Yu Christine Chen

A Method to Study the Effect of Renewable Resource Variability on Power System Dynamics

This paper proposes a set-theoretic method to assess the effect of variability associated with renewable-based electricity generation on power system dynamics, with a focus on time-scales involving electromechanical phenomena. Performance requirements define a set within which the values of certain system variables, e.g., synchronous generator speeds, system frequency, or bus voltages, must remain at all times. To address this problem, reachability analysis techniques are used; for a given time frame, if the reach set, i.e., the set that contains all possible system trajectories, is within the set defined by performance requirements, then it may be concluded that variability arising from in renewable-based electricity generation does not have a significant impact on system dynamics. The proposed method is illustrated through several case studies, including the 39-bus New England system model.

Analysis of Power System Dynamics Subject to Stochastic Power Injections

We propose a framework to study the impact of stochastic active/reactive power injections on power system dynamics with a focus on time scales involving electromechanical phenomena. In this framework, the active/reactive power injections evolve according to a continuous-time Markov chain (CTMC), while the power system dynamics are described by the standard differential algebraic equation (DAE) model. The DAE model is linearized around a nominal set of active/reactive power injections, and the combination of the linearized DAE model and the CTMC forms a stochastic process known as a stochastic hybrid system (SHS). The extended generator of the SHS yields a system of ordinary differential equations that governs the evolution of the power system dynamic and algebraic state moments. We illustrate the application of the framework to the computation of long-term power system state statistics, and to short-term probabilistic dynamic performance/reliability assessment.

Power system line outage detection and identification — A quickest change detection approach

A method to detect and isolate power system transmission line outages in near real-time is proposed. In particular, a linearized power system model is presented and a statistical model for line outage detection and isolation is developed using this model. To detect and isolate the line outage quickly, algorithms based on statistical quickest change detection are employed.

Measurement-Based Estimation of Linear Sensitivity Distribution Factors and Applications

In this paper, we propose a method to compute linear sensitivity distribution factors (DFs) in near real-time. The method does not rely on the system power flow model. Instead, it uses only high-frequency synchronized data collected from phasor measurement units to estimate the injection shift factors through linear least-squares estimation, after which other DFs can be easily computed. Such a measurement-based approach is desirable since it is adaptive to changes in system operating point and topology. We further improve the adaptability of the proposed approach to such changes by using weighted and recursive least-squares estimation. Through numerical examples, we illustrate the advantages of our proposed DF estimation approach over the conventional model-based one in the context of contingency analysis and generation re-dispatch.

Scalable Optimization Methods for Distribution Networks With High PV Integration

This paper proposes a suite of algorithms to determine the active- and reactive-power setpoints for photovoltaic (PV) inverters in distribution networks. The objective is to optimize the operation of the distribution feeder according to a variety of performance objectives and ensure voltage regulation. In general, these algorithms take a form of the widely studied ac optimal power flow (OPF) problem. For the envisioned application domain, nonlinear power-flow constraints render pertinent OPF problems nonconvex and computationally intensive for large systems. To address these concerns, we formulate a quadratic constrained quadratic program (QCQP) by leveraging a linear approximation of the algebraic power-flow equations. Furthermore, simplification from QCQP to a linearly constrained quadratic program is provided under certain conditions. The merits of the proposed approach are demonstrated with simulation results that utilize realistic PV-generation and load-profile data for illustrative distribution-system test feeders.

Quickest Line Outage Detection and Identification

A method is proposed to detect and identify power system transmission line outages in near real-time. The method exploits the statistical properties of the small random fluctuations in electricity generation and demand that a power system is subject to as time evolves. To detect and identify transmission line outages, a linearized incremental small-signal power system model is used in conjunction with high-speed synchronized voltage phase angle measurements obtained from phasor measurement units. By monitoring the statistical properties of voltage phase angle time-series, line outages are detected and identified using techniques borrowed from the theory of quickest change detection. As illustrated through case studies, the proposed method is effective in detecting and identifying single- and double-line outages in an accurate and timely fashion.

A set-theoretic framework to assess the impact of variable generation on the power flow

The increased penetration of renewable resources, such as wind and solar, into existing power systems introduces significant uncertainties in the generation side. We propose a method to assess whether power system static state variables, i.e., bus voltage magnitudes and angles, remain within acceptable ranges (with some confidence level), as dictated by system operational requirements, while the system is subject to variations in electricity generation arising from the uncertain nature of renewable resources. These variations are assumed to be unknown but constrained to lie (with some confidence level) within some bounded set. Through set operations, we propagate this set through the power flow model, and the result is another set that contains the possible values that (with some confidence level) the state variables (voltage magnitudes and angles) may take. The proposed method is applied to the IEEE 34-bus and 123-bus benchmark distribution systems.

Linear approximations to AC power flow in rectangular coordinates

This paper explores solutions to linearized power-flow equations with bus-voltage phasors represented in rectangular coordinates. The key idea is to solve for complex-valued perturbations around a nominal voltage profile from a set of linear equations that are obtained by neglecting quadratic terms in the original nonlinear power-flow equations. We prove that for lossless networks, the voltage profile where the real part of the perturbation is suppressed satisfies active-power balance in the original nonlinear system of equations. This result motivates the development of approximate solutions that improve over conventional DC power-flow approximations, since the model includes ZIP loads. For distribution networks that only contain ZIP loads in addition to a slack bus, we recover a linear relationship between the approximate voltage profile and the constant-current component of the loads and the nodal active-and reactive-power injections.

Online computation of power system linear sensitivity distribution factors

Linear sensitivity distribution factors (DFs) are commonly used in power systems analyses, e.g., to determine whether or not the system is N-1 secure. This paper proposes a method to compute linear sensitivity distribution factors (DFs) in near real-time without relying on the system power flow model. Instead, through linear least-squares estimation (LSE), the proposed method only uses high-frequency synchronized data collected from phasor measurement units (PMUs) to estimate the injection shift factors (ISFs). Subsequently, ISFs can be used to compute other DFs. Such a measurement-based approach is desirable since it is adaptive to changes in system operating point and topology. We illustrate the value of the proposed measurement-based DF estimation approach over the traditional model-based method through several examples.

Assessing the Impact of Wind Variability on Power System Small-Signal Reachability

We propose a method to assess the impact on power system dynamic performance of operational uncertainty caused by variability in the system supply side. Operational uncertainty is not new to power systems, e.g., demand variability. However, with the increased penetration of renewable-based generation, operational uncertainty will extend to a significant portion of the supply side, which may have an impact on system dynamic performance, e.g., frequency or voltage deviations beyond prescribed operational requirements. To address the problem, we propose the use of reachability analysis techniques, which will provide bounds on worst-case deviations of system variables that must remain within certain bounds. The method is illustrated with several examples.