Search Results (8)

The Economic Dispatch Problem (EDP) plays a critical role in power system operations by trying to allocate power generation across multiple units at minimal cost while satisfying complex operational constraints. Traditional optimization techniques struggle with the non-convexities introduced by factors such as valve-point effects, prohibited operating zones, and spinning reserve requirements. While metaheuristics methods have shown promise, they often suffer from convergence issues and constraint-handling limitations. In this study, we introduce a novel application of Group Relative Policy Optimization (GRPO), a reinforcement learning framework that extends Proximal Policy Optimization by integrating group-based learning and relative performance assessments. The proposed GRPO approach incorporates smart initialization, adaptive exploration, and elite-guided updates tailored to the EDP’s structure. Our method consistently produces high-quality, feasible solutions with faster convergence compared to state-of-the-art metaheuristics and learning-based methods. For instance, in the case of the 15-unit system, GRPO achieved the best cost of USD 32,421.67/h with full constraint satisfaction in just 4.24 s, surpassing many previous solutions. The algorithm also demonstrates excellent scalability, generalizability, and stability across larger-scale systems without requiring parameter retuning. These results highlight GRPO’s potential as a robust and efficient tool for real-time energy scheduling in smart grid environments. Full article

With the soaring demand for electric power and the limited spinning reserve in the power system in Taiwan, the comprehensive management of both thermal power generation and load demand turns out to be a key to achieving the robustness and sustainability of the power system. This paper aims to design a demand bidding (DB) mechanism to collaborate between customers and suppliers on demand response (DR) to prevent the risks of energy shortage and realize energy conservation. The concurrent integration of the energy, transmission, and reserve capacity markets necessitates a new formulation for determining schedules and marginal prices, which is expected to enhance economic efficiency and reduce transaction costs. To dispatch energy and reserve markets concurrently, a hybrid approach of combining dynamic queuing dispatch (DQD) with direct search method (DSM) is developed to solve the extended economic dispatch (ED) problem. The effectiveness of the proposed approach is validated through three case studies of varying system scales. The impacts of tie-line congestion and area spinning reserve are fully reflected in the area marginal price, thereby facilitating the determination of optimal load reduction and spinning reserve allocation for demand-side management units. The results demonstrated that the multi-area bidding platform proposed in this paper can be used to address issues of congestion between areas, thus improving the economic efficiency and reliability of the day-ahead market system operation. Consequently, this research can serve as a valuable reference for the design of the demand bidding mechanism. Full article

This paper presents a novel sorting algorithm for modular multilevel inverters (MMCs) with integrated batteries, designed to ensure the uninterrupted operation of electric vehicles (EVs) under post-fault conditions. The proposed system structure consists of an MMC with four full-bridge modules per phase, where one module acts as a spinning reserve during normal operation. The algorithm addresses a single switch fault per phase by operating the faulted module in half-bridge mode, ensuring all batteries remain operational and maintaining full power output and battery capacity without any noticeable changes for the vehicle operator. Unlike conventional fault-tolerant strategies that often reduce power output or disable affected modules, the proposed algorithm isolates the faulty switch while preserving system output. This approach avoids derating and eliminates the need for immediate maintenance, enabling the EV to continue operating under fault conditions. Simulation and experimental results validate the effectiveness of the algorithm under a single switch fault scenario, demonstrating its ability to maintain autonomy and consistent power delivery. This work demonstrates a fault-tolerant MMC principle, offering a robust and scalable solution for enhancing reliability and user satisfaction in EV power systems. Full article

The integration of renewable energy is rapidly leading the existing grid systems toward modern hybrid power systems. These hybrid power systems are more complex due to the random and intermittent nature of RE and involve numerous operational challenges. This paper presents the operational model for solar integrated power systems to address the issues of economical operation, reliable solar share, energy deficit in case of contingency events, and the allocation of system spinning reserve. A mixed-integer optimization is formulated to minimize the overall cost of the system operation and to maximize the solar share under robust system spinning reserve limits as well as various other practical constraints. A Pareto-optimal solution for the maximization of the number of solar power plants and minimization of the solar cost is also presented for reliable solar share. Further, a decomposition framework is proposed to split the original problem into two sub-problems. The solution of joint optimization is obtained by exploiting a Lagrange relaxation method, a binary search Lambda iteration method, system spinning reserve analysis, and binary integer programming. The proposed model was implemented on an IEEE-RTS 26 units system and 40 solar plants. Full article

A chance-constrained programming-based optimization model for the dynamic economic emission dispatch problem (DEED), consisting of both thermal units and wind turbines, is developed. In the proposed model, the probability of scheduled wind power (WP) is included in the set of problem-decision variables and it is determined based on the system spinning reserve and the system load at each hour of the horizon time. This new strategy avoids, on the one hand, the risk of insufficient WP at high system load demand and low spinning reserve and, on the other hand, the failure of the opportunity to properly exploit the WP at low power demand and high spinning reserve. The objective functions of the problem, which are the total production cost and emissions, are minimized using a new hybrid chaotic maps-based artificial bee colony (HCABC) under several operational constraints, such as generation capacity, system loss, ramp rate limits, and spinning reserve constraints. The effectiveness and feasibility of the suggested framework are validated on the 10-unit and 40-unit systems. Moreover, to test the robustness of the suggested HCABC algorithm, a comparative study is performed with various existing techniques. Full article

The requirement for energy sustainability drives the development of renewable energy technologies and gas-fired power generation. The increasing installation of gas-fired units significantly intensifies the interdependency between the electricity system and natural gas system. The joint scheduling of electricity and natural gas systems has become an attractive option for improving energy efficiency. This paper proposes a robust day-ahead scheduling model for electricity and natural gas system, which minimizes the total cost including fuel cost, spinning reserve cost and cost of operational risk while ensuring the feasibility for all scenarios within the uncertainty set. Different from the conventional robust optimization with predefined uncertainty set, a new approach with risk-averse adjustable uncertainty set is proposed in this paper to mitigate the conservatism. Furthermore, the Wasserstein–Moment metric is applied to construct ambiguity sets for computing operational risk. The proposed scheduling model is solved by the column-and-constraint generation method. The effectiveness of the proposed approach is tested on a 6-bus test system and a 118-bus system. Full article

Distributed generation (DG) is an important method of energy generation that accelerates the decentralization process of centralized systems, and has been widely deployed in modern society due to its economical, sustainable, and environmentally friendly characteristics. However, with the tremendous development of DG, system reliability operations are facing increasingly severe challenges because of the fluctuations of the renewable generation. In this paper, a novel spinning reserve optimization method is proposed to maximize the maximum allowance of system uncertainty (MAoSU) under the premise of satisfying the preset system operational cost. Then, the success rate of DG off-grid operation is calculated by comparing the magnitude of optimal spinning reserve capacity with the power exchange between the main grid and the distributed grid. The simulation results show that decision-makers need to increase the operational cost to compensate for system uncertainty, and the percentage increase of the operational cost is in proportional to the MAoSU and system renewable energy penetration rate. Additionally, with the increase of the MAoSU, the system needs to prepare more spinning reserve capacity to maintain system reliability operations. Finally, with the decrease of the MAoSU, the success rate of system off-grid operation decreases sharply, especially when the MAoSU is less than 0.5. Full article

This paper proposes an energy and reserve joint dispatch model based on a robust optimization approach in real-time electricity markets, considering wind power generation uncertainties as well as zonal reserve constraints under both normal and N-1 contingency conditions. In the proposed model, the operating reserves are classified as regulating reserve and spinning reserve according to the response performance. More specifically, the regulating reserve is usually utilized to reduce the gap due to forecasting errors, while the spinning reserve is commonly adopted to enhance the ability for N-1 contingencies. Since the transmission bottlenecks may inhibit the deliverability of reserve, the zonal placement of spinning reserve is considered in this paper to improve the reserve deliverability under the contingencies. Numerical results on the IEEE 118-bus test system show the effectiveness of the proposed model. Full article