Vaibhav Donde

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.

Optimization Strategies for the Vulnerability Analysis of the Electric Power Grid

Identifying small groups of lines, whose removal would cause a severe blackout, is critical for the secure operation of the electric power grid. We show how power grid vulnerability analysis can be studied as a bilevel mixed integer nonlinear programming problem. Our analysis reveals a special structure in the formulation that can be exploited to avoid nonlinearity and approximate the original problem as a pure combinatorial problem. The key new observation behind our analysis is the correspondence between the Jacobian matrix (a representation of the feasibility boundary of the equations that describe the flow of power in the network) and the Laplacian matrix in spectral graph theory (a representation of the graph of the power grid). The reduced combinatorial problem is known as the network inhibition problem, for which we present a mixed integer linear programming formulation. Our experiments on benchmark power grids show that the reduced combinatorial model provides an accurate approximation, to enable vulnerability analyses of real-sized problems with more than 16,520 power lines.

Severe Multiple Contingency Screening in Electric Power Systems

We propose a computationally efficient approach to detect severe multiple contingencies. We pose a contingency analysis problem using a nonlinear optimization framework, which enables us to detect the fewest possible transmission line outages resulting in a system failure of specified severity, and to identify the most severe system failure caused by removing a specified number of transmission lines from service. Illustrations using a three-bus system and the IEEE 30-bus system aim to exhibit the effectiveness of the proposed approach.

Identification of severe multiple contingencies in electric power networks

In this paper we propose a two-stage screening and analysis process for identifying multiple contingencies that may result in very severe disturbances and blackouts. In a screening stage we form an optimization problem to find the minimum change in the network to move the power flow feasibility boundary to the present operating point and that will cause the system to separate with a user-specified power imbalance. The lines identified by the optimization program are used in a subsequent analysis stage to find combinations that may lead to a blackout. This approach is applied to a 30-bus system with encouraging results.

Power System Extreme Event Screening using Graph Partitioning

We propose a partitioning problem in a power system context that weighs the two objectives of minimizing cuts between partitions and maximizing the power imbalance between partitions. We then pose the problem in a purely graph theoretic sense. We offer an approximate solution through relaxation of the integer problem and suggest refinement using stochastic methods. Results are presented for the IEEE 30-bus and 118-bus electric power systems.

SHOOTING METHODS FOR LOCATING GRAZING PHENOMENA IN HYBRID SYSTEMS

Hybrid systems are typified by strong coupling between continuous dynamics and discrete events. For such piecewise smooth systems, event triggering generally has a significant influence over subsequent system behavior. Therefore, it is important to identify situations where a small change in parameter values alters the event triggering pattern. The bounding case, which separates regions of (generally) quite different dynamic behaviors, is referred to as grazing. At a grazing point, the system trajectory makes tangential contact with an event triggering hypersurface. The paper formulates conditions governing grazing points. Both transient and periodic behaviors are considered. The resulting boundary value problems are solved using shooting methods that are applicable for general nonlinear hybrid (piecewise smooth) dynamical systems. The grazing point formulation underlies the development of a continuation process for exploring parametric dependence. It also provides the basis for an optimization technique that finds the smallest parameter change necessary to induce grazing. Examples are drawn from power electronics, power systems and robotics, all of which involve intrinsic interactions between continuous dynamics and discrete events.

Dynamic performance assessment: grazing and related phenomena

Performance specifications place restrictions on the dynamic response of many systems, including power systems. Quantitative assessment of performance requires knowledge of the bounding conditions under which specifications are only just satisfied. In many cases, this limiting behavior can be related to grazing phenomena, where the system trajectory makes tangential contact with a performance constraint. Other limiting behavior can be related to time-driven event triggering. In all cases, pivotal limiting conditions can be formulated as boundary value problems. Numerical shooting methods provide efficient solution of such problems. Dynamic performance assessment is illustrated in the paper using examples drawn from protection operation, transient voltage overshoot, and induction motor stalling.

Identification of Market Power in Large-Scale Electric Energy Markets

Market power potential is a serious concern for efficient and competitive operation of centrally-dispatched electricity markets. Traditional measures for market power ignore underlying physical characteristics of the electric grid that may be exploited for local advantage. In our prior work we have proposed a revenue sensitivity-based approach for identifying market participants with market power potential, and we demonstrated detailed cases using a 30-bus system[1] [2] [3]. In this paper we address computational challenges for scaling our method to large systems, and we present practical extensions to a portion of our work that enables the evaluation of very large, RTO-scale electric power grids.

Grazing bifurcations in periodic hybrid systems

Grazing bifurcations occur when a small parameter variation induces a change in the event sequence of a hybrid system, i.e., a system where continuous dynamics and discrete events strongly interact. At such a bifurcation, the system trajectory makes tangential contact with (grazes) an event triggering hypersurface. This bounding case separates regions of (generally) quite different dynamic behaviour. The paper formulates the conditions governing grazing bifurcation points, and extends those conditions to limit cycles. A shooting method is used to solve for bifurcating limit cycles. The approach is applicable for general nonlinear hybrid systems.

Shooting for border collision bifurcations in hybrid systems

Border collision bifurcations refer to situations where a small parameter variation induces a change in the event sequence of a hybrid system. At such a bifurcation, the system trajectory makes tangential contact with an event triggering hypersurface. This bounding case separates regions of (generally) quite different dynamic behaviour. In the paper, the conditions governing bifurcation points are formulated as a boundary value problem. A shooting method is used to solve that problem. The approach is applicable for general nonlinear hybrid systems.