Robert A. Schlueter

A voltage stability security assessment method

A voltage stability security assessment method is developed that can identify (i) each region that experiences voltage collapse and (ii) the equipment outages that cause voltage collapse in each of these regions. The method establishes whether the voltage collapse caused by a contingency is due to clogging voltage instability or loss of control voltage instability. The advantages of the method is that it requires little computation and is comprehensive in attempting to find all regions with voltage collapse problems and all single and double equipment outages that cause voltage collapse in each region.

On the behaviour of optimal linear sampled-data regulators†

Abstract Optimal sampled-data controls for linear processes with quadratic criteria are determined through application of the discrete minimum principle. The effect of sampling on the closed-loop systems performance is investigated and the asymptotic behaviour of the optimal cost for large sampling periods is determined. The resulting design method is applicable to continuous, sampled-data and discrete regulators.

Methods for determining proximity to voltage collapse

Theoretical results have shown that PQ controllability is sufficient to insure that every known test for prevention of voltage collapse is satisfied. This result unifies the theoretical basis for voltage collapse, since these tests were developed based on radically different power system models, tested very different matrices and conditions, and were based on different theoretical approaches. This theoretical foundation is used to develop methods of determining the proximity to voltage collapse. An algorithm for computing voltage control areas, which are groups of interconnected buses, is developed. It is shown that proper system and operation planning must be undertaken in each voltage control area if voltage collapse is to be prevented. A measure of the proximity to voltage collapse is shown to be the reactive reserves in a voltage control area boundary. >

Bifurcation subsystem and its application in power system analysis

The paper extends the concept of a bifurcation subsystem that experiences, produces, and causes the bifurcation in the full system model, and systematically describes a bifurcation subsystem method. The motivation for finding a bifurcation subsystem and its advantages over model reduction, slaving, and finding the center manifold dynamics are discussed. By using the theoretical results of the persistence on saddle-node and Hopf bifurcation of a full system model with both fast and slow singularly perturbed dynamics, a more precise definition of what constitutes a bifurcation subsystem for both saddle-node and Hopf bifurcation is given. Persistence of the center manifold for the reduced models of singularly perturbed fast and slow external dynamics thus is shown. These results are then used to show that the center manifold of the saddle-node and Hopf bifurcation lies in the bifurcation subsystem or is contained within the bifurcation subsystem if additional conditions are satisfied. The test conditions for the existence of a bifurcation subsystem are: 1) quickly reviewed and 2) then applied to compute a saddle-node and a Hopf bifurcation subsystem for a multiple machine differential algebraic example system. The results computationally validate the bifurcation subsystem method.

Computational Algorithms for Constructing Modal-Coherent Dynamic Equivalents

Recent research has shown that the most desirable features of conventional modal and coherent dynamic equivalents can be combined ina single equivalent when an rms coherency measure and a robust, random system disturbance are used to determine structurally coherent groups for coherency-based aggregation. In particular, a modal-coherent equivalent can be derived which preserves not only the coherent groups of the original system model, but also the modes of group to group oscillations. A modal-coherent equivalent represents a valuable tool for transient stability analysis since it is constructed only once for a given utility and can then be used in the transient stability study of any disturbance that might occur in that utility. Previous works have presented theoretical developments which explain the structural coherency mechanism on which the modal-coherent approach to dynamic equivalents is based, and have neglected the computational aspects of constructing modal-coherent equivalents. This paper extends the value of the modal-coherent approach by developing efficient computational algorithms for evaluating the rms coherency measure for the required random disturbance and for determining the structurally coherent groups using the computed values of the measure. These algorithms will allow modal-coherent equivalents to be constructed for large power systems at a reasonable cost.

Modification of Power System Operation for Significant Wind Generation Penetration

The purpose of this paper is to discuss modification of unit commitment, economic dispatch, regulation and frequency regulation controls when the level of wind generation capacity is significant. A wind farm penetration constraint is determined, that limits worst case wind generation change from an array due to a thunderstorm to be less than the worst first contingency loss of conventional generation resource or commitment. The farm penetration constraint only acts as an indicator that additional spinning reserve, load following, and unloadable generation capability is required through adjustment of unit commitment and AGC controls if the farm penetration constraint was violated. A discussion of the methodology, costs, and benefits of changing unit commitment when WECS generation is significant (and either satisfies or violates this farm penetration constraint) is then discussed. A further discussion of the modification of regulation and economic dispatch controls to exploit the changes in response rate capability provided by the unit commitment is also discussed. A modified echelon penetration constraint that limits instantaneous rate of change and change from a wind array that must be handled by governor frequency regulation and regulation controls. This constraint is imposed to limit cycling of units which can incur additional operating and maintainance costs on conventional steam units and possibly safety concerns on nuclear units.

Modal-Coherent Equivalents Derived from an RMS Coherency Measure

An algebraic formula is derived which relates the rms coherency measure, evaluated over an infinite interval for step disturbances in mechanical input power, to the parameters of the power system state model and the disturbance vector. This expression eliminates the need for simulation to determine the coherency measure as is required when a max-min coherency measure is used to identify coherent groups. It is shown that specific probabilistic disturbances cause the rms measure to be a function of system structure alone, allowing coherent equivalents to be constructed which do not depend on the location of any particular disturbance when these probabilistic disturbances are used to determine the coherent generators for aggregation.

/spl mu/-synthesis power system stabilizer design using a bifurcation subsystem based methodology

A /spl mu/ synthesis power system stabilizer (MPSS) design is presented for a two-area system in this paper. The uncertainty is modeled based on structural information of the system and the bifurcation parameter induced nonlinear change in the bifurcation subsystem that experiences, produces, and causes the full system bifurcation. The control objective is to damp out the interarea oscillation as well as maintaining the bus voltages for the variation of the uncertainty parameter. The determination of the robust control device location that is expected to give better control performance is discussed. The performance index definition reflects the desired control purpose. A very flexible robust control configuration that can be easily applied for different control designs is shown. The RGA matrix is studied to evaluate the robust power system stabilizer design. RGA matrix information suggests that the control structure and capability of disturbance rejection have been drastically improved by MPSS design. The time simulation verifies the improvement of control performance and robustness.

Method of identifying weak transmission network stability boundaries

Methods of determining weak transmission stability boundaries are developed based on the strong controllability and observability properties of power systems. This theory has been previously applied to a dynamical model of the generators and network. It was established previously that the network and generator states associated with a cluster of generator and load buses surrounded by weak transmission boundaries are strongly controllable and observable for a single measurement and control at generators or load buses in that bus cluster. Such a bus cluster is called the control area. Two methods of determining control areas, where strong controllability and observability hold, are developed. Both methods attempt to determine weak transmission stability boundaries that encircle control areas. The groups of generators identified as belonging to each control area is identical to the groups of coherent generators determined using a RMS coherency measure evaluated for the set of all inertial load flow contingencies. >

Identification of generic bifurcation and stability problems in power system differential-algebraic model

Based on the structurally represented power system differential-algebraic model and its Jacobian matrix. This paper develops a much more complete and systematic classification of the types of bifurcation and stability problem in the power system model. It is theoretically shown that bifurcations cannot occur due to the row dependence of the network Jacobian matrix (causality matrix) associated with the rows of the active and reactive power balance equations at a single bus or at a subset of buses, resulting in several of the classified bifurcations being nongeneric. The generic types of bifurcation and instability problems are then identified: static bifurcation dynamic bifurcation, loss of causality, and loss of single-machine stability; the later two are further shown to be very improbable. This paper also proposes an equivalent test for static bifurcation-static/algebraic bifurcation test whose advantages are disclosed. The identification of generic bifurcation and stability problems in power systems provides the foundation of the further study on static and dynamic voltage-angle stability problems. >