A Solution to Economic Dispatch Problem of MERALCO and NPC using Piece-wise Linear Programming Method

I. Background and Objective
II. Background of the Problem
III. Formulation of the Solution using Linear Programming (LP)
IV. Solution and Description of the Analysis Tool Used
V. Results
VI. Discussion of the Results and Conclusion

III. Formulation of the Solution using Linear Programming (LP)

The Objective Function

Take note that the cost function that we are modeling is the cost function of the power for MERALCO’ s point of view. Thus, the cost function of the generators can be viewed as composed of two significant parts, the fixed cost and the variable cost. The fixed cost represents the cost of the contracted energy of MERALCO to the generators that is converted into a contracted capacity in one month by dividing the contracted energy by 720 hours while the variable cost is the cost per MWh when the demand exceeds the contracted capacity. It is important to emphasize that whether MERALCO consume the contracted capacity or not, they must still pay for it. That is, if MERALCO contracted X amount of power, the amount that they will be paying is the same even if the dispatch schedule is somewhere in between 0 and X. Thus, the cost curve of generators is piece-wise and showed bellow;

Figure 1: The typical piece-wise cost curve of MERALCO IPP’s which is composed of contracted capacity as a fixed cost (0-X) and variable cost
The following table shows the list of MERALCO IPP’s and the amount of equivalent contracted capacity (fixed cost) and the cost per MWh of the power that exceeds the contracted capacity. Take note that these are 1998 data because these are the only data that is available for this paper;
Table 1: MERALCO IPP contracted capacity data
Only 40% of MERALCO’s demand must be sourced from these generators. The remaining 60% must be purchased from NPC. During this time, the cost of electric energy from NPC would be Php1012. This is based from the assumption that the generators of NPC and its IPP’s are dispatched in an optimal manner. Take note also that during that time (1998), there is no way to determine the cost of energy from NPC, only until the passage of RA 9136 when the unbundling of rates was promulgated by the Energy Regulatory Commission (ERC).Since the objective function that is needed for LP is just the algebraic sum of the cost function of the IPP’s of MERALCO and the cost per MWh of the power from NPC, the equation of objective function will be,

Our objective is to minimize this cost such that the resulting cost of electricity will be the lowest possible. Take note that the Pn1’s does not appear in the objective function because the cost of this power is fixed for a contracted capacity.

Equality Constraints

To maintain the security and stability of the system, the total power generation and load must be equal at all times, thus;

Where, PL is the instantaneous load of the system. The 24 hour typical load profile of MERALCO in 1998 base from peak demand is approximated as follow,

Table 2: A typical MERALCO load profile base from the peak demand in 1998.

Pn1 is the magnitude of the contracted capacity of generator n while Pn2 is the magnitude of the power that exceeds the contracted capacity. The total power generation of generator n is equal to Pn1 + Pn2.

Inequality Constraint

The first set of inequality constraints only shows that Pn1 must be less than the contracted capacity as illustrated in the piece-wise cost curve. Further more, Pn1 must be greater than the generators rated minimum output power.

The second set shows that Pn2, which is the remaining capacity of the generator after the contracted capacity has been subtracted, when added to the contracted capacity, must not exceed the rated capacity of the generator. Thus,

Lastly, and the most important part, as we have stated, MERALCO can only purchase 40% of its demand from its own IPP’s. Thus,

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