With the increasing development of smart grid, multiparty cooperative computation between several entities has become a typical characteristic of modern energy systems. Traditionally, data exchange among parties is inevitable, rendering how to complete multiparty collaborative optimization without exposing any private information a critical issue. This paper proposes a fully privacy-preserving distributed optimization framework based on secure multiparty computation (SMPC) secret sharing protocols. The framework decomposes the collaborative optimization problem into a master problem and several subproblems. The process of solving the master problem is executed in the SMPC framework via the secret sharing protocols among agents. The relationships of agents are completely equal, and there is no privileged agent or any third party. The process of solving subproblems is conducted by agents individually. Compared to the traditional distributed optimization framework, the proposed SMPC-based framework can fully preserve individual private information. Exchanged data among agents are encrypted and no private information disclosure is assured. Furthermore, the framework maintains a limited and acceptable increase in computational costs while guaranteeing optimality. Case studies are conducted to demonstrate the principle of secret sharing and verify the feasibility and scalability of the proposed methodology.

Using thermal inertia in district heating systems (DHSs) to improve the dispatch flexibility and economy of integrated heat and electricity systems (IHESs) is a research hotspot and difficulty. In most existing studies, the partial differential equations (PDEs) of thermal inertia are approximated by discrete-time models, making it difficult to accurately describe the continuous dynamic processes. In this paper, we propose a novel generalized phasor method (GPM) for thermal inertia in DHSs with constant mass flow. Based on the analytical solution of the PDEs and the Fourier transform, the intractable PDEs are transformed into a series of complex algebraic equations represented by phasors. The GPM has higher accuracy compared to traditional discrete models because it is essentially a continuous model in the time domain. Then, we present a different representation of an integrated heat and electricity dispatch (IHED) model combining a DHS model in phasor form and a traditional electrical power system model. The IHED model is a convex programming problem and can be easily solved. The effectiveness of the proposed GPM and dispatch model is verified in three test systems. Compared with traditional methods for modeling the thermal inertia, the proposed GPM is more accurate.