5. Objective Function and Constarints

The objective function contains power generation unit costs and transferred electrical energy costs. Furthermore, the objective function is considered as a statistic problem using probability scenarios:
(1)
Where Qs (t ) is the cost of diesel generator produced power at the time t and scenario s,PsFC (t ) is the amount of power produced by the fuel cell at time t and scenario s,PsW (t ) is the amount of wind generated power at the time t and scenario s,PsPV (t ) is the amount of generated power of photovoltaic at time t and scenario s,PsBSC (t ) is the battery storage level at time t and scenario s,PsBSDC (t ) is the battery discharge rate at time t and scenario s,PsUE (t ) is the amount of energy not supplied in time t and scenario s,PsEE (t ) is the amount of energy transferred to the grid at time t and scenario s andNs is the number of scenarios. Constraints are also listed below:
- First Kirchhoff Law or Power Balance in each period t and scenario s:
(2)
- Wind generation limit in each period t and scenario s:
(3)
- Photovoltaic generation limit in each period t and scenario s:
(4)
- Fuel cell generation limit in each period t and scenario s:
(5)
- Diesel generation limits in each period t and scenario s:
(6)
- Storage battery limit in each period t and scenario s:
(7)
- Storage battery maximal discharge in each period t and scenario s:
(8)
- Storage battery maximal charge in each period t and scenario s:
(9)
- The battery cannot be charged and discharged at the same time in each period t:
(10)
- Storage battery maximal discharge in period t and scenario s with respect to the battery storage in period t-1:
(11)
- Storage battery maximal charge in period t and scenario s with respect to the battery storage in period t-1:
(12)
- Power balance for battery:
(13)
- Initial power of the battery:
(14)
- Undelivered power limit in each period t and scenario s:
(15)
It should be noted that: