Ian A. Hiskens

Achieving Controllability of Electric Loads

This paper discusses conceptual frameworks for actively involving highly distributed loads in power system control actions. The context for load control is established by providing an overview of system control objectives, including economic dispatch, automatic generation control, and spinning reserve. The paper then reviews existing initiatives that seek to develop load control programs for the provision of power system services. We then discuss some of the challenges to achieving a load control scheme that balances device-level objectives with power system-level objectives. One of the central premises of the paper is that, in order to achieve full responsiveness, direct load control (as opposed to price response) is required to enable fast time scale, predictable control opportunities, especially for the provision of ancillary services such as regulation and contingency reserves. Centralized, hierarchical, and distributed control architectures are discussed along with benefits and disadvantages, especially in relation to integration with the legacy power system control architecture. Implications for the supporting communications infrastructure are also considered. Fully responsive load control is illustrated in the context of thermostatically controlled loads and plug-in electric vehicles.

Distributed MPC Strategies With Application to Power System Automatic Generation Control

A distributed model predictive control (MPC) framework, suitable for controlling large-scale networked systems such as power systems, is presented. The overall system is decomposed into subsystems, each with its own MPC controller. These subsystem-based MPCs work iteratively and cooperatively towards satisfying systemwide control objectives. If available computational time allows convergence, the proposed distributed MPC framework achieves performance equivalent to centralized MPC. Furthermore, the distributed MPC algorithm is feasible and closed-loop stable under intermediate termination. Automatic generation control (AGC) provides a practical example for illustrating the efficacy of the proposed distributed MPC framework.

Trajectory sensitivity analysis of hybrid systems

The development of trajectory sensitivity analysis for hybrid systems, such as power systems, is presented in the paper. A hybrid system model which has a differential-algebraic-discrete (DAD) structure is proposed. This model forms the basis for the subsequent sensitivity analysis. Crucial to the analysis is the development of jump conditions describing the behavior of sensitivities at discrete events, such as switching and state resetting. The efficient computation of sensitivities is discussed. A number of examples are presented to illustrate various aspects of the theory. It is shown that trajectory sensitivities provide insights into system behavior which cannot be obtained from traditional simulation.

Simulation and Optimization in an AGC System after Deregulation

In this paper, the traditional AGC two-area system is modified to take into account the effect of bilateral contracts on the dynamics. The concept of DISCO participation matrix to simulate these bilateral contracts is introduced and reflected in the two-area block diagram. Trajectory sensitivities are used to obtain optimal parameters of the system using a gradient Newton algorithm.

Decentralized charging control for large populations of plug-in electric vehicles

The paper develops a novel decentralized charging control strategy for large populations of plug-in electric vehicles (PEVs). We consider the situation where PEV agents are rational and weakly coupled via their operation costs. At an established Nash equilibrium, each of the PEV agents reacts optimally with respect to the average charging strategy of all the PEV agents. Each of the average charging strategies can be approximated by an infinite population limit which is the solution of a fixed point problem. The control objective is to minimize electricity generation costs by establishing a PEV charging schedule that fills the overnight demand valley. The paper shows that under certain mild conditions, there exists a unique Nash equilibrium that almost satisfies that goal. Moreover, the paper establishes a sufficient condition under which the system converges to the unique Nash equilibrium. The theoretical results are illustrated through various numerical examples.

Control Lyapunov Functions for Controllable Series Devices

Controllable series devices (CSDs), i.e., series-connected flexible ac transmission systems (FACTS) devices, such as the unified power controller (UPFC), controllable series capacitor (CSC), and quadrature boosting transformer (QBT) with a suitable control scheme can improve transient stability and help to damp electromechanical oscillations. For these devices, a general model, which is referred to as an injection model, is used. This model is valid for load flow and angle stability analysis and is helpful for understanding the impact of the CSD on power system stability. Also, based on Lyapunov theory a control strategy for damping of electromechanical power oscillations in a multimachine power system is derived. Lyapunov theory deals with dynamical systems without inputs. For this reason, it has traditionally been applied only to closed-loop control systems, that is, systems for which the input has been eliminated through the substitution of a predetermined feedback control. In this paper, however, we use Lyapunov function candidates in feedback design itself by making the Lyapunov derivative negative when choosing the control. This control strategy is called control Lyapunov function (CLF) for systems with control inputs.

A Robust Control Strategy for Shunt and Series Reactive Compensators to Dame Electromechanical Oscillations

This paper examines the enhancement of power system stability properties by use of thyristor controlled series capacitors (TCSCs) and static var systems (SVCs). Models suitable for incorporation in dynamic simulation programs used to study angle stability are analyzed. A control strategy for damping of electromechanical power oscillations using an energy function method is derived. Using this control strategy each device (TCSC and SVC) will contribute to the damping of power swings without deteriorating the effect of the other power oscillation damping (POD) devices. The damping effect is robust with respect to loading condition, fault location, and network structure. Furthermore, the control inputs are based on local signals. The effectiveness of the controls is demonstrated for model power systems.

Sensitivity, Approximation, and Uncertainty in Power System Dynamic Simulation

Parameters of power system models, in particular load models, are seldom known exactly, yet dynamic security assessment relies upon simulation of those uncertain models. This paper proposes a computationally feasible approach to assessing the influence of uncertainty in simulations of power system dynamic behavior. It is shown that trajectory sensitivities can be used to generate accurate first-order approximations of trajectories that arise from perturbed parameter sets. The computational cost of obtaining the sensitivities and perturbed trajectories is minimal. The mathematical structure of the trajectory approximations allows the effects of uncertainty to be quantified and visualized using worst-case analysis and probabilistic approaches

Energy functions, transient stability and voltage behaviour in power systems with nonlinear loads

This paper presents preliminary results in a program aimed at energy function analysis of transient behaviour of power systems with nonlinear loads. The model, which preserves the network structure, is of differential-algebraic type. This introduces some new analytical issues, but the concepts enable the establishment of a connection between transient (angle) stability, multiple stable equilibria and voltage behaviour. A practical method for determining and classifying equilibrium points of the model is developed.

Exploring the Power Flow Solution Space Boundary

A knowledge of the structure of the boundary of solutions of the power flow problem is important when analyzing the robustness of operating points. This paper proposes a predictor-corrector technique to assist in exploring that structure. Points on the solution boundary satisfy the power flow equations together with an equation that forces the power flow Jacobian to be singular. Curves of such points result from freeing two parameters of the system. The proposed technique follows those curves. A simple example is used to illustrate the complex nature of the power flow solution space.