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The optimum allocation of LM program is of great practical interest. This paper ... work-driven load management (NDLM), reliability evaluation, sensitivity indices ...



Allocation of Network-Driven Load-Management Measures Using Multiattribute Decision Making Payam Teimourzadeh Baboli, Student Member, IEEE, and Mohsen Parsa Moghaddam, Member, IEEE

Abstract—In restructured power systems, the independent system operator (ISO) has to maintain system reliability at an acceptable level. In addition to the expected energy not supplied (EENS) as a reliability index, the total grid losses are another system operators’ anxieties. Load management (LM) is an effective mean to achieve a suitable network operational condition. The optimum allocation of LM program is of great practical interest. This paper presents a multiattribute decision-making for allocation of network-driven load-management (NDLM) measures. The objectives of the optimization problem are defined as minimization of the EENS, minimization of total grid losses, and maximization of load-management capacity. It has been shown that these objectives are conflicting aspects of an NDLM program which is solved by the STEM interactive method. The IEEE reliability test system is used to demonstrate the effectiveness of the proposed methodology.

For functions and variables Importance coefficient of objective . Relative importance coefficient of objective . MINIMAX function. Failure rate of th component. Repair rate of th component. Curtailable load of bus . Total curtailable load. Feasible search region in

Index Terms—Multiattribute decision making (MADM), network-driven load management (NDLM), reliability evaluation, sensitivity indices, STEM interactive method.

th iteration.

EENS of system before load reduction. EENS of system after th load reduction. EENS of system after total load reduction.


Expected energy not supplied at hour .

SET of all possible contingencies.

Total EENS of the dispatch period.

Index for units.

Coefficient of the objective function

Index for buses.

Amount of demand in th bus before load reduction.

th objective function.

Index for lines.

Amount of demand in the th bus after load reduction.

Index for selected buses.

Total amount of demand before load reduction.

Index for iterations. NB

Number of buses.


Number of lines.


Number of selected buses.


Total amount of demand after load reduction. Total grid losses before load reduction. Total grid losses after th load reduction.

Number of hours in the dispatch period. Index for hours in the dispatch period.

Total grid losses after total load reduction. Load supplying factor of bus at hour . LT

System lead time. Demand of bus

Manuscript received July 05, 2009; revised December 02, 2009. First published April 19, 2010; current version published June 23, 2010. Paper no. TPWRD-00490-2009. The authors are with the Department of Electrical and Computer Engineering of Tarbiat Modares University, Tehran, Iran (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier 10.1109/TPWRD.2010.2045517 0885-8977/$26.00 © 2010 IEEE

at hour .

Average power flow of line at hour . Probability of each contingency. Grid losses at hour . Total grid losses. Resistance of line .



Nodal EENS sensitivity index. Nodal grid losses sensitivity index. Total EENS sensitivity index. Total grid losses sensitivity index. Unavailability of the th component. th optimization variable. Vector of optimization variables. Vector of compromise solution in iteration.




HE INTEGRATED use of demand- and supply-side resources has been peformed by electric utilities, because of its potential attractiveness, both at operation and economic levels [1], [2]. Cost and emission reduction, decrease of overseas fuel dependency, increase in power system reliability, and an increase in revenues are some of the benefits a utility can obtain from such integration. In the demand side, the “resources” can be used by changing the regular working cycle of some individual loads and, thus, changing the demand shape at more aggregate levels. Under deregulation, the scope of load-management (LM) programs has considerably been expanded to include demand-response programs [3]. There are three types of demand-side management (DSM) based on the overall purpose of the DSM program [4]: 1) environmentally driven: achieves environmental and/or social goals by reducing energy use, leading to increased energy efficiency, and/or reduced greenhouse gas emissions; 2) network driven: deals with challenges in the electricity network by reducing demand in ways that maintain the system reliability in the immediate term and over the longer term, deferring the need for network augmentation; 3) market driven: provides short-term responses to electricity market conditions (e.g., by reducing load during periods of high market prices caused by reduced generation or network capacity) (e.g., demand-response programs). Considerable research has been performed in which the impacts of LM on generation and transmission system reliability have been investigated (see, for example, [5]–[7]). These works focus on the accumulate load curve of the system and none of them described the allocation problem. Practically, when an LM program is implemented in a grid, the selection of the optimum combination of buses, which has the most impact on network’s characteristics, is too important. In this paper, the allocation problem of the network-driven load management (NDLM) program implementation for the enhancement of the composite system reliability as well as reduction of total grid losses are addressed. The techniques for composite system reliability evaluation are well developed in the literature [8]–[11]. In this study, expected energy not supplied (EENS) is considered as an index of composite system reliability evaluation, which can be considered an important net-

work operator’s concern. It shows how problems of minimization of EENS and minimization of total grid losses may conflict with each other. Furthermore, a multiattribute decision-makingbased (MADM-based) methodology is presented for the aforementioned conflicting problems. Via a MADM approach, the decision maker (DM) may grasp the conflicting nature of the objectives where tradeoffs are made in order to obtain satisfactory compromise solutions [12]. In this paper, the step method (STEM) [13] interactive method has been adopted to provide decision support to select the best combination of network buses for NDLM program implementation. This optimization method is used because of the simplicity of its computation and dialog phases as well as its capability to deal with integer variables. In this paper, optimum allocation of NDLM programs implementation is proposed, considering minimization of the EENS and minimization of the total grid losses while the capacity of NDLM programs is maximized. The reminder of this paper is organized as follows. Section II provides a brief introduction of NDLM programs. Section III describes the impacts of load management on system reliability. Section IV presents the problem formulation. Section V describes the optimization procedure. Section VI presents numerical results of the case study and finally, Section VII concludes this paper. II. NETWORK-DRIVEN LOAD MANAGEMENT (NDLM) Network-driven load management is concerned with reducing demand on electricity networks in specific ways which maintain the system’s reliability in the short term and defer the need for network augmentation in the long term [4]. Problems in electricity networks are becoming significant in countries where electricity demand is increasing and network infrastructure is aging. As loads grow and infrastructure reaches the end of its economic life, the potential cost of augmenting and providing support services for electricity networks increases significantly. Two prime purposes for NDLM programs are as follows [4]. 1) In the long term, relieve constraints on electricity distribution and/or transmission networks at lower costs than building new infrastructures. 2) In the short term, provide operational support services for electricity networks, achieving peak load reductions with various response times. This paper focuses on the impact of NDLM programs’ implementation on network characteristics. III. IMPACTS OF LM ON COMPOSITE SYSTEM RELIABILITY The impacts of LM on composite system reliability can be summarized as follows [11]. 1) Improve reserve capacity of power system during onpeak hours. LM measures can be treated as one of the contributors for improving the system adequacy with the dominant characteristic of rapidness. 2) To make better use of transmission capacity, it is possible to change power flows on some heavily loaded lines with proper LM projects.



is chosen which can be used for reliability enhancement in planning studies as detailed in [16]. EENS, in megawatt hours per year, is the total amount of energy which is expected not to be delivered to the loads during the dispatch period. The EENS at hour can be calculated by

Fig. 1. Two-state model of the ith power system’s component.

3) Improve components’ running condition by reducing the difference between peak load and low load to keep effective operation of the components. 4) Improve system security, because LM and energy conservation can extend the components’ lifetime and improve system security. Among the aforementioned four operating benefits, the first two are the main contributors to improve the system reliability.

(2) is a binary variable which indicates the supplying where state of the th load in hour (i.e., is equal to 1 when the th load is supplied or 0 when the load is shedded). The value is determined by running the optimal power flow for of each considered state of the system. Thus, minimizing total EENS can be stated as

A. Basic Procedure of Composite System Reliability Evaluation


The composite system reliability assessment is a complex calculation procedure, which generally includes the following steps [14]: Step 1) determination of component failures and load curve models; Step 2) selection of system states; Step 3) identification and analysis of system problems; Step 4) calculation of reliability indices. Both state enumeration and Monte Carlo simulation methods can be applied to the composite system reliability evaluation. These two methods use different approaches to select system states and have different types of formulas to calculate reliability indices. The techniques of identifying and analyzing problems in a system state are the same. These include power flow and contingency analysis for problem recognition and optimal power flow for remedial actions. In our study, the state enumeration simulation method is adopted to select system states. B. Generating Units and Transmission Network Reliability Model

subject to


B. Optimization of Total Grid Losses In order to minimize the total grid losses, the following objective function is used: (4a) subject to


where (5)

C. Optimization of Total NDLM Capacity

In this investigation, from the reliability analysis viewpoint, the two-state model shown in Fig. 1 is chosen to represent each system component’s reliability model. of the th According to this model, unavailability (known as system’s component during a short-time interval the system lead time presented in [15]) is given by (1)

This objective function shows the total curtailable load in system buses. Actually, the capacity of NDLM will increase if this objective function is maximized. Also, by maximizing this objective function, and become smaller. This objective function can be formulated as (6) where (7)

IV. PROBLEM FORMULATION As was mentioned before, three objectives are considered in this optimization problem. The first objective is minimization of EENS, the second one is minimization of total grid losses, and the last one is maximization of total NDLM capacity. These objective functions can be formulated as follows. A. Optimization of the EENS The EENS index is selected for measuring the composite system reliability. In this paper, the annualized reliability index

D. Nodal and Total Sensitivity Indices In this section, certain sensitivity indices are addressed for analyzing the impact of load reduction on decreasing EENS and total grid losses. In this respect, first, two nodal sensitivity indices are introduced which will be used for evaluation of the impact of the th load reduction on the variation of EENS and total grid losses. Then, two total sensitivity indices are proposed to evaluate the impact of total load reduction on decreasing of




4) Total Grid Losses Sensitivity Index: This index shows the variation of total grid losses when 1 MW of total load in selected buses is curtailed as defined by the following equation: (11)

V. OPTIMIZATION PROCEDURE Multiattribute models have the advantage of accurately representing the real multiattribute nature of certain situations. The mathematical formulation of a typical multiobjective linear programming (MOLP) problem can be stated as follows:

subject to

(12a) (12b)

where (13) Fig. 2. Flowchart of the optimization procedure.

EENS and total grid losses in those buses which are selected for implementing NDLM programs. 1) Nodal EENS Sensitivity Index: This index shows the variation of EENS when 1 MW of the th load is curtailed and is defined as (8) 2) Nodal Grid Losses Sensitivity Index: This index shows the variation of the grid’s losses when 1 MW of the th load is curtailed as defined by the following equation: (9) 3) Total EENS Sensitivity Index: This index shows the variation of EENS when 1 MW of total load in selected buses is curtailed and is defined as (10)

Let D be the feasible search region defined by constraints in (12b). In general, there are no feasible solutions such that all can simultaneously take their maximum value within the feasible region D. In this study, the STEM interactive method [13] is used in the optimization procedure because of the simplicity of its computation and its capability to deal with integer variables. STEM is an iterative exploration procedure, where the best compromise is reached after a certain number of iterations [13]. First, each objective is optimized individually to determine the maximum or minimum possible value. Then, an iterative procedure will be commenced. Each iteration is made up of a calculation phase and a decision-making phase. During the decision-making phase, the DM examines the results of the calculation phase and from this examination, he or she may impose new adjustments to achieve his or her goals. Fig. 2 shows the flowchart of the optimization procedure. A. Individual Optimization Before the first iteration, the optimum value for each objective is determined by using the nodal sensitivity indices. These optimum values are then used for constructing the pay-off table T as indicated in Table I. Row of Table I corresponds to the solution vector which maximizes the objective function , under the con-



give the relative importance of the disThe coefficients tances to the ideal solutions. is the Let us consider column in the payoff table T. If maximum value of the column and is the minimum value of the corresponding objective; then and can be calculated as follows: (15)


C. Decision Phase is propped to the DM, which The compromise solution with , the ideal one. compares his or her objective vector are satisfactory and others If some of the components are not, the DM must accept a certain amount of relaxation of to allow an improvement of the una satisfactory objective satisfactory ones in the next iteration. So, he is asked to indicate can be relaxed, and the amount of relaxation can which be accepted. For the next iteration, the feasible region is modified as following:

Fig. 3. Single-line diagram of the RTS-79 [18].



. (17)


straints (12b). So function when

is the corresponding value of the objective reaches its maximum value.

B. Calculation Phase For each iteration, the feasible combination of buses which is the “nearest” to the ideal solution is selected, in the MINIMAX (minimizing the maximum distance) sense as follows: (14a) subject to (14b)

The 24-bus IEEE Reliability Test System (RTS-79) is used as a case study system [17]. The single-line diagram of the test system is given in Fig. 3. This test system describes a load model, generation system, and transmission network which can be used to test or compare methods for composite reliability analysis of power systems. The test system has 32 generators, 33 transmission lines, 5 transformers, and 17 load buses with the total generation capacity of 3405 MW, and the maximum load of 2850 MW. The generating unit data and the associated components’ reliability data can be found in [17]. The bus-load data at the time of system peak load are shown in Table II. No data on load uncertainty or load diversity between the buses are provided. For those times other than the annual system peak, the bus loads are assumed to have the same proportional relation to system load as at the peak load condition. These restrictions on bus loads (no uncertainty, no diversity, constant power factor) are the assumptions usually made in reliability evaluations. It is assumed that all loads could participate in NDLM programs, exactly 10% of the demand for each bus can be curtailed and the study period is considered to be one year. The percentage of bus loads is given in the last column of Table II. Ten percent of this value demonstrates the capacity of the NDLM program implementation of the corresponding bus.





Fig. 4. Normalized total EENS and grid losses sensitivity indices and normalized total NDLM capacity.


Fig. 5. Normalized sensitivity indices and bus-load percentage of total system load.

Table III gives the EENS and total grid losses before implementing any NDLM program. Nodal EENS and grid losses sensitivity indices for each bus are calculated by using (8) and (9), respectively, and are shown in Table IV. As can be seen in Table IV, there are some conflicts between the objectives, i.e., there are some buses like Load15 which has but negative or Load16 with big but a big . So, due to existing conflicts, the problem should be small solved by a multiattribute optimization method. It is assumed that 5 buses are chosen for implementing NDLM programs. The solutions that individually optimize each objective function and the corresponding 5 selected buses are presented in Table V which shows the pay-off table T. The underlined values denote the optimal value of each objective. The results of Table V indicate that when the selected buses for implementing NDLM programs are changed, different values for EENS and total grid losses will be obtained. The amount of load reduction in different buses are not similar therefore, comparison of decreasing in EENS and grid losses should be made with respect to the amount of load reduction. For instance, even the value of EENS in optimal solution F3 is less than its value in optimal solution F1, but the variation in EENS in optimal solution F1 is bigger when we consider the amount of load reduction as it is pointed in Fig. 4. Investigation

of Fig. 4 and Table V indicate that the decrease in EENS or total grid losses strongly depend on the both of the amount and location of load reduction. By considering the last column of Table V, it can be seen that there are just a few common buses in three rows of the mentioned column. For example, bus 15 and 10 are common between rows 1 and 3, and bus 18 is common between rows 2 and 3. This can be interpreted as conflict among the objectives of the problem. In Fig. 5, the nodal sensitivity indices and bus load percentage of total system load are normalized with respect to their maximum value to make a better comparison. This figure indicates the conflicts between these indices, e.g., in some buses, one index has high value but the rest of the indices have small values and just in a few load points, all the indices are in an acceptable level, as judged by the DM. So, the DM has to compromise between the objectives and choose a preferable combination of buses to obtain satisfactory nondominated solution. The nondominated solution and corresponding five selected buses computed by STEM interactive method are summarized in Table VI. If the DM weighs all of the objective functions as well as their importance degree, then the amount of EENS and total grid losses are less than the optimal values indicated in Table V, with an acceptable load reduction level as shown in Table VI.



VII. CONCLUSION In this paper, the importance of the allocation problem of NDLM programs and their impacts on composite system reliability and total grid losses have been illustrated. The IEEE reliability test system (RTS-79) has been analyzed to illustrate the proposed technique. The objectives were defined as minimization of the EENS, minimization of total grid losses and maximization of load-management capacity. Due to the conflicting aspects of the objectives, the optimization problem has been solved by a multiattribute decision-making method. The STEM interactive method has been adopted to provide decision support in selecting the best combination of buses for NDLM implementation. This optimization method has been used because of the simplicity of its computation and its capability to deal with integer variables. The allocation of NDLM programs described in this paper can be extended to applications in real power systems. REFERENCES [1] I. Apolinario, C. C. de Barros, H. Coutinho, L. Ferreira, B. Madeira, P. Oliveira, A. Trindade, and P. Verdelho, “Promoting demand-side management and energy efficiency in portugal 2 years of experience,” in Proc. 5th Int. Conf. Eur. Electricity Market, 2008, pp. 1–6. [2] M. Ashari, W. L. Keerthipala, and C. V. Nayar, “A single phase parallely connected uninterruptible power supply/demand side management system,” IEEE Trans. Energy Convers., vol. 15, no. 1, pp. 97–102, Mar. 2000. [3] “Assessment of demand response and advanced metering,” FERC, Staff Rep., 2006. [Online]. Available: www. FERC. Gov [4] “Worldwide survey of network-driven demand-side management projects,” Task XV of the IEA-DSM Res. Rep. No. 1, 2006. [5] L. Goel, V. P. Aparna, and P. Wang, “A framework to implement supply and demand side contingency management in reliability assessment of restructured power systems,” IEEE Trans. Power Syst., vol. 22, no. 1, pp. 205–212, Feb. 2007. [6] E. Hirst, “Reliability benefits of price-responsive demand,” IEEE Power Eng. Rev., vol. 22, no. 11, pp. 16–21, Nov. 2002. [7] L. Goel, W. Qiuwei, and P. Wang, “Reliability enhancement of a deregulated power system considering demand response,” in Power Eng. Soc. IEEE General Meeting, Oct. 2006, pp. 1–6. [8] R. Billinton and W. Li, “A system state transition sampling method for composite system reliability evaluation,” IEEE Trans. Power Syst., vol. 8, no. 3, pp. 761–770, Aug. 1993.


[9] R. Billinton, H. J. Koglin, and E. Roos, “Reliability equivalents in composite system reliability evaluation,” Proc. Inst. Elect. Eng., Gen., Transm. Distrib., vol. 134, no. 3, pp. 224–232, May 1987. [10] R. Billinton, S. O. Faried, and M. Fotuhi-Firuzabad, “Composite system reliability evaluation incorporating a six-phase transmission line,” Proc. Inst. Elect. Eng., Gen., Transm. Distrib., vol. 150, no. 4, pp. 413–419, Jul. 2003. [11] M. Zhou, G. Li, and P. Zhang, “Impact of demand side management on composite generation and transmission system reliability,” Proc. IEEE Power Eng. Soc. PSCE, pp. 819–824, 2006. [12] H. Jorge, C. H. Antunes, and A. G. Martins, “A multiple objective decision support model for the selection of remote load control strategies,” IEEE Trans. Power Syst., vol. 15, no. 2, pp. 865–872, May 2000. [13] R. Benayoun, I. de Montgolfier, J. Tergny, and O. Laritchev, “Linear programming with multiple objective functions: Step method (STEM),” Math. Programming, vol. 1, pp. 366–375, 1971. [14] L. Wenyuan, Risk Assessment of Power Systems-Models, Methods and Applications. Hoboken, NJ: Wiley, 2005. [15] R. Billinton and M. Fotuhi-Firuzabad, “Generating system operating health analysis considering stand-by units, interruptible load and postponable outages,” IEEE Trans. Power Syst., vol. 9, no. 3, pp. 1618–1625, Aug. 1994. [16] N. Samaan and C. Singh, “A new method for composite system annualized reliability indices based on genetic algorithms,” in Proc. Power Eng. Soc. Summer Meeting, Jul. 2002, vol. 2, pp. 850–855. [17] P. M. Subcommittee, “IEEE reliability test system,” IEEE Trans. Power Syst., vol. PAS-98, no. 6, pp. 2047–2054, Nov. 1979. [18] L. Goel, Q. Wu, and P. Wang, “Nodal price volatility reduction and reliability enhancement of restructured power systems considering demand-price elasticity,” Elect. Power Syst. Res., vol. 78, no. 10, pp. 1655–1663, Oct. 2008. Payam Teimourzadeh Baboli (S’09) was born in Babol, Iran, in 1985. He received the B.Sc. degree in electrical engineering from the Noshirvani University of Technology (NIT), Babol, Iran, in 2007, the M.Sc. degree in power engineering from Tarbiat Modares University (TMU), Tehran, in 2009, and is currently pursuing the Ph.D. degree in power engineering at TMU. His research interests include demand-side management, multiobjective programming, and electricity markets.

Mohsen Parsa Moghaddam (M’05) was born in Iran in 1956. He received the B.Sc. degree in electrical engineering from Sharif University of Technology, Tehran, Iran, in 1980, the M.Sc. degree from Toyohashi University of Technology, Japan, in 1985, and the Ph.D. degree from Tohoku University, Japan, in 1988. Currently, he is an Associate Professor in the Department of the Electrical Engineering, Tarbiat Modares University, Tehran. His research interests include power system planning and control, energy management, and power system restructuring.

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