Coordinated operations of electricity and district heating networks offer a potential for mitigating inherent variability of renewable energy sources (RES) in the ongoing transition to smart grids. This paper proposes a two-stage distributionally robust optimization (DRO) approach to determine the optimal day-ahead unit commitment in coordinated electricity and district heating networks with variable RES power output. The proposed formulation is to minimize the worst-case expected total cost over an ambiguity set comprising a family of probability distributions with given support and moments of RES power output. As such, the proposed DRO approach can overcome the limitations of stochastic programming in its inherent dependence of exact probability distributions along with a huge computational burden, but also becomes less conservative than conventional robust optimization. The pertinent DRO model is eventually reformulated as a tractable mixed-integer second-order cone (SOC) programming after employing linear decision rules and the SOC duality. Simplified affine policies are utilized to further improve computational tractability and performance. Finally, case studies are conducted based on Barry Island electricity and district heating networks. The numerical results validate the computational improvement of the proposed approach by employing simplified affine policies.

Extreme weather events pose a serious threat to energy distribution systems. We propose a distributionally robust optimization model for the resilient operation of the integrated electricity and heat energy distribution systems in extreme weather events. We develop a strengthened ambiguity set that incorporates both moment and Wasserstein metric information of uncertain contingencies, which provides a more accurate characterization of the true probability distribution. We first recast the proposed model into an equivalent framework which is similar to a conventional two-stage robust model and then utilize a modified column-and-constraint generation algorithm to solve the recast model. Numerical results from three test systems validate the enhanced resilience of the distributionally robust approach, the reduced conservatism of the strengthened ambiguity set, and the computational efficiency of the proposed solution algorithm.

The combined operations of power distribution and district heating networks catalyze the ongoing transition to smart cities. This paper proposes a data-driven distributionally robust energy and reserve co-optimization approach for combined power distribution and district heating networks. In particular, smart buildings are modeled as equivalent storage devices as cost-effective resources to enhance operational flexibility and provide additional reserves in power systems. Uncertainties pertaining to renewable energy source (RES) power and ambient temperature are captured within an ambiguity set that comprises a variety of statistical characterizations (e.g., expected value, variance, covariance) to generate more trustworthy and less conservative solutions. Linear decision rules and the second-order cone duality are employed to enhance computational tractability by transforming the original problem into a second-order cone program. Finally, numerical results based on the real-world Barry Island system demonstrate the risk-reduction and economic benefits of the proposed approach.

This study implements a rolling look-ahead unit commitment scheme in a combined PDN and DHN energy system to exploit the operational flexibility of rapid-response combined heat and power (CHP) units under significantly variable renewable energy source (RES) power output. The scheme is formulated as a multistage distributionally robust (DR) unit commitment model that respects the non-anticipativity of decision variables for sequential revelations of uncertainties. In contrast to the moment-based ambiguity sets employed in conventional DR models, the present framework constructs an ambiguity set based on probabilistic forecasts. In this regard, compatibility between DR approaches and probabilistic forecasts is achieved by incorporating probability measures of uncertain RES power output stemming from probabilistic forecasts. The computational challenge associated with the proposed multistage DR model is addressed by applying linear decision rules. Moreover, a new constraint reformulation approach is utilized to increase the computational speed and tractability. The pertinent model is cast into a tractable mixed-integer linear programming problem. The effectiveness of the proposed method in capturing the probabilistic forecast of RES power output and reducing system operation costs is demonstrated by case studies carried out on the Barry Island multi-carrier energy system.