Alva J. Svoboda

Short-term resource scheduling with ramp constraints [power generation scheduling]

This paper describes a Lagrangian relaxation-based method to solve the short-term resource scheduling (STRS) problem with ramp constraints. Instead of discretizing the generation levels, the ramp rate constraints are relaxed with the system demand constraints using Lagrange multipliers. Three kinds of ramp constraints, startup, operating and shutdown ramp constraints are considered. The proposed method has been applied to solve the hydro-thermal generation scheduling problem at PG&E. An example alone with numerical results is also presented.

Short-term resource scheduling in multi-area hydrothermal power systems

Abstract This paper describes the short-term resource scheduling problem in multi-area large-scale hydrothermal power systems. The description of the problem is comprehensive, providing information on important operating considerations and constraints which need to be modelled in practice. A rigorous and concise formulation of the problem is presented. The solution algorithm, which is based on Lagrangian relaxation, is described and its salient features are discussed. Numerical results and our experience with the solution algorithm are also presented.

Equity and efficiency of unit commitment in competitive electricity markets

Abstract We examine the effects of competition and decentralized ownership on resource scheduling. It is shown that centralized scheduling of multi-owned resources under imperfect information may face difficulties that do not arise when resources are centrally owned. A simulation case study is performed using a Lagrangian relaxation-based unit commitment algorithm modified to simulate proposed second-price pool auction procedures. We show that variations in near optimal unit commitments that have negligible effect on total costs could have significant impact on the profitability of individual resources. These results raise serious questions regarding the feasibility of proper mechanisms to oversee the efficiency and equity of a mandatory centrally dispatched pool.

Scheduling hydro power systems with restricted operating zones and discharge ramping constraints

An optimization-based algorithm is presented for scheduling hydro power systems with restricted operating zones and discharge ramping constraints. Hydro watershed scheduling problems are difficult to solve because many constraints, continuous and discrete, including hydraulic coupling of cascaded reservoirs have to be considered. Restricted or forbidden operating zones as well as minimum generation limits of hydro units result in discontinuous preferred operating regions, and hinder direct applications of efficient continuous optimization methods such as network flow algorithms. Discharge ramping constraints due to navigational, environmental and recreational requirements in a hydro system add another dimension of difficulty since they couple generation or water discharge across time horizon. Integrated consideration of the above constraints is very challenging. The key idea of this paper is to use additional sets of multipliers to relax discontinuous operating region and discharge ramping constraints on individual hydro units so that a two-level optimization structure is formed. The low level consists of a continuous discharge scheduling subproblem determining the generation levels of all units in the entire watershed, and a number of pure integer scheduling subproblems determining the hydro operating states, one for each unit. The discharge subproblem is solved by a network flow algorithm, and the integer scheduling problems are solved by dynamic programming with a small number of states and well-structured transitions.

A transmission-constrained unit commitment method in power system scheduling

This paper presents a transmission-constrained unit commitment method using a Lagrangian relaxation approach. Based on a DC power flow model, the transmission constraints are formulated as linear constraints. The transmission constraints, as well as the demand and spinning reserve constraints, are relaxed by attaching Lagrange multipliers. A three-phase algorithmic scheme is devised including dual optimization, a feasibility phase and unit decommitment. A large-scale test problem with more than 2200 buses and 2500 transmission lines is tested along with other test problems. q 1999 Elsevier Science B.V. All rights reserved.

Price-based adaptive spinning reserve requirements in power system scheduling

In a deregulated electricity market such as the California WEPEX, spinning reserves must be explicitly identified as an ancillary service and priced. Additionally, scheduling coordinators who match suppliers and demands may either self-provide spinning reserves, or rely on the Independent System Operator (ISO) to provide reserves at the spot price. The deregulated market structure makes explicit the implicit softness that has always been recognized in the reserve constraints: additional reserves may have value even when a minimum reserve requirement has been met. In this paper we formulate the spinning reserve requirement (SRR) as a function of the endogenously determined marginal values of reserves. The spinning reserve requirement depends, according to a non-increasing response function, on a price/value signal. We present three power system scheduling algorithms in which this price/value signal is updated at each iteration of a dual optimization. Game theory is used to interpret the proposed algorithms. Numerical test results are also presented.

Energy delivery capacity and generation scheduling in the deregulated electric power market

The generation schedules obtained in traditional hydrothermal scheduling or unit commitment programs are in hourly generation levels. In the new deregulated power market, the power transactions are processed in terms of hourly energy delivery. Failing to fulfil scheduled energy delivery may result in a penalty to the power producers. This paper shows that although ramp-rate constraints are satisfied in hydrothermal scheduling, taking a generation level schedule as an energy delivery schedule may not be realizable. Based on the maximum principle in optimal control theory, the energy delivery capacity across the scheduling horizon is established as a set of recursive equations with given ramp-rate constraints. A sufficient and necessary condition is obtained to check if an energy delivery schedule is realizable. Based on this condition, two cases, where ramp-rate constraints are both satisfied, are analyzed and an unrealizable energy delivery schedule is observed.

Self-Commitment of Combined Cycle Units Under Electricity Price Uncertainty

Summary form only given. Day-ahead energy market clearing relies on a deterministic equivalent model with a limited time horizon, which may lead to inefficient scheduling of generating units from the point of view of generators. For this reason, generators may wish to assume the risk of self-committing their units with the hope of securing greater profits. This phenomenon may reduce the room for economic signals in the day-ahead market. In this paper we investigate the influence of risk aversion and price volatility on the decision of generators to self-commit units. We present a stochastic programming model for self-committing combined cycle units under price uncertainty with a conditional value at risk criterion. We use Benders decomposition to solve the problem and present results on a case study to draw conclusions.

A unit decommitment method in power system scheduling

This paper presents a unit decommitment method for power system scheduling. Given a feasible unit commitment, our algorithm determines an optimal strategy for decommitting overcommitted units based on dynamic programming. This method is being developed as a possible post-processing tool to improve the solution quality of the existing unit commitment algorithm used at PG&E. It can also be integrated into any other unit commitment method or used as a complete unit commitment algorithm in itself. The decommitment method can also be used as a tool to measure the solution quality of unit commitment algorithms. The proposed method maintains solution feasibility at all iterations. In this paper we prove that the number of iterations required by the method to terminate is bounded by the number of units. Numerical tests indicate that this decommitment method is computationally efficient and can improve scheduling significantly.

Volatility of unit commitment in competitive electricity markets

We examine the effects of competition and decentralized ownership on resource scheduling. We show that centralized scheduling of multi-owned resources under imperfect information may face difficulties that do not arise when resources are centrally owned. We perform a simulation case study using a Lagrangian relaxation-based unit commitment algorithm modified to simulate proposed second-price pool auction procedures. This algorithm is based on the Hydro-Thermal Optimization (HTO) program used in short-term resource scheduling at PG&E. We demonstrate both the volatility of simulation outcomes for resources not base loaded, and the especially negative consequences of volatility for marginal resources (i.e., resources that frequently determine system marginal costs). Specifically, we show that variations in near optimal unit commitments that have negligible effect on total costs could have significant impact on the profitability of individual resources. These results raise serious questions regarding the feasibility of proper mechanisms to oversee the efficiency and equity of a mandatory centrally dispatched pool.