Antony Schellenberg

Cumulant-based probabilistic optimal power flow (P-OPF) with Gaussian and gamma distributions

This paper introduces the cumulant method for the probabilistic optimal power flow (P-OPF) problem. By noting that the inverse of the Hessian used in the logarithmic barrier interior point can be used as a linear mapping, cumulants can be computed for unknown system variables. Results using the proposed cumulant method are compared against results from Monte Carlo simulations (MCSs) based on a small test system. The Numerical Results section is broken into two sections: The first uses Gaussian distributions to model system loading levels, and cumulant method results are compared against four MCSs. Three of the MCSs use 1500 samples, while the fourth uses 20 000 samples. The second section models the loads with a Gamma distribution. Results from the proposed technique are compared against a 1000-point MCS. The cumulant method agrees very closely with the MCS results when the mean value for variables is considered. In addition, the proposed method has significantly reduced computational expense while maintaining accuracy.

A survey of load control programs for price and system stability

Load control and demand side load management programs have been implemented in a large number of competitive power markets. These programs can provide enhanced system security and many benefits to participants. This paper reviews and compares existing economically driven programs.

Optimal power flow with complementarity constraints

This paper proposes a mathematical program with complementarity constraints to better model the relationship between the base, or current, operating point and the maximum loading point in a power system when solving maximum loading problems.

Classification of Future Electricity Market Prices

Forecasting short-term electricity market prices has been the focus of several studies in recent years. Although various approaches have been examined, achieving sufficiently low forecasting errors has not been always possible. However, certain applications, such as demand-side management, do not require exact values for future prices but utilize specific price thresholds as the basis for making short-term scheduling decisions. In this paper, classification of future electricity market prices with respect to pre-specified price thresholds is introduced. Two alternative models based on support vector machines are proposed in a multi-class, multi-step-ahead price classification context. Numerical results are provided for classifying prices in Ontarios and Albertas markets.

Enhancements to the Cumulant Method for Probabilistic Optimal Power Flow Studies

This paper introduces two extenstions to the cumulant method (CM) for probabilistic optimal power flow (P-OPF) studies; the first is an enhancement to provide improved handling of limits within the P-OPF problems and the second is a way to include correlated variables. The first enhancement is termed the Limit corrected cumulant method (LCCM) which specifically addresses errors in the existing CM when limits, away from the mean solution, are encountered while solving a P-OPF problem. The LCCM approach relies on the CM to produce multiple probability density functions (PDFs) and then combines these PDFs together to generate final PDFs. The second enhancement for incorporating correlated variables into P-OPF problems is based on the composition of correlated variables from several independent ones. The proposed approaches are verified against Monte Carlo simulations (MCS) consisting of 10 000 samples and demonstrate significant improvements when compared with traditional CM results.

Introduction to cumulant-based probabilistic optimal power flow (P-OPF)

This letter introduces the cumulant method for the probabilistic optimal power flow (P-OPF) problem. The proposed adaptation of the cumulant method to the P-OPF problem is given.

Cumulant-based stochastic nonlinear programming for variance constrained voltage stability analysis of power systems

This paper proposes a Cumulant Method-based solution to solve a maximum loading problem incorporating a constraint on the maximum variance of the loading parameter. The proposed method takes advantage of some properties regarding saddle node bifurcations to create a linear mapping relationship between random bus loading variables and all other system variables. The proposed methodology is tested using a sample system based on the IEEE 30-bus system using random active and reactive bus loading. Monte Carlo simulations consisting of 10 000 samples are used as a reference solution for evaluation of the accuracy of the proposed method.

The Value of Intra-Day Markets in Power Systems With High Wind Power Penetration

In this paper, the value of intra-day markets in managing wind power uncertainty in competitive electricity markets is analyzed. A competitive electricity market model consisting of a day-ahead market and a number of intra-day markets is considered. Real-time operation adjustment is also taken into account. Stochastic programming is used to model decision making under wind power uncertainty. Numerical simulations based on two test systems are presented.

Residential Energy Management Using a Two-Horizon Algorithm

The increasing demand for electricity and the emergence of smart grids have presented new opportunities for residential energy management systems (REMS) in demand response market. Several techniques are available for optimizing the operation schedules and decisions of REMS. However, it can be challenging for REMS to capture sufficient resolution and horizon to make good short-term and long-term decisions, respectively, under limited computing resources. We propose a two-horizon algorithm, which can achieve high resolution schedules with reasonable value of energy services while limiting computation time. Simulation results are provided to confirm the validity of the proposed approach.

Cooling Devices in Demand Response: A Comparison of Control Methods

Demand response plays an important role in the development of the smart grid, which can effectively manage societys energy consumption. Cooling devices, such as refrigerators and freezers, are ideal devices for demand-response programs because their energy states can be controlled without reducing the lifestyle and comfort of the residents. Conversely, managing air conditioning and space heating would affect a residents comfort level. Direct compressor control and thermostat control methods have been proposed in the past for controlling cooling devices but they are never studied concurrently. This paper proposes a new control mechanism and compares the effectiveness of the three control mechanisms for cooling devices in demand response. In addition, this paper illustrates the need for a damping strategy to mitigate demand oscillations that occur from synchronous fleet control.