# Power system - Economic dispatch

Quick concept related question, I have a system with 5 generation units and I have to find the maximum demand that the system can support and still be N-1 secure.

their max outputs are:

Unit A= 155, Unit B = 195, Unit C = 165, Unit D = 305 and Unit E = 280

Considering the reserve constrain their max outputs are:

Unit A= 155, Unit B = 195, Unit C = 165, Unit D = 175 and Unit E = 205

The approach I took was to create a matrix and Tripp one unit per time and sum their max outputs like as follows:

                                                    Max demand supported
**Unit A Tripping**         Unit B  Unit C  Unit D  Unit E  740
**Unit B Tripping** Unit A          Unit C  Unit D  Unit E  700
**Unit C Tripping** Unit A  Unit B          Unit D  Unit E  730
**Unit D Tripping** Unit A  Unit B  Unit C          Unit E  720
**Unit E Tripping** Unit A  Unit B  Unit C  Unit D          690


However discussing with two other friends, each one has a different approach, one of them summed all the max outputs of each unit regardless any constraint, the second summed all the max outputs regarding the reserve constrain finding 895MW

I wonder, who got it right, and what is it meant by N-1 then.

Thanks

• This looks like a Transport Model problem in Management Science... – Solar Mike Oct 20 '17 at 13:16

The correct answer is the sum of the constrained generators minus the largest constrained generator (895 - 205 =) 690.

Perhaps you can be a bit more clear about the reserve constraints you are considering?

Usually, the dispatch + reserves for each unit must be within the unit's "max output" (first constraint).

Without losing any unit, the total dispatch must meet the total demand D (second constraint).

Then, to guarantee N-1 security, that is, to make sure the system can still meet the total demand D when any single unit is lost, we require that, for each lost unit k, the total reserve without unit k is greater than or equal to the output of the lost unit k (third constraint). So if we lose a single unit, we always have enough reserves on the remaining units to meet the demand.

So, if I understand you correctly, this is the linear program that corresponds to the problem you are trying to solve: \begin{align} \max_{D,p_i,r_i} D\\ \text{subject to}\\ p_i+r_i &\leq p_i^M,\\ \sum_{j=1}^5p_j &=D,\\ \sum_{\substack{j=1\\j\neq k}}^5r_j &\geq p_k, \quad k=1,\ldots,5\\ i=1,...,5 \end{align}

I won't solve this for you, as I don't know what your reserve constraints are, but I think this should give you an idea of how to proceed.