System incremental cost calculations using the participation factor load-flow formulation

The load-flow problem is reformulated such that the use of a slack-bus generator is included only as a special case. This reformulation, known as the participation factor load-flow, includes a total mismatch variable and a defined participation vector, which, in general, distributes this mismatch to all system buses. The slack-bus constraint can still be obtained be defining a particular participation vector. In using the participation factor load-flow in the transpose Jacobian approach to the economic optimal dispatch problem, it is shown that the value of the system- lambda can be controlled such that this value represents the minimal incremental change in generation costs per unit change in system total demand with this demand distributed according to the specified participation vector. Methods using the conventional B-coefficient loss formulas or slack-bus load-flows give system- lambda values whereby the unit change in demand must be placed on a fictitious single load-bus or on the slack-bus, respectively. An extensive 28-bus, 8-generator system is included to illustrate these results.>