Probabilistic ranking of large scale transmission projects

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Electric Power Systems Research 42 (1997) 21-25

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Probabilistic ranking of large scale transmission projects K. Tinnium, P. Rastgoufard *, P.F. Duvoisin Electric Power Research Laboratory, Department of Electrical Engineering, Tulane University, New Orleans, LA 70118, USA

Received 14 February 1995

Abstract

The purpose of this investigation is to determine an appropriate way of probabilistically prioritizing transmission system alternatives. Three approaches widely exercised by different electric utilities are studied and compared to the methodology proposed and developed in this paper. Utilizing the appropriate methodology, transmission system alternatives are prioritized and the best alternative is placed on the top of a ranking table. An analysis of qualitatively identifying the different transmission system benefits is performed. Some of the qualitative benefits are quantified and used in our methodology. The proposed methodology is tested on the IEEE 25 bus reliability test system (RTS). TRELSS (transmission reliability evaluation of large scale systems), a software package developed by Electric Power Research Institute (EPRI) is utilized in determining the probabilistic indices that are used in the proposed approach. © 1997 Elsevier Science S.A. Keywords: Probabilistic ranking; Transmission system; Prioritization; Reliability evaluation

I. Introduction

The basic function of a power system is to supply electrical energy to both large and small customers as economically as possible, and with an acceptable degree of reliability and quality. As described in [1-5] reliability is the ability of a power system to provide service to customers while maintaining the quality and price of electricity at an acceptable level. Past utility operating experiences have shown that prioritization of transmission system alternatives is important in that transmission line design planners are constantly in need of finding appropriate indices that will facilitate prioritization of transmission alternatives. Prioritization is necessary for transmission line design planners in order to determine the 'best' alternative, i.e., the alternative that produces the maximum return for a given cost. Deterministic approaches that include a set of predefined criteria were in use during the past. Probabilistic approaches that take into consideration the probability of occurrence of an outage and the stochastic nature of the power system have come into study in recent years. Probabilistic load flow and stability tech* Corresponding author. Tel.: + 1 504 8655785. 0378-7796/97/$17.00 © 1997 Elsevier ScienceS.A. All rights reserved. PII S0378-7796(96)011 72-8

niques are used to study power systems [6-8]. Electric utility planners, though convinced that probabilistic approaches are suitable, are still facing a problem of determining, probabilistically, the 'best' alternative. Qualitative identification and quantification of the benefits of modifying a power system by probabilistically modelling the effects of addition or deletion of transmission capability is a major issue in this regard. The former issue is given importance in this paper. Work done by different electric utilities in the past indicates that the following three approaches are useful. 1. Project Cost Approach: The capital cost of the project is an index for determining the order of priority of different transmission system alternatives. 2. The Total Cost Approach: The total cost is defined as CC (Capital Cost) + CIC (Customer Interruption Cost) + FC (Fuel Cost). The benefits come in the form of a reduction in customer interruption cost. In this approach, the total cost is utilized as a measure in the ranking of the alternatives. 3. Cost/Risk ratio: In this approach, all the costs that are quantifiable in dollars are considered in the numerator and the risks which are not quantifiable in dollars are placed in the denominator in KWH.

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K. Tinnium et al./Electric Power Systems Research 42 (1997) 21-25

The alternative that has the least Cost/Risk ratio is chosen. We propose a methodology in this paper that identifies the transmission system benefits and establishes a Cost-Benefit ratio in analysing the transmission system and identifying the best alternative.

2. Mathematical development The proposed mathematical formula that encompasses the existing methodologies is given by Eq. (1). Cost Benefit

PTC A+B+C+D+E+F+O

(1)

where PTC is the Project Total Cost A B C D E FO -

Benefits due to Benefits due to Benefits due to Benefits due to Benefits due to Benefits due to Other benefits

Reduced Customer Claims Increased Revenue Reduced Fuel Costs Reduced O&M Costs Reduced Fines Reduced Equipment damage

To obtain an appropriate Cost/Benefit ratio, one needs to qualitatively identify and properly quantify all the above mentioned transmission system benefits. Eq. (1) is applied to each transmission project alternative and projects are ranked in a ranking table according to their Cost/Benefit ratio. The project that is the most beneficial to the electric utility will be placed on the top of the ranking table followed by the less beneficial projects. The next section provides a brief description of the above benefits and illustrates ideas regarding the quantification of the above benefit parameters.

3. Qualitative analysis of benefits In this section we present a listing of benefits associated with the implementation of transmission system improvements (new alternatives). The following are the transmission system benefits that are identified and qualitatively assessed. 3.1. Reduced customer claims

A new alternative will result in improved reliability (less load shedding and forced outages) of the power system and hence customer complaints will be reduced. Addition of a transmission line results in improvement in the mean time to failure (MTTF) which in turn results in reduced customer claims. Improvement of M T T F will be utilized as an index in the quantification of Cost/ Benefit analysis. The ability of a power system to maintain constant frequency and to reduce voltage magnitude fluctuation

is improved by the implementation of the new transmission. These improvements result in reduced customer claims or other additional benefits. This parameter can be quantified by considering the change in expected unserved energy (EUE) and multiplying it with the customer's perceived cost. To appropriately evaluate these benefits, different customer classes needs to be considered at every bus in the system. Investigations of the Customer's perception of the cost of the interruption have shown that figures vary widely from one customer to another but also depend on considerations that are purely subjective. Cost of losses due to interruptions are not always readily deduced from the direct economic consequences of interruptions. There are also indirect effects, which are often difficult to observe, analyze and predict. This is discussed in detail in [9-12]. 3.2. Increased revenue

This can be obtained from evaluating the amount of power that is supplied to another power company due to increased transmission capacity. The increased revenue can be evaluated by treating the neighbouring utilities as new loads. 1. Adding a transmission line to provide better service to existing customers, 2. Adding a transmission line to provide service to new customers. The above cases lead to benefits as reflected by the lost and recovered revenues. Increased Wheeling also plays a major role in assessing the benefits due to increased revenue. This item can be quantified by considering the change in the transmission capability and the power system loadability before and after the implementation of the alternative. This change in transmission capability can then be multiplied by the load factor and the appropriate cost that is associated with the wheeling of power. 3.3. Reduced j h e l costs

The following benefits are all associated with reduced I2R losses and improved utilization of least cost genera-

tion (optimum dispatch). The following two cases arise. 1. For the same output power, the transmission improvement is just to improve the system transmission capability, but serve the same load. In this case the input is dependent upon the I2R losses. Since the transmission improvement results in reduced I2R losses, the system efficiency, and consequently benefits, will increase. 2. If the new alternative results in serving more load than before the implementation of the alternative, it may as well result in more utilization of fuel. However, the benefit in increased revenue will overcome the cost associated with the increased fuel.

K. Tinnium et al./Electric Power Systems Research 42 (1997) 21 25 Improvements in the transmission system reduce the number of times various system equipment has to be maintained, resulting in a reduction in the O&M costs. For example, a transmission system project will result in a reduction in circuit overloads existing in the power system. This in turn results in reduction in the O&M costs of the transmission towers associated with the transmission lines. Reduction in fuel costs can be estimated by performing an economic dispatch and determining the I2R losses before and after the implementation of the alternative. The savings in losses reflects the savings in terms of fuel.

3.4. Reduced equipment damage Addition of transmission lines and transmission improvements will increase the reliability of the transmission network and consequently decrease the expected unserved energy at different load centers. The increase in reliability will affect the following aspects of system behaviour as far as the equipment damage is concerned. Improved stability and security invariable results in a reduction in the equipment damage costs. The benefits due to reduced equipment damage can be probabilistically quantified by determining the reduction in overloads on transmission lines and transformers. The reduction in life of a piece of equipment, for example a transformer, can be evaluated from the reduction in the temperature caused by the reduction in circuit overloads.

3.5. Reduced fines The ability of any new facility to reduce regulatory fines will contribute to the overall system benefit. NRC fines depend on the particular alternative that is to be undertaken. If a new customer arrives in an area to which a particular power company supplies load, the power company is obliged to serve the new customer. If fines can be related to voltage violations due to outages, then the reduction in fines can be modeled from an estimate of the reduction in voltage violations. The resultant reduction in fines can be translated to benefit in terms of dollar benefits.

3.6. Other benefits The other benefits include the benefits due to: reduced fines (BRF), reduced cost of carrying additional generation (BRCG), reduction in environmental impact costs (BRE), reduction in voltage fluctuation cost (BRVF) and reduced restart of generation cost (BRRG). These need to be quantified based on the best practices exercised by electric utilities. Details of the benefits that were discussed in the previous section can be found in [13]. In [14], three transmission projects

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were studied for Central Louisiana Electric Company and were prioritized by using formula (1).

4. Simulation results The methodology for cost-benefit analysis (CBA) discussed earlier was implemented on a 25 bus test system incorporated into TRELSS (transmission reliability evaluation of large scale systems). The input data and the various parameters of the test system are provided in TRELSS and we assume that their accuracy has been verified by EPRI. Two alternatives exhibiting first level generator contingencies are studied. Memory requirements and the computational time required restrict the analysis of multiple contingencies involving more than one generator and one circuit. Case 1. The original IEEE 25 bus RTS. Case 2. The transmission system used in case 1 was modified by the addition of a transmission line between buses 21 and 23. Case 3. A new transmission line is added between buses 16 and 22. The numerical values chosen for most of the parameters are hypothetical and do not represent a real situation. However, to display the usefulness of our methodology, we have chosen some numerical values to allow the evaluation of the ranking table of alternatives according to the proposed CBA. However, a realistic situation is documented in Ref. [13]. The 25 bus system consists of 4l generating units, 11 generator buses, 39 lines and 6 transformers and the contingency analysis is performed for this system. The following tables show the sample output reports obtained from TRELSS for the case studies. Only the benefits due to reduced customer claims are considered in evaluating the cost/benefit ratio.

5. Analysis The benefits due to reduced customer claims are calculated in the following manner, EUE is calculated at a given load point. Multiplying it by the customer interruption cost (or the customer perceived value) evaluated at the average outage duration for that load point and dividing by the average duration gives that load point's contribution to the total cost in dollars per year. ~/i

C= L

L

2 fJ 2 M~Ck(do)

i=lj=l

(2)

k=l

where C is the expected cost due to unserved energy, n is the number of load points under study, Mi is the

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K. Tinnium et al. ,/Electric Power Systems Research 42 (1997) 2 1 - 2 5

Table 1 Reliability load bus summary for Case 1

Table 3 Change in EUE for Alternative # 2

Load bus

EUE (MWh year - I )

Bus No.

AEUE (MWh year 1)

30 40 60 100 150 160 180 190 200

0.008 0.002 0.031 0.092 0.096 8.072 1956.09 17.296 0.105

30 60 100 150 160 180 190 200

-0.029 -0.012 0.016 -0.08 8.072 1130.032 11.096 -0.018

Total

1150.047

Total

1981.29

number of contingencies affecting the ith load point, f j is the frequency of unserved load due to contingency j on the load point i. Mo.k is the kW of load at bus i in the customer class K and L is the number of customer classes. The customer type dependence is reflected by The benefits due to increased revenue, reduced O&M cost, reduced equipment damage costs and reduced fines need to be quantified and used and in the denominator of the cost/benefit formula. The increased revenue is related to the increase in transmission capability, reduced O&M costs and damage costs may be related to a reduction in circuit overloads due to the implementation of an alternative, and reduced fines may be related to the reduction in voltage violations associated with each alternative. Table 1 gives the EUE at each load point in the original IEEE 25 bus system. Tables 2 and 3 give the change in EUE due to implementation of alternatives 1 and 2 respectively. To perform the proposed CBA for the test system, the following alternatives are considered. The base case is the original IEEE 25 bus system. Base Case (Case 1): The original IEEE 25 bus system. Table 2 Change in EUE for Alternative # 1 Bus No.

AEUE (MWh year - I )

20 30 60 100 150 160 180 190 200

-0.001 -0.029 -0.038 0.024 -0.099 4.093 698.733 8.768 0.0029

Tot~

711.48

Alternative 1 (Case 2): The original system is modified by adding a transmission line between buses 21 and 23. The impedance and rating of this line is similar to the line connecting buses 21 and 22 of the test system. Alternative 2 (Case 3): A transmission line is added between buses 16 and 22 of the test system. The data of the line connecting buses 16 and 17 is chosen as the data for the added line. Analysis of Alternative # 1 indicates that the change in EUE equals 711.48 MWh per year. From [15], it is seen that the composite customer perceived cost is $5.26 per kWh. Therefore the benefit in dollars due to a reduction in EUE equals $3 472 384. It may be noted here that a more detailed analysis can be performed by considering the ratio of customer classes at each load bus and multiplying the change in EUE for each customer class by the corresponding customer perceived cost. Analysis of Alternative # 2 indicates that the change in EUE equals 1150.047 MWh per year. Therefore the benefits in dollars due to a reduction in EUE equals $6 049 247. The above analysis indicates that the benefits due to reduced customer claims associated with Alternative # 2 are higher. However, to determine which alternative deserves higher priority, one needs to use Eq. (1), after quantifying the other qualitatively identified transmission system benefits. 6. Conclusions

This paper presents a methodology for prioritizing transmission system alternatives. The methodology is tested on the IEEE 25 bus system and the appropriate results are presented in the paper. The identification of different customer classes and determination of the costs associated with the different system failures is a major concern. This paper has used some generic values; however, a realistic data base that leads to appropriate customer perceived values is currently being compiled.

K. Tinnium et al. //'Electric Power Systems Research 42 (1997) 21-25

C u r r e n t l y we are w o r k i n g on q u a n t i f y i n g the system benefits a s s o c i a t e d with each t r a n s m i s s i o n alternative. These will then be i n t e g r a t e d into a m o r e realistic cost/benefit formula. E n t e r g y ' s t r a n s m i s s i o n system is being a n a l y z e d using m o r e detailed cost/benefit indices.

Acknowledgements T h e Electric P o w e r R e s e a r c h L a b o r a t o r y ( E P R L ) has received the s u p p o r t o f E n t e r g y Services Inc. for the p a s t three years. E n t e r g y ' s s u p p o r t o f the research activities o f E P R L at T u l a n e U n i v e r s i t y in general a n d s u p p o r t for this project in p a r t i c u l a r are greatly a p p r e ciated.

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[4] R. Billinton, Composite system reliability evaluation, Trans. IEEE Power Appar. Syst., 88 (1969) 276 281. [5] R. Billinton, Power System Reliability Evaluation, Gordon and Breach, New York, 1974. [6] O. Alsac and B. Stott, Optimal load flow with steady state security, Proc. IEEE Power Eng. Soc. Summer Meet., July, 1973, pp. 745 751. [7] A. Meliopolous, G.J. Cokkinides and X.Y. Chao, A new probabilistic power flow analysis method, Trans. IEEE Power Syst., 5 (1990) 182 189. [8] B. Borkowska, Probabilistic load flow, Proc. IEEE Power Engineering Soc. Summer Meet., July, 1973, pp. 752-759. [9] R.K. Subramaniam, R. BiUinton and G. Wacker, Factors affecting the development of an industrial customer damage function, Trans, 1EEE Power Appar. Syst., 104 (1985) 3209-3215. [10] G. Wacker, E. Wojczynski and R. Binninton, Interruption costs methodology and results--A Canadian residential survey, Trans. IEEE Power Appar. Syst., 102 (1983) 3385 3391. [11] E. Wojczynski, R. Billinton and G. Wacker, Interruption costs methodology and results--A Canadian commercial and small industrial survey, Trans. IEEE Power Appar. Syst., 103 (1984). [12] E.M. Mackay and L.H. Berk, Costs of Power Interruptions to Industry Survey Results, November 1986, pp. 469-477. [13] P. Rastgoufard, P.F. Duvoisin and K.N. Tinnium, Probabilistic prioritization of transmission system alternatives, Technical Report, Tulane University, July 1993. [14] P. Rastgoufard, P.F. Duvoisin and K.N. Tinnium, Probabilistic prioritization of transmission system projects, Technical Report, Tulane University, February 1994. [15] R. Billinton and R. Allan, Reliability Assessment of Large Electric Power Systems, Kluwer, Dordrecht, 1988.