A Fast Scalable Quasi-Static Time Series Analysis Method for PV Impact Studies Using Linear Sensitivity Model

Understanding the impact of distributed photovoltaic (PV) resources on various elements of the distribution feeder is imperative for their cost effective integration. A year-long quasi-static time series (QSTS) simulation at 1-second granularity is often necessary to fully study these impacts. However, the significant computational burden associated with running QSTS simulations is a major challenge to their adoption. In this paper, we propose a fast scalable QSTS simulation algorithm that is based on a linear sensitivity model for estimating voltage-related PV impact metrics of a three-phase unbalanced, nonradial distribution system with various discrete step control elements including tap changing transformers and capacitor banks. The algorithm relies on computing voltage sensitivities while taking into account all the effects of discrete controllable elements in the circuit. Consequently, the proposed sensitivity model can accurately estimate the state of controllers at each time step and the number of control actions throughout the year. For the test case of a real distribution feeder with 2969 buses (5469 nodes), 6 load/PV time series power profiles, and 9 voltage regulating elements including controller delays, the proposed algorithm demonstrates a dramatic time reduction, more than 180 times faster than traditional QSTS techniques.

I. Introduction

Over the past decade, distribution networks have seen a significant increase in the penetration of distributed energy resources (DERs). Installations of PV systems alone have seen an average annual growth rate of 68% per year in the United States over the past 10 years [1]. This unprecedented growth has been primarily attributed to the decreasing cost of PV systems as well as federal and state incentives [2]. However, due to high temporal and spatial variability of PV power production, significant penetration of PV systems can have undesired impacts on the distribution circuit elements. Feeders with high PV penetration can suffer from voltage violations, thermal overloading and excessive reverse power flow into the substation [3]. In addition, voltage regulators and capacitors banks in particular, can suffer from an excessive increase in the number of operations and potential oscillatory behavior. These effects can drastically reduce their life expectancy. Currently, scenario-based simulation is commonly used by utilities for screening potential issues while evaluating PV interconnection requests [4]. This process essentially involves solving a small set of static power flows designed to simulate extreme scenarios such as light and peak loading, min/max PV output etc. However, due to the complex locational and temporal interdependence of the PV systems, identifying a limited set of scenarios that capture all their potential impacts is statistically impossible. Furthermore, the impact on discrete step, time dependent controllable elements such as voltage regulators and capacitor banks cannot be accurately captured using static scenario-based simulations [5].