Question

How do you setup this problem is Excel Solver to solve the problem?

21. Star Power Company is a power company in the Midwest region of the united States. Star
buys and sells energy on the spot market. Star can store power in a high-capacity battery
that can store up to 60 kWh (kilowatt hours). During a particular period, Star can buy or sell
electricity at the market price known as LMP (Locational Marginal Price). The maximum
rate that power can be injected or withdrawn from the battery is 20 kWh per period. Star
has forecasted the following LMPs for the next 10 periods:
period LMp ($/kWh)
1 $ 5
2 $27
3 $ 2
4 $25
5 $22
6 $29
7 $24
8 $20
9 $61
10 $66
The battery is full at the beginning of period 1; that is, at the start of the planning horizon,
the battery contains 60 kWh of electricity.
a. Develop a linear programming model Star Power can use to determine when to buy
and sell electricity in order to maximize profit over these 10 weeks. What is the maximum
achievable profit?
b. Your solution to part (a) should result in a battery level of 0 at the end

of period 10. Why
does this make sense? Modify your model with the requirement that the battery should
be full (60 kWh) at the end of period 10. How does this impact the optimal profit?
c. To further investigate the impact of requirements on the battery level at the end of
period 10, solve your model from part (b) with the constraint on the ending battery
level varying from 0 kWh to 60 kWh in increments of 10 kWh. Develop a graph with
profit on the vertical axis and required ending battery level on the horizontal axis.
Given that Star has not forecasted LMPs for periods 11, 12, and so on, what ending
battery level do you recommend that Star use in its optimization model?How do you solve this problem with Solver?

Answer 1

(a)

Formulation of LPP -

Variable

Xi : the power traded in period i

Pi : the price of power in period i for selling

- Pi : the price of power in period i for buying

Objective

Constraints

1. -20 <= Xi  <=20

2. Battery power at any point of time should be less than 60

(b)

resulting into 0 power after period 10

resulting into 60 power after period 10

(c)

Depends upon the price in period 11, if it is greater than 60, they should save 20.