Optimising Reactive Power Margin

The traditional objective function of an optimal power flow problem (OPF) is to minimise the active power generation subject to meeting system demand and network constraints. In OATS, it is quite straight forward to modify the objective function depending on the needs of the problem. In this example, we demonstrate modifying the objective function of an OPF to optimise reactive power margin.

The traditional objective function of an OPF is given as:

\[\sum_{g \in G} c_g(p^{G}_{g})\]

where \(c_g\) defines a function, which is normally a monotonically increasing quadratic or a linear function of active power generation.

Let \(Q^{min}_g, Q^{max}_g\) be the minimum and maximum reactive power generation bounds of a generator \(g\). Let \(q_g\) be reactive power generation from generator \(g\). The following quadratic term is the square of the distance from the mid-point of each generation reactive power capability.

\[m_g = \sum_{g \in G} \left(q_g - \left(\frac{Q^{min}_g+ Q^{max}_g}{2}\right)\right)^2\]

Now we can modify the objective function in the OPF as follows:

\[\gamma_1\sum_{g \in G}c_g(p^{G}_{g}) + \gamma_2\sum_{g \in G} m_g(q^{G}_{g})\]

where \(\gamma_i, (i=1,2)\) are weights and can be changed depending on the importance associated to the active power cost and reactive power margins.

Now, the question is that how can we achieve all the above within OATS. The first step is to define new parameters, set and variables. In this problem, we only need to define the following two new parameters.

model.gamma1 = Param(within=NonNegativeReals) # weight for active power
model.gamma2 = Param(within=NonNegativeReals) # weight for reactive power

Once the above two parameters are defined, we can modify the objective function as follows:

def objective(model):
    obj = model.gamma1*sum(model.c2[g]*(model.baseMVA*model.pG[g])**2+model.c1[g]*model.baseMVA*model.pG[g]+ model.c0[g] for g in model.G)+\
    sum(model.VOLL[d]*(1-model.alpha[d])*model.baseMVA*model.PD[d] for d in model.D)+\
    model.gamma2*sum(model.qG[g]-0.5*(model.QGmin[g]+model.QGmax[g]))^2
    return obj