You will be needing the following information from the previous rounds:

From the previous rounds: Your coal plant capacity is 600 MW, your nuclear plant 1000 MW, and your wind plant 1000 MW. You have learned to bid on the nuclear plant at -500.00 EUR/MWh and the wind plant at 0.00 EUR/MWh. For the coal plant, we take the earlier variable cost and add the CO2 cost, we round it so that your bid is 100.00 EUR/MWh. Your weighted average cost of capital, WACC, is 6.1 %.

a) Market equilibrium. In this market, the demand is fluctuating between two levels, low demand, and high demand. The demand curve is given by the following equation P=a−bQP=a−bQ. In the low period, a=3650a=3650, and in the high period, a=4450a=4450. The slope is always the same b=2b=2. The supply curve is given by your supply, i.e. the bid levels and capacities in Source 1 above. (You could think of this as a residual demand, i.e. actual demand reduced with other supply.) We assume that all plants are available at full capacity throughout (it's very windy!).

You can calculate the correct answers, but here you can also find the correct answer by drawing the supply and demand curves. (It may be useful to visualize in any case, the supply should look almost the same as in the lecture video on storage, you just have nuclear in addition.)

--> Market price with the low demand in EUR/MWh = ?

-->Market price with the high demand in EUR/MWh = ?

b) Efficient storage. Your boss has heard about the possibility of battery storage coming and asked you about the potential implications to the market. You promise to make a simple calculation: What would be the minimum capacity of storage that evens out the prices and where would the prices end up to be, i.e. makes the prices in both demand levels equal? It is enough to consider only the capacity in MWh that stores energy from one period to the other. No need to get technical, do not worry about how quickly the storage can be charged or discharged, nor about the losses i.e. the efficiency of the charge/discharge cycle, etc.

For the new market equilibrium price, you may need to do a light calculation or draw carefully near the new equilibrium, but no need to do optimizations. Two tips: 1) use the fact that the storage buys from the low demand and sells an equal amount to the high demand period, as we ignore losses, 2) both of these answers are integer numbers.

-->The efficient storage size in MWh is =?

-->The new market price in EUR/MWh is =?

c) Levelized cost for storage. Now instead of the free storage above, you are asked to consider the private economics of a storage investment. You call your buddy Elon Musk for advice and hear that the current cost is 132 EUR per invested kWh of storage capacity (roughly the real price for a battery pack, ignoring system costs).

As a first step calculate the annuity payments from investing a 1 MWh unit of storage (e.g. using the example from Lecture 8 or in Excel function PMT or in R package FinCal or by hand). You need three values: 1) interest rate, which is the WACC from above, 2) the number of periods, which you can assume to be 10 years, 3) the present value of the asset, this is the current investment cost from Mr. Musk. The result is cash payments in EUR/invested kWh/year. As you are investing 1 MWh, so multiply by 1000 to arrive at a EUR/year value.

--> Capital cost from investment in EUR/year is (with two decimal points accuracy) =?

d) Unit cost of storage. The final step is to calculate the costs so that you can compare them with market prices directly. For this, we assume that the battery can have two full cycles per day, i.e. it can be charged fully and discharged fully twice a day. This gives you the amount of energy per year (365 days).

--> Cost of investment in EUR/MWh is (with two decimal points accuracy) =?

e) Market impact. Given the cost level from d), you invest to as much capacity as is profitable for you. What are the new price levels in the new equilibriums?

Note! I am not expecting you to optimize this, gets unnecessarily tricky. Instead, you should be able to deduct the right answers using only answers from a) and d).

--> New market price with the low demand in EUR/MWh =?

--> New market price with the high demand in EUR/MWh =?