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Standard computations reveal that locational marginal prices (LMPs), being Lagrange multipliers in an optimization problem, must lie in the null space of a Jacobian matrix evaluated at the optimal power flow solution, augmented by columns associated with active line flow limits. The impact of network power flow and active line limit constraints is to confine the LMPs in a subspace that satisfies necessary conditions for optimality. Optimal market clearing can then proceed as a minimization over offer curves confined to admissible LMPs in this subspace. When no line limits are active and losses neglected (e.g., in a dc power flow representation), the matrix in question has a generalized Laplacian structure, and admits only a vector of all equal elements in its null space (verifying the well-known equal incremental cost condition). As line flow limits become active, the null space grows in dimension. Among the phenomena of interest as the dimension of admissible LMPs grows is that of 'load pockets'; that is, admissible LMP vectors that can show patterns in which buses partition into zones of approximately equal LMPs, with significant differences between zones. This paper explores an approach to admissible LMP calculation that isolates the topological role of active line flow constraints, independent of offer curve prices. Identification of this admissible subspace can then greatly facilitate computations such as clustering to identify potential zones of differentiated LMPs. Index Terms--Coherency, Fiedler vector, locational marginal prices (LMPs), synchrony, zonal prices.

This paper explores synchrony, a recently introduced generalization of the concept of slow-coherency, and outlines how it can form the basis for efficient construction of dynamic equivalents by aggregation. We describe a novel approach for selecting the inter-area modes that are to be represented by the aggregate model. A clustering algorithm for recognizing approximate synchrony is presented, and improvements over the standard slow-coherency recognition algorithm are noted. Using for illustration a 23-generator power system model with 325 state variables, the paper demonstrates the effectiveness of a synchrony-based approach to decomposing the eigenanalysis of the electromechanical modes, separating the computation of inter-area and intra-area modes in the style of multi-area Selective Modal Analysis. Key Words - Synchrony, Coherency, Slow-Coherency, Aggregation, Dynamic Equivalencing, Eigenanalysis, Selective Modal Analysis.

Energy methods have shown promise as measures for quantifying the vulnerability of power systems to problems of voltage instability and collapse. However, to make such measures more useful as a security assessment tool in an operational environment, it is important to provide physical interpretations of the quantitative measure. This paper will demonstrate that for certain basic load models, the energy based security measure is equal to the area enclosed by a familiar Q-V curve, with a change of scale on the voltage axis. This interpretation has the added benefit of providing easily computed approximations to the maximum real and reactive power loadability both at individual buses and for the system as a whole. Results are demonstrated in detail on the IEEE 118 bus system, with additional tests on a 415 bus sample system.

This paper examines dynamic behavior in system models that reflect reasonably detailed (third order) HVDC dynamics along with ac system models that include reactive flows, and frequency and voltage dependent load models. A vector Lyapunov function approach is employed to define a system wide energy function that can be used for general security analysis. The paper describes the derivation of individual component Lyapunov functions for simplified models of HVDC links connected to 'infinitely strong' ac systems, along with a standard ac only system Lyapunov function. A novel method of obtaining weighting coefficients to sum these components for the overall system energy function is proposed. Use of the new energy function for transient stability and security analysis is illustrated in a test system. Keywords: HVDC, Lyapunov functions, transient energy functions, transient stability, dynamic security assessment.

An analytical method to study voltage instability and collapse in AC/DC power systems using bifurcation theory is presented. It measures the distance in state space to the point of collapse and obtains a more accurate value of the minimum load. Models for the transient behavior of the system are developed and mathematically simulated to determine the load values for a given bifurcation point. The proposed method is used in a simplified AC/DC system.

The use of market mechanisms to determine generation dispatch, and the natural tendency to seek improved economic efficiency through rapid market updates, raises a critical issue. As the frequency of market-based dispatch updates increases, there will inevitably be interaction between the dynamics of markets determining the generator dispatch commands, and the physical response of generators and network interconnections. This paper examines questions of stability in such coupled systems by means of numeric tests using various market update models, (including detailed generator/turbine/governor dynamics) for the New England 39 bus test system. The results highlight the nature of potential instabilities and show the interaction modes between physical and market quantities through eigen-analysis. Understanding of potential modes of instability in such coupled systems is crucial both for designing suitable rules for power markets, and for designing physical generator controls that are compatible with market-based dispatch. Index Terms--Dynamic coupling, eigenvalues, market dynamics, power system dynamics.