## Monte Carlo Simulation (MCS) in Supply & Demand Forecasting and Financial & Process Modeling

**Monte Carlo Simulation (MCS) in Supply & Demand Forecasting and Financial & Process Modeling**

The conventional or usual approach to forecasting supply & demand of power, energy and goods and services is to use deterministic modeling technique which uses fixed or static data – quantity, price and growth rate.

The same is true with financial & process modeling – fixed or static data is used in estimating plant output (production rate, output, power to GDP elasticity ratio), revenues (growth rate, price escalation), capital and operating costs, financing costs (equity returns, debt interest, commitment fees, front-end fees) and capital structure (% equity, % debt).

However, at best, static data used in deterministic models, provides only static results for equity returns (NPV, IRR, PAYBACK), project returns (NPV, IRR, PAYBACK), net present value of income after tax, discounting rate pre-tax WACC, and the unit tariff (selling price, electricity price, energy price).

Thus, static inputs and outputs from deterministic models provide very little insight into the risk profile of a given project being analyzed for possible investment decisions – go or no go.

This is where stochastic (probabilistic) modeling, instead of static or deterministic modeling, is the better if not superior approach in estimating the most probable value of the statistic being forecasted (mean and its standard deviation, and resulting min and max values of the statistic).

Thus, the use of Monte Carlo Simulation (MCS), which started in 1964, has gained wide prominence in the power generation industry to provide a better estimate of the risk profile of supply & demand forecasting and in determining the technical and economic feasibility of proposed projects, especially of capital-intensive power generation project using conventional, fossil, nuclear and renewable energy technologies.

In supply forecasting, the deterministic model is converted to an stochastic model using the following transformation:

Capacity (sto.) = Capacity (det.) x [ min% + (max% – min%) x rand() ]

Total Capacity = sum (of all capacity from each power generation technology or power plant)

where min% = 60%, max% = 100% and rand() = random function of MS EXCEL (gives value from 0.0 to 1.0).

In demand forecasting, the deterministic model is likewise converted to an stochastic model using the formula:

AGR(sto.) = AGR(det.) x [ min% + (max% – min%) x rand() ]

Demand(t) = Demand(t-1) x [ 1 + AGR(sto.) ]

where min% = 90% , max% = 110%; which simulates the annual growth rate (AGR) from its 100% value

t = time period, year

Hence, the net capacity surplus/(deficit) is given by:

Net Capacity Surplus(t) = Total Capacity(t) – Demand(t)

In power plant project finance modeling, the main determinants (variables that have greatest impact on the equity IRR) are listed below.

In a coal-fired power plant, a 20% swing (-10% to +10%) provides the following changes (delta) on the equity IRR, from the largest positive determinant – tariff (6.33%), followed by capacity factor (4.67%), efficiency (1.68%), debt ratio or % debt (1.29%), installed capacity (0.24%).

On the other hand, the largest negative determinant is capital cost or Capex (-4.27%), fuels & chemical costs (-1.66%), debt interest or loan interest (-1.13%) and O&M or Opex costs (-0.45%).

6.33% | Tariff |

4.67% | Capacity Factor |

1.68% | Efficiency |

1.29% | Debt Ratio |

0.24% | Capacity |

-0.45% | Opex |

-1.13% | Debt Interest |

-1.66% | Fuels |

-4.27% | Capex |

As an example, the Tariff and other main determinants, including foreign exchange rate, are modeled as follows:

Tariff = (5.500 PhP/kWh net) x [ 90% + (110% – 90%) x rand() ]

Net Capacity Factor = (85% installed capacity) x [ 90% + (110% – 90%) x rand() ]

Plant Thermal Efficiency = (42.00% of GHV) x [ 90% + (110% – 90%) x rand() ]

Debt Ratio = % Debt = (70% capital cost) x [ 90% + (110% – 90%) x rand() ]

Installed Capacity = (135 MW gross per unit) x [ 90% + (110% – 90%) x rand() ]

Var O&M Costs = (Var Opex, PhP/kWh net) x [ 90% + (110% – 90%) x rand() ]

Fix O&M Costs = (Fix Opex, PhP/kW/year) x [ 90% + (110% – 90%) x rand() ]

Debt Interest = Loan Interest = (7.00% p.a.) x [ 90% + (110% – 90%) x rand() ]

Fuel Cost = Coal Cost = ($85.00 per MT) x [ 90% + (110% – 90%) x rand() ]

Overnight Capital Cost = (Capex, $/kW) x [ 90% + (110% – 90%) x rand() ]

Forex Rate = (44.00 PhP/US$) x [ 90% + (110% – 90%) x rand() ]

where net = gross – own use & losses (applies to both MW capacity and MWh generation).

Sample results of the Monte Carlo Simulation after 1,000 trials in a project finance modeling exercise are shown below:

Stochastic Model | |||

Equity Returns (30% Equity, 70% Debt) | |||

press ctrl + W to run | NPV | IRR | PAYBACK |

1,000 | 264,230 | 16.56% | 7.72 |

Mean | 80,363 | 16.26% | 8.14 |

Standard error | 41,555 | 0.10% | 0.06 |

Median | -5,224 | 15.99% | 8.17 |

Standard deviation | 1,314,093 | 3.15% | 1.96 |

Variance | 1,726,840,158,606 | 0.10% | 3.85 |

Skewness | 0.307 | 0.384 | -0.046 |

Kurtosis | 2.540 | 2.606 | 2.009 |

Expected value = | 80,363 | 16.26% | 8.14 |

The standard deviation*1.96 = | 2,575,622 | 6.18% | 3.84 |

95% of all outcomes, max = | 2,655,985 | 22.43% | 11.99 |

95% of all outcomes, min = | -2,495,259 | 10.08% | 4.30 |

Stochastic Model | |||

Project Returns (100% Equity, 0% Debt) | |||

press ctrl + W to run | NPV | IRR | PAYBACK |

1,000 | (2,793,242) | 13.00% | 6.33 |

Mean | -2,727,555 | 12.76% | 6.55 |

Standard error | 48,386 | 0.06% | 0.03 |

Median | -2,790,486 | 12.68% | 6.49 |

Standard deviation | 1,530,092 | 1.77% | 0.87 |

Variance | 2,341,181,104,103 | 0.03% | 0.77 |

Skewness | 0.106 | 0.204 | 0.276 |

Kurtosis | 2.494 | 2.491 | 2.519 |

Expected value = | -2,727,555 | 12.76% | 6.55 |

The standard deviation*1.96 = | 2,998,980 | 3.48% | 1.71 |

95% of all outcomes, max = | 271,425 | 16.24% | 8.26 |

95% of all outcomes, min = | -5,726,535 | 9.28% | 4.83 |

Stochastic Model | Net Profit | pre-Tax | Electricity |

After Tax | WACC | Tariff | |

press ctrl + W to run | Million PhP | % | PhP/kWh |

1,000 | 12,015 | 13.06% | 5.752 |

Mean | 10,480 | 12.92% | 5.447 |

Standard error | 48 | 0.04% | 0.010 |

Median | 10,479 | 12.81% | 5.459 |

Standard deviation | 1,523 | 1.35% | 0.312 |

Variance | 2,318,825 | 0.02% | 0.098 |

Skewness | 0.090 | 0.382 | -0.057 |

Kurtosis | 2.637 | 2.606 | 1.801 |

Expected value = | 10,480 | 12.92% | 5.447 |

The standard deviation*1.96 = | 2,985 | 2.65% | 0.612 |

95% of all outcomes, max = | 13,465 | 15.57% | 6.059 |

95% of all outcomes, min = | 7,496 | 10.28% | 4.835 |

Deterministic models as well as Deterministic + Stochastic models are available for the following power generation technologies:

Biomass cogeneration (power + steam + hot water/air + chilled water/refrigeration/air conditioning)

Biomass direct combustion (boiler steam + hot water/air)

Biomass gasification (pyrolysis)

Biomass IGCC (integrated gasification combined cycle)

Biomass WTE (waste to energy)

Coal-fired CFB (circulating fluidized bed)

Coal-fired PC (pulverized coal) subcritical

Coal-fired PC (pulverized coal) supercritical

Coal-fired PC (pulverized coal) ultrasupercritical

Diesel Engine Genset (diesel, gas oil, bunker, fuel oil)

Oil Thermal (bunker, fuel oil)

Gas Thermal (natural gas)

Simple Cycle (Open Cycle) Gas Turbine (Natural Gas, Oil such as diesel, gas oil, kerosene, naptha)

Combined Cycle Gas Turbine (Natural Gas, Oil such as diesel, gas oil, kerosene, naptha)

Geothermal (flash, binary)

Nuclear (PHWR)

Ocean Thermal Energy Conversion (OTEC)

Solar PV

Wind (Onshore, Offshore)

Large Hydro

Pumped Hydro

Mini-Hydro

The reader is advised to search the internet for the definition of the above statistical terms (mean, standard error, median, standard deviation, variance, skewness and Kurtosis).

Please email energydataexpert@gmail.com should you have any questions.

You may request also for sample project finance models with Monte Carlo Simulation.

But you must have a Monte Carlo Simulation add-in excel program for the above MCS models to run in excel.

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energydataexpert@gmail.com

Purchase any model for USD 500 and remit via PayPal (use my gmail account above) or via bank / wire transfer (BPI current account which I will email you once you confirm your order).

Cheers,

Energy technology selection expert

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