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• A data-driven distributionally robust optimization approach for the optimal dispatching is proposed. • A trunked spatial correlation model is developed to describe the correlation of multiple wind farms' power. • The trunked spatial correlation combines the advantages of pair-copula and probability forecasting. • The ISODATA clustering algorithm is utilized to generate typical scenarios. • Demand response is considered to improve the flexibility of the power grid system. With the increasing penetration of large-scale wind power into the power grid, it is crucial to develop a precise model to accurately depict the stochasticity and correlation among wind farm outputs, which is highly important for ensuring the safe and efficient utilization of wind energy in grid dispatching. In this article, a data-driven distributionally robust optimization (DDRO) dispatching approach that accounts for spatial correlations among outputs from multiple wind farms is proposed. The proposed approach is applied to a source-network-load-storage grid system to ascertain unit start-stop schedules and resource allocation effectively. First, a truncated spatial correlation model is proposed, enabling a comprehensive representation of spatial correlations and output constraints between distinct wind farms. Second, the ISODATA clustering algorithm is employed to generate typical scenarios, reduce model complexity, and expedite the computation process. Third, a unit commitment model considering the demand response is constructed and solved using the DDRO approach. Finally, the proposed model is applied to the IEEE 30-bus system to test its robustness and cost-effectiveness compared to the traditional robust optimization model. Additionally, it is applied to the IEEE 118-bus system to demonstrate its scalability and stability. [ABSTRACT FROM AUTHOR]

In recent years, the development of hydrogen energy has been widely discussed, particularly in combination with renewable energy sources, enabling the production of "green" hydrogen. With the significant increase in wind power generation, a promising solution for obtaining green hydrogen is the development of wind-to-hydrogen (W2H) systems. However, the high proportion of wind power and electrolyzers in a large-scale W2H system will bring about the problem of renewable energy consumption and frequency stability reduction. This paper analyzes the operational characteristics and economic feasibility of mainstream electrolyzers, leading to the proposal of a coordinated hydrogen production scheme involving both a proton exchange membrane (PEM) electrolyzer and an alkaline (ALK) electrolyzer. Subsequently, a coordinated control based on Model Predictive Control (MPC) is proposed for system frequency regulation in a large-scale W2H islanded microgrid. Finally, simulation results demonstrate that the system under PEM/ALK electrolyzers coordinated control not only flexibly accommodates fluctuating wind power but also maintains frequency stability in the face of large disturbances. Compared with the traditional system with all ALK electrolyzers, the frequency deviation of this system is reduced by 25%, the regulation time is shortened by 80%, and the demand for an energy storage system (ESS) is reduced. The result validates the effectiveness of MPC and the benefits of the PEM/ALK electrolyzers coordinated hydrogen production scheme. [ABSTRACT FROM AUTHOR]

Virtual power plant (VPP) has become a promising technique to facilitate distributed energy resources (DERs) to participate in the power markets. Considering the respective interests of the VPP agent and distribution system operator (DSO), a bi-level optimisation model for VPP bidding in multiple retail markets (including active power, reactive power and spinning reserve market) as price-maker is formulated. In the upper layer, taking into account various DERs, the VPP agent aims to develop hourly bidding prices and quantities of multiple market commodities to maximise its operation profits. In the lower layer, DSO conducts the retail market clearing to minimise the system operation cost considering the network constraints and bidding plans of the market participants. Moreover, the quadratic coupling constraints among different market commodities due to capacity limitation of distributed generators and branches are formulated explicitly in the proposed model. The hybrid simulated annealing-genetic algorithm with self-adaptive parameters is adopted to cope with the non-linearity and compute the economic bidding plans for VPP. The effectiveness of the proposed approach is verified under different scenarios through case studies, which indicate its superiority and great potential for implementation. [ABSTRACT FROM AUTHOR]

Virtual power plant (VPP) has become a promising technique to facilitate distributed energy resources (DERs) to participate in the power markets. Considering the respective interests of the VPP agent and distribution system operator (DSO), a bi‐level optimisation model for VPP bidding in multiple retail markets (including active power, reactive power and spinning reserve market) as price‐maker is formulated. In the upper layer, taking into account various DERs, the VPP agent aims to develop hourly bidding prices and quantities of multiple market commodities to maximise its operation profits. In the lower layer, DSO conducts the retail market clearing to minimise the system operation cost considering the network constraints and bidding plans of the market participants. Moreover, the quadratic coupling constraints among different market commodities due to capacity limitation of distributed generators and branches are formulated explicitly in the proposed model. The hybrid simulated annealing‐genetic algorithm with self‐adaptive parameters is adopted to cope with the non‐linearity and compute the economic bidding plans for VPP. The effectiveness of the proposed approach is verified under different scenarios through case studies, which indicate its superiority and great potential for implementation. [ABSTRACT FROM AUTHOR]

The environmental/economic dispatch (EED) of power systems addresses the environmental pollution problems caused by power generation at the operational level, offering macroscopic control without requiring additional construction and remediation costs, garnering widespread attention in recent years. This paper undertakes a comprehensive review of existing EED models, categorizing them according to the control of atmospheric pollutants into total air pollutant control (TAPC) and control considering the spatial and temporal diffusion (STD) of atmospheric pollutants. In addition, various methods employed to address the EED problems, as well as the current state of research on multi-area EED models, are presented. Finally, this paper analyzes and summarizes the literature on existing EED models, highlighting the deficiencies of the current work and future research directions. Through these explorations, the authors find that controlling the EED model by considering TAPC is more suitable for general macro planning, whereas the EED model considering the STD of air pollutant emissions enables more precise and effective control. Summarizing such models and techniques is conducive to developing dispatch plans adapted to local conditions, which is significantly beneficial for public welfare and government management, promoting sustainable and environmentally friendly power system dispatch methods. [ABSTRACT FROM AUTHOR]

With increasing heating demand and installed capacity of wind farms, combined heat and power (CHP) systems with inflexible generation are confronted with a major challenge for the efficient utilization of the wind power. Distributed heat sources (DHSs), such as electric boilers and heat storage, offer an effective way to enhance wind power penetration in a combined heat and power system by reducing the electric-heat coupling of the CHP unit. In this paper, an assessment approach for the wind power penetration of a CHP system with DHSs is proposed, and a two-stage multiple types of DHSs optimal configuration strategy to realize the minimum construction cost at a certain permissible wind power curtailment rate is established. After that, the proposed strategy is applied to a case study of a practical CHP system with in-depth analysis and detailed discussion, which reveals the effectiveness of the proposed strategy and indicates its promising applications for DHS configuration. [ABSTRACT FROM AUTHOR]

• An economic dispatch framework for combined heat and power systems is proposed. • A polytope-based aggregation and disaggregation method is developed. • The aggregation model includes feasible region and equivalent cost parameters. • The proposed approach can manage numerous thermal controllable residents. • Uncertainty is modeled by the distributionally robust chance-constrained program. Thermal controllable residents possess great potential of thermal inertia to improve the system renewable generation accommodation capability. Nevertheless, a high-dimensional optimization problem with huge computational burden emerges if a large number of small thermal controllable residents are modeled individually. In light of this, a polytope-based inner approximate aggregation approach for thermal controllable residents with heterogeneous parameters is proposed, which can unlock the potential operational flexibility offered by numerous small thermal controllable residents and satisfy their various operational constraints. Moreover, a day-ahead economic dispatch framework for combined heat and power systems coordinating with thermal controllable residents' aggregation and disaggregation processes is proposed to further utilize the thermal controllable residents' flexibility and promote the wind energy accommodation. The object is to reduce the overall operation cost while ensuring users' comfort and diversified system operational constraints. Simulation analyses are conducted on the 14-bus electric system and 7-node district heating system, which substantiate that the proposed approach can efficiently improve the system economy and relieve the wind power curtailment through aggregate management of numerous thermal controllable residents. [ABSTRACT FROM AUTHOR]

Distribution network scheduling (DNS) is the basis for distribution network management, which is computed in a periodical way via solving the formulated mixed-integer programming (MIP). To achieve the online scheduling, a provably robust learn-to-optimize approach for online DNS is proposed in this paper, whose key lies in the transformation of the MIP-based DNS into the simple linear program problem with a much faster solving time. It formulates the parametric DNS model to construct the offline training dataset and then proposes the provably robust learning approach to learn the integer variables of MIP. The proposed learning approach is adversarial to minor perturbation of input scenario. After training, the learning model can predict the integer variables to achieve online scheduling. Case study verifies the acceleration effectiveness for online DNS. [ABSTRACT FROM AUTHOR]

To maintain the system's real-time balance, mature electricity markets generally tend to raise the frequency of market clearing. Given the shrinking time lag between the price update process and underlying electromechanical dynamics, it inevitably considers the two in a unified, dynamical framework. However, the relationship between market activities and the evolution of electricity networks has received scant attention in pertinent research. Inspired by the primal-dual gradient method and modern control theory, we propose a novel multi-rate hybrid model that simultaneously accounts for the continuous nature of physical system dynamics and the discrete nature of market clearing. To maintain the asymptotical convergence of the proposed model, we derive the explicit constraints on the upper bounds of market clearing and bidding intervals. These bounds can be determined without prior knowledge of the Nash equilibrium, and even the time schedules don't have to be periodic, which dramatically improves the applicability of the proposed model in practical market operation. The whole model provides a new perspective to study economic-physical problems, which can be readily implemented in a distributed way and achieve social welfare maximization along with frequency regulation. • A novel economic-physical model is established for the market operation coupled with the power networks' dynamics. • The proposed hybrid model considers frequency evolution's continuous nature and bidding's discrete nature. • We derive the upper bounds on the time lengths of consecutive bidding and market clearing. • The multi-rate hybrid system can maximize social welfare and regulate frequency. [ABSTRACT FROM AUTHOR]

• In conventional game theory, it is assumed that all players instantly respond the best actions to the market signal (e.g. price or demand). However, players cannot react so quickly. To better depict the economic behavior of players, we take the adjustment speed of market price into account and characterize the market price as the state variable using a sticky price model. • Compared with the day-ahead market, the real-time market is always in a disequilibrium process. Hence, Nash equilibrium cannot tell the players how to optimize their production in a disequilibrium market. Given that, we establish an N-player non-cooperative differential game model with finite-horizon is established to optimize the generation strategy of all generators before they reach an equilibrium. The units' capacity and power flow constraints constitute the boundary of control variables. We construct a state-feedback information structure in which the existence of Markovian Nash equilibrium and the uniqueness of optimal state trajectory is proved in detail. It will help other scholars to build an effective non-cooperative differential game model in the real-time market. • Commonly, the diagonalization algorithm is used to calculate Nash equilibrium, but it needs to collect global information. Subjected to privacy protection issues, we proposed a distributed algorithm based on consensus theory to solve the Hamiltonian functions with coupled constraints. The whole solving process only needs local boundary information, which greatly protects the privacy of players. Based on the optimal control theory, we provide a new perspective on the study of the electricity market. Continuous liberalization of electricity markets makes a strong correlation between the economic behaviors of market participants and their profits. To guide the production of generators before the market reaches equilibrium, a new framework is proposed to model the real-time electricity market with help of optimal control theory. The market price is described as the dynamic state using a sticky price model. We establish an N-person non-cooperative differential game model, where all participants try to maximize their profits independently only by observing power prices. The existence of feedback Nash equilibrium and uniqueness of optimal price trajectory are proved in detail, which will help other scholars build an effective differential game model. To protect the privacy of all generators, a distributed algorithm is proposed based on neurodynamic and consensus theory, which only requires information exchange among neighboring participants. Furthermore, a special case of a duopoly power market is investigated in detail and we provide a feedback time-continuous solution for each generator. Compared with the commercial Cplex solver, the proposed distributed algorithm performs better in convergence speed. [ABSTRACT FROM AUTHOR]

Intelligent home energy management system (IHEMS) manages various home appliances depending on user preferences in order to save energy cost and assure user satisfaction. To realize cooperation between the distribution system operator (DSO) and end-user, a two-stage scheduling optimization model is developed based on the flexibility quantification, with the user privacy in demand-side management in a specific cluster taken into account. It also aids to reduce the network operation cost, and the distribution system's uncertainty caused by wind power is represented using chance constraints. The user uploads the IHEMS-calculated offered flexibility to DSO via cluster; DSO optimizes the optimal flexibility to minimize the operation cost; then, clusters distribute the flexibility requirement based on the flexibility index; finally, the user updates the optimal schedule. The numerical results using MATLAB are provided to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

• Provide a new perspective to study the market operation based on control theory. • Establish a dynamic economic-physical model for the market operation. • The game action is described by state equations derived from the primal-dual method. • The whole trading process can be executed in a distributed way. • The stability analysis relies on the Lyapunov function and incremental passivity. With the emergency of competitive markets as central operational mechanisms, the real-time market clearing results are used to determine the optimal power dispatch. It inevitably strengthens the coupling between the market update process and the physical response of the generators and networks. It necessitates the development of stability analysis for such coupled systems. Based on the primal–dual gradient method, an economic cybernetic model is established to simultaneously characterize the market operation and electromechanical power system dynamics. Inspired by modern control theory, the proposed dynamic model constructs a state space in which the actions of market participants are control signals, and the system states, such as nodal prices, bus voltages, and frequency, are treated as state variables. To promote the expandability, we also formulate the coupled dynamics in port-Hamiltonian form and provide detailed proof and sufficient conditions for its asymptotic stability by using properties of incremental passive systems. The whole transaction process implemented in a distributed manner aims at maximizing social welfare and frequency regulation when the economic-physical system reaches its equilibrium point. [ABSTRACT FROM AUTHOR]