Optimal load curtailment as a bi-criteria program
Introduction
Deregulation has significantly changed the functioning of the power systems of today. With the evolution of different market structures in various countries, the independent system operators (ISOs) can be placed in two basic categories, depending upon their responsibilities and the functions performed. The first one is the PoolCo model, wherein ISO is responsible for market settlement and transmission system management including transmission pricing and security aspects. This form of the market exists in different forms in UK, Australian, Latin American, and some of the US markets [1]. The other structure is that of open access which is dominated by bilateral transactions and can be found to be predominant in Nordic countries. Here, ISO is only responsible for system operation and has no role in generation scheduling and dispatch.
In a PoolCo model, the members of the pool, namely the sellers and buyers, submit bids to sell/purchase power. These bids would be based on an economic criterion such that the bid reflects the maximum profitability for the individual seller/buyer. ISO (or an equivalent entity) would take into account all the submitted bids and dispatch generation to meet the demand. This initial dispatch is the one based on the market clearing process, where the decisions taken are such that the generation satisfies the demand at the lowest cost. This has been the key premise for the implementation of deregulation that the increased competition will eventually lower energy prices for the end user. However, on various occasions it has been observed that during periods of increased demand, energy prices have spiked unreasonably. A feature common in many of these high-price incidents is the inability of the transmission networks to carry power without violating the limits of secure operation. This is known as network congestion. Consequently, this least-cost schedule would not necessarily be optimal from the point of view of transmission network security and could result in various potential problems.
Ref. [2] describes some challenging problems in the design of real-time competitive markets. For each problem, potential solutions are presented, explained, and compared. Shirmohammadi et al. [3] define a system of advanced analytical methods and tools for secure and efficient operation of the power system.
Transmission network congestion is one of the major problems faced by system operators. Hence, under such circumstances, ISO has to resort to an out-of-merit re-dispatch of generation which, although not the most economic, will relieve the transmission network of the congestion. Adjustable or curtailable loads can play a similar role in the congestion management process [4]. The maintenance of the reliability and security of the transmission network is the prime responsibility of any system operator.
As noted earlier, network limitations can create a distorted power market situation, where local generators have an advantage due to reduced competition. Interruptible load schemes offer an alternative to local generation in such cases to alleviate congestion. Interruptible load consists of customers who agree to have their demand curtailed when the security of the system is at stake [5]. These customers are compensated by benefits from reduction in energy costs and from other incentives provided by the utility/ISO. Loads of large industrial customers having backup generation or having a demand that can be easily rescheduled can fall under the interruptible load category. Ref. [6] presents an expert system for alleviation of overloads in the network. The proposed methodology resorts to phase-shifting transformers and rescheduling of generation/curtailable load, if required. Various trade curtailment schemes for the purpose of security control of the transmission network are discussed in Ref. [7]. Another aspect of interruptible loads is that they can assist the utility in maintaining an online reserve (substitute for spinning reserve) that can be activated fast enough [1]. Optimal bidding strategies for competitive generators and large consumers to maximize social welfare are presented in Ref. [8]. Ferrero and Shahidehpour [9] show that the optimum solution from the perspective of individual participants in a PoolCo does not necessarily coincide with the optimum scheduling from the Pool's perspective.
A market for interruptible load contracts called callable forward is proposed in Ref. [10]. This involves a forward contract, which makes it binding for the utility to deliver certain energy E to the consumer as per the contract, and a call on the same energy, wherein the consumer is required to relinquish a portion of the delivered energy at a predetermined price (say $M). Thus, a consumer owning a callable forward is guaranteed to receive from the utility, either the required energy E or $M (and no energy) at the discretion of the utility.
Load curtailment programs are functional in various markets across the world. In Alberta, Canada, availability of curtailable system load is viewed as an ancillary service [11]. Load curtailment program started in late 1998 and has been invoked three times till date in order to help maintain system security. The National Grid in the Republic of Ireland has implemented an interruptible load scheme to assist in frequency control and provision of stability following major system incidents such as an unexpected loss of a large generator [12]. A program to curtail load from interruptible load customers in one control area and supply other control areas, experiencing a deficit, has been proposed in the WSCC (Western Systems Coordinating Council) region of North America [13]. Strbac et al. [14] discuss demand reduction scheduling where the demand-side has an opportunity to compete with generators, through the demand-side bidding scheme, in UK and Wales Pool.
This paper presents a methodology to optimally curtail load, to maximize the stability margin, in the event of a shortage of generation. Two approaches are proposed—an iterative, successive optimization solution procedure and a one-step direct solution, for optimizing the security margin. In addition, considering a scenario similar to the callable forward market, a bi-criteria programming problem model is developed that considers two objectives simultaneously—maximizing the security margin and minimizing the cost incurred in the process. The plot of the two objective values in the objective space, using the set of non-dominated solutions obtained, seeks to give a tradeoff between the reduction in the security margin and the cost incurred.
Section snippets
Background and theory
Load curtailment would have to be resorted to, in the event of a contingency, say loss of generation to ensure secure operation of the transmission network. Other reasons for resorting to interruption of loads could include congestion management, security enhancement, or improvement of the voltage profile [1]. The scenario considered in the proposed work is that of loss of generation in the system. In order to dispatch curtailable loads optimally, to maximize the security margin (w.r.t voltage
The LP model
The objective is to maximize the post-dispatch security margin of the system from the point of view of voltage stability. As mentioned earlier, this would imply minimizing the maximum stability index among all the buses in the load set wherein interruptible load schemes are offered to the customers. Let buses a, b, and c be the customers who are willing to have their load interrupted, with the following specifications:
Maximum demand: .
Curtailable portion of the total demand: {ΔP′
Solution procedure
Due to the dependence of the state variables of the system on the decision variables, an iterative solution would be most accurate. This would involve successive optimization. The procedure would start with an initial guess for the decision variables (ΔP). The state of the network with this value of ΔP would be determined using the load flow. The terms of the coefficient matrices (Ak and SIk01) would be computed using the updated state variables. LP given in Eq. (7) would then be solved to
Bi-criteria optimization
As mentioned earlier, in the context of callable forward markets, where interruptible load schemes are implemented, the utility/ISO would have to provide the customer with some benefit/incentive for his willingness to allow the curtailment. This can be viewed as a “cost” to the utility. The primary aim of load curtailment would be to safeguard the system security. At the same time, it would be beneficial to minimize the “cost” incurred in the curtailment. The “cost” is taken to be a linear
Results
The proposed approach was implemented on two test systems—a 6-bus system [16] and the IEEE-118 bus system [17]. The data (assumed) for the customers in the ILS set and the generation available after the contingency (loss of generation) for each of the test systems are given in Table 1 below.
The individual demand is taken in proportion to the original load on the bus. The cost of curtailment is assumed to be {0.01, 0.02, 0.04} monetary units per MW, respectively, for each of the customers in the
Discussion
In the PoolCo, ISO plays a key role in the proper functioning of the market. He has to take care of the market (economic) activities, like receiving bids from various participants and setting up the market clearing price, and also has to shoulder the responsibility of ensuring system security and undertaking congestion management. The phenomenon of congestion is such that it can adversely affect the physical transmission network and the related economics to a significant extent. Therefore,
Conclusions
A methodology is proposed that seeks to optimally dispatch interruptible load in the face of a loss of generation such that the voltage stability margin is maximized. Iterative and non-iterative solution procedures employing successive optimization and one-step optimization, respectively, are presented. The results obtained from both the approaches are fairly close, although the one-step method results in a drastic reduction in computation time. A BCP is also developed which takes into account
Durgesh P. Manjure was born in Mumbai, India, in 1976. He received his Bachelor of Engineering (Electrical Engineering) degree from the University of Bombay in 1997 and his Master's degree in Electrical Engineering from Clemson University in December 1999. His Master's research involved the study of the effect of nonlinear loads on power system harmonics. This included the comparison of time domain and frequency domain methods of harmonic analysis and the effect of nonlinearity and unbalance on
References (17)
- et al.
Optimal bidding strategies for competitive generators and large consumers
Electrical Power Energy Syst.
(2001) - et al.
Optimality conditions in power transactions in deregulated power pools
Electrical Power Syst. Res.
(1997) - et al.
Operation of Restructured Power Systems
(2001) - G.A. Angelidis, A.D. Papalexopoulos, On the operation and pricing of real-time competitive electricity markets, in:...
- et al.
Transmission dispatch and congestion management in the emerging energy market structures
IEEE Trans. Power Syst.
(1998) - et al.
Restructured Electrical Power System: Operations, Trading and Volatility
(2001) - C.D. Vournas, Interruptible load as a competitor to local generation for preserving voltage security, in: Proceedings...
- Bansilal, D. Thukaram, K. Parthsarathy, An expert system for alleviation of network overloads, Electrical Power Syst....
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Durgesh P. Manjure was born in Mumbai, India, in 1976. He received his Bachelor of Engineering (Electrical Engineering) degree from the University of Bombay in 1997 and his Master's degree in Electrical Engineering from Clemson University in December 1999. His Master's research involved the study of the effect of nonlinear loads on power system harmonics. This included the comparison of time domain and frequency domain methods of harmonic analysis and the effect of nonlinearity and unbalance on power factor. Currently, he is pursuing his Ph.D. degree at Clemson, and is involved in studies related to steady-state security assessment in deregulated power systems. He is a student member of the IEEE and the PES, and served as the Secretary for the PES, Clemson Chapter from 1997 to 1999.
Elham B. Makram received her Ph.D. from Iowa State University in 1981. She worked in industry for about 11 years and then joined Clemson University in 1985. She is presently South Carolina Gas and Electric Professor of Power Engineering in the Holcombe Department of Electrical and Computer Engineering at Clemson University. She is teaching power courses such as power system analysis, electric power distribution, power system harmonics, and computer applications in power systems. She is a Senior Member in IEEE Society, Member in Sigma Xi, Member in Women's Engineering Society, Member in CIGRE, and a Member in American Society for Engineering Education (ASEE). She is the recipient of the 1991 Alumni Research Award, the 1992 NSF/FAW Award, the 1993 SWE Distinguished Engineering Educator Award, the 1994 Outstanding Faculty Award at Clemson University, and the 1996 Provost's Award for Scholarly Achievement. Her research interests include computer simulation of power systems, power system harmonics, and optimal operation and design of power systems.