the use of life cycle cost analysis to determine the most effective cost of installation 500 kv of...

E1.6 9th International Conference on Insulated Power Cables E1.6

Jicable'15 - Versailles 21-25 June, 2015 1/6

The Use of Life Cycle Cost Analysis to Determine the Most Effective Cost of Installation 500 kV of Java-Sumatra Power Interconnection System

Herry NUGRAHA , Zivion SILALAHI ; PLN Indonesia, Bandung Institute of Technology, Indonesia, [email protected], [email protected] Ngapuli SINISUKA ; Bandung Institute of Technology, [email protected] ABSTRACT In order to transfer 3,000 MW capacity of the electricity from the Mine-Mouth Coal-fired Power Plants in South Sumatra to the load center in Java, PLN Indonesia intends to build the Java-Sumatra Power Interconnection System. The scopes of these works of the Power Interconnection System are including: HVAC 500 kV Transmission Line in Java, HVAC 500 kV Transmission Line in Sumatra, HVDC 500 kV Transmission Line in Java, HVDC 500 kV Transmission Line in Sumatra, and HVDC 500 kV Java-Sumatra submarine cables. This paper will analyze the financial feasibility study to ensure if the project has economic benefit, and the asset would be used effectively and efficiently along its benefit period using Life Cycle Cost Analysis (LCCA). In this paper, a LCCA will be simulated to analyze three alternatives and to decide which alternative is the most profitable. Cash Flow and Monte Carlo simulations for a period of 30 years operation of the Interconnection System are part of the LCC models to achieve the objectives of this paper.

KEYWORDS

Life Cycle Cost Analysis; LCCA; Java-Sumatra 500kV DC; Power Transmission Submarine Cables; Monte Carlo.

1. INTRODUCTION

Electricity in Indonesia is currently experienced a rapid development along with the high growth in industry as well as residential demand. The characteristic between one area to another is significantly different. In Java as most populated island, 2000 MW of electric power need to be added to meet the increasing demand. Most of the major power plants are using coal as the energy source. In order to supply this energy, most of the coals are transported from other islands (Sumatera and Kalimantan). These schemes are considered to have many disadvantages, such as the high transportation cost, and also the limitation caused by the fluctuation of weather condition.

Regarding to this issue, the Java-Sumatra HVDC Interconnection System is now under construction in order to transfer power from Mine-Mouth Coal-fired Power Plants at South Sumatra to the load center in Java. The scopes of these works of the Power interconnection system are including: HVDC 500 kV transmission line in Sumatra, and HVDC 500 kV Java-Sumatra submarine cables, HVAC 500 kV transmission line in Java, HVAC 500 kV transmission line in Sumatra, HVDC 500 kV transmission line in Java,. Configuration of this system is provided in figure 1.

In Java-Sumatra transmission (especially in the HVDC sequence), several configuration can be designed regarding to the engineering and economic issues.

Fig.1: Configuration of Java-Sumatra HVDC Interconnection System

In this paper, it will be discussed how to calculate and chose the most effective cost of Java-Sumatra Power Interconnection System. The scopes of these works of the Power Interconnection System during its life cycle (LCC). The objective of the LCC is to choose some alternatives of the most cost effective approach to determine the lowest long term cost of ownership [6].LCC is the total cost of ownership including the cost of the project or asset acquisition, operation & maintenance, and disposal. LCC includes both deterministic costs (such as acquisition costs, yearly maintenance costs and disposal costs) and probabilistic costs (such as the cost of failure, repairs costs, and energy not served (ENS)). Most of the probabilistic costs associated directly with the reliability and maintenance characteristics of the system. Monte Carlo simulation techniques are used to join probability chance for failure, probability of ENS and economic data to solve problems of uncertainty. Failure costs FC are incurred by each year as they fail using a Monte Carlo simulation of failure or success to cover the uncertainty.

2. METHODS

2.1 Life Cycle Cost

The method which will be discussed in this paper includes the scenario of the design decision; parameter of performance; risk calculation; and computation of all associated costs of capital, maintenance and failure costs based on the probability of chance for failure. The method is proposed to analyze failure data using appropriate cost profile in order to represent the fact that each scenario of design and each failure have different prices, in different time periods at an economic cycle. These steps can be described briefly as follows:

1. Specify scope, boundaries, environments and functions.



2. Determine several alternatives of the costs structure. 3. Use Monte Carlo simulation of probability success or

failure of sub-system to calculate Simulated Chance for Failure of the system. Both parallel model and series model chance for failure are explained as follow:

a. Parallel Model The system survives if any one element survives and fails if both elements fail simultaneously. In a parallel system each element must be capable of carrying the full load or else percentage of load capacity.

Mean Time to Failure (MTTF) is calculated using Monte Carlo simulation based on the value of Weibull Shape Factor β and Weibull Characteristic Life η for each sub-system. Time of failure TF is a function of value criterion of failure F(t). The equations to calculated TF and MTTF are:

T� = η �− ln�1 − F�t ��

[1]

MTTF�� = ∑�� !!"�"��#��"$�∑��%��"$�� [2]

Describe decision of the success value as 1 if RAND() > TF else the value of failure as 0. During Monte Carlo simulation calculation, the values of TF and MTTFsystem are always changing in line with random numbers F(t) = RAND () generated by computer.

b. Series Model In a series system, failure of any item causes the system to fail. For system success, all elements of the system

must be successful simultaneously. To calculate Simulated Chance for Failure of series equipment using Monte Carlo simulation can be explained as follow:

1. Describe the value of chance for failure of equipment U1, U2, …, Un.

2. Describe decision equipment En of the success value as 1 if RAND() > Un else the value of failure as 0.

3. Calculate assembly of two series equipment:

If 100% capacity of E1 = 1 and 100% capacity of E2 = 1 than the decision system reliable 100% at 1st simulation S100%,1 = 1.

If c% capacity of E1 = 1 and 100% capacity of E2 = 1 than the decision system reliable c% of capacity at 1st simulation Sc%,1 = 1, or if 100% capacity of E1 = 1 and c% capacity of E2 = 1 than the decision system reliable c% of capacity at 1st simulation Sc%,1 = 1.

If E1 = 0 or E2 = 0 than the decision system unreliable at 1st simulation S0%,1 = 1.

Moreover, the reliability and unreliability can be calculated as follow:

n

SR

n

nx

x

∑= 1

,

[3]

4. Gather cost estimates and cost models, where all the details are assembled. In this step, the result of Simulated Chance for Failure of 500 kV AC and 500 kV DC using Monte Carlo simulation techniques

discussed in step 3 are jointed to the economic data to solve problems of uncertainty. Yearly cost breakdown structure, ENS, Failure Costs (FC), and Net Present Value (NPV) are incurred by each year as they fail to cover the uncertainty. The following are the formulas for calculating costs estimates and NPV:

ENS = SFR x P x ART x LC [4]

FC = SFR x RCF [5]

Where: SFR = Simulated Failure Rate P = Electric Price ($/kWh) ART = Average Repair Time (hours) LC = Load Capacity (MW) RCF = Repair Cost per Failure ($)

∑

=+

=T

tr

Ct

tNPV1

)1( [6]

where: Ct = cost during the t period r = discount rate, and t = number of time periods

5. Present the calculation result to the chart, table or graphic as tools of decision maker, such as: Break-even charts, Pareto charts, Effectiveness, and graphic of sensitivity analysis.

6. Select preferred course of action using LCC to get right decision.

2.2 Effectiveness

Effectiveness of the system can be numerically analyzed using Reliability, Availability, Maintainability, Capability (RAMC) parameter of each alternative. All of these parameters give the critical combination and complex integration of the systems that regard the consequence frequent failure, where high risks of the integrity of installation are encountered.

2.2.1 Reliability

Reliability is the probability that a cable is fulfilling its purpose adequately for the period of time intended. Reliability associated with effort to reduce frequency of failures during the interval of time and measure probability of failure-free operation during the specified time interval. Reliability is expressed as [7]:

&�' = (�)*

+,,-� = (�)./ [7]

2.2.2 Availability

Availability is that aspect of system reliability that takes equipment maintainability into account. Availability in this paper will evaluate the consequences of unsuccessful operation or performance of the submarine cable and the critical requirements necessary to restore operation or performance to design expectations. The latter are including the time needed to have the system routinely maintained. To measure the availability in whole system, the availability factor is being used. Availability factor (AF)is the ratio between the hours of the transmission to be operated in a given period [7].

U1

U2

U1 U2



AF= µ/(µ+λ) [8]

Where µ is mean time to failure (MTTF). Both of MTTR and MTTF value are obtained by Monte Carlo as will be explained in the next section.

2.2.3 Maintainability

Maintainability deals with duration of maintenance outages or how long it takes to achieve (ease and speed) the maintenance actions compared to a datum. The key figure of merit for maintainability is often the mean time to repair (MTTR) and a limit for the maximum repair time (t) [7].The formula is defined as follows:

M=1-exp(-t/λ) [9]

Maximum repair time for the system is usually obtained from general experiences. For the case of submarine cable, this value is determined as 87 days [4]. Based on this formulation, the failure rates and the maintenance scheme will affect the maintainability value of each alternative.

2.2.4 Capability

In electrical power system, capability deals with productive output compared to inherent productive output which is a measure of how well the production activity is performed compared to the datum. Often the term is the synonymous with productivity which is the product of efficiency multiplied by utilization. Efficiency measures the productive work output versus the work input. Utilization is the ratio of time spent on productive efforts to the total time consumed [6]. In this paper, the capability C is defined as probability of power interconnection system which is capable to meet grid requirement. The condition is based on the success probability of each component that configure the system, as showed in figure 2.

Fig. 2: Logic diagram of system’s capability Each of these parameters has a probability based on the operational data as shown in the diagram. Based on the configuration, all parameters are calculated by using following formulas [6]:

P(AND) =p1× p2 [10]

P(OR) = 1−(q1×q2) [11]

Where p is the probability of each component to be failure, and q is the complement of p.

3. GENERATING ALTERNATIVES

3.1 The Data

A number of reliability surveys have been established by CIGRE for HVDC converter stations. The data cover utilization and availability of many HVDC systems around the world. The data also represents mean time before failure (MTBF) and mean time to repair (MTTR) for overall system and converter station The data cover 7.000 km of subsea power cable both HVDC and HVAC technologies. The failure rates are defined by insulation technology, operating voltage level, and internal/external failures for both underground and subsea cables. The utilization of the HVDC systems was 53.4% and 53.3% in 2009 and 2010 respectively. The average availability from CIGRE study was 95.2% and 91.9% in 2009 and 2010 respectively [2].

Failure to subsea power cables are grouped in two categories: external failures and internal failures. Most damage is caused by external violence which can be classified by failures caused by natural causes and human activities. Internal failures are due to joint failures or electrical damage. Natural causes of damage are mainly due to tides and waves and moving materials on the seabed. That causes corrosion and abrasion, respectively. Other natural causes are movement of the sea bottom, tsunami and shark bites. The external violence to subsea power cables is mainly caused by anchors and fishing equipment. Ocean dumping of material and other cables can also be harmful to subsea cables [2].

The total cost for maintenance is estimated at less than 100.000 SEK (or less than 12.000 EUR) per year for each HVDC link. However, subsea cable repair is very expensive. The experience from Svenska Kraftnät shows that a subsea cable repair will cost something between 65-85 MSEK (or 7,5-10 million EUR). Investment cost for HVDC systems is estimated at 1.0 million EUR per km, according to Table 4.4. Repair cost for one failure of a 500 km long cable is then almost 20% of the total investment cost. The average repair time for Swedish cable links is 65 days. Failure rate for large HVDC cable systems are 0,264 failures/year/100 cable kilometers for mechanical faults and 0.0143 failures/year/100 cable kilometers for internal faults. The average time to repair damage is approximately 60 days [2].

3.2 The Alternatives

Three alternatives that are being analyzed in this paper are shown in figure 3. The specification of each alternative is as follow: 1. Alternative 1.

Each of negative and positive paths of the transmission are using a single cable. These cables have a delivery capacity of 3,000 MW. One identical cable are served as a spare in case one of the operating cables undergoes a failure condition.

2. Alternative 2. In this configuration, double cable is used to form positive and negative path of the transmission. Single cable has a capacity of 1,500 MW, to give the total capacity equal to 3,000 MW. One spare cable that has a same capacity (1,500 MW) is provided as a spare.



3. Alternative 3. The configuration is similar to alternatives 2, except that no spare cable is provided.

Fig. 3: Three alternatives installation

4. SIMULATION AND ANALYSIS

Refer to equations and models discussed in chapter 2; alternative generated, data and assumptions discussed in chapter 3; Monte Carlo simulation, LCCA and effectiveness calculation can be explained as follow:

1. In this case study, the scopes, boundaries, environments and functions are Java-Sumatra Power Interconnection System. Figure 1 show the configuration of the system which is explaining the specified scope of alternative 1.

2. In this paper, three alternatives discussed in chapter 3 are alternatives scenario of quantity and type of 500 kV DC Cable as a basis of analysis and calculation and summarized in table 1.

3. Refer to equations and models at step 3 of the methods discussed in chapter 3 and based on scenarios, data and assumptions discussed in chapter 3, Monte Carlo simulation technique and calculation using Microsoft Excel are implemented to get the results of HVAC 500 kV Transmission Line in Sumatra system’s Simulated Reliability as shown in table 2. The next step is compile chance for failure of 2 Converter units, HVDC 500 kV Transmission Line in Sumatra & Java-Sumatra submarine cables and 2 Converter units which has parallel and series combination of the system. Results of Monte Carlo simulations are always different for each trial; however, results from many trials will show an overall direction and trend. Table 3 show the sample of results of alternative 1 that tell us probability success of 100% load, 50% load and failure of the HVDC System Simulated Chance for Failure calculated from probability chance for failure of Sumatra Converter, HVDC 500 kV Cable, and Sumatra Converter for 51,032 number simulation.

Case in alternative 1, when the random number of Sumatra Converter #1 is 0.026086, it means 0.026086 < 0.06, make the items fail become 0 or failure. Moreover, the random number of Sumatra Converter #2 is 0.432784 (> 0.06) � Sumatra Converter #2 is success � Assembly of Sumatra Converter is 50% success.

Then, the random number of HVDC 500 kV Cable #1 is 0.961848 (>0.0174) � HVDC 500 kV Cable #1 is success, also HVDC 500 kV Cable #2 and #3 are success � Assembly of HVDC 500 kV Cable is success.

Also, both of Java Converters are success, so the Assembly of Java Converter is success.

Regarding to three conditions above, the HVDC System is 50% success.

Finally after 51,032 number simulations the total number of HVDC System of success is 39,708 times, so the HVDC System Simulated Chance for Failure calculated by 39,708 divided by 51,032 than the result is 0.7781. Other alternatives are calculated and simulated with similar step.

4. Table 4 show sample of result of gathering cost estimates and cost models where all the details are assembled including: Land Acquisition, Project Cost, Yearly Maintenance Cost, ENS, FC, Disposal cost, and Net Present Value (NPV) alternative 1. In this step, yearly cost calculated and simulated for 40 years but the yearly costs from 2nd to 39th are not shown at table 4 cause of paper space. Other alternatives are calculated and simulated with similar step.

5. Figure 3 shows Break-even chart which is made by calculation result of step 5. This chart tell us picture of cost profile of Java-Sumatra HVDC Interconnection System of each alternative and clearly explain us that LCC of all alternative are built parallel curve without break even.

6. Pareto charts as shown in figure 4 tell us that Project cost are dominant cost contributor to the Java-Sumatra HVDC Interconnection System, and it also tell us that ENS cost and FC as probabilistic cost have contribution to explore hidden cost even it is not significant compare to Project cost.

7. Refer to Break-even Chart and Pareto Chart discussed above, it is indicated that the value failure rates of 0.1114 failures/(year/100 circuit kilometers) or 0.0174 unreliability is only small effect to contribute LCC of cable system of all alternative discussed. Based on the fact founded, sensitivity calculation of unreliability estimated by design (1/38 failure per year), unreliability based on statistic data (0.0174 [2]) and extended to 0.08 versus probability the system to meet maximum load (3,000 MW) is conducted. The result is provided in figure 5.

8. Table 5 shows the result of Effectiveness calculations that measure reliability, availability, maintainability and capability; and also present LCCs all alternative which equal with NPVs of each alternative respectively with condition that it is simulated at assumption the unreliability of the HVDC 500 kV Cable system is 0.08.

9. Consider to the results as discussed at step 5 to step 8, it is reasonable if we choose alternative 1 or 2 as a decided installation with considering to moderate LCC but low risk for long term. Even alternative 3 has lowest LCC, it is advised as a second priority to choose because the probability to meet maximum load will decrease exponentially related to unreliability of the HVDC 500 kV Cable system.

10. In case of cable installation system, the decision is made by choosing the highest value of probability to meet maximum load and effectiveness. Figure 5 and table 5 tell us that alternative 1 and 2 which has spare can be considered as the best to be applied rather than without spare.



Table 1: Project cost estimation

Table 2: Simulation result of system effectiveness

Table 3: Sample of results of probability success alternative 1

Table 4: Sample LCC calculation result

Fig.3: Break-even Chart of Java-Sumatra HVDC

Interconnection System

Fig.4: Pareto Chart of Java-Sumatra HVDC

Interconnection System

1 2 3

1 Land Acquisition 70.00 100.00 90.00

2 Project Cost

a. AC/DC Converter Station (Sumatra Side) 500.00 490.00 480.00

b. Converter Station, Electrode Station, Landing Point & Submarine Cable Switching Station (Jawa)

500.00 490.00 480.00

c. 500 kV DC Submarine Cable (40 km) 400.00 410.00 390.00

d. 500 kV DC Overhead T/L Sumatra (354 km) 220.00 230.00 215.00

e. 500 kV DC Overhead T/L Jawa (110 km) 75.00 90.00 80.00

f. 500 kV AC Transmission Line 200.00 200.00 200.00

3 Disposal 50.00 70.00 60.00

4 Discont Rate 12% 12% 12%

No Cost DescriptionAlternative

HVDC System 3 Cables Simulations # (n): 51032

Item FailsSumatra

ConverterSubmarin

e CableJava

ConverterHVDC

System

Σ HVDC

System

HVDC System

Simulated Chance

For Failure

0=Failure Failure Failure Failure Failure Failure Failure1=Success 50% 50% 50% 50% 50% 50%

Success Success SuccessSucces

sSuccess Success

1 Sumatra Converter #1 0.06 0.026086 0 02 Sumatra Converter #2 0.06 0.432784 1 1

01 HVDC 500 kV Cable #1 0.0174 0.961848 1 0 0 385 0.0075 2 HVDC 500 kV Cable #2 0.0174 0.182256 1 0 1 10939 0.2144 3 HVDC 500 kV Cable #3 0.0174 0.360583 1 1 0 39708 0.7781

1 Java Converter #1 0.06 0.541774 1 02 Java Converter #2 0.06 0.397868 1 0

1

No Component

Item Chance

For Failure

Random #

Alternative 1

0 1 40

1 Land Acquisition 70.00

2 Project Cost

a. Converter Station, Electrode Station, Landing Point & Submarine Cable Switching Station (Sumatra)

500.00

b. Converter Station, Electrode Station, Landing Point & Submarine Cable Switching Station (Jawa)

500.00

c. 500 kV DC Submarine Cable (40 km) 400.00

d. 500 kV DC Overhead T/L Sumatra (354 km) 220.00

e. 500 kV DC Overhead T/L Jawa (110 km) 75.00

f. 500 kV AC Transmission Line 200.00

3 Yearly Maintenance 0.015 0.015

4 Energy not served 0.029390 0.06 1,368 7.24 7.24

5 Failure 0.071152 10 0.712 1

6 Disposal 50

Total 1,965.00 7.96 58.0

Discount Rate = i 0.12 12%

Future Value = FV 1,965.00 7.96 57.96

Discount Factor = (1+i)n 1.12 93.05

Present Value = FV/(1+i)n 1,965.00 7.11 0.62

NPV = Σ (FV/(1+i)n) 2,031.19

Annual Cost (Millions)Electric

Price

($/kWh)

No Cost Description

CFPP

Simulated

Chance

For Failure

Repair Cost

/Failure

($Millions/

Failure)

Average

Repair

Time

(hours)

1,500

1,600

1,700

1,800

1,900

2,000

2,100

2,200

0 5 10 15 20 25 30 35 40

Co

st (

Mil

lio

ns)

Year

Life Cycle Cost of

500 kV DC of Java-Sumatra Power Interconnection System

Break-even Chart

Alt. 1

Alt. 2

Alt. 3

$0.00 $500.00 $1,000.00 $1,500.00 $2,000.00

Alt. 1

Alt. 2

Alt. 3

Alt. 1

Alt. 2

Alt. 3

Alt. 1

Alt. 2

Alt. 3

Alt. 1

Alt. 2

Alt. 3

Alt. 1

Alt. 2

Alt. 3

Alt. 1

Alt. 2

Alt. 3

Lan

d A

cqu

isit

ion

Pro

ject

Co

st

Ye

arl

y

Ma

inte

na

nce

En

erg

y n

ot

serv

ed

Failu

reD

isp

osa

l



Fig.5: Sensitivity Chart

Table 5: Simulation result of system effectiveness

5. CONCLUSION

Based on the data, formulas, scenarios, calculation, simulation of Installation 500 kV of Java-Sumatra Power Interconnection System using combination technique of LCCA, effectiveness and Monte Carlo, it has demonstrated strong correlation among project cost, failure, maintenance and risk of ENS with financial benefit and also the risk. It is shown that HVDC installation especially submarine cable need high cost for project capital (1.0 million EUR per km) but has very low probability failure during operation (0.1114 failures/ (year/100 circuit kilometers)). LCC profile of Java-Sumatra HVDC Interconnection System of each alternative and clearly explain us that LCC of all alternative are built parallel curve without break even, it can be concluded that focus on high quality installation during construction is more importance than focus on maintenance.

Sensitivity chart for Probability 500 kV DC to Meet Maximum Load (3,000 MW) tell us the correlation between failure rate, reliability and the design of quantity of cable (with or without spare) and it can be concluded that cable installation with spare is more low risk.

The application of Monte Carlo simulation gives a great advantage in handling dependancy of many parameters and sub-system, but in case of submarine cable it is needed more and more data statistics collected for more accurate of the evaluation.

ACKNOWLEDGEMENTS

This paper is part of a research study funded by PLN Indonesia.

REFERENCES

[1] H. Nugraha; N. I. Sinisuka, 2013, “The Application of RAMS to analyze Life Cycle Cost on the Operation of Power Generation”. Safety, Reliability and Risk Analysis: Beyond the Horizon – Steenbergen et al. (Eds) © 2014 Taylor & Francis Group, London, ISBN 978-1-138-00123-7

[2] S.H. Karlsdóttir, 2013, Experience in Transporting Energy through Subsea Power Cables: The case of Iceland, University of Iceland, Reykjavic, Iceland

[3] N. Sinisuka; I. Felani; N.Erdiansyah, 2012, “The Use of Life Cycle Cost Analysis to Determine the Most Effective Cost of Installation High Voltage Undersea Cable Bali Strait”, Journal of Energy and Power Engineering 6,IJEPE,2082-2089

[4] R.F. Stapelberg,2009. Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design. Springer-Verlag, London, England

[5] D. Sudarmadi, G. C. Paap, L. v.d. Sluis, 2007, Review of steady state analysis of HVDC Interconnection of Java-Sumatera, Proceedings of the International Conference on Electrical Engineering and Informatics Institut Teknologi Bandung, Indonesia.

[6] Barringer, H. P. 2003. A Life Cycle Cost Summary, International Conference of Maintenance Societies (ICOMS-2003), Maintenance Engineering Society of Australia, A Technical of the Institution of Engineers, Australia

[7] P. Barringer, 1997, Availability, Reliability, Maintainability, and Capability, Barringer & Associates, Inc., Texas, USA

[8] M. Nakamura; N. Nanayakkara; H. Hatazaki; K. Tsuji, 1992, "Reliability Analysis of Submarine Power Cables and Determination of External Mechanical Protection", Transactions on Power Delivery, IEEE, vol.7, 895-902

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

0.0041 0.0117 0.0174 0.0312 0.0625 0.0800

Pro

ba

bil

ity

Unreliability of 500 kv DC Cable

Sensitifity Chart for Probability 500 kV DC

to Meet Maximum Load (3000 MW)

Alt. 1

Alt. 2

Alt. 3

1 2 3

Reliability R Simulated 98.88% 98.80% 98.82%

Availability A Simulated 93.32% 93.32% 93.34%

Maintainability M Simulated 99.10% 98.99% 99.04%

Capability C Simulated 75.02% 72.36% 54.33%

Effectiveness Eff. R x A x M x C 68.60% 66.04% 49.63%

LCC LCC = NPV 2,031.19$ 2,075.53$ 2,000.11$

Parameter Symbol FormulaAlternative

the use of life cycle cost analysis to determine the most effective cost of installation 500 kv of...

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