Rajesh Rajaraman

The effect of demand elasticity on security prices for the PoolCo and multi-lateral contract models

Optimum power flows and security constrained power flows assume that customer demand is a fixed quantity. In the new competitive environment, it is necessary to assume that demand is elastic and will vary as a function of price. A critical element in any competitive model, whether it be a PoolCo or a multi-lateral contract model, is for a system operator to ensure reliability and feasibility of the power system operating point. Security pricing for feasibility was first advanced by Schweppe et al for the case of line flow constraints for a PoolCo model. Using geometry, this paper generalizes the approach to include any security constraint for a general competitive model. The paper discusses interpretations of security pricing and its possible implementation in energy management systems.

Understanding price volatility in electricity markets

The paper illustrates notions of volatility associated with power systems spot prices for electricity. The paper demonstrates a frequency-domain method useful to separate out periodic price variations from random variations. It then uses actual observed price data to estimate parameters such as volatility and the coefficient of mean reversion associated with the random variation of prices. It also examines spatial volatility of prices.

Nonlinear dynamics and switching time bifurcations of a thyristor controlled reactor circuit

We study a thyristor controlled reactor circuit used for static VAR control of utility electric power systems. The circuit exhibits switching times which jump or bifurcate as fold or transcritical bifurcations. We study the nonlinear dynamics of the circuit using a Poincare map and demonstrate that the Poincare map has discontinuities and is not invertible. The circuit has multiple attractors, moreover, the basin boundary separating the basins of attraction intersects with the Poincare map discontinuities. These novel properties illustrate some of the basic features of dynamical systems theory for thyristor switching circuits.

Damping estimates of subsynchronous and power swing oscillations in power systems with thyristor switching devices

The authors extend the torque per unit velocity method for estimating the modal damping of subsynchronous oscillations to general power systems with thyristor switching devices. This allows damping of SSR by thyristor controlled series capacitors to be obtained from time domain simulations of only the electrical part of the system. Their method generalizes to the case of multiple torsional modes with the same natural frequency. A new method is used to estimate the damping and frequency of the swing mode. Torque per unit velocity methods are easier than exact eigenvalue analysis and testing on the IEEE first benchmark SSR model shows excellent agreement with exact eigenvalue analysis.

Inefficiencies of NERC`s transmission loading relief procedures

Abstract NERC’s recent proposal for transmission loading relief procedures effectively addresses engineering concerns pertaining to network security, but it also provides opportunities for gaming that may lead to higher price volatility. A process for obtaining location-based transmission prices can reduce these gaming opportunities.

Nonlinear dynamics and switching time bifurcations of a thyristor controlled reactor

The authors study a thyristor controlled reactor circuit used for static volt ampere reactive (VAR) control of electric power systems. The circuit exhibits switching times which jump or bifurcate. The nonlinear dynamics of the circuit are studied using a Poincare/spl acute/ map and it is demonstrated that the Poincare/spl acute/ map has discontinuities and is not invertible. These novel properties illustrate some of the basic features of dynamical systems theory for switching circuits.<<ETX>>

Open transmission access: an efficient minimal role for the ISO

This paper presents a vision of an efficient minimal role for an independent system operator (ISO) in a competitive market for electric power. The ISO framework could be achieved during the final stages of the transition to the deregulated environment. The chief responsibility of the ISO will be to maintain system reliability at all times. To achieve this end, ISO only requires information about the expected status of the system and scheduled transactions. There is no need for the ISO to engage in transactions in the bulk power market except for comparatively small amounts of power required to maintain reliability. The ISO will coordinate the actions of various market participants using technically sound rules, classified according to time frames. These rules include procedures by which the ISO can estimate congestion costs and allow markets to efficiently ration scarce flow capability. The paper also touches upon the ISOs key role in the ancillary services market. Finally, the paper discusses the regulated transmission company, and concludes that ISO-determined congestion costs should be collected by the transmission company.

Justification of torque per unit velocity methods of analyzing subsynchronous resonance and a swing mode in power systems

Torque per unit velocity is a practical method to study the subsynchronous resonance instability of electric power systems. The torque per unit velocity method is justified as an eigenvalue perturbation technique and extended to power systems with thyristor switching devices and multiple torsional modes. A new method to estimate the damping of the swing mode is proposed.

Damping and incremental energy in thyristor switching circuits

Thyristor controlled reactors provide controllable inductances in utility power lines and are increasingly used for static var control and flexible AC transmission. The size of a perturbation from a nominal periodic steady state can be measured by its incremental energy. This paper shows that incremental energy of a small perturbation increases when a thyristor switches on and decreases when a thyristor switches off. This observation aids in understanding how perturbations are damped by thyristor switchings and highlights some problems with representing the small signal dynamics of thyristor controlled reactors with impedances.

Profiting from Operating Reserves

Abstract Virtually all proposed pricing schemes for reserve consumption are inefficient because they fail to capture the insurance aspect of operating reserves. Power traders who offer low reserve prices to “good” reserve customers will shift costs to other power traders, will undermine inefficiently organized reserve markets, and will drive these markets toward more efficient segmentation of reserve customers.