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

II. Background of the Problem

Power Purchase Agreement (PPA)

The Power Purchase Agreement (PPA) can be also viewed as a Bilateral Contract between the supplier and off-taker of electricity. The “juice” of PPA between supplier and off-taker is that both parties agreed that the off-taker guarantied a certain amount of electricity that it will purchase for a specified period of time (i.e., one month) such that, whether the off-taker consumed or not consumed the contracted capacity, they will still pay for it. It can be a contracted capacity (MW) or a contracted energy (MHW). The difference between contacted capacity and contracted energy is that, for a contracted capacity, a specified magnitude of output power (in MW) must be available in the system so that whether the system needed it or not, there is an assured available capacity. Contracted energy, on the other hand, the generating plant should supply, (or the reverse side, the buyer should consume), a specified amount of energy (in MWh) within a specified period of time, usually, one moth or one year.

This kind of agreement reduces the financial risk on the supplier side and reduces the risk on the continuity of service on the off-taker side. However, the reduction of risk on the other side may incur additional risk on the other side and vise-versa. The risk in the electricity business is further increased by the fact that the electricity cannot be stored and the balance between supply and demand must be maintained all the time.

The PPA between the NPC and IPP’s has became popular in the past years because of the alleged anomalous contracts that pass the economic risk of the IPP’s to NPC which latter added to the NPC’s multi-billion worth of debt and liabilities.

On the other hand, just like NPC, MERALCO has also a PPA with its own IPP’s which some are operated by its own sister companies.

The MERALCO’s source of Power

MERALCO’s purchase of electricity to its own IPP’s is limited to 40% of its demand. The remaining 60% must be purchased from NPC. Also in the past years, MERALCO has been vocal on contesting that the cost of electricity will be lower if their purchase of power to its own IPP is not restricted to 40%.

This claim of MERALCO, maybe, has some basis since some of their IPP’s has a lower cost per MWh compared with the selling price of NPC’s electricity. Likewise, there are also some of its IPP’s with higher electricity cost than NPC’s. The PPA between MERALCO and its own IPP’s is also a deciding factor.

The Optimal Power Flow and Economic Dispatch

The optimal power flow (OPF) is an extension of economic dispatch. The output of an economic dispatch calculation is an optimal dispatch of generators while satisfying all necessary constraints like the minimum and maximum output power of the power plant and the demand and supply balance. The objective of the economic dispatch is, basically, to minimize the cost of generation, which is mostly a function of the operating cost of the plant, thus minimizing its selling price to utilities and consumers. The cost function can be approximated into a linear function of the output power. Various power plants, specially, if they have different types of fuel, has different cost function. That is why they have different selling price of electricity.

Linear Programming Method

Once the objective function can be approximated linear, the optimize solution can be solve using linear programming. Linear programmer is also suitable for a constraint optimization problem which involves both equality and inequality constraints. Linear Programming model has the following forms;
General Linear Programming Problem: Find the values of x1, x2, …, xn that will

Maximize or minimize
Subject to the restrictions ,

where;
x1, x2, …, xn = decision variables
c1, c2, …, cn = cost coefficients
, ith technological constraint (i = 1,2, …, m)
aij = technological coefficients (i = 1,2, …, m and j =1,2, …, n)
bi = right-hand-side coefficients

Standard Form: Find the values of x1, x2, …, xn that will

Maximize

Subject to the restrictions,

Canonical Form: Find the values of x1, x2, …, xs that will

Maximize

Subject to the restrictions,