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Value of Lost Load A Critical Parameter for Optimum Utility Asset Investment

Amir Hisham Hashim Power Engineering Centre Universiti Tenaga Nasional

Daniel Andrew Sen Dept. of Electrical Engineering Universiti Tenaga Nasional

Radzian A Rahman Transmission and Dist. Dept TNB Research

Abstract: In today’s demanding business environment, determining the value of lost load (VoLL) is important in order for utilities to make the right decision when it embarks on any form of asset expansion. The VoLL is the aggregated or average value of outage costs across the whole range of customers in the electricity supply industry (ESI). Determining the VoLL offers utilities tangible numbers that can be used in balancing the cost of outages against the cost of investing in the network to ensure system adequacy and security. This paper covers the uses and advantages of using VoLL, particularly in determining optimum asset investment. Finally a demonstration of VoLL application in utility asset evaluation will be shown where certain system expansion options will be evaluated. Keywords: Value of Loss Load, Power System Reliability, Power System Economics, Utility Asset Investment. 1.

Introduction

Utilities are responsible for the generation, transmission, and distribution of electricity to customers. Part of this responsibility is ensuring that system adequacy and security criteria are fulfilled. However, this must be balanced against the investment and operating costs, which are increasingly important factors to remain competitive. Utility planning has traditionally been based on the electricity load demand forecast. The demand for electricity initiates actions by the utilities to add or retire generation, transmission, or distribution assets [1]. Retiring assets can be done fairly quickly, however, there is a long lead time required to plan and construct new utility equipment. Decisions may need to be made from 2-10 years in advance [1] for the need of a new utility plant. System reliability is a central criterion during the planning stage. Reliability is the need to provide both system adequacy and security. Adequacy is the existence of sufficient facilities such as generators, lines, and control systems within a system to satisfy customer demand, whereas, system security is the ability for the system to respond against a disturbance in the system such as the loss of a generator or a lightning strike. The VoLL can be used in both adequacy and security assessment but this paper will concentrate on the adequacy part. While these criteria have served the ESI well in the past, the present environment requires a balance between the planning and operation criteria, and the economic value customers assign to reliability in establishing target reliability levels [2]. Customers’ needs range from those who would not mind paying a premium for a highly reliable supply (because they would suffer a very large loss when there are disruptions in their power supply) to the vast majority of customers who do not mind tolerating outages in exchange for lower prices. Often, there is a mix of customers with various reliability needs located in close geographic proximity. Therefore, it can be quite hard for the utility to decide on the optimum reliability level. One method of optimization is through value based planning, which is matching the level of investment in reliability with customers’ reliability preferences [2]. Taking into account the economics during the planning stage allows utilities to optimize their investment by investing in assets to boost reliability where customers expect higher reliability levels than the status quo.

2.

Background of Asset Optimization

In mathematics, optimization is the discipline which is concerned with finding the maxima and minima of functions, possibly subject to constraints [3]. When applied to asset investment in the ESI, optimization is the process of trying to maximize the utility’s profit while, at the same time minimizing the cost of adequacy and security. Planning engineers are constantly analyzing and managing risks and the costs associated with those risks. Two common methods of analyzing risks are the probabilistic approach and the deterministic approach. The probability approach aims to determine the probability of an event occurrence using statistical data. In this process, a sampling method is selected. To avoid biases, researchers employ random sampling procedures [4]. Through statistical methods, for a given sample size, the mean, standard deviation, coefficient of variation, and the level of precision can be calculated. This method allows utilities to gauge damage perceived by customers due to a power interruption. The deterministic approach, on the other hand, plans for contingency scenarios such as n-1 criteria and largest generator tripping. In utilizing this method, the utility plans for various potential contingencies and estimates the damage to the affected customers. Reliability worth according to Billington [5] is the outage cost can be divided into three categories: • Outage Cost to Utility – this includes loss of revenue, loss of goodwill, loss of future potential sales and increased expenditure for maintenance and repair. • Outage Cost to Industry- this includes lost of production, damaged machineries and products and corrective maintenance. • Outage Cost to Residential – this includes lost of frozen foods, alternative energy cost. Often outage cost to Industry and Residential outweigh the outage cost to utility. However, the outage cost can be reduced through measures such as the construction of parallel lines which connect a power source to the load. Figure 1 below illustrates the costs utilities face in planning for asset investment. In the figure, there are 2 types of costs: the reliability cost and reliability worth. The reliability cost is related to the cost of purchasing and installing new equipment to increase the utility’s reliability. This cost increases with increasing reliability. The reliability worth is the value the customer is willing to pay for increasing power supply reliability. This cost decreases with increasing reliability. The total cost to the consumer is the sum of the utility cost, which the consumer pays for through the electricity bill, and the consumer cost due to outages [6].

Cost

Utility asset investment centers on reducing risk by increasing system reliability to provide system adequacy and security. However, optimization would show that investment beyond point A is economically inefficient because it leads to higher total cost. At the same time, investment below point A would result in a lower than optimum reliability level, which also results in higher total cost.

Total Cost Reliability Cost (utility) Reliability Worth (consumer) A

Reliability Figure 1: Utility Asset Investment: Balancing Reliability Cost and Reliability Worth [7].

3.

Value of Loss Load (VoLL)

The Value of Loss Load (VoLL) is the estimated amount that customers receiving electricity with firm contracts would be willing to pay to avoid a disruption in their electricity service [8]. The value of these losses can be expressed as a CDF. A CDF is defined [9] as: Loss ($/kW) = f(duration, season, time of day, notice)

$/kW interrupted

Based on the calculated outage cost, a customer damage function (CDF) can be obtained for various customer groups. Typically, there are three distinct groups of customers: residential, small and medium commercial/industry and large commercial/industrial [10]. Figure 2 below illustrates the incremental CDFs of these three groups.

Small & Medium C/I Large C/I Residential

Outage Duration Figure 2: Example Customer Damage Functions [10]. The CDF relates the magnitude of customer losses (per kW interrupted) for a given duration of a power outage. While the general shapes of all three curves are similar, the magnitude of loss varies dramatically depending on the customer’s size. Based on VoLL data from an EGAT survey in March and April 2000 [11], it was estimated that the customers’ costs in the first hour for residential customers was Baht 11.45/kW. For large C/I and small & medium C/I customers, the cost in the first hour was Baht 29.55/kW and Baht 89.50 /kW respectively. Another research from EPRI [10] indicates that residential customers’ cost tend to peak at USD 1.50/kW in the first hour and falls of to USD 0.46/kW in subsequent hours. On the other hand, large C/I and small & medium C/I suffer much higher losses of USD 10/kW and USD 38/kW respectively in the first hour. This falls to USD 4/kW and USD 9/kW respectively in the subsequent hours. The CDF predicts the loss per interrupted kW based on factors that influence the outage. The CDF is usually calculated based on defined market segments such as residential, commercial, and industrial. This is done because there are large variations of costs across the utility market segments. However, in a large area it is a normal practice that the interruption cost is aggregated to represent a general picture of the load losses. The aggregated interruption cost is called the composite CDF. To illustrate the interruption costs, the CDF values are derived from a U.K. Survey by Billington (1982, 1985 and 1987). The customer interruption cost expressed in kilowatts of annual peak demand ($/kW) is tabulated as below.

User Sector Large User Industrial Commercial Agricultural Residential Government Office

Table 1: Interruption Cost with respect to Interruption Duration Interruption Duration 1 hour 2 hour 2.5 hour 5 hours 1.005 1.508 2.225 3.968 1.625 3.868 9.085 25.163 0.381 2.969 8.552 31.317 0.060 0.343 0.649 2.064 0.001 0.093 0.482 4.914 0.044 0.369 1.492 6.558 4.778 9.878 21.065 68.830

8.3 hours 8.240 55.808 83.008 4.120 15.690 26.040 119.160

4.

Application of VoLL for Power System Investment Optimization

A power system experiences a blackout when all paths between a load point and its sources are disconnected. It assumes that any branch is capable of carrying all the load demanded of it. The term used to describe this situation is total loss of continuity (TLOC). When TLOC occurs, the load is permanently lost for a period of blackout. This loss contributes to outage cost A simple schematic and VOLL survey data based on different customer segments may be used to illustrate the concept of VOLL. In this example, the number of parallel power lines that connect a generator and the loads is varied to simulate networks of different reliability levels. Figure 3 illustrates the reduction of outage cost by increasing reliability through the added number of parallel lines. The example considers outage cost to the consumers. Figure 3 shows a simple power system which consists of a source (generator) that supplies electricity to three load points Load 1, Load 2, and Load 3. To further simplify this example, we assume that all loads have the same value. This power system has three sub-networks: • the first sub-network consists of three parallel lines supplying Load 1, the n-2 case • the second sub-network consists of two parallel lines supplying Load 2, the n-1 case • the third sub-network is a spur line supplying Load 3

G

Lines 2, 3, and 4

Component 8: Busbar

Generator

Lines 5 and 6

Load 1

Component 9: Busbar

Component 1: Busbar

Line 7

Load 2

Component 10: Busbar Load 3

Figure 3: Example of three networks with different reliability levels. Each sub-network is made up of several components, such as busbars and lines, which have varying individual failure rates, λ. Taking into account the individual failure rates, the overall reliability of each subnetwork can be calculated. Reliability indices can be defined as below: = Failure rate per year (frequency/year) r = Number of outage hours (hours) U = r = Number of hours per year (hours/year) L = Load supplied (MW) E = Annual outage time at load point (MWh/year) C I = Interruption cost per kW ($/MW) C A= Annual customer interruption cost ($/year)

An example system with these parameters is used to reflect the power system illustrated by the previous diagram. The total loss of continuity for each load based on the failure of individual component can be tabulated as shown below. Failure Event Electricity to Load 1 Failure of 1 Failure of 2,3 and 4 Failure of 8 Electricity to Load 2 Failure of 1 Failure of 5 and 6 Failure of 9 Electricity to Load 3 Failure of 1 Failure of 7 Failure of 10

Table 2: Example Failure Events r U

L

E

0.01 8.00×10-6 0.01

2 5 2

0.02 4.00×10-5 0.02

10 10 10

0.2 4.00×10-4 0.2

0.01 4.00×10-4 0.01

2 5 2

0.02 2.00×10-3 0.02

10 10 10

0.2 0.02 0.2

0.01 0.02 0.01

2 5 2

0.02 0.1 0.02

10 10 10

0.2 1 0.2

As in any other indices, a composite CDF is aggregated through the usage of weightage which resembles the load composition of the service area. This is based on the annual peak demand and annual energy consumption for each customer segment. The load composition weightage based on annual peak demand and annual energy consumption adopted from R. Billington (1995) showed that for 2-hour and 5-hour durations, a VoLL of $1560/MW and $12140/MW was incurred respectively. Using this value, the annual customer interruption cost, CA ($/year) can be calculated using the formular below; CA = λ×CI×L Failure Event Electricity to Load 1 Failure of 1 Failure of 2,3 and 4 Failure of 8

Table 3: Annual Customer Interruption Cost r CI λ

L

CA

0.01 8.00×10-6 0.01

2 5 2

1560 12140 1560

Electricity to Load 2 Failure of 1 Failure of 5 and 6 Failure of 9

10 10 10 Total

156 0.9172 156 312.92

0.01 4.00×10-4 0.01

2 5 2

1560 12140 1560

Electricity to Load 3 Failure of 1 Failure of 7 Failure of 10

10 10 10 Total

156 48.56 156 360.56

0.01 0.02 0.01

2 5 2

1560 12140 1560

10 10 10 Total

156 2428 156 2740

5.

Discussion of Result

By adding more lines, alternative supply paths are created. The calculation tabulated above show that, statistically, the increase of power lines is proven to reduce the annual outage time at a load point, and thus the outage costs incurred. However, building lines incurs investment cost and these costs have to be balanced against the outage cost. The quoted total price to lay an XLPE underground cable to supply a 10MW load was RM500/meter [12]. Assuming the distance is 100m, the capital cost of building an additional line would be RM50,000. The savings derived from adding another line to the spur network so that it becomes a double circuit is RM2740.00 – RM360.56 or RM2379.44 per year. Therefore, the initial investment of RM50,000 can be recovered in a period of 21 years of service. Since most cable manufacturers recommend that cables be replaced every 40 years, this represents a cost saving investment in the long run. However, adding another line for a triple circuit or 3 feeder network is not cost effective because the additional savings of RM46.64 per year derived from adding a third line is marginal and does not justify the large capital cost. Therefore, the optimum topology in this particular example case is a double circuit network. VoLL is not the only factor in determining asset expansion. Current assets will have to be upgraded and new nodes will have to be constructed due to increasing demand and the need for added system security and adequacy. Current spur networks, as shown in this example, will have to be upgraded to double circuit networks eventually. This means that there will come a time when the utility will have no choice but to construct an additional line. This inherent necessity is a mitigating factor when considering the capital cost of asset expansion as described in this example. 6.

Conclusion

This paper has illustrated the use of the VoLL in an asset expansion scenario. Since this analysis can give an indication of the cost of outage, it allows for reliability levels to be quantified which in turn forms the core of a cost-benefit analysis. In this case, the 2 feeder option is deemed as the best option among the 1, 2 and 3 feeder options. The variation of VoLL can also affect the solution. For instance, the 3 feeder option can be the selected if the VoLL is really high, particularly for sensitive loads such as semiconductor plants. Thus, this leads to the possibility of using VoLL for asset expansion in specific geographic areas, given the mix of customer loading and will lead to an optimum investment solution. References [1] H.G. Stoll, “Least-Cost Electric Utility Planning”, John Wiley & Sons, 1989, pp 167. [2] Sullivan, M.J. and Keane, D.M., “Outage Cost Estimation Guidebook”, EPRI Research Project 2878-04 Final Report, December 1995, pp 1-1. [3] “Optimization - Wikipedia, the free encyclopedia”, http://en.wikipedia.org/wiki/Optimization, 27 October 2005. [4] Sullivan, M.J. and Keane, D.M., “Outage Cost Estimation Guidebook”, EPRI Research Project 2878-04 Final Report, December 1995, pp 6-1. [5] R. Billington and R.N. Allan, “Reliability Evaluation of Power Systems”, Plenum Press.New York and London, 1994, pp. 302 - 326 and pp.443 – 473. [6] H.G. Stoll, “Least-Cost Electric Utility Planning”, John Wiley & Sons, 1989, pp 363-365. [7] A.H. Hashim, “MEE Course Notes”, Universiti Tenaga Nasional, 2005. [8] Vassilopoulos, P., “Models for the Identification of Market Power in Wholesale Electricity Markets”, Industrial Organization, D.E.A 129, September 2003 pp 46 - 47.

[9] Sullivan, M.J. and Keane, D.M., “Outage Cost Estimation Guidebook”, EPRI Research Project 2878-04 Final Report, December 1995, pp 1-4. [10] Sullivan, M.J. and Keane, D.M., “Outage Cost Estimation Guidebook”, EPRI Research Project 2878-04 Final Report, December 1995, pp 8-13. [11] “Electricity Outage Cost Study”, http://www.eppo.go.th/power/ERI-study-E/ERI-ExeSummaryE.html, 19 November 2005. [12] Teleconversation with Mr. Norazman Atib, Tenaga Nasional Berhad (Distribution) on 16 November 2005.