Pablo A. Ruiz

Uncertainty Management in the Unit Commitment Problem

Uncertainty in power systems operations has been traditionally managed by multistage decision making and operating reserve requirements. A familiar example of multistage decisions is day-ahead unit commitment and real-time economic dispatch. An alternate approach for managing uncertainty is a stochastic formulation, which allows the explicit modeling of the sources of uncertainty. This paper compares stochastic and reserve methods and evaluates the benefits of a combined approach for the efficient management of uncertainty in the unit commitment problem. Numerical studies show that unit commitment solutions obtained for the combined approach are robust and superior with respect to the traditional approach in terms of both economics and reliability metrics.

Wind power day-ahead uncertainty management through stochastic unit commitment policies

Day-ahead uncertainty management in power systems has traditionally been approached by means of multistage decision making and operating reserve requirements. An alternate approach for managing uncertainty is a stochastic formulation, which allows the explicit modeling of the sources of uncertainty. The large investments in wind power has increased the importance of operations uncertainty management due to the considerable operational uncertainty wind plants have. This paper evaluates the benefits of a combined approach that uses stochastic and reserve methods for the efficient management of uncertainty in the unit commitment problem for systems with significant amount of wind power. Numerical studies on a model of the PSCo system show that the unit commitment solutions obtained for the combined approach are robust and superior with respect to the traditional approach in terms of economic metrics and curtailed wind power.

Tractable Transmission Topology Control Using Sensitivity Analysis

The standard economic generation dispatch (ED) minimizes generation costs subject to transmission constraints, where the status of each line, i.e., open or closed, is fixed. Recent research shows that, by optimally dispatching the network topology along with generation resources, significant congestion costs may be avoided. Optimal topology control, i.e., appropriate changes of transmission-line status, for real-sized power networks requires the solution of a computationally intractable mixed-integer linear program; however, it appears that much of the cost savings may be attained by changing the status of just a few lines. This paper proposes tractable transmission topology control policies, which employ sensitivity information readily available from the ED to select candidate lines to change status while maintaining system connectivity. Implementation on the IEEE 118-bus test system found that our best performing policy captured an average of 96% of the potential cost savings. Moreover, the limited computational effort required suggests that these policies could be employed in real-system operations.

Voltage and Reactive Power Estimation for Contingency Analysis Using Sensitivities

Operational reliability is normally checked using contingency analysis, thus requiring the solution of the power flow problem under a wide variety of system conditions. As power flows are computationally expensive and approximate solutions are usually acceptable, fast estimation methods are used. Real power distribution factor methods provide a good trade-off between accuracy and speed. Reactive power and voltage sensitivities-based methods have not been as successful, partially because equipment limits are ignored. This paper discusses the estimation of post-contingency voltages and reactive power generation and flows using sensitivities. Employing piecewise linear estimates, the effect of equipment limits on the estimates is effectively captured. Representative results are presented using the IEEE 14 and 57-bus test systems. The results show that VAr limits have a significant influence in post-contingency voltages and reactive outputs and flows

Reduced MIP formulation for transmission topology control

The standard optimal power flow minimizes generation costs subject to a fixed transmission network topology. Although the co-optimization of network topology and generation resources results in significant congestion cost avoidance, it requires the solution of a mixed integer program (MIP), which is in general intractable for even moderate size systems. The current MIP formulations use the Bθ power flow model, which does not scale with the number of switchable lines or with the number of monitored/contingent facilities, and as such is not amenable to developing tractable topology control (TC) heuristics. This paper introduces the shift factor MIP formulation of the TC problem, where line openings are emulated through the use of flow-cancelling transactions. The shift factor formulation is very compact and its size is a function of the number of pairs of monitored/contingent transmission elements and the number of switchable lines. Simulation results on the IEEE 118-bus test system show the superior computational performance of the shift factor formulation as compared to the Bθ formulation for small to medium switchable sets.

Modeling Approaches for Computational Cost Reduction in Stochastic Unit Commitment Formulations

Although stochastic commitment policies provide robust and efficient solutions, they have high computational costs. This letter considers two modeling approaches for the reduction of their computational effort: the relaxation of the integrality constraint of fast-start units, and the modeling of generation outages as load increments. These approaches are shown to reduce the computational cost while maintaining the good properties of stochastic policies.

On fast transmission topology control heuristics

The standard optimal power flow (OPF) problem minimizes generation costs over one study period assuming a fixed system topology. The prospect of a smart grid incorporating extensive cyber capabilities enabling significant progress in economic efficiency, reliability and environmental sustainability, ought to transform the OPF problem accordingly. This paper discusses the inclusion of tractable dynamic transmission topology control in the OPF problem based on heuristic control policies derived from individual transmission “line profit” criteria. Simulations on the IEEE 118-bus test system demonstrate the effectiveness of the heuristic policies in reducing production costs. As the algorithms requisite information to identify promising candidate elements for switching is standard output of the OPF solution, the computational effort is up to four orders of magnitude better than dynamic transmission topology control performance reported in the literature.

An Effective Transmission Network Expansion Cost Allocation Based on Game Theory

The expansion of transmission systems impacts many entities in the market environment. Each entity may fare better or worse as a result of congestion relief in the presence of new investments. Negatively affected firms exert their influence to prevent the expansion from taking place. The opposition of these firms and the lack of appropriate incentives results in insufficient investments in transmission assets. The network is being frequently used at its maximum limits, leading to economic inefficiencies and reduced reliability. Hence, there is a need for effective incentive schemes for network expansion. In this paper, we propose a game theory-based scheme for the allocation of transmission expansion costs among market entities. The allocation takes into account both the physical and economic impacts of the new transmission assets and the influence of each firm on the expansion decision. This is the first scheme designed to give all market participants explicit incentives to support the expansion. The application of the allocation solution to the Garver six-bus system is presented to illustrate the capabilities of the proposed method

Valuation of Reserve Services

Spinning reserve is idle capacity connected to the system with the purpose of balancing power demand and supply in real-time and ensuring reliable system operations in the case of equipment outages. The reserve has an economic value since it reduces the load shedding costs. This value is impacted by the reliability and dynamic characteristics of system components, the variability of the load from its forecast, the system operation policies, and economic aspects such as the risk preferences of the demand. In this paper, we take into account all these aspects to estimate the reserve value. The results require little computational effort, and are useful in the development of reserve demand functions and optimal reserve requirements.

Spinning Contingency Reserve: Economic Value and Demand Functions

Spinning contingency reserve is idle capacity connected to the system to ensure reliable operations in the case of equipment outages. The reserve has an economic value since it reduces the outage costs. In several electricity markets, reserve demand functions have been implemented to take into account the value of reserve in the market clearing process. These often take the form of a step-down function at the reserve requirement level, and as such they may not appropriately represent the reserve value. The value of spinning contingency reserve is impacted by the reliability and dynamic characteristics of system components, the system operation policies, and the economic aspects such as the risk preferences of the demand. In this paper, we take into account these aspects to approximate the reserve value and construct reserve demand functions. The results are obtained in closed form. Illustrative examples show that the demand functions constructed have similarities with those implemented in some markets.