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District heating systems can provide considerable flexibility for electric power systems through combined heat and power units and heat pumps. This paper proposes a chance-constrained two-stage energy and multi-type reserves scheduling scheme for integrated electricity and heating systems to handle both wind power forecast errors and the outage of the largest generator. The combined heat and power units and heat pumps not only provide following reserves for offsetting wind power forecast errors under normal conditions, but also provide primary frequency response reserves for arresting system frequency decline after the outage of the largest generator. The primary frequency response reserves from combined heat and power units and heat pumps are optimized satisfying system steady-state frequency requirement while considering the reserve costs. To manage the risk level of load shedding caused by wind power forecast errors, chance constraints are adopted to achieve the trade-off between the sufficiency of following reserves and system economic efficiency. The nonlinear and nonconvex scheduling model is reformulated as a mixed-integer linear program via linearization and convex approximation based on conditional value-at-risk. The effectiveness of the proposed scheduling scheme in improving the system frequency regulation, system economic efficiency, and wind power integration is verified through the case studies on a 6-bus and 6-node integrated electricity and heating system and a regional large-scale test system. • A joint energy and multi-type reserves scheduling scheme is proposed for IEHSs. • CHP units and HPs provide both following reserves and primary frequency response reserves. • A chance-constrained program is used to manage the risk level of load shedding. • System frequency regulation is further enhanced by utilizing reserves from heat pumps. • The system economic efficiency and wind power integration are improved. [ABSTRACT FROM AUTHOR]

• An enhanced wind power scenario generation and evaluation method is proposed. • A non-separable covariance function is incorporated to capture spatial and temporal correlations. • A more accurate parameter estimation method with fluctuation-based clustering is proposed. • New scenario evaluation indices from the perspective of system operators are introduced. Short-term wind power scenarios significantly affect the economic efficiency of the stochastic power system scheduling. In order to better capture the nonlinear spatio-temporal correlations of wind power, this paper proposes a scenario generation method integrated with non-separable spatio-temporal covariance function and fluctuation-based clustering for short-term wind power output. By taking advantage of well-calibrated marginal distribution modeled by Gaussian mixture model, the non-separable covariance function is incorporated in the scenario generation method to capture the complex interactions between spatial and temporal components of wind power. To estimate the covariance matrix more precisely, the historical data is grouped into K clusters with different fluctuations using the K-means clustering algorithm. Two indices are proposed to evaluate the scenarios in capturing the spatial and temporal correlations from the perspective of system operators. The proposed method is applied to a modified IEEE-118 system with four wind farms. Simulation results verify the superiority of the proposed method in capturing spatial and temporal correlations, and validate the economic benefits for the power system operation. [ABSTRACT FROM AUTHOR]

The growing uncertainty caused by the increasing wind power penetration brings an urgent need of increased reserve capacity to ensure the secure operation of power systems. The interconnection of multiple integrated electricity and heating systems (IEHSs) allows resource sharing among them and the district heating system can provide additional reserves to the electric power system. In this paper, a decentralized robust energy and reserve co-optimization for multiple IEHSs is proposed to handle wind power uncertainty in a more economic and efficient way. In each IEHS, the day-ahead energy and reserve scheduling is formulated as a two-stage adaptive robust optimization, where the feasibility of day-ahead reserve deployment in the real-time operation is guaranteed. Then, a decentralized methodology is developed based on the alternating direction method of multipliers (ADMM) to achieve the synergistic yet independent operation by exchanging tie-line power flows with adjacent IEHSs. In order to accelerate the convergence of the decentralized operation and reduce the communication demand, the improved ADMM with locally adaptive penalty parameters is adopted. Simulation results demonstrate the effectiveness of the proposed decentralized robust energy and reserve optimization scheme in terms of improving the economic efficiency and ensuring the secure operation for IEHSs, as well as preserving information privacy. • A decentralized energy and reserve co-optimization for multiple IEHSs is proposed. • The feasibility of reserves is guaranteed with the two-stage robust optimization. • An improved ADMM algorithm with adaptive penalty parameters is adopted.. • The economic efficiency of IEHSs is improved and information privacy is preserved. [ABSTRACT FROM AUTHOR]

• A two-stage adaptive robust energy and reserve co-optimization scheme is proposed. • The spatial correlation of wind uncertainty is used to control the conservatism of robust solutions. • The available reserve capacity of combined heating and power units is fully utilized. • Electrical boiler and buildings' thermal inertia are introduced to increase the reserve capacity. The uncertainty and variability of wind power pose significant challenges to secure and reliable operation of power systems. Coordinated operation of the electric power system and district heating system, which can provide sufficient reserve capacity and flexibility, is an effective way to cope with the uncertainty. This paper proposes an adaptive robust energy and reserve co-optimization for the integrated electricity and heat system to minimize the total system cost under the worst-case realization of wind uncertainty considering spatial correlations of wind uncertainties. The available reserve capacity and flexibility provided by the district heating system is fully used by exploiting the regulation capabilities of combined heat and power units and electrical boilers, as well as utilizing the building thermal inertia. To reduce the conservatism of the robust solution, the spatial correlation of wind uncertainties is considered in the uncertainty set. The column-and-constraint generation algorithm is adopted to solve the adaptive robust model iteratively by reformulating the second stage with its Karush-Kuhn-Tucker conditions. Simulation results demonstrate that the economic efficiency is improved by utilizing the reserve flexibility from the district heating system and considering wind farm spatial correlations. Compared with the conventional single-stage optimized model, the feasibility of the two-stage robust solution is always guaranteed by considering the real-time operation constraints of the electric power system and district heating system. [ABSTRACT FROM AUTHOR]

• Explore benefits of using large-scale heat pumps to provide following and regulating reserves. • Stochastic optimization of the integrated electricity and heat system co-optimizes energy, reserve, and heat regulation. • Identify inactive transmission line constraints using an analytical calculation algorithm. Integrating power and heat sectors can increase the flexibility of wind power integration. Power-to-heat devices powered by renewables can promote the electrification and decarbonization of the heat sector. This paper explores the feasibility and benefits of using large-scale heat pumps for reserve provision. A two-stage stochastic optimization model is proposed for the day-ahead centralized scheduling of the integrated electricity and heat system considering wind power uncertainties, with reserve provision of large-scale heat pumps, combined heat and power units, and thermal power units. The model co-optimizes energy, following reserve, regulating reserve, and heat regulation to handle wind power uncertainties. To reduce the computational complexity of the scenario-based stochastic optimization problem, inactive transmission line constraints are identified and removed based on an analytical calculation method, which considers the influence of power consumption of large-scale heat pumps on the power flow of transmission lines. The benefits of using reserves from large-scale heat pumps are tested on the modified IEEE-118 bus integrated electricity and heat system. The simulation results show that using large-scale heat pumps to provide the following reserve and regulating reserve show similar impacts on saving cost and reducing wind energy curtailment, and the acceleration algorithm can save computation time by approximately 64%. [ABSTRACT FROM AUTHOR]

• Wind power forecast uncertainty in integrated electricity and natural gas systems are modelled. • The spatial-temporal correlation of wind power plants power uncertainty is considered. • A distributionally-robust chance constrained model controls the dispatch robustness to the wind power forecast errors. • An interval optimization model considers the uncertainty in natural gas network. With increasing penetrations of gas-fired generation in power systems because of reducing gas prices and emissions regulations, the interdependent and coordinated operation of integrated electricity and natural gas systems (IEGSs) is becoming an urgent research topic. Meanwhile, the significantly increasing deployment of wind power necessitates that IEGSs operation considers wind power output uncertainty. How to model the impact of wind power uncertainty on IEGSs power and gas flows dispatch is challenging. In this paper, a hybrid distributionally-robust chance-constrained and interval optimization (DRCC-IO) based model is proposed to consider the influence of wind power uncertainty and its spatial-temporal correlation on IEGSs operation. First, the DRCC-OPF model is proposed to obtain reliable economic dispatch solutions for the electricity network considering the wind power forecast errors. The spatial-temporal correlation of the wind power plant (WPP) forecasts is considered with a sparse correlation covariance matrix. Then, the interval optimization (IO) model is used to model the impacts of the power variations of gas-fired units on the natural gas network. Finally, the proposed model considers the impacts of wind power uncertainty on both the electricity and natural gas networks. Case studies performed on a six-bus power system coupled with a seven-node gas system and an IEEE 118-bus power system with a 14-node gas system verify the effectiveness of the proposed method to improve system security and reduce costs of the IEGSs. The robustness of the wind power forecast errors can be controlled in the proposed model to trade off the security and costs of the IEGSs. [ABSTRACT FROM AUTHOR]