Wide development of the heat and electricity integrated energy system (HE-IES) has provided flexible multi-energy optimization management, which improves energy efficiency and benefits the environment. It is essential to calculate energy flow quickly, accurately, and reliably as the system scale and complexity increase. To handle this problem, we propose a partitional decoupling method based on a decomposed energy flow model for the large-scale HE-IES. The computation mechanisms are presented considering various system scales and topologies, which consist of decoupling mode to solve the non-convergence caused by hydraulic initialization and the iteration mode to correct the variables at common nodes of decoupled systems. Moreover, a unit conversion method is introduced to solve the non-convergence problem in energy flow calculation under extreme scenarios. Case studies show that the proposed method provides accurate energy flow calculations with higher efficiency regard-less of system scale and topology, especially in looped systems. Numerical simulation further verifies the effectiveness of the proposed method for non-convergence.

Intensified interaction between electric power system (EPS) and district heating network (DHN) has raised an urgent requirement of security control to ensure the regular operation of the heat and electricity integrated energy system (HE-IES). However, the implicit expressions of thermal dynamics remain an obstacle to building the quantitative relationships between the EPS and the DHN. To solve this, this paper proposes a novel dynamic model of the district heating network, which contains the equivalent pipe model and the analytical thermal source-load function (TSLF). Then, the interaction between EPS and DHN is divided into the energy flow calculation at the control points and the dynamic simulation during the control intervals to investigate the coupling effect. On this basis, the dynamic characteristics in HE-IES are employed to quantitatively establish the security control strategy using the combined sensitivity analysis. Case studies verify the accuracy and efficiency of the proposed method.

The dynamic simulation of the integrated electricity and gas system (IEGS) is effective for accurate operational guidance. However, the IEGS model governed by partial and ordinary differential-algebraic equations (PDAE) is challenging for analysis, because it poses heterogeneous properties, high dimensionality, and strong nonlinearity. To eliminate the nonlinear terms, this paper firstly derives the expression of average flow velocity (AFV) and reformulates the gas flow dynamics into the variable-coefficient partial differential equations (VC-PDE), whose consistency, stability, and convergence can be theoretically guaranteed. Then, a novel adaptive step size control (ASC) strategy is developed for VC-PDE solvers to improve computational efficiency and accuracy. Finally, this paper builds a framework for the simulation of IEGS considering the dynamics in the natural gas network (NGN) and coupling units, where the bidirectional interaction between the electric power system (EPS) and NGN is investigated. Case studies verify the superiority of the proposed VC-PDE solver with ASC regarding accuracy, stability, convergence, and efficiency in different systems.

The worldwide promotion of electric heating improves the operational flexibility of the power system (PS). However, it also increases the risk of cascading failure due to the bi-directional interaction with the heating system (HS). To prevent such contingencies and facilitate prompt post-outage adjustments, the steady-state security region (SSR) of the integrated energy system (IES) will be a valuable and effective tool. This article derives an accurate SSR model for the heat and electricity IES, composed of a novel combined heat and power (CHP) unit model, the AC power flow model, and the dynamic HS model. An equivalence-based hyperplane method (EHM) is then proposed to solve the SSR model. The EHM treats the SSR as the intersection of the time-invariant and time-varying parts, and each part is described with a set of hyperplanes. On this basis, the sequential SSR (SSSR) is defined for IES to characterize the impact of CHP and HS integration, with which the time-varying process resulting from the thermal dynamics is divided into three periods for investigation. Numerical studies verify the accuracy and efficiency of the SSSR and EHM and demonstrate the influences of the CHP, HS integration, and thermal dynamics on the secure operation of the PS.

The ability to operate across multiple timescales is vital for the flexibility enhancement of integrated electricity and heating systems (IEHS). Nonetheless, the common dependence on numerical solvers operating in discrete spaces poses a challenge in accurately representing their inherent multi-timescale properties, thereby compromising system security. In response, this paper proposes a novel multi-timescale matching method in continuous space to get rid of resolution constraints, circumventing discretization issues while deriving an explicit formulation for thermal dynamics. This forms the groundwork for establishing the global sensitivity factors to quantify the interdependencies within the IEHS. On this basis, a rolling security evaluation and regulation strategy that is cognizant of the asynchronous behaviors in power and heating systems is tailored. Case studies validate the effectiveness and efficiency of the proposed method to ensure the IEHS’s security.

The deepening digitalisation of infrastructure has significantly increased the interconnection between power systems (PS) and gas systems (GS), rendering integrated electricity and gas systems (IEGS) more vulnerable to cyber-physical contingencies (CPC). This paper pioneers the investigation into N-1 contingency evaluation for cyber-physical IEGS to identify critical failures that pose threats to operational security. To accurately model various CPCs in IEGS, we introduce a nonlinear partial differential-algebraic equation (PDAE) model, which redefines CPCs as discontinuities and abrupt changes in simulation boundaries. We further propose a variable-coefficient analytical method (VC-AM) designed to robustly and efficiently handle these reformulated boundaries during CPC simulations. Building on this foundation, an N-1 evaluation framework is established to explore the contingency impact propagation and detect resultant violations, incorporating several performance indexes to quantify and rank the impacts of diverse contingencies. Case studies reveal that cyber-physical interdependence notably amplifies the effects of contingencies, underscoring the potential of VC-AM for real-time N-1 evaluation. In contrast, traditional methods are hindered by high computational complexity and convergence challenges.