Soumya Kundu

Distributed control of reactive power from photovoltaic inverters

As new devices and technologies enter the electrical distribution grid, decentralized control algorithms will become increasingly important. Unlike centralized control where standard optimization procedures can ensure optimal system performance, control algorithms for distributed systems may take a variety of forms. This paper derives a decentralized algorithm that regulates the reactive power output from highly distributed photovoltaic (PV) sources. An objective function is constructed that minimizes voltage deviations and line losses. It is shown that this objective function is minimized by a local control law that regulates the reactive power output of PV inverters. Optimality of the derived control law is tested against central optimization solutions.

Safe protocol for controlling power consumption by a heterogeneous population of loads

Recent studies on control of aggregate power of an ensemble of thermostatically-controlled-loads (TCLs) have been concentrated on shifting the temperature set points of each TCL in the population. A sudden shift in the set point, however, is known to be associated with undesirable power oscillations which require closed-loop control strategies to regulate the aggregate power consumption of the population. In this article, we propose a new approach which we term as a “safe protocol” to implement the shift in temperature set point. It is shown analytically and verified numerically that by shifting the set point “safely” the aggregate power consumption can be changed to a different value within a time frame of the order of a TCLs cycle duration and avoid the undesired oscillations seen otherwise in a “sudden” shift. We discuss how the excess aggregate energy transferred under a safe shift in the set point could potentially mitigate the burden due to abnormal energy generation within a short time span.

Overvoltages due to Synchronous Tripping of Plug-in Electric-Vehicle Chargers Following Voltage Dips

Plug-in electric vehicle (PEV) charging equipment incorporates protection that ensures that grid disturbances do not damage the charger or vehicle. When the grid voltage sags below 80% of nominal, undervoltage protection is likely to disconnect the charging load from the grid. Most PEV charging will occur overnight, when non-PEV load is at a minimum. This paper argues that PEV voltage-sag response, when synchronized across large numbers of PEVs, could result in the loss of a significant proportion of the total load. It is shown that this load loss can lead to unacceptably high voltages once the initiating event has been cleared. This paper explores the nature of this voltage-rise phenomenon. Analysis tools are developed to assist in determining PEV loading conditions that demarcate acceptable postdisturbance voltage response from unacceptable outcomes. Two examples, based on standard distribution test systems, are used to illustrate PEV-induced overvoltage behavior, and demonstrate applications of the analysis tools.

Hysteresis-based charging control of plug-in electric vehicles

The paper develops a hysteresis-based charging control strategy for plug-in electric vehicles (PEVs) that is capable of regulating charging load to satisfy system-wide services, including filling the overnight demand “valley” and balancing fluctuations in renewable generation. The actual state-of-charge (SoC) of a PEV battery follows a nominal SoC profile within a small hysteresis band. This leads to a sequence of ON and OFF cycles for the charger. The paper shows that in steady-state the probability distributions of SoC in the ON and OFF states, normalized around the nominal profile, follow a uniform distribution over the hysteresis deadband. Based on this steady-state behavior, a linearized state-space model has been developed to capture the response of aggregate electricity demand to shifts in the nominal SoC profile. A feedback control law is designed based on this linearized model.

Stability and control of power systems using vector Lyapunov functions and sum-of-squares methods

Recently, sum-of-squares (SOS) based methods have been used for the stability analysis and control synthesis of polynomial dynamical systems. This analysis framework was also extended to non-polynomial dynamical systems, including power systems, using an algebraic reformulation technique that recasts the systems dynamics into a set of polynomial differential algebraic equations. Nevertheless, for large scale dynamical systems this method becomes inapplicable due to its computational complexity. For this reason we develop a subsystem based stability analysis approach using vector Lyapunov functions and introduce a parallel and scalable algorithm to infer the stability of the interconnected system with the help of the subsystem Lyapunov functions. Furthermore, we design adaptive and distributed control laws that guarantee asymptotic stability under a given external disturbance. Finally, we apply this algorithm for the stability analysis and control synthesis of a network preserving power system.

Sustainability, Resiliency, and Grid Stability of the Coupled Electricity and Transportation Infrastructures: Case for an Integrated Analysis

AbstractElectrified vehicles (EVs) couple transportation and electrical infrastructures, impacting vehicle sustainability, transportation resiliency, and electrical grid stability. These impacts occur across timescales; grid stability at the millisecond scale, resiliency at the daily scale, and sustainability over years and decades. Integrated models of these systems must share data to explore timescale dependencies, and reveal unanticipated outcomes. This paper examines EV adoption for sustainability, resiliency, and stability effects. Sustainability findings, consistent with previous studies, indicate that electrification generally reduces lifecycle greenhouse gas (GHG) emissions, and increases SOx and NOx. Electrified vehicles enhance vehicle resiliency (ability of vehicle to complete typical trips during fuel outage). Coupled results enhance EV resilience research, finding that a 16-km (10-mi) all-electric range plug-in hybrid EV improves resiliency ∼50% versus a gasoline-only vehicle. Increasing EV m...

Computation of linear comparison equations for stability analysis of interconnected systems

Sum-of-squares (SOS) methods have been shown to be very useful in computing polynomial Lyapunov functions for systems of reasonably small size. However for large scale systems it is necessary to use a scalable alternative using vector Lyapunov functions. Earlier works have shown that under certain conditions the stability of an interconnected system can be studied through suitable comparison equations. However finding such comparison equations can be non-trivial. In this work we propose an SOS based systematic procedure to directly compute the comparison equations for interconnected system with polynomial dynamics. With an example of interacting Van der Pol systems, we illustrate how this facilitates a scalable and parallel approach to stability analysis.

A sum-of-squares approach to the stability and control of interconnected systems using vector Lyapunov functions

Stability analysis tools are essential to understanding and controlling any engineering system. Recently, sum-of-squares (SOS) based methods have been used to compute Lyapunov based estimates for the region-of-attraction (ROA) of polynomial dynamical systems. But for a real-life large scale dynamical system this method becomes inapplicable because of growing computational burden. In such a case, it is important to develop a subsystem based stability analysis approach which is the focus of the work presented here. A parallel and scalable algorithm is used to infer stability of an interconnected system, with the help of the subsystem Lyapunov functions. Locally computable control laws are proposed to guarantee asymptotic stability under a given disturbance.

Nonlinear Dynamics of Hysteresis-Based Load Controls

Abstract Direct load control can be achieved by varying the hysteresis band of switchable loads, thereby changing their on/off durations. Such hysteresis-based control methods may, however, display complex dynamics that must be thoroughly understood in order to design safe control mechanisms. This paper explores the dynamical behavior of a group of hysteresis-based PEV chargers. Of interest is the change in the total power demand of the group as the hysteresis- band limits are varied. A detailed state-space model is used to capture the dynamics of the load aggregation. This model suggests that for certain control inputs, e.g. periodic ramp signals, the system may display rich dynamical behavior. It is observed that structural stability of the system may be disrupted as certain characteristics of the input signal are varied. The paper explores these phenomena through a bifurcation analysis of the load population dynamics. The results identify performance limitations that govern the responsiveness of fast-acting demand control.