Resource

Virtual power plants can effectively integrate different types of distributed energy resources, which have become a new operation mode with substantial advantages such as high flexibility, adaptability, and economy. This paper proposes a distributionally robust optimal dispatch approach for virtual power plants to determine an optimal day-ahead dispatch under uncertainties of renewable energy sources. The proposed distributionally robust approach characterizes probability distributions of renewable power output by moments. In this regard, the faults of stochastic optimization and traditional robust optimization can be overcome. Firstly, a second-order cone-based ambiguity set that incorporates the first and second moments of renewable power output is constructed, and a day-ahead two-stage distributionally robust optimization model is proposed for virtual power plants participating in day-ahead electricity markets. Then, an effective solution method based on the affine policy and second-order cone duality theory is employed to reformulate the proposed model into a deterministic mixed-integer second-order cone programming problem, which improves the computational efficiency of the model. Finally, the numerical results demonstrate that the proposed method achieves a better balance between robustness and economy. They also validate that the dispatch strategy of virtual power plants can be adjusted to reduce costs according to the moment information of renewable power output.

Distributionally robust optimal dispatch modelling of renewable-dominated power system and implementation path for carbon peak

The renewable-dominated power system has a high proportion of renewable generation, which promotes the achievement of the carbon peak and carbon neutrality objectives in the power industry. However, renewable generation is dependent on volatile and unpredictable natural resources. Moreover, the renewable resources and load demands are inversely distributed in some countries such as China. Besides, renewable generation is not in sync with load demands. Therefore, the renewable-dominated power system needs a high proportion of cross-region power transmission and requires more reliable dispatching to maintain the generation/load balance than conventional systems. At first, the renewable-dominated power system is divided into three levels in this paper, the cross-regional transmission level, renewable generation level, and thermal power generation level. A moment uncertainty set is employed to indicate the uncertainty caused by fluctuations in renewable generation. Furthermore, the distributionally robust conditional value-at-risk (DRCVaR) is presented to show the risk of abandoning renewable generation under different weather conditions. Based on the three-level construction and other constraints, a distributionally robust optimal dispatch model is proposed to minimize the carbon emission and the abandonment of renewable generation in the system. Then, the proposed dispatch model is converted into a semidefinite programming problem by the dual optimization theory, which can be easily solved. Finally, the proposed dispatch model is verified with a receiving power system in China. Additionally, the implementation path for the carbon peak of the power industry is proposed. The analysis results show that renewable generation reaches 59% in 2025, and the carbon peak reaches its peak value in 2030. In other words, the carbon peak target can be achieved via the renewable-dominated power system with the proposed dispatch model.

Distributionally robust optimal dispatch of CCHP campus microgrids considering the time-delay of pipelines and the uncertainty of renewable energy

Considering the time-delay of energy transmission in cooling/heating pipelines and the uncertainty of renewable energy (RE), a distributionally robust optimal (DRO) dispatch model of combined cooling, heating and power campus microgrids (CCHP-CMG) is established. The method of characteristics is used to obtain the analytical algebraic solution of the partial differential equation (PDE) describing the energy transmission in pipelines and to add the solution to the optimal dispatch model. Based on the Jensen–Shannon divergence distance, an ambiguity set including the probability distribution (PD) information of the actual historical data is proposed to describe the uncertainty of RE outputs, and a min–max bi-level DRO dispatch model is established. An alternative iteration method is proposed to solve the bi-level model to obtain the solution that satisfies the constraints for the worst PD of uncertain variables. Additionally, a method for reconstructing the inner-layer problem is proposed to significantly reduce the computational complexity. Test results for an actual CCHP-CMG demonstrated the high computational accuracy and efficiency of the method of characteristics in solving the PDE compared to the finite difference method. The proposed reconstruction method is accurate and efficient, and the proposed DRO method can easily adjust the conservativeness of the obtained dispatch scheme.

Adaptive robust optimal dispatch of microgrid based on different robust adjustment parameters

This paper proposes a microgrid adaptive robust optimal dispatch model with different robust adjustment parameters to improve the operating economy and safety of large-scale renewable distributed energy integration into the microgrid system. Through a robust equivalent process, considering the uncertain characteristics of the renewable energy output and load demand in the microgrid, the uncertain parameters are converted into corresponding definite parameters. A two-stage robust optimization model is established to minimize the operating cost of the microgrid under the premise of ensuring the robustness of the microgrid. An improved Benders algorithm is proposed to solve the established optimization model. The different robust adjustment parameters can be obtained adaptively through the optimization program. The optimized adaptive robust adjustment parameters can better reflect the balance between the economy and robustness of the microgrid operation, and are more suitable for the operation of the microgrid. The improved Benders algorithm can effectively speed up the solution and improve the efficiency of the solution. The simulation of the modified IEEE39-bus system verifies the rationality of the proposed optimization model and the advantages of the improved algorithm.

Robust optimal dispatch of interconnected micro-energy network based on cooperative game

The micro-energy network is a subset of the electricity, gas, and heat energy grid. Due to its limited capacity, the energy and spare capacity of micro-energy network should be shared through interconnection. It can not only reduce the operating cost of the micro-energy network caused by power interchange deviation but also increase the consumption rate of intermittent distributed generation (IDG). On account of this assumption, a control structure and a double-layer dispatch model of the interconnected micro-energy network system are proposed in this paper. An economic dispatch model based on adaptive robust optimization is proposed to deal with the uncertainty produced by IDG and minimize the operation cost. Then, a cooperative game model of an interconnected system is built to allocate the profits obtained. Simulation results demonstrate that the proposed scheduling method can significantly reduce the cost of a single micro-energy network and interconnected system. In addition, compared to the noninteractive model and traditional deterministic method, it is proved that the proposed method has a strong capability to deal with uncertain risks, improve the consumption rate of IDG, and realize the coordinated economic optimal operation of multiple micro-energy networks.

Robust optimal dispatch of power grid considering uncertainty of wind power output and electric vehicles

With the extensive grid connection of wind power and the massive access of electric vehicles, their random nature has aggravated the difficulty of grid dispatching. In this paper, the idea of robust optimization is used to consider the uncertain factors faced by power grid dispatch, and the objective function is to minimize the total cost in extreme scenarios to establish a max-min optimization model for robust optimal dispatch of power grid. By adopting the column and constraint generation (C&CG) decomposition algorithm, the max-min double-layer optimization problem is decomposed into the main problem and the sub-problem iteratively, and a robust optimal scheduling scheme for dealing with uncertain factors is obtained. Finally, the IEEE 33-bus power system is taken as an example to carry out simulation analysis, and compared with the deterministic optimization scheduling method. The simulation results verify the effectiveness of the robust optimization scheduling model and solution algorithm in this paper.

Robust day‐ahead dispatch of CAES for mitigating fluctuation of net load in the distribution network

Compressed air energy storage (CAES) can balance the fluctuation of renewable generation. In this study, the CAES is used as an energy storage system in the distribution network with wind power generation (WPG). Considering the forecasting error of WPG and load, a robust day-ahead optimal dispatch scheme for the CAES is developed in this study. The characteristics of the CAES are modelled in detail for the expansion/compression operation during the robust optimal dispatch (ROD). The aim is to minimise the fluctuation of the net load in the distribution network. Robust dynamic programming is employed to solve the optimisation problem in this study. The developed scheme is tested with the IEEE-RBTS load profile and real WPG data. The deterministic and ROD-ahead dispatch scheme are simulated and compared. The fluctuation of the net load is compared with different weights of the variation and uncertainty set.