IF statement in decision variables OpenSolver

**ExcellerenUU** · 04-20-2023, 04:15 AM

Hi everyone,

I'm just new to this forum so forgive me if I not up to speed of any customs or rules of conduct or anything..

I have a problem which I can't seem to fix on my own.

I'm trying to optimize a problem right now, using the OpenSolver. In short: the optimization problem is minimizing costs of electricity use of electric vehicles (EVs) which have a certain driving pattern. The goal is to simulate an optimal charging strategy during the hours that the EV is connected to the grid, where electricity prices vary per hour. Since the EVs have batteries, they also allow electricity to be sold back to the grid. The decision variables contain the electricity extracted/sold back to the grid per specific hour.

So for example: the car is connected to the grid at 10PM at 10 kWh and needs to be charged with 50 kWh the next morning at 09AM. The OpenSolver needs to find in which hours it is the cheapest to charge the vehicle. If prices between hours vary enough, it may also be possible that it discharges (earns money with the electricity) to reduce charging costs further.

Here comes the catch: the price for electricity when discharging the vehicle differ from the price when charging. I want to include an IF-statement here to account for this (i.e. IFS(charge in hour I <0; charge* charge price; charge in hour I >0; charge*discharge price). The solver however does not recognize this since (I think) the IF statement is based on the decision variables. I've tried many things, but can't seem to work around an IF statement that is (in)directly based on the decision variables..

Anyone that might know how to help?

**Hydraulics** · 04-22-2023, 09:05 AM

This question is more related to Operation Research than to Excel, anyhow...

There are a number of ways to model your problem. When IF statements are introduced, usually we rely on additional binary variables (you may want to search for "MILP indicator variable", or something like that).

In your problem, we can split the cost function to be optimized into two terms, the first for energy bought in each time interval, the second for energy sold. We introduce two real variables, and two binary variables (linked to the real ones) that will tell us IF we are buying or selling. A simple constraint will force OpenSolver to either buy or sell.

Have a look at the attached file for a basic setup. As I wrote, this is not the only approach we can follow.

HTH,

Francesco

**ExcellerenUU** · 04-24-2023, 10:46 AM

Thanks for the help. I set up my model similar to yours, and it should be working I guess. However, all decision variables have 0s in them, but the battery keeps charging anyway. Any idea what might be the problem?

I use the OpenSolver since I have more than 200 variables.