The authors present a method of finding a continuum of power flow solutions starting at some base load and leading to the steady-state voltage stability limit (critical point) of the system. A salient feature of the so-called continuation power flow is that it remains well-conditioned at and around the critical point. As a consequence, divergence due to ill-conditioning is not encountered at the critical point, even when single-precision computation is used. Intermediate results of the process are used to develop a voltage stability index and identify areas of the system most prone to voltage collapse. Examples are given where the voltage stability of a system is analyzed using several different scenarios of load increase. >

The continuation power flow: a tool for steady state voltage stability analysis

Optimal power flow using particle swarm optimization

The authors discuss the voltage stability analysis of large power systems by using a modal analysis technique. The method computes, using a steady-state system model, a specified number of the smallest eigenvalues and the associated eigenvectors of a reduced Jacobian matrix. The eigenvalues, each of which is associated with a mode of voltage/reactive power variation, provide a relative measure of proximity to voltage instability. The eigenvectors are used to describe the mode shape and to provide information about the network elements and generators which participate in each mode. A simultaneous iteration method, which is well suited to applications involving large power systems, is used for selective calculation of appropriate eigenvalues. Results obtained using a 3700 bus test system are presented illustrating the applicability of the approach. >

Voltage Stability Evaluation Using Modal Analysis

Estimating the proximity of power systems to voltage collapse in real-time still faces difficulties. Beside the data management and computational issues, any central-control method is subject to the reliability of long-distance data communications. In the paper, the authors describe a new data-processing method to estimate the proximity to voltage collapse. The method (code-named SMARTDevice, for Stability Monitoring And Reference Tuning Device) employs only local measurements-bus voltage and load current-and calculates the strength of the transmission system relative to the bus. The collapse occurs when the local load approaches this value. The method is simple enough so that it can be implemented in a numerical relay. The performance of SMARTDevice is compared against the conventional undervoltage relays. It is shown that the latter can misoperate while the new device does not. SMARTDevice is in fact a new breed of voltage relay whose setpoint is automatically tuned to the power system condition.

Use of local measurements to estimate voltage-stability margin

Optimal power flow using gravitational search algorithm

A method for the online testing a power system is proposed which is aimed at the detection of voltage instabilities. Thereby an indicator L is defined which varies in the range between 0 (noload of system) and 1 (voltage collapse). Based on the basic concept of such an indicator various models are derived which allow to predict a voltage instability or the proximity of a collapse. The indicator uses information of a normal load flow. The advantage of the method lies in the simplicity of the numerical calculation and the expressiveness of the result.

Estimating the Voltage Stability of a Power System

Estimating the voltage stability of a power system

For the purposes of on-line security calculations a method for deriving steady-state network equivalents is presented which is based on a radial tree-shaped structure. This is not able to give a perfect replica of the original network, but the accuracy of the representation of different network regions is controllable. The impedances and the structure of the radial equivalent are found by a search procedure directed at minimizing an error function on the transfer impedances to be matched by the equivalent. Injections are treated in terms of the REI-network. Results for practical power systems are given, which show the feasibility of this reduction method with security calculations.

H. Glavitsch

Papers

Estimating the Voltage Stability of a Power System

Estimating the voltage stability of a power system

Graneq - A Radial, Internal Network Equivalent for Power System Security Calculations