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Right modeling question

  • 4 August 2023
  • 4 replies
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O
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Good day to you.

I am modeling a situation in AIMMS and I have a situation but do not know how to handle it. 

The situation is that I am modeling variable 'P_Discharging(agg,t)' and I do not want it to discharge after the battery gets to <= 0.3501 and at the same time, variable 'P_Charging(agg,t)' and I do not want it to charge at >= 0.949. To achieve this, I have these figures:

 

My main aim is to formulate a linear program. Just asking if what I have done is right or if I should model it using a 'Constraint' rather than ‘variable’. Moreso, I do not know how to model it into a 'Constraint'. Please, can you help me look into this?

 

Thank you.

 

Olusegun

 

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Best answer by Marcel Hunting 7 August 2023, 15:37

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Marcel Hunting
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hi @olusegun.adeniji. Seems to me that you want to model for P_Discharging(agg,t): If SOC(agg,t-1) < 0.3501 then P_Discharging(agg,t) = 0.

Linear models cannot handle strict inequalities (<) so you have to use some kind of small (epsilon) value to transfer them into <=.

For P_Discharging(agg,t) you need a new binary variable, say X(agg,t). Then you need these new constaints:

SOC(agg,t-1) <= 0.3501 - eps + M*X(agg,t)

SOC(agg,t-1) >= 0.3501*X(agg,t)

Here M is some big value and eps a small (positive) value close to 0. Now you need one more constraint, namely

P_Discharging(agg,t) <= M*X(agg,t)

Now we have modelled:

  • If X(agg,t) = 0 then SOC(agg,t-1) <= 0.3501 - eps, and P_Discharging(agg,t) = 0.
  • If X(agg,t) = 1 then SOC(agg,t-1) >= 0.3501.

The current definition of P_Discharging should be removed.

The variable P_Charging you can be reformulated in a similar way.

Marcel - AIMMS Optimization Specialist
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Thank you for your prompt response. I have implemented the P_Charging part as follows:

SOC(agg, t -1)  >=  0.949 + eps + M*Y(agg, t);

SOC(agg, t - 1)  <=  0.949 * Y(agg, t);

P_Charging(agg, t)  >=  M*Y(agg, t).

So if:

  • Y(agg, t) = 0, then SOC(agg,t)  >=  0.949 + eps, and P_Charging (agg,t) = 0
  • Y(agg, t)  = 1, then SOC(agg,t)  <= 0.949.

But when I used a high value for M in the formulation, it returned that a high value cannot be implemented.

Olusegun

Marcel Hunting
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Userlevel 5
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I think you should be using

P_Charging(agg, t)  <=  M*Y(agg, t).

(so different type). The M does not have to be very large. It suffices to make the M in the first constraint equal to an upper bound on SOC, so you can use Max_SOC(t). The M in the third constraint can be equal to Max_P_Discharge, because that defines an upper bound on P_Charging.

Marcel - AIMMS Optimization Specialist
O
Badge +3

Hi,

By design, I modelled the P_Charging to be negative while P_Discharging is positive. So, the range of P_Charging is ((Min_Active_Power(agg, t), 0) while the range of P_Discharging is (0, Max_P_Discharge(agg,t)). The range of SOC(agg,t) is (Min_SOC(t), Max_SOC(t)). Both the ranges on SOC(agg, t) are positive.

So I think this will be finally right:

For Discharging:

SOC(agg,t -1) <= 0.3501 - eps + (Min_SOC(t) * X(agg,t))

SOC(agg,t -1) >= 0.3501 * X(agg,t)

P_Discharging(agg,t) <=  Max_P_Discharge(agg,t) * X(agg,t)

 

For Charging:

 

SOC(agg, t -1)  >=  0.949 + eps + Max_SOC(t) * Y(agg, t);

SOC(agg, t - 1)  <=  0.949 * Y(agg, t);

P_Charging(agg, t) <= Min_Active_Power(agg,t) * Y(agg, t).

 

I would appreciate if you could make necessary comments on the above formulation.

 

Thanks

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