Probabilistic Energy Flow Calculation through the Nataf Transformation and Point Estimation

Abstract

Featured Application: The work presented in this paper provides methods for probabilistic energy flow calculations and will serve as a reference for the operation and maintenance of integrated energy systems.Abstract: With the increasing capacity of renewable energy sources, uncertainties regarding renewable energy and other dynamic loads in integrated energy systems (IESs) are increasing. Thus, it is necessary to study the probabilistic energy flow (PEF) of IESs. However, existing PEF calculation methods such as the point estimate method (PEM) are computationally inefficient when there are many random variables and estimated points; moreover, relatively large errors can occur when the estimated points are outside their limits. Hence, this paper presents a calculation method that addresses these problems. Because there are correlations among the variables, the Nataf transformation is employed to control the correlation quickly and effectively. A model for an IES that is interconnected with natural gas and electricity systems and accounts for the uncertainties of wind plants, photovoltaic power plants, and dynamic gas loads is presented. Correlations between wind plants and photovoltaic power plants are handled using the Nataf transformation. Finally, a modified PEM is developed to solve the PEF. For situations in which the estimated points exceed their boundaries, the power transformation and equal constraint transformation methods are used. The results of time-domain simulations demonstrate the effectiveness of the proposed approach.Appl. Sci. 2019, 9, 3291 2 of 23 challenges in terms of energy uncertainties arise. The uncertainties come from the intermittency of RESs; additionally, the volatility of the loads in different energy structures aggravate the energy uncertainties in IESs [9], which creates significant challenges for the operation and maintenance of IESs. We can determine the probabilistic distribution of each node state in the IESs by calculating the probabilistic energy flow, which provides guidance to address possible risks. Therefore, the probabilistic energy flow (PEF) in IESs must be studied.The basis of PEF is the calculation of steady-state energy flow (SSEF), which has been studied extensively. Because of the similarity between the SSEF model of the power system and the gas network, Newton's method can be used to solve the SSEF of the gas network. When the initial point of Newton's method is near the equilibrium point, the method has good and fast convergence. Moreover, the IES mostly works near the equilibrium point. Therefore, Newton's method is a commonly used method for solving the energy flow problem. Moreover, the solutions obtained using this method for multiple energy systems can be divided into two forms according to the Jacobian matrices used in the solution, i.e., separate Newton iterations for each system [10] or a unified Newton iteration for all systems [11]. In [10], each energy system (e.g., power system or natural gas system) is represented by its own Jacobian matrix and inde...

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