Fernando L. Alvarado

Point of collapse and continuation methods for large AC/DC systems

The implementation of both point of collapse (PoC) methods and continuation methods for the computation of voltage collapse points (saddle-node bifurcations) in large AC/DC power systems is described. The performance of these methods is compared for real systems of up to 2158 buses. Computational details of the implementation of the PoC and continuation methods are detailed, and the unique problems encountered due to the presence of high-voltage direct-current (HVDC) transmission, area interchange power control, regulating transformers, and voltage and reactive power limits are discussed. The characteristics of a robust PoC power flow program are presented, and its application to detection and solution of voltage stability problems is demonstrated. >

Sensitivity of the loading margin to voltage collapse with respect to arbitrary parameters

Power system loading margin is a fundamental measure of a systems proximity to voltage collapse. Linear and quadratic estimates to the variation of the loading margin with respect to any power system parameter or control are derived. Tests with a 118-bus system indicate that the estimates accurately predict the quantitative effect on the loading margin of altering the system loading, reactive power support, wheeling, load model parameters, line susceptance and generator dispatch. The accuracy of the estimates over a useful range and the ease of obtaining the linear estimate suggest that this method will be of practical value in avoiding power system voltage collapse.

Interval arithmetic in power flow analysis

Power flow analysis is the fundamental tool for the study of power systems. The data for this problem are subject to uncertainty. Interval arithmetic is used to solve the power flow problem. Interval arithmetic takes into consideration the uncertainty of the nodal information, and is able to provide strict bounds for the solutions to the problem: all possible solutions are included within the bounds given by interval arithmetic. Results are compared with those obtainable by Monte Carlo simulations and by the use of stochastic power flows. Object-oriented programming techniques makes it possible to use interval arithmetic with minimal modifications to existing software. However, to reduce the conservatism inherent in all interval arithmetic computations, an iterative method is used to obtain the hull of the solution set. >

Computation of closest bifurcations in power systems

Voltage collapse and blackout can occur in an electric power system when load powers vary so that the system loses stability in a saddle node bifurcation. This paper computes load powers at which bifurcation occurs and which are locally closest to given operating load powers. The distance in load power parameter space to this locally closest bifurcation is an index of voltage collapse and a minimum load power margin. The computations are illustrated for several power systems. Monte-Carlo optimization techniques are applied to obtain multiple minimum load power margins. The use of load power margin sensitivities to select system controls is discussed. >

Parallel processing in power systems computation

The availability of parallel processing hardware and software presents an opportunity and a challenge to apply this new computation technology to solve power system problems. The allure of parallel processing is that this technology has the potential to be cost effectively used on computationally intense problems. The objective of this paper is to define the state of the art and identify what the authors see to be the most fertile grounds for future research in parallel processing as applied to power system computation. As always, such projections are risky in a fast changing field, but the authors hope that this paper will be useful to the researchers and practitioners in this growing area.

Contingency ranking for voltage collapse via sensitivities from a single nose curve

The change in the loading margin to voltage collapse when line outages occur is estimated. First a nose curve is computed by continuation to obtain a nominal loading margin. Then linear and quadratic sensitivities of the loading margin to each contingency are computed and used to estimate the resulting change in the loading margin. The method is tested on a critical area of a 1390 bus system and all the line outages of the IEEE 118 bus system. The results show the effective ranking of contingencies and the very fast computation of the linear estimates.

Point of collapse methods applied to AC/DC power systems

The authors describe an extension of the point of collapse method developed for studies of AC systems to the determination of saddle-node bifurcations in power systems including high voltage direct current (HVDC) transmission. Bus voltage profiles are illustrated for an AC/DC test system. They significantly differ from the profiles of pure AC systems for typical system models. In particular, voltage dependent current order limits are shown to affect the voltage profiles and the loadability margin of the system. It is also shown that Hopf bifurcations, which are possible in purely AC lossless systems with second-order generator models, become plausible when the dynamics for the HVDC system are included. >

SVC placement using critical modes of voltage instability

The location of SVC (static VAr compensators) and other types of shunt compensation devices for voltage support is an important practical question. This paper considers a tool based on the determination of critical modes. Critical modes are computed by studying the system modes in the vicinity of the point of collapse. System participation factors for the critical mode are used to determine the most suitable sites for system reinforcement. Because the method does not rely on base case linearizations, the method is able to properly consider all system limits and nonlinear effects. The paper tests the proposed method by performing an assessment of the impact of the addition of static VAr compensators to a 1380 bus model of the BC Hydro system. >

Using Utility Information to Calibrate Customer Demand Management Behavior Models

In times of stress customers can help a utility by means of voluntary demand management programs if they are offered the right incentives. The incentives offered can be optimized if the utility can estimate the outage or substitution costs of its customers. This paper illustrates how existing utility data can be used to predict customer demand management behavior. More specifically, it shows how estimated customer cost functions can be calibrated to help in designing efficient demand management contracts.

Sensitivity of Transfer Capability Margins with a Fast Formula

Bulk power transfers in electric power systems are limited by transmission network security. Transfer capability measures the maximum power transfer permissible under certain assumptions. Once a transfer capability has been computed for one set of assumptions, it is useful to quickly estimate the effect on the transfer capability of modifying those assumptions. This paper presents a computationally efficient formula for the first order sensitivity of the transfer capability with respect to the variation of any parameters. The sensitivity formula is very fast to evaluate. The approach is consistent with the current industrial practice of using dc load flow models and significantly generalizes that practice to more detailed ac power system models that include voltage and VAR limits. The computation is illustrated and tested on a 3357 bus power system.