2.3.2. Operational Costs

First, for the WT-DGs, the operational cost is the summation of two parts. The first part refers to the cost of the actual output power of the WT. The second part is the penalty cost of unavailable wind output power that refers to the deviation between the available and scheduled wind powers. At time *t*, the total operational costs of each WT (*i*) can be represented, as in [56], as

$$\mathcal{C}\_{pw,i,t} = \begin{cases} c\_w P\_{w,i,t} + c\_{pw} (P\_{wav,i,t} - P\_{w,i,t}) \text{, if } P\_{w,i,t} < P\_{wav,i,t} \\ c\_w P\_{w,i,t} + c\_{rw} (P\_{w,i,t} - P\_{wav,i,t}) \text{, if } P\_{w,i,t} > P\_{wav,i,t} \end{cases} \tag{23}$$

where *Cpw,i,t* is the total operating cost of the wind, *c<sup>w</sup>* is the operational cost of the wind output (\$/kW), *cpw* is the penalty costs for under-estimation power of the WT (\$/kW), *Pwav,i,t* is the available *i*th WT power at time t (kW), and *crw* is the reserve cost for overestimation wind turbine power (\$/kW).

Second, for the PV units, the operational costs for each unit (*i*) at each time (*t*) are described as in [56]:

$$\mathcal{C}\_{pv,i,t} = \begin{cases} \mathcal{c}\_{pv} P\_{v,i,t} + \mathcal{c}\_{pvv} (P\_{pv\\_av,i,t} - P\_{pv,i,t}), \text{ if } P\_{pv,i,t} < P\_{pv\\_av,i,t} \\\mathcal{c}\_{pv} P\_{v,i,t} + \mathcal{c}\_{vpv} (P\_{pv,i,t} - P\_{pv\\_av,i,t}), \text{ if } P\_{pv,i,t} > P\_{pv\\_av,i,t} \end{cases} \tag{24}$$

where *Cpv,i,t* is the total operating cost of the PV, *cpv* is the operational cost of the PV units (\$/kW), *cppv* and *crpv* are, respectively, the penalty costs for under-estimation and overestimated powers (\$/kW), and *P pv\_av,i,t* is the available power that can be produced (kW).

The first parts of Equations (23) and (24) represent the cost based on the actual PV and WT generation power, while the second part represents the costs due to under-estimation or over-estimation. The under-estimation costs are related to penalties due to the generated PV, and WT output power is less than the scheduled one, whereas the over-estimation costs are related to the reserve costs in case the scheduled output power is greater than the available generated power for both PV and WT.
