Abstract:
A nunber of mathematical programming methods have been applied for the generation expansion planning problems by various authors (as described the review work). The -cost of operation of energy produced depends upon the following factors. A part of the cost is directly proportional to the power injected at the generating Buses. A part is proportional to square of the power at these buses and there is fixed cost. Considering the above the generation planning problem shall be formulated as quadratic
programming problem. The constraints are that the sum of the generated powers at these Buses is greater than or
equal to the total demand at the load buses. At each Bus the power that can be injected is limited by maximun value.
The Be ales algo rth im is applied to the
generation planning problem for which the results are available by other method. In this method the quadratic cost function is represented by an upper Triangular matrix. This results in saving of Computer spacej compare to other type of programming. Therefore the memory is comparatively
not more as the constraint matrix is represented in the same way except that Zeroth row of _4 (Constraint) matrix is not used. In this method these are no artificial constants used for optimization purpose. A feasible basic solution has to be chosen in this problem for choosing initial values of injected power are taken equal to the original injected power (for the previous stage) plus additional demand distributed equally among generating buses. It is found that for the five Bus system to which this algorithm is applied the optimal solution is obtained in one iteration only.
The uncertainity of generation is taken into account in the following way. The loss of load probability at each generating bus is calculated using the recurssive convolution Integral equation. The injected power at each bus is consider as equivalent load. The probability of this load exceeding the installed capacity gives the LOW.,
