The dynamic gas flow model with static electric-driven compressor (EDC) model has been widely studied in coordinated analysis of integrated electricity-gas system (IEGS). However, as a crucial coupling unit, the boost characteristics of the EDC change dynamically with gas state, which may lead to unstable operation mode and then affect safe operating of IEGS. Meanwhile, its nonlinear model greatly increases the difficulty of analysis. This paper proposes a reduced-order transfer function model that considers EDCs for an accurate and efficient dynamic analysis of the IEGS. Firstly, a general two-port model in the Laplace-domain is derived to jointly analyze the pipeline and EDCs dynamic characteristics. The model based on transfer function, explicitly gives the relation between the pressures and flows state at ports. On this basis, to concisely analyze state variations of crucial nodes, the multiple cascaded pipelines and compressors are aggregated and to form an equivalent model. Meanwhile, to reduce the computational burden of the high-order Laplacian “s” in the aggregated process, a reduced-order method is developed based on Jordan continued-fraction expansion by preserving the main gas dynamic feature. Then the analytical expression of state fluctuation can be conveniently derived to analyze the underlying impact and interaction between power system and gas system. Finally, case studies are conducted to prove the effectiveness of proposed model and reduction method.

The integrated energy system (IES) combined electric power grid, natural gas network (NGN) and district heating network (DHN) is widely concerned because of its high efficiency and environmentally friendly. The accurate energy flow calculation of IES is the key to simulation analysis, operation optimization and control. This paper studies the dynamic energy flow of IES considering the different time-scale among the electric power, heat and gas networks. Firstly, a discretization method based on the delay characteristics of pipelines for DHN is proposed. By using this method, the selected temporal and spatial step sizes can be adaptively selected for thermal dynamic equation with application to different networks. Secondly, a discretization method for NGN is developed by considering the temporal step size of DHN as sampling period, so that the data interactions between two slow dynamic systems can be addressed in a same time series. Thirdly, a multi-rate energy flow calculation method with different temporal step sizes is presented for IES, which integrates the NGN and DHN considering different time-scale features to retain the state of IES as intact as possible. Simulation results illustrate the effectiveness of the proposed method, which provides dispatchers with more decision-making information.

With renewable energy becoming more and more important, the heat and electricity integrated energy system (HE-IES) has been widely used because of its potential benefit in accommodating renewable energy. This work for the first time formulated a dynamic optimal energy flow (OEF) problem for the HE-IES with hybrid AC/DC sources. Firstly, to effectively and accurately assess the operation state of district heating network (DHN), the temperature dynamics are focused and solved with a set of difference equations where an adaptive discretization method is proposed. The method based on the delay characteristics of pipelines is proposed to select temporal and spatial steps for reasonable approximation of DHN, and to achieve satisfactory accuracy results with a lower computational burden. Secondly, a two-stage OEF model for HE-IES with new linear approximations is developed. In this model, a detailed converter station model coupled AC grid and DC grid is investigated, and a linearization constraint method is proposed to handle the highly nonlinear of converter station by adding extended branches to the AC grid. Finally, simulations demonstrate that the effectiveness of the proposed model, which can provide more intact information of state variables for optimal planning. Note to Practitioners—This work is motivated by the demand for optimal energy management in heat and electricity integrated energy system (HE-IES). On the one hand, the slow dynamic characteristic of the district heating network (DHN) is crucial for calculating the optimal results. On the other hand, the improvement of electronic technology has diversified energy supplies and enriched the way of using electricity, such as converter-based generators for electric power grid (EPG) and converter-based boilers for DHN. Therefore, the model of HE-IES exhibits highly nonlinearity, which brings huge challenges to optimal energy flow analysis, especially for the real-time OEF analysis with state information updated every 15-30 min. Existing studies focus on computing optimal energy flow without considering the slow dynamic characteristic of DHN or the hybrid AC/DC scenarios brought by the converter-based sources. This paper presents an optimal energy flow problem that integrates the slow dynamic characteristic and the converter-based sources to retain the complete state information of the system as much as possible in the optimization process. The work is used on an integrated IEEE-33 bus and Denmark-61 node system to show the effectiveness.

The district heating network (DHN) can provide flexibility for electric power system (EPS) to accommodate power because of its slow dynamic and thermal energy storage characteristics. However, the traditional flexibility quantifications neglect the thermal temporal-spatial dynamic propagation and uncertainty parameters of DHN, resulting in inaccurate assessment of available flexibility capabilities. To address this issue, this article proposes a dynamic flexibility quantification method. First, three flexibility metrics including capacity, amplitude, and duration of power integration are modeled by simultaneously considering the temperature temporal and spatial dynamic propagation. Then, the discretized criteria are designed to reasonably linearize the temporal and spatial dynamic variables in the metrics. Thus, the evolution of flexibility metrics over time and space can be captured. Furthermore, the uncertainty parameters (e.g., mass flow, thermal resistance) in the metrics are modeled to account for their impact on the flexibility results. To this end, the maximum entropy principle combined with the probabilistic cumulant is developed to construct the probability distributions of metrics. With these effects, the flexibility provided by DHN can be elaborately quantified. Finally, case studies and simulation analysis are carried out on China Luhua network and Denmark 61-node network to verify the effectiveness of the proposed quantification method.