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With the large-scale integration of single-phase distributed photovoltaic systems into distribution grids, issues such as mismatched generation and load, overvoltage, and three-phase imbalance may arise in the distribution network. A multi-objective optimization method for flexible distribution networks incorporating a four-leg soft open point (F-SOP) is proposed based on fuzzy chance constraints. First, a mathematical model for the F-SOP’s loss characteristics and power control was established based on the three-phase four-arm topology. Considering the impact of source load uncertainty on voltage regulation, a multi-objective complementary voltage regulation architecture is proposed based on fuzzy chance constraint programming. This architecture integrates F-SOP with conventional reactive power compensation devices. Next, a multi-objective collaborative optimization model for distribution networks is constructed, with network losses, overall voltage deviation, and three-phase imbalance as objective functions. The proposed model is linearized using second-order cone programming. Finally, using an improved IEEE 33-node distribution network as a case study, the effectiveness of the proposed method was analyzed and validated. The results indicate that this method can reduce network losses by 30.17%, decrease voltage deviation by 46.32%, and lower three-phase imbalance by 57.86%. This method holds significant importance for the sustainable development of distribution networks.

The large-scale integration of new energy is an inevitable trend to achieve the low-carbon transformation of power systems. However, the strong randomness of wind power, photovoltaic power, and loads poses severe challenges to the safe and stable operation of systems. Existing studies demonstrate insufficient integration and handling of source-load bilateral uncertainties in wind–solar–fossil fuel storage complementary systems, resulting in difficulties in balancing economy and low-carbon performance in their energy storage configuration. To address this insufficiency, this study proposes an optimal energy storage configuration method considering source-load uncertainties. Firstly, a deterministic bi-level model is constructed: the upper level aims to minimize the comprehensive cost of the system to determine the energy storage capacity and power, and the lower level aims to minimize the system operation cost to solve the optimal scheduling scheme. Then, wind and solar output, as well as loads, are treated as fuzzy variables based on fuzzy chance constraints, and uncertainty constraints are transformed using clear equivalence class processing to establish a bi-level optimization model that considers uncertainties. A differential evolution algorithm and CPLEX are used for solving the upper and lower levels, respectively. Simulation verification in a certain region shows that the proposed method reduces comprehensive cost by 8.9%, operation cost by 10.3%, the curtailment rate of wind and solar energy by 8.92%, and carbon emissions by 3.51%, which significantly improves the economy and low-carbon performance of the system and provides a reference for the future planning and operation of energy systems.

Building operational energy consumption accounts for a significant share of global energy consumption, and it is crucial to promote renewable energy self-sufficiency and operational optimization for zero-carbon buildings. However, scheduling strategies relying on day-ahead forecasts have limitations, and ignoring the ambiguity of short-term source-load forecasts is prone to the risk of scheduling failures. To address this issue, this study proposes an intraday optimization method for zero-carbon buildings under the source-load fuzzy space, which innovatively constructs a fuzzy chance constraint model of Photovoltaic (PV) output and load demand, enforces energy self-sufficiency as a constraint, and establishes a multi-objective optimization framework with thermal comfort as the main objective and power adjustment balance as the sub-objective, so as to quantify the decision risk through intraday energy optimization. Experiments show that the proposed method quantifies the decision-maker’s risk preference through fuzzy opportunity constraints, balances conservatism and aggressive strategies, and improves thermal comfort while safeguarding energy independence, providing a risk-controllable scheduling paradigm for the decarbonized operation of buildings.

Because of their renewable and non-polluting characteristics in power production, distributed photovoltaics have been developed, but they have also been criticized for the volatility of their output power. In this paper, an integrated energy system optimal dispatching model is proposed to improve the local absorption capacity of distributed photovoltaics. First, an integrated energy system consisting of electricity, heat, cooling, gas, and hydrogen is modeled, and a mathematical model of the system is constructed. After that, the uncertainty of distributed photovoltaic power and load demand is modeled, and a typical scenario data set is generated through Monte Carlo simulation and K-means clustering. Finally, an optimal dispatching model of the integrated energy system is constructed to minimize the daily operating cost, including energy consumption, equipment operation and maintenance, and curtailment penalty costs, as the optimization objective. In the objective, a segmented curtailment penalty cost is Introduced. Moreover, this paper presents a chance constraint to convert the optimization problem containing uncertain variables into a mixed integer linear programming problem, which can reduce the difficulty of the solution. The case shows that the proposed optimal dispatching model can improve the ability of photovoltaics to be accommodated locally. At the same time, due to the introduction of the segmented curtailment penalty cost, the system improves the absorption of distributed photovoltaic generation at peak tariff intervals and enhances the economy of system operation.

Integrated energy systems are central to advancing efficient energy utilization and low-carbon transformation. In the current context, the inherent variability of high-penetration renewable sources (e.g., wind and solar) and the volatility of multi-energy loads (electricity, gas, heat, hydrogen) introduce significant uncertainties into integrated energy system dispatch from both supply and demand sides. To enhance renewable energy integration, operational economy, and low-carbon performance, this paper proposes a low-carbon optimal dispatch method for regional integrated energy systems that considers wind–solar uncertainty and dynamic hydrogen pricing. The significance of this study lies in addressing issues such as the difficulty of fixed hydrogen prices in guiding demand-side responses, insufficient incentives from traditional carbon pricing mechanisms, and the poor robustness of dispatching schemes under uncertainties. The price is dynamically adjusted according to the output of renewable energy and the level of hydrogen storage needed to stimulate the elastic response of hydrogen load. Secondly, a mechanism was proposed to constrain the carbon cost. Finally, the uncertainties stemming from wind and solar power output and multiple loads are addressed by employing fuzzy opportunistic constrained programming. Comparative analysis results of different scenarios indicate that the proposed strategy cuts down the system’s carbon emissions by 12.48%, increases hydrogen sales revenue by 9.96%, and lowers operating costs by 13.69%. Research has confirmed that this method not only enhances the system’s adaptability to uncertainty but also effectively balances the system’s economic efficiency with a cleaning objective. The novelty of this paper resides in the integration of dynamic hydrogen pricing mechanisms, tiered carbon trading schemes, and fuzzy opportunistic constrained programming for the first time, offering an innovative solution for the economic operation of regional integrated energy systems under uncertain scenarios.

Demand uncertainty is an important issue that influences the strategic, tactical, and operational-level decision making in the transportation/logistics/supply chain planning. In this study, we explore the effect of demand uncertainty on the operational-level freight routing problem in the capacitated multimodal transportation network that consists of schedule-based rail transportation and time-flexible road transportation. Considering the imprecise characteristic of the demand, we adopt fuzzy set theory to model its uncertainty and use trapezoidal fuzzy numbers to represent the fuzzy demands. We set multiple transportation orders as the optimization object and employ soft time windows to reflect the customer requirement on on-time transportation. Under the above situation, we establish a fuzzy mixed integer nonlinear programming (FMINLP) model to formulate the capacitated road–rail multimodal routing problem with demand uncertainty and time windows. We first use the fuzzy expected value model and credibility measure based fuzzy chance-constrained programming to realize the defuzziness of the model and then adopt linearization technique to reformulate the crisp model to finally generate an equivalent mixed integer linear programming (MILP) model that can be solved by standard mathematical programming software. Finally, a numerical case is presented to demonstrate the feasibility of the proposed method. Sensitivity analysis and fuzzy simulation are combined to quantify the effect of demand uncertainty on the routing problem and also reveal some helpful insights and managerial implications.

This study focuses on a renewable energy power plant equipped with electrolytic hydrogen production system, aiming to optimize energy management to smooth renewable energy generation fluctuations, participate in peak shaving auxiliary services, and increase the absorption space for renewable energy. A multi-objective energy management model and corresponding algorithms were developed, incorporating considerations of cost, pricing, and the operational constraints of a renewable energy generating unit and electrolytic hydrogen production system. By introducing uncertain programming, the uncertainty issues associated with renewable energy output were successfully addressed and an improved particle swarm optimization algorithm was employed for solving. A simulation system established on the Matlab platform verified the effectiveness of the model and algorithms, demonstrating that this approach can effectively meet the demands of the electricity market while enhancing the utilization rate of renewable energies.

This paper addresses the deregulated electricity market arising in a distribution system with an electricity transaction. Under such an environment, the distribution system operator (DSO) with a distributed generator faces the challenge of electricity price uncertainty in a spot market. In this context, a credibility theory-based robust optimization model with multiple transactions is established to hedge the uncertain spot price of the DSO. Firstly, on the basis of credibility theory, the spot price is taken as a fuzzy variable and a risk aversion-based fuzzy opportunity constraint is proposed. Then, to exploit the resiliency of multiple transactions on hedging against uncertain spot price, the spot market, option contract and bilateral contract integrating power flow constraints are studied, because it is imperative for DSO to consider the operational constraints of the local network in the electricity market. Finally, the clear equivalence class is adopted to transform the risk aversion constraint into a deterministic robust optimization one. Under the premise of considering the expected cost of the DSO, the optimal electricity transaction strategy that maximizes resistance to uncertain spot price is pursued. The rationality and effectiveness of the model are verified with a modified 15-node network. The results show that the introduction of option contracts and bilateral contracts reduces the electricity transaction cost of DSO by USD 28.5. In addition, under the same risk aversion factor, the cost of the proposed model is reduced by USD 195.18 compared with robust optimization, which avoids the over-conservatism of traditional robust optimization.

With the rapid development of wind power generation and photovoltaic power generation, the phenomenon of wind and solar abandoning becomes more and more serious in the operation of power systems, and the microgrid is a new operating mode of power systems which provides a new consumption mode for wind power generation. With the increasingly close connection among energy resources and people’s increasing awareness of environmental protection, this paper establishes a microgrid optimal scheduling model with a combined heat and power system, in consideration of environmental costs. This model aims at the lowest comprehensive cost, at the same time taking into account the emission reductions of SO2 and NOx, considering the cost of power generated by the micro-generator, environmental cost, the related cost of battery, operation and maintenance cost of wind power, and photovoltaic power generation. The related constraints of thermal balance and power balance are also considered during microgrid system operation. The established model is solved with an improved particle swarm algorithm. At last, taking a microgrid system as an example, the validity and reliability of the proposed model are verified.

As the low-carbon economy continues to expand, wind power, as one form of clean energy, promotes the low-carbon power development process. In this paper, a multi-objective environmental economic dispatch (EED) model is proposed considering multiple uncertainties of the system. Carbon trading costs and green certificate trading costs are introduced into the economic costs. Meanwhile, the objective function of pollutant emissions is taken into account in the model, which can further promote the reduction of pollutant emissions in the system scheduling. The output of wind turbines is uncertain and volatile, so it brings new challenges to the power system EED once the large-scale wind power accesses the power grid. For the multiple uncertainties of the system, fuzzy chance-constrained programming is introduced, and the output of the wind turbines and the load are regarded as fuzzy variables. We use the clear equivalence forms to clarify the fuzzy chance constraints. The improved multi-objective standard particle swarm optimization (SPSO) algorithm is used to solve the optimization problem effectively. The feasibility and effectiveness of the proposed model and algorithm are verified by an example of a 10-unit system with two wind farms.