Search Results (38)

Current technical approaches find it challenging to reduce hydrogen production costs in combined cooling, heating, and power (CCHP) microgrids integrated with hydrogen refueling stations (HRS). Furthermore, the stability of such systems is significantly impacted by multiple uncertainties inherent on both the source and load sides. Therefore, this paper proposes a two-stage robust optimization for bi-level game-based scheduling of a CCHP microgrid integrated with an HRS. Initially, a bi-level game structure comprising a CCHP microgrid and an HRS is established. The upper layer microgrid can coordinate scheduling and the step carbon trading mechanism, thereby ensuring low-carbon economic operation. In addition, the lower layer hydrogenation station can adjust the hydrogen production plan according to dynamic electricity price information. Subsequently, a two-stage robust optimization model addresses the uncertainty issues associated with wind turbine (WT) power, photovoltaic (PV) power, and multi-load scenarios. Finally, the model’s duality problem and linearization problem are solved by the Karush–Kuhn–Tucker (KKT) condition, Big-M method, strong duality theory, and column and constraint generation (C&CG) algorithm. The simulation results demonstrate that the strategy reduces the cost of both CCHP microgrid and HRS, exhibits strong robustness, reduces carbon emissions, and can provide a useful reference for the coordinated operation of the microgrid. Full article

Extreme damage poses a serious challenge to the safe operation of power grids. Optimizing the allocation of defense resources to improve the grid’s disaster resistance capabilities is the main concern of the power system. In this paper, a distributed robust optimal defense resource allocation method based on the defender–attacker–defender model is proposed to improve the disaster resilience of power grids. This method takes into account the uncertainty of restoration time due to different damage intensities and improves the efficiency of restoration resource scheduling in the restoration process. Meanwhile, a set covering-column and constraint generation (SC-C&CG) algorithm is proposed for the case that the mixed integer model does not satisfy the Karush–Kuhn–Tucker (KKT) condition. A case study based on the IEEE 24-bus system is conducted, and the results verify that the proposed method can minimize the system dumping load under the uncertainty of the maintenance time involved. Full article

As the integration of renewable energy sources into microgrid operations deepens, their inherent uncertainty poses significant challenges for dispatch scheduling. This paper proposes a hybrid game-theoretic optimization strategy to address the uncertainty of renewable energy in microgrid scheduling. An energy trading framework is developed, involving integrated energy microgrids (IEMS), shared energy storage operators (ESOS), and user aggregators (UAS). A mixed game model combining master–slave and cooperative game theory is constructed in which the ESO acts as the leader by setting electricity prices to maximize its own profit, while guiding the IEMs and UAs—as followers—to optimize their respective operations. Cooperative decisions within the IEM coalition are coordinated using Nash bargaining theory. To enhance the generality of the user aggregator model, both electric vehicle (EV) users and demand response (DR) users are considered. Additionally, the model incorporates renewable energy output uncertainty through distributionally robust chance constraints (DRCCs). The resulting two-level optimization problem is solved using Karush–Kuhn–Tucker (KKT) conditions and the Alternating Direction Method of Multipliers (ADMM). Simulation results verify the effectiveness and robustness of the proposed model in enhancing operational efficiency under conditions of uncertainty. Full article

This paper proposes a novel sparse twin parametric insensitive support vector regression (STPISVR) model, designed to enhance sparsity and improve generalization performance. Similar to twin parametric insensitive support vector regression (TPISVR), STPISVR constructs a pair of nonparallel parametric insensitive bound functions to indirectly determine the regression function. The optimization problems are reformulated as two sparse linear programming problems (LPPs), rather than traditional quadratic programming problems (QPPs). The two LPPs are originally derived from initial L1-norm regularization terms imposed on their respective dual variables, which are simplified to constants via the Karush–Kuhn–Tucker (KKT) conditions and consequently disappear. This simplification reduces model complexity, while the constraints constructed through the KKT conditions— particularly their geometric properties—effectively ensure sparsity. Moreover, a two-stage hybrid tuning strategy—combining grid search for coarse parameter space exploration and Bayesian optimization for fine-grained convergence—is proposed to precisely select the optimal parameters, reducing tuning time and improving accuracy compared to a singlemethod strategy. Experimental results on synthetic and benchmark datasets demonstrate that STPISVR significantly reduces the number of support vectors (SVs), thereby improving prediction speed and achieving a favorable trade-off among prediction accuracy, sparsity, and computational efficiency. Overall, STPISVR enhances generalization ability, promotes sparsity, and improves prediction efficiency, making it a competitive tool for regression tasks, especially in handling complex data structures. Full article

Within the context of global warming, the frequent occurrence of extreme weather may lead to problems, such as a sharp decrease in new energy output, insufficient system backups, and an increase in the amount of energy consumed by users, resulting in large-scale power shortages within the grid for a short period of time. With the increase in the numbers of electric vehicles (EVs) and microgrids (MGs), which are resilient resources, the ability of a system to participate in demand response (DR) is further improved, which may make up for short-term power shortages. In this paper, we first propose a charging and discharging model for EVs during the onset of a cold wave, and then perform load forecasting for EVs during cold wave weather based on user behavioral characteristics. Secondly, in order to accurately portray the flexible regulation capability of microgrids with massively flexible resource access, this paper adopts the convex packet fitting expression based on MGFOR to characterize the flexible regulation capability of MGs. Then, the Conditional Value at Risk (CVaR) is used to quantify the uncertainty of wind and solar power generation, and a two-layer model with the objective of minimizing the operation cost in the upper layer and maximizing the rate of new energy consumption in the lower layer is proposed and solved using Karush–Kuhn–Tucker (KKT) conditions. Finally, the proposed method is verified through examples to ensure the economic operation of the system and improve the new energy consumption rate of the system. Full article

In this paper, we study the optimality conditions and perform a stability analysis for the second-order cone constrained variational inequalities (SOCCVI) problem. The Lagrange function and Karush–Kuhn–Tucker (KKT) condition of the SOCCVI problem is given, and the optimality conditions for the SOCCVI problem are studied. Then, the second-order sufficient condition satisfying the constrained nondegenerate condition is proved. The strong second-order sufficient condition is defined. And the nonsingularity of Clarke’s generalized Jacobian of the KKT point, the strong regularity of the KKT point, the uniform second-order growth condition, the strong stability of the KKT point, and the local Lipschtiz homeomorphism of the KKT point for the SOCCVI problem are proved to be equivalent to each other. Then, the stability theorem of the SOCCVI problem is obtained. Full article

Against the backdrop of a “dual-carbon” strategy, the use of photovoltaic storage charging stations (PSCSs), as an effective way to aggregate and manage electric vehicles, new energy sources, and energy storage, will be an important primary component of the electricity market. The operational characteristics of the aggregated resources within a PSCS determine its bidding space, which has an important influence on its bidding strategy. In this paper, a novel bidding space model is constructed for PSCSs, which dynamically integrates electric vehicles, photovoltaic generation, and energy storage. A two-stage bidding strategy for multiple PSCSs is established, with stage I aiming at achieving the lowest cost for the power purchased by a PSCS to optimize the power generation and power plan and stage II aiming at achieving the lowest cost of the grid operator’s power purchase to optimize the system’s power balance. Thirdly, the two-stage model is transformed into a single-layer, mixed-integer linear programming problem using dyadic theory and Karush–Kuhn–Tucker (KKT) conditions, enabling the derivation of the optimal bidding strategy. Finally, the example analysis verifies that the proposed model can achieve a reduction in the PSCS’s day-ahead power purchase cost and flexibly dispatch each resource within the PSCS to maximize revenue, as well as reducing power consumption behavior during peak tariff hours, to enhance the market power of the PSCS in the electricity market. Full article

As a crucial path to promote the sustainable development of power systems, shared energy storage (SES) is receiving more and more attention. The SES generates carbon emissions during its manufacturing, usage, and recycling process, the neglect of which will introduce a certain extent of errors to the investment of SES, especially in the context of the large-scale integration of renewable energy and dramatic increase in demand for SES capacity. To enhance the accuracy of SES investment, we propose a double-layer optimization model to compute the optimal configuration of a shared energy storage station (SESS) considering its life-cycle carbon emission. First, the service mode, settlement method, profit mechanism, and application scenarios of SESS are introduced. Second, the life-cycle assessment approach is used to calculate the life-cycle carbon emission of SESS, and the uncertainty of supply and demand is considered. Then, a double-layer optimization model that considers the economic operation of multi-microgrid systems and the optimal allocation of SESS is established. The lower-layer model’s Karush–Kuhn–Tucher (KKT) condition is derived to convert the double-layer model into a single-layer one. Finally, a combined heat and power (CHP) three-microgrid system is used to demonstrate the validity of our proposed model, and the economy of SESS investment is analyzed from multiple perspectives. The results show that considering the life-cycle carbon emission of SESS can provide more accurate guidance for investing in and measuring the carbon emission and reduction for SESS. Full article

The proposal of the energy-consuming right (ECR) market may lead to generation companies (GenCos) facing the risk of being overcharged due to the inaccurate calculation of carbon emission reduction, since it claims the same credit as the carbon market does. To estimate the carbon emission reduction accurately for the GenCos that participate in electricity, carbon, and ECR markets simultaneously, this paper proposes a market framework where a flexible exchange mechanism between the ECR and carbon markets is specially considered. To investigate the influence of the allocation and exchange of ECR and carbon credits on the behavior of GenCos that participate in multi-type markets, a bi-level model based on the leader–follower game theory is proposed. In the upper level of the proposed model, a decision problem for maximizing the profit of GenCos is developed, which is especially constrained to the primary allocation of ECR and carbon credits. While the multi-type market clearing model and an exchange mechanism between the ECR and carbon credits are proposed in the lower level of the model. The bi-level problem is converted into the mathematical program with equilibrium constraints (MPECs) through the Karush–Kuhn–Tucker (KKT) condition to solve. The results illustrate that the interaction between the ECR market and the carbon market can improve the energy efficiency and reduce the carbon emissions of GenCos. Full article

The advancement of hydrogen technology and rising environmental concerns have shifted research toward renewable energy for green hydrogen production. This study introduces a novel tri-level transaction methodology for microgrid clusters, addressing uncertainties and price fluctuations in hydrogen. We establish a comprehensive microgrid topology with distributed power generation and hydrogen production facilities. A polygonal uncertainty set method quantifies wind and solar energy uncertainties, while an enhanced interval optimization technique refines the model. We integrate a sophisticated demand response model for hydrogen loading, capturing users’ behavior in response to price changes, thereby improving renewable energy utilization and supporting economically viable management practices. Additionally, we propose a tri-level game-theoretic framework for analyzing stakeholder interactions in microgrid clusters, incorporating supply–demand dynamics and a master–slave structure for microgrids and users. A distributed algorithm, “KKT & supply-demand ratio”, solves large-scale optimization problems by integrating Karush–Kuhn–Tucker conditions with a heuristic approach. Our simulations validate the methodology, demonstrating that accounting for uncertainties and dynamic hydrogen prices enhances renewable energy use and economic efficiency, optimizing social welfare for operators and economic benefits for microgrids and users. Full article

Energy storage (ES) units are vital for the reliable and economical operation of the power system with a high penetration of renewable distributed generators (DGs). Due to ES’s high investment costs and long payback period, energy management with shared ESs becomes a suitable choice for the demand side. This work investigates the sharing mechanism of ES units for low-voltage (LV) energy prosumer (EP) communities, in which energy interactions of multiple styles among the EPs are enabled, and the aggregated ES dispatch center (AESDC) is established as a special energy service provider to facilitate the scheduling and marketing mechanism. A shared ES operation framework considering multiple EP communities is established, in which both the energy scheduling and cost allocation methods are studied. Then a shared ES model and energy marketing scheme for multiple communities based on the leader–follower game is proposed. The Karush–Kuhn–Tucker (KKT) condition is used to transform the double-layer model into a single-layer model, and then the large M method and PSO-HS algorithm are used to solve it, which improves convergence features in both speed and performance. On this basis, a cost allocation strategy based on the Owen value method is proposed to resolve the issues of benefit distribution fairness and user privacy under current situations. A case study simulation is carried out, and the results show that, with the ES scheduling strategy shared by multiple renewable communities in the leader–follower game, the energy cost is reduced significantly, and all communities acquire benefits from shared ES operators and aggregated ES dispatch centers, which verifies the advantageous and economical features of the proposed framework and strategy. With the cost allocation strategy based on the Owen value method, the distribution results are rational and equitable both for the groups and individuals among the multiple EP communities. Comparing it with other algorithms, the presented PSO-HS algorithm demonstrates better features in computing speed and convergence. Therefore, the proposed mechanism can be implemented in multiple scenarios on the demand side. Full article

In this article, we investigate a class of non-smooth semidefinite multiobjective programming problems with inequality and equality constraints (in short, NSMPP). We establish the convex separation theorem for the space of symmetric matrices. Employing the properties of the convexificators, we establish Fritz John (in short, FJ)-type necessary optimality conditions for NSMPP. Subsequently, we introduce a generalized version of Abadie constraint qualification (in short, NSMPP-ACQ) for the considered problem, NSMPP. Employing NSMPP-ACQ, we establish strong Karush-Kuhn-Tucker (in short, KKT)-type necessary optimality conditions for NSMPP. Moreover, we establish sufficient optimality conditions for NSMPP under generalized convexity assumptions. In addition to this, we introduce the generalized versions of various other constraint qualifications, namely Kuhn-Tucker constraint qualification (in short, NSMPP-KTCQ), Zangwill constraint qualification (in short, NSMPP-ZCQ), basic constraint qualification (in short, NSMPP-BCQ), and Mangasarian-Fromovitz constraint qualification (in short, NSMPP-MFCQ), for the considered problem NSMPP and derive the interrelationships among them. Several illustrative examples are furnished to demonstrate the significance of the established results. Full article

In this paper, we investigate constraint qualifications and optimality conditions for multiobjective mathematical programming problems with vanishing constraints (MOMPVC) on Hadamard manifolds. The MOMPVC-tailored generalized Guignard constraint qualification (MOMPVC-GGCQ) for MOMPVC is introduced in the setting of Hadamard manifolds. By employing MOMPVC-GGCQ and the intrinsic properties of Hadamard manifolds, we establish Karush–Kuhn–Tucker (KKT)-type necessary Pareto efficiency criteria for MOMPVC. Moreover, we introduce several MOMPVC-tailored constraint qualifications and develop interrelations among them. In particular, we establish that the MOMPVC-tailored constraint qualifications introduced in this paper turn out to be sufficient conditions for MOMPVC-GGCQ. Suitable illustrative examples are furnished in the framework of well-known Hadamard manifolds to validate and demonstrate the importance and significance of the derived results. To the best of our knowledge, this is the first time that constraint qualifications, their interrelations, and optimality criteria for MOMPVC have been explored in the framework of Hadamard manifolds. Full article

Integrated Energy Systems (IESs) interconnect various energy networks to achieve coordinated planning and optimized operation among heterogeneous energy subsystems, making them a hot topic in current energy research. However, with the high integration of renewable energy sources, their fluctuation characteristics introduce uncertainties to the entire system, including the corresponding indirect carbon emissions from electricity. To address these issues, this paper constructs a two-stage, three-layer robust optimization operation model for IESs from day-ahead to intra-day. The model analyzes the uncertainties in carbon emission intensity at grid-connected nodes, as well as the uncertainty characteristics of photovoltaic, wind turbine, and cooling, heating, and electricity loads, expressed using polyhedral uncertainty sets. It standardizes the modeling of internal equipment in the IES, introduces carbon emission trading mechanisms, and constructs a low-carbon economic model, transforming the objective function and constraints into a compact form. The column-and-constraint generation algorithm is applied to transform the three-layer model into a single-layer main problem and a two-layer subproblem for iterative solution. The Karush–Kuhn–Tucker (KKT) condition is used to convert the two-layer subproblem into a linear programming model. A case study conducted on a park shows that while the introduction of uncertainty optimization increases system costs and carbon emissions compared to deterministic optimization, the scheduling strategy is more stable, significantly reducing the impact of uncertainties on the system. Moreover, the proposed strategy reduces total costs by 5.03% and carbon emissions by 1.25% compared to scenarios considering only source load uncertainty, fully verifying that the proposed method improves the economic and low-carbon performance of the system. Full article

This article deals with a class of nonsmooth interval-valued multiobjective semi-infinite programming problems with vanishing constraints (NIMSIPVC). We introduce the VC-Abadie constraint qualification (VC-ACQ) for NIMSIPVC and employ it to establish Karush–Kuhn–Tucker (KKT)-type necessary optimality conditions for the considered problem. Regarding NIMSIPVC, we formulate interval-valued weak vector, as well as interval-valued vector Lagrange-type dual and scalarized Lagrange-type dual problems. Subsequently, we establish the weak, strong, and converse duality results relating the primal problem NIMSIPVC and the corresponding dual problems. Moreover, we introduce the notion of saddle points for the interval-valued vector Lagrangian and scalarized Lagrangian of NIMSIPVC. Furthermore, we derive the saddle-point optimality criteria for NIMSIPVC by establishing the relationships between the solutions of NIMSIPVC and the saddle points of the corresponding Lagrangians of NIMSIPVC, under convexity assumptions. Non-trivial illustrative examples are provided to demonstrate the validity of the established results. The results presented in this paper extend the corresponding results derived in the existing literature from smooth to nonsmooth optimization problems, and we further generalize them for interval-valued multiobjective semi-infinite programming problems with vanishing constraints. Full article