D. Lefebvre

Design of load shedding schemes against voltage instability using combinatorial optimization

This paper proposes a methodology for the design of automatic load shedding against voltage instability. In a first step, the authors describe a method allowing to find the minimal shedding required in a given unstable scenario. In a second step, they describe the structure of various controllers and identify the parameters to be optimized. Next, they present an optimization approach to find the controller parameters which optimize an overall performance objective. Results are presented on the Hydro-Quebec system, in which load shedding is presently planned.

Design of load shedding schemes against voltage instability

This paper proposes a methodology for the design of automatic load shedding against long-term voltage instability. In a first step, a set of training scenarios is set up, corresponding to various operating conditions and disturbances. Each scenario is analyzed to determine the minimal load shedding which stabilizes the system, with due consideration for the shedding location and delay. In a second step, the parameters of a closed-loop undervoltage load shedding scheme are determined so as to: (i) approach as closely as possible the optimal sheddings computed in the first step, over the whole set of scenarios; (ii) stabilize the system in all the unstable scenarios; and (iii) shed no load in the stable ones. The corresponding optimization problem is solved using a (micro-)genetic algorithm. A detailed example is given on the Hydro-Quebec system in which load shedding is presently planned.

Quasi steady-state models for long-term voltage and frequency dynamics simulation

The quasi steady-state (QSS) approximation of long-term dynamics relies on time-scale decomposition and consists of replacing faster phenomena by their equilibrium conditions, in order to reduce the complexity of the whole model and increase the computation efficiency of time simulations. This paper describes the extension of a QSS model extensively used in long-term voltage stability studies, to readily incorporate the frequency dynamics that takes place over the same time scale. This extended QSS model relies on a common-frequency assumption. Its advantages, limitations and possible improvements are discussed through simulation results on the hydro-Quebec system, where it has been compared to full time scale simulations. Disturbances with an impact on either frequency or voltages are considered and the coupling between these two aspects of long-term dynamics is briefly discussed.

Undervoltage load shedding scheme for the Hydro-Quebec system

In recent years, Hydro-Quebec has undertaken a major program to upgrade the reliability of its transmission system. Much effort has been focused on increasing the systems ability to withstand extreme contingencies, usually caused by multiple incidents or the successive tripping of transmission lines. This work deals with the conception and the control logic of an undervoltage load shedding scheme aimed at protecting the Hydro-Quebec system against long-term voltage instability. Various results showing the impact of the operation of these automatisms on the system stability are provided in this paper.

Load shedding controllers against voltage instability: a comparison of designs

This paper discusses and compares three types of undervoltage load shedding closed-loop controllers in terms of performances and design computational effort. The authors first describe the various controllers and identify the parameters to be optimized. Next, they present an optimization methodology applicable to all three types of controllers. This approach allows to find the controller parameters which optimize an overall performance objective. Results are presented on the Hydro-Quebec system, in which load shedding is presently planned.

A time-scale decomposition-based simulation tool for voltage stability analysis

This paper proposes a time domain simulation tool combining full time scale (FTS) simulation in the short-term period following a contingency and quasi steady-state (QSS) approximation for the long-term phase. A criterion is devised to automatically switch from FTS to QSS simulation as soon as sufficient damping of short-term dynamics is reached. Various comparisons with FTS simulations have been performed on the Hydro-Quebec system. The proposed method is shown to combine accuracy of FTS with computational efficiency of QSS. Sensitivity of simulations to load model and the need for updating the whole model with frequency variations are also discussed.

Modelling the short-term and long-term aggregate response of multiple loads fed through a sub-transmission network

This paper addresses the problem of representing the aggregate response to voltage changes of a set of loads fed through distribution transformers connected by a sub-transmission network. A simple, while accurate equivalent is proposed. The latter involves standard network components and includes a single internal bus. This equivalent matches both the short-term and the long-term response of the original system, the long-term dynamics coming from the load tap changers that control the distribution voltages. A procedure to identify its parameters from step responses of unreduced system is detailed. The method is illustrated and validated on a large sub-transmission-distribution system of Hydro-Quebec