In line with their corporate responsibility targets, DataAnalytics, an analytics firm, has committed to satisfy 100% of its electricity demand using clean energy in the year 2022. They are currently in the process of planning how to achieve this target.

In order to hedge against possible variations in the price of electricity in 2022, DataAnalytics plans to contract solar capacity from SolarNow, a nearby solar farm, through a Corporate Power Purchase Agreement (CPPA). SolarNow has offered two possible CPPA contracts:

Contract A: 100 MW of capacity; DataAnalytics must purchase all the output of its contracted 100 MW of solar capacity at a price of 50/MWh.

Contract B: 150 MW of capacity; DataAnalytics must purchase all the output of its contracted 150 MW of solar capacity at a price of 40/MWh.

However, because of variations in weather, the amount of electricity output that SolarNows solar panels will produce is uncertain. In particular, every MW of capacity is projected to produce MWh of electricity per year, where has a mean of 1500 MWh and a standard deviation of 120 MWh. The distribution is symmetric around its mean.

Given the current work-from-home arrangements under which DataAnalytics is operating, it is unclear how many employees will be working from home versus in the offices in 2022. With probability 25%, all their employees will be back in the office and the firms 2022 electricity demand will be 210,000 MWh. With probability 75%, only half their employees will be back in the office, and the electricity consumption will be 140,000 MWh.

If DataAnalytics electricity demand falls short of the amount of electricity delivered by the contract, they must still honour the terms of the contract and pay SolarNow the entire amount, as per the contract terms. However, if exceeds the amount of electricity delivered by the contract, they must make up the shortfall by purchasing wind or solar energy from the spot market at a price /MWh.

Problem Setup and Scenario Analysis

a) For each of the contracts, write an expression for DataAnalytics total cost in terms of the uncertain production, demand and spot price.