3.Model Implementation

The constraints in the above problem formulation are comprised of the following aspects: 1) Maximum and minimum constraints of generator output power; 2) Number of particular type of generators in each given time interval; 3) Load power is satisfied in each given time interval; 4) The maximum output power is no less than 120% of the power rating. Meanwhile, the total generation cost is comprised of: 1) Total starting cost of all the generators; 2) Total fixed cost of all the generators; 3) Total marginal cost of all the generators.

The constraints and objective in this optimization formulation are detailed as follows:

Define that and.

The upper and lower limits of output power of each generator is shown as:

\({P_{i\min }} \le {P_{ijk}} \le {P_{i\max }}\)(1)

The total number of Type #i generator is limited by:

\(0\le N_{ij} +N'_{ij}\le N_{i\max}\)\(\)\(\)(2)

In the given time interval, the total output power of all the generators should meet the load requirements, which is shown as:

\(\sum\limits_{i = 1}^4 {\sum\limits_{k = 1}^{{N_{ij}} + {N_{ij}}'} {{P_{ijk}}} } {\rm{ = }}{P_{dj}}\)(3)

The maximum output power should not be lower than 120% of the load requirements:

\(\sum\limits_{i = 1}^4{{P_{imax}} }({N_{ij}} + {N_{ij}}'){\ge}{1.2P_{dj}}\)\(\)(4)