1. Review of Electricity Analysis Class

2. Some of the Subjects Addressed in the Class
Overview of electricity value drivers and LCOE with example of how to evaluate wind power at off-shore platforms
How can we evaluate the amount of oil production and other strategies for electricity by simulating short term marginal cost
How can you measure the value of oil plants in a merchant plant environment through measuring profits that are earned from historic merchant prices
What are the costs of oil plants compared to other plants at different capacity factors in screening analysis
How can you evaluate the cost of different electricity strategies for off- shore platforms that accounts for outage costs.
How much oil, gas, hydro and other units would be built in an optimal system.

3. Sources of Data – USB Drive with Materials

4. Load Factor, Capacity Factor, Availability Factor
Average Demand/Peak Demand
Annual Energy/8760/Peak Demand
Capacity Factor for Plant
Average Generation/Possible Generation
Annual Generation/8760/Capacity
Availability Factor
Hours Available/Total Hours

5. Example of Cost and Benefit of Wind on Oil Platform using LCOE and Variable Operating Cost

6. Using LCOE to Evaluate Value of Wind at Off-Shore Platform
Demonstrate that you can use LCOE to evaluate the cost and benefit of putting wind farm at off-shore wind platform

7. Key Conclusions of LCOE Analysis
It is easy to compute LCOE yourself if you have the cost/kW, the capacity factor, the O&M and the carrying charge rate.
For issues like computing the cost and benefits of wind at platforms, the fact that renewable energy is intermittent must be accounted for.
For an oil platform you cannot compare the total LCOE of wind with oil because of this issue.
You must compare:
Rule: Compare LCOE of wind including capital cost with only the variable cost of oil not including capital cost.
This is because you still need the oil plant as back-up when the wind is not blowing

8. Analysis of Wind Value on Off-Shore Platform
Compute Cost of Electricity from Wind versus Cost from Electricity Plant on Platform
Concept of LCOE – Levelised Cost of Electricity can be used
To Compute LCOE for Wind or Solar or Hydro, you need
Cost/kW
Fixed O&M cost/kW-year (FOM)
Capacity Factor
Carrying Charge Factor
LCOE (USD/MWH) =
(Cost/kW x CCR + Fixed O&M)/(8760 x CF)
The carrying charge is computed later and includes effect of cost of capital, taxes plant life and other factors.

9. LCOE of Thermal
To compute the LCOE of thermal you need to add the variable cost. The variable cost include the fuel cost and the O&M.
Fuel cost can be compute with the heat rate as follows
Fuel cost/MWH = HR x Fuel Cost/MMBTU
HR = MMBTU/MWH = kBTU/kWh= 1000 x BTU/kWh
It is normal to see BTU/kWh for Thermal
MMBTU/MWH = Normal HR (BTU/kWh) x 1000
Variable O&M/MWH can be found from other sources
So, LCOE for Thermal
LCOE = (Cap cost/kW x CCR + FOM)/(8760 x CF) +
Fuel/MWH + Var O&M/MWH
CCR is discussed later

10. Converting Heat Rate to Efficiency and Vice Versa
You can convert heat rate to efficiency using the following conversion factor.
3412 BTU/kWh or 3412 kbtu/mwh or mmbtu/mwh
Eg. NGCC heat rate is 6,400 btu/kwh. This is input/output.
This is 6.4 mmbtu/mwh
If you want efficiency you need output/input or mWh/BTU
To get efficiency you can multiply x to get MWH out/MWH in
This means that the efficiency is 3.412/heat rate = 3.412/6.4 = 53.3%

11. Lazard Study – Benchmarks for Electricity Cost Factors

12. IEA Study of Real Plants

13. Example with Excel
In this example the LCOE for Wind is lower than the LCOE for Plant on the oil platform.
Oil cost is 71/MWH and Wind cost is only 33/MWH

14. LCOE is not a Good way to Make Comparison of Intermittent Plants with Dispatchable Plants
The problem with wind is that it is not always windy and the capacity factor is below 100%. In the case of the off-shore platform, you still need electricity for the platform when it is not windy.
This means that you still need a dispatchable plant for when the wind is not blowing and you still have to pay for the fixed costs of the dispatchable plant.
The implication of this is that you should compare the total cost of wind including the capital cost with only the variable cost of thermal (you still need the fixed costs).
This kind of analysis can be extended from the oil platform to other types of systems including large integrated electricity systems

15. Example of Comparing the cost Wind with only variable cost
You still need the fixed cost of the thermal plant for when the Wind does not blow. But the Wind can be compared to only the variable cost.

16. Wind Depends a lot on CCR and Capacity Factor
A case with lower capacity factor and high CCR. In the case below the Wind is not economic because LCOE is more than variable cost of oil operation.

17. Note on Colouring
You can make the colour with a file named generic macros and then press CNTL, ALT, C

18. Example of Measuring Oil Use with Short-run Marginal Cost Analysis

19. Issues that can be addressed with SRMC
This section moves to evaluating electricity costs with marginal cost. The marginal cost analysis is central to evaluating many issues that include, for example:
What is the value of new NGCC in a system and how does the new NGCC affect costs to consumers
What is the effect of a low hydro year on the amount of oil generation
What is the effect or removing a nuclear plant from service and replacing the plant with renewable energy or thermal plants
What is the effect of new wind or solar generation on the cost of electricity to consumers

20. Illustration of Different Supply Curves – Economics of Strategies are Different with Different Supply Curves
A key idea of this section is that the economics of different strategies depend importantly on the shape of the supply curve.
For example, the economics of nuclear power is much higher if the gas price is high. Alternative supply curve shapes are illustrated below. 
With the steep supply curve, small changes in capacity and in demand and in other factors have a big effect on the marginal and total cost of electricity. 
In the case with flat supply curves all of these factors have a minor effect.

21. Illustration of Different Supply Curves
Three different supply curves with different mixes of capacity, different gas prices, different heat rates and other factors are illustrated below.

22. Difficulty of Using Short-term Marginal Cost to Predict Oil Production
Oil depends on the operation of other plants on a system and it is one of the last plants to dispatch.
Examples
More hydro, less oil dispatch
Hydro peak shaving reduces oil dispatch compared to run of river
Wind generation reduces oil generation, but the wind generation must occur in high load hours
Changes in the load shape affect how much oil is produced and changes in the load shape affect oil production
Capacities of other thermal plants affect the amount of electricity production of oil
Plant outages and reliability of other plants affect the amount of oil production
If you can get data, you can make an hour by hour analysis
Data on capacity, hourly load, Wind, hourly hydro is available in many countries by going to ISO website.
BUT NOT IN BRAZIL, it seems very difficult to get the good data

23. Setting-up Marginal Cost Analysis
Required Data
Hourly Loads
Plant by Plant Capacity, Heat Rates, Fuel Costs, Variable O&M
Wind, Hydro and Solar Production by Hour
Outage Rates
Steps to Computing Hour by Hour Production
Create Sheet for Single Hour with Ranking of plants
Accumulate the Capacity
Relate Net Demand to Accumulated Capacity
Compute Total Cost

24. Example of Thermal Supply Inputs
The screenshot demonstrates the inputs the you should input to establish the supply curve. You need heat rates, capacity and fuel prices

25. Step by Step Analysis for Computing Supply Curve
Once you get the data, you can compute a supply curve with the following steps:
Step 1: Sort the Data by Cost and find a match key
Step 2: Accumulate the Capacity
Step 3: Find the marginal unit with the MATCH function
Step 4: Use the Index Command to Find the Price of the Marginal Unit
Step 5: Use TRUE and FALSE switch to Find Unit which is Dispatched and Unit on the Margin
Step 6: Compute the total generation cost using the switches
Step 7: Construct Counter by 2 to Create Step Graph
Step 8: Add the Demand to the Graph

26. Basic Steps for Supply Curve
Step by Step Instructions for Basic Supply and Demand
1. Sort the plants according to their cost and accumulate the total capacity
2. Use the small command on the marginal cost of each plant
3. The small command creates a sort key
4. Use the INDEX command with the sort key to compute the sorted capacity
5. Accumulate the sorted capacity

27. Technical Details of Creating Supply Stack
Match the demand and the supply
1. You can match the input demand with the accumulated capacity to find the marginal price
2. You must adjust this because the match command gives the last plant not the next plant
3. You must also adjust through reducing the demand by an increment so if the demand matches an increment of supply the marginal cost will be the exact number
4. Once you have matched the demand with the supply, use the INDEX command to find the price -- the index command is used with the COST

28. Calculation of Supply Stack
With the inputs you can compute the supply stack including the fully dispatched plants and the partially dispatched plants.

29. Pricing at Marginal Cost versus Average Cost
Forecasting oil generation depends on everything else

30. Note on Saudi Supply Curve
You may think the supply curve for Saudi is very flat because of low natural gas prices and oil prices that are used in PPA agreements.
But it is essential to use the opportunity cost of gas and oil.
If the gas was not used in plants, could it be sold to somebody else in the world with LNG
Or, would the gas just be left in the ground that implies a shadow price which reflects the price that future natural gas could be sold at.

31. Problems with Finding Inputs for Brazil
Given the difficulty in computing oil production because of finding all of the inputs, it may be advisable to make a different forecast of production.
An alternative would be to do the following:
Use last period production
Remove changes from wind production
Add changes from increased demand
Evaluate the possible changes in hydro and their effect on oil production
You can make a simple equation
Oil production t = Oil Production t-1 +/- changes in wind +/- other

32. Problem with Forecasting Oil production from Hourly Analysis
Oil is at the end of the supply stack
This means the rest of the supply stack must be accurate to make a forecast
The items that must be correct include
Hydro generation
Outages of other plants
Capacity of Wind
Demand Changes
Before trying this, you should see if you can simulate a historic year

33. Technical Details of Computing Supply Stack
Adjustments for plants with the same cost
1. Make an additional column for adjusted costs
2. The adjusted costs are the input costs plus a very small random number (RAND() x )
3. Use the SMALL command with the adjusted costs rather than the input costs

34. Creating a Step Function on the Graph
Graphing the Supply and Demand
1. To graph the supply curve, set up columns as usual with the x-axis (the accumulated capacity) in the first column and the y-axis (the sorted cost) in the second column
2. Put a title on the y-axis so that when excel uses the F11 key, it will know what to do.
3. Press the F11 key and then modify the chart type to and X/Y chart
4. To add the demand to the chart, make a column for the demand that has a constant number
5. Modify the chart and use the demand as the x-axis and the sorted cost as the y-axis

35. Technical Details of Creating Supply and Demand Graph
Compute the generation and the total cost
1. Computing the total generation is a little tricky because the plant that is on the margin does not produce its full output
2. To differentiate between plants that are on the margin and those operating at full capacity, you can create two switches
3. The full dispatch switch is a TRUE/FALSE switch that is TRUE when the plant number is less than MATCH for the dispatch unit computed above
4. The marginal dispatch switch is a TRUE/FALSE switch that is TRUE when the unit number equals the MATCH for the marginal dispatched unit
5. The total generation is dispatch switch multiplied by the capacity plus the marginal dispatch switch multiplied by the difference between the total load and the prior accumulated capacity.

36. Advanced Issues – Incorporating Heat Rate Curve
To incorporate marginal heat rates you can divide plants into separate parts or blocks.
The cost of running a plant is less at full load because the plant is more efficient.
The real marginal cost depends on which block of the plant is running.
You can make a bigger portfolio of plants where you still sort plants, but you sort the plants on a block by block basis.

37. Compensation from Marginal and Average Heat Rate Instead of Average Heat Rate
Efficient dispatch should reflect the marginal heat rate:
Measures the additional fuel used when additional energy is produced
Plants should be dispatched on a portfolio basis after they are committed
Plant with lowest marginal heat rate should be dispatched first
Compensation should be on the basis of average heat rates
The average heat rate measures the total fuel used relative to the total energy produced
If compensation is based on the marginal heat rate, added revenues should be collected through the capacity payment

38. Representing Thermal Plants with a Curve for Average Heat Rates
An equation for the average heat rate at different levels of capacity is demonstrated below. The screenshot demonstrates how an average heat rate can be represented by an equation with a constant, a slope and a square factor.Test

39. Computation of Incremental and Average Heat Rate

40. Example of Heat Rate Curves
If the plant is dispatched at different levels, the incremental heat rate should change. To compute the marginal heat rate curve, you can split the plant up and compute the average heat rate that declines. Then, for each block level you can compute the MMBTU input and the MWH output. The incremental heat rate is the change in MMBTU divided by the change in output for different levels of plant operation.

41. Supply Curve with Incremental Heat Rates
The supply curve with incremental heat rates looks a lot like the supply curve discussed to this point. To model incremental heat rates, you must assume that a plant is on or off. This is why there is a day ahead analysis as well as an hour by hour analysis.

42. Demand Response when Capacity is Near Demand
One of the things that is not done by the supply curve so far is to determine what happens when there is a high level of demand relative to supply. It may be the case that you can reduce demand for a certain price through interruptible rates or demand response mechanisms or with smart meters. The idea of finding more and more load at higher prices is illustrated below.

43. Advanced Issues – Demand Elasticity
To perform the calculations of demand elasticity you can use the following equations that are based on the elasticity.
Elasticity = Ln(Q/Qo)/Ln(P/Po)
Demand = Base Demand - Elasticity x Qo
Ln(Demand) = Base Demand - Elasticity x Qo
Ln(Demand) = Base Demand + Ln(P/P0) * Elasticity * LN(Base)
Demand = EXP((Ln(P/P0) * Elasticity) * Prior Q
Ln(P/Po) x Elasticity = Ln(Q/Qo)
EXP (Ln(P/Po) x Elasticity) = Q/Qo
EXP (Ln(P/Po) x Elasticity) x Qo = Q

44. Incorporating Demand Elasticity in the Supply and Demand Analysis
The manner in which demand elasticity can be included in the analysis is demonstrated below.

45. Simulation of Demand and Supply over Many Hours

46. Demand Analysis and Hour by Hour Forecast
Once you have the supply stack build with the marginal cost and the total cost for a single hour, you can repeat the process for many hours.
To extend the analysis to multiple hours, you can use a data table.
A data table takes a variable output like the total cost for an hour and can repeat the calculation as many times as you want.
In this case, you want to repeat the calculation of marginal cost and total cost many times for different amounts of load.
A data table must be structured in a particular manner where the output such as the total cost or the marginal cost must be put in one place and the load such as on a row. The load then must be in a column.

47. Demonstration of Technical Aspects of Making a Data Table to Simulate Hour by Hour
The illustration below demonstrates how you can make a datatable that simulates costs on an hour by hour basis using a data table. The number on the top and the right is from the supply curve analysis. The demand is the Column Input in the data table.

48. Example of Load Data (Need for Brazil)

49. Technical Note
You can use INDEX and Developer Tab to make dropdown box to select loads

50. More Efficient Hour by Hour Cost with VBA
Data tables have a number of problems for simulation. Instead of using the data tables you create VBA code. The VBA code avoids the necessity to put the data table in a single sheet and it can be used to make the tables more flexible. The code below is an illustration of how to create the VBA.

51. Adjustments for Solar, Wind and Hydro

52. Adjusting Demand for Renewable Energy
In working through the details of an hour by hour production simulation, you need the amount of the load and also the hour by hour amount of the load reduction caused by solar, wind and hydro.
For solar, you can get the solar patterns of the day from websites and then adjust for the amount of the capacity
For wind, you can do something similar, but the analysis is more complex because of power curves
For hydro, the analysis depends if the hydro is run of the river or storage hydro. This is explained below.

53. Evaluating the Costs and Benefits of Renewable Energy
If you want to measure how much solar, wind or hydro power will save for people in the country, you can do the following:
First, allocate the amount of solar, wind or hydro power to each hour using weather data as explained below.
Second, incorporate the renewable energy as a reduction in demand so the thermal will dispatch against the net demand and not the gross demand as illustrated on the charts of supply and demand below.
Third, add up the cost for each hour with and without different renewable strategies. When you add up the cost with a lot of solar, and the cost with not much solar, you can see the effect on costs.
Fourth, compare the cost savings from solar with the fixed cost of solar where the fixed cost of solar includes the capital cost (cost/kW x CCR) and the fixed O&M cost – Cost/kW-year.

54. Computing Net Demand with Renewables
The screenshot below illustrates how you can incorporate renewables into the hour by hour cost analysis. You need the pattern of solar, wind or hydro power. You can start with the general patter in different hours and different seasons and then convert the data to percentages. The percentages can then be multiplied by the renewable capacity.

55. Production and Price depend on the shape of the supply curve and the level of demand net of wind, solar and hydro
You can illustrate production issues in a single hour with a supply and demand graph. In this case there is a relatively small amount of renewable energy.

56. Supply and Demand with More Renewable
The graph below illustrates a case where capacity is increased and the same shapes are applied. In this case the marginal declines as the net demand pushes down.

57. Mechanics of Net Demand
When working through demand, the hour by hour solar, wind and hydro should be subtracted from the load to see how much is left for the thermal load.

58. Renewable and German Merchant Price Example
The effect of renewables is demonstrated on the graph below of German electricity and natural prices. Note the margin between electricity and gas has turned around after renewable capacity has entered the market.

59. Solar Power Patterns
Solar power patterns are predictable and stable. The month by month solar for a project is illustrated below.

60. Year by Year Variation in Solar with EU website
Compute the P90 level from standard deviation and average using NORMINV

61. Solar Capacity for a Day from EU Website
Solar Variation in Different Hours
Need to Ramp up the Diesel Plant when the clouds come

62. Weekly Solar Irradiation

63. On-shore Wind Speed – Look up World Wind Map in Google

64. Wind Speed and Electricity Price
The scatter chart shows some relationship but not strong

65. Wind Capacity Factor

66. Hydro Resource Assessment
The amount of power depends on flow and head as shown on the adjacent diagram:
Power (kW)=
Flow Rate (m/s)
x Head (m)
x Gravitational Constant (9.8 m/sec^2)
x Efficiency

67. Residual Flow
9 September 2011 67

68. Example of Variation in Hydro Capacity Factor – Applies to Wind, Solar and Tidal
Finding Data on DVD and downloading directly to excel using
WORKBOOKS.OPEN

69. Variability in Hydro and Thermal Generation – Georgia Example

70. Hydro Reservoir
The graph shows how you can use a peak shaving method to compute the amount of hydro. This demonstrates that the peaking capacity is allocated to peak hours and the remaining peak is flatter.

71. Using Set-Point to Compute Peak Shaving
The screenshot below illustrates how you can use the MIN and MAX and a set point to compute the total energy when you are peak shaving.

72. Valuation of Plants in Merchant Markets

73. Implication for Brazil Oil Production Analysis - 1
If you want to see the value of oil plants without trying to simulate every hour in the future, you could do the following:
First, find a database of merchant power prices. For most markets as shown below you can get the historic data.
Second, make an assumption for the heat rate, the variable operating and maintenance cost
Third, find the oil price. If you have USD/BBL you can convert it to USD/MMBTU if you divide by 5.8 (you can see the convert spreadsheet)
Fourth, compute the total variable cost per MWH as the oil price per MMBTU x Heat Rate + Variable Cost
Fifth, Compute the Margin for every single hour with the formula MAX(price – variable cost,0). Note that you could add a capacity price if there is a capacity price in the market.

74. Valuing Plant from Merchant Markets Continued
Once you have the margin per hour (which cannot be negative because of the option to not dispatch), add the margin for the entire year (use the SUMIF as explained below).
When you add the margins for every hour, you get the value per MW per year instead of the value per MWH.
After you compute the value per MW-year you can divide the number by 1000 to get the value per kW-year.
Finally, compare the value per kW-year to the fixed cost. The fixed costs are discussed in the LCOE section. Fixed cost is typically stated in money (e.g. USD) per kW-year. It includes capital cost as USD/kW x CCR and O&M per kw-year.

75. Valuing Plants from Merchant Markets Continued
If the amount or the margin in USD/kw-year from merchant markets (including capacity price) exceeds the fixed cost (O&M and capital) you should theoretically build new plants. For example if the Oil margin + capacity charges is more than the oil cost, then build new plants.
If the margin you make from markets is less than the fixed O&M on an existing plant, then you should theoretically retire plants.

76. Valuation of Plants from Merchant Analysis
Get database on hour by hour prices
For different plants, compute the margin from the price less the fuel cost
Use heat rates from plant characteristics and current fuel costs
Accumulate the margin for different plants to compute value per kW- year
Compare the value per kW-year with the capital and fixed operating cost per kW-year

77. Volatility in Energy Value for NGCC – PJM Market

78. Example of Computing Plant Value in Merchant Market
The example below illustrates how to compute the value of merchant plants in a merchant market. Alternative heat rates can be input and you can see what the value of the plant is on an annual basis. The key is understanding that you can evaluate capital costs and fixed O&M costs (e.g. USD/kW-year)

79. Simulation of Merchant Prices with Bidding Game
When a lot of demand, bid at the next highest cost
When the demand is very high, markets can fall apart
Solutions to the problem:
Cap prices
Make Capacity Markets
But Capacity Markets are Artificial
California Crisis Discussion
Start with low hydro
Remove capacity with outages
Limited demand response
Transmission and game playing
Market power and manipulation of gas and electricity prices

81. California Supply and Demand During a Typical Day – A lot of Reserve

82. California: No Dramatic Increase in Demand Trends in Electricity Demand

83. Electricity Usage in California

84. Actual Costs of Wholesale Power
Total Cost $/Billion
Average Cost ¢/Billions
ISO Control Area, ISO Department of Market Analysis
$40 BILLION MORE !!

85. Monthly Electricity and Gas Prices – In General you Cannot Evaluate Electricity Prices without Evaluating Gas Prices

86. Price History
California Crisis with Very High Prices that Lasted a Long Time

87. Electricity Prices Relative to Natural Gas Prices
The California crisis can be demonstrated by the implied heat rate.
Electricity price USD/MWH divided by gas price USD/MMBTU gives you MMBTU/MWH

88. Similar Problems in New Zealand

89. Comments on Risks Associated with Surplus Supply
A destructive consequence of operating in a fragmented industry with low barriers to entry is a susceptibility to “book-bust” cycles, not unlike mining, chemical, and pulp and paper industries.
The lumpiness with which new generation enters the market and its longevity may threaten extended time frames at the bottom of the merchant business cycle.
As merchant power industry appears to be reaching the end of a build-out period, energy merchants will likely have to confront surplus reserve margins for years to come.

90. UK Oversupply in Merchant Market – Caused many Bankruptcies

91. Simulation of Market Prices with Bid Data
You can find bid data in some markets (after the fact). Then you can use the bids instead of cost to create a supply curve.

92. Supply and Demand from Bids Instead of Cost
The simulated supply and demand in the PJM market is illustrated on the graph below. It applies the same principles as the supply curve based on cost.

93. Screening Analysis

94. General Notion of Screening Analysis
For thermal plants the economics of a plant depends on the fixed and variable cost.
With varying net loads (i.e. loads after hydro), the optimal plant in a system depends on how much you need to run it.
For plants with a high capital cost, you still have to pay for the plants no matter how much they run. So if you only need to run the plants for a small part of the year (a peaking plant), it is not worth paying the high fixed costs that must be allocated to a few hours.
For base load plants where you run them a lot, you care more about variable cost.

95. Implications of Screening Analysis for Brazil Oil Analysis
You can use the screening and load duration curve analysis to evaluate the amount of oil that is optimal to have in a system.
With hydro that has a reservoir, the shape of the load duration curve will change and cut-off the top as illustrated below.
You can use this to evaluate future needs for oil plants compared to other plants.

96. Basic Notion of Screening Analysis – Compare Fixed and Variable Cost for Different Capacity Factors
The graph below demonstrates screening analysis where you can change the carrying charge rate and the gas price which are very big drivers in the analysis. The y-axis is the cost per MWH and the X-axis is the capacity factor.

97. Carrying Charge Rates

98. Basics of Carrying Charge Rate
Carrying Charge Rates Depend on the IRR required on the project and the life of the project.
You can demonstrate this with the PMT function or a goal seek function.
More detailed issues include:
Inflation
Debt and Equity
Taxes
Construction Period
Decommissioning
You can use the carrying charge rate to determine the real price that will produce a given IRR. O&M costs and Fuel costs in current currency can then be added to the capital cost recovery.

99. Location of Carrying Charge File
The file with the carrying charge calculator can be found in Chapter 5 of the USB drive as illustrated below.

100. File to Compute Carrying Charge Rate
The carrying charge file can be used to evaluate carrying charges given various assumptions. Some of the assumptions and the outputs are shown below.

101. Proof of Carrying Charge Calculator
The lower section of the sheet demonstrates that the equity IRR target which you entered is the same as the result of a project finance model.

102. Long-run Marginal Cost

103. Peaker Method
Assume that peaker cost should be allocated on the basis of demand, then compute the surplus cost over and above a peaking plant for each type of plant.
The peaking cost is allocated on the basis of demand
The surplus cost above the cost of a peaking plant is allocated on the basis of energy
Difficult to find the cost of peaking plants for older plants
Related Method: On-peak and off-Peak Method for allocating energy costs

104. Step by Step Method for Evaluating Optimal Capacity and Long-run Marginal Cost
Step 1: Create a load duration curve where you sort from the lowest value to the highest value (note that this is the opposite of a typical load duration curve).
Step 2: Compute the overall capacity factor as the percent of time for each hour.  This is a simple calculation where you count the hours and divide by For example, the second hour when you sort from low to high is 8759/8760 or more than 99%.  A plant operating in this increment of load would have a capacity factor of more than 99%.
Step 3: Once you have the capacity factor for each increment, use the lookup function to find the plant number that matches the capacity factor from the screening analysis.  The screening analysis is discussed below and produces a list of plants that are optimal to run for different capacity factors.
Step 4: Transpose the plants from the screening analysis to the load duration curve and put the code number for each plant at the top.  Then make a switch for whether the plant is the incremental plant running.  This switch is used by comparing the code number from step 3 above to the code number at the top of the page.
Step 5: For each load value (e.g. 8760), compute the increment of the load and the accumulated percent of time at the particular load.  For the minimum load or the first load value, the increment is the load itself.  For subsequent higher loads, the incremental load is the load of the row you are on minus the previous load.
Step 6: Compute the accumulated generation for each plant type.  When the switch is true the generation is accumulated.  When the switch is not true the accumulation stops.
Step 7: Compute the marginal cost per hour.  To do this you can use the lookup function again, but this time lookup against the variable cost from the screening analysis.

105. Backwards Load Duration and Optimal Capacity
The graph can also be used to evaluate the short-run and long-run marginal cost.  The short term marginal cost is the running cost of each of the plant types for the different loads.  The long- run marginal cost is the weighted average cost of the different types of units where the capacity cost is weighted by the amount of capacity and the energy cost is weighted average cost of running capacity for the amount of time it is running. Note that this is a somewhat simplistic analysis because reserve margins and cost of outages should be included in the analysis.

106. Outage and Reliability Analysis

107. Value of Reliability
There are many situations in which you may want to compute the value of reliability in electricity. Some examples include:
The amount of capacity needed to provide consumers with reasonable reliability
Cost of reliability versus value of reliability
Can evaluate the loss of load probability and put a cost on the time that load is not served
Other examples
What kind of capacity should be built to assure that an off-shore platform will have sufficient reliability
Measure the cost of an outage as the cost of lost margin from the platform

108. Causes of Variation in Availability
Random or Forced Outage
Scheduled Maintenance Outage
Submit schedule for approval from off-taker
Coordination with other plants
Calculation of optimal maintenance period
Requirements for maintenance outage
Penalties can be imposed for maintenance during peak periods
Problems with Preventative Maintenance
Poor Operations

109. Definition of Forced Outage
"Total Forced Outage" - during periods other than Planned Outages or Maintenance Outages, the Facility is unable to engage in Dispatch Operation, or the Facility is declared by Seller to be in a Total Forced Outage for what would otherwise be a Partial Forced Outage.
"Partial Forced Outage" - during periods other than Planned Outages or Maintenance Outages, the Facility is partially able to engage in Dispatch Operation, and has not been declared by Seller to be in a Total Forced Outage

110. Valuation of Outages
Theory: Marginal Value of Energy and Outage During Hour of Outage
Similar to Problem of Valuing Capacity
Valuation approaches:
Peaker Method
Value of Lost Supply
Depends on Supply Curve
Depends on Season of Year
Depends on Hydro Availability
Depends on amount of Surplus Capacity

111. Theoretical Formula for Penalty
Penalty for replacement power should be:
Penalty/MWH = (Replacement – Fuel)
Penalty/kW-year =
Penalty/MWH x 8760/1000

112. Computing the Value of Reliability
Cost of outage is the cost of and outage multiplied by the probability that the outage occurs.
The value of an outage can be compared to the cost of avoiding the outage
Strategies to reduce the outage cost could be building redundant plant or building smaller plants
The cost of an outage can be measured by using Monte Carlo Simulation.
In Monte Carlo Simulation, you use a random number to assign when the outage occurs and then run the analysis over and over again and accumulate the total amount of outages and cost.

113. Example of Reliability Analysis - Inputs
Inputs for different strategies. More reliability with smaller plants but the cost may be higher.

114. Reliability - Results
This page demonstrates the results of different strategies with the trade off between cost and value of reliability.

115. Reliability Analysis – Monte Carlo Simulation
This page illustrates the simulation.

116. Example of Monte Carlo Simulation
To illustrate how to compute the value of reliability, consider the example of a refinery that has a high outage cost and different possible strategies. The more expensive strategy has a higher cost but more reliability.

117. Monte Carlo Simulation
The illustration below demonstrates how to make a Monte Carlo simulation to compute outage costs. A random number from 0 to 1 is put into the spreadsheet. When the random number is lower than the forced rate, the plant is assumed to be out. When the random number is above the forced outage rate, the plant is assumed to be available. This process is illustrated below.

118. VBA Code for Monte Carlo Simulation
Sub simulate() '
' simulate Macro
Number = InputBox("number of simulation")
For i = 1 To Number
Cells(i + 16, 11) = Range("i26")
Cells(i + 16, 12) = Range("i42")
Cells(i + 16, 13) = Range("i58")
Next i
End Sub