Since all the generating units that are
online have different costs of generation, it is necessary to find
the generation levels of each of these units that would meet the load
at the minimum cost. This has to take into account the fact that the
cost of generation in one generator is not proportional to its
generation level but is a nonlinear function of it.

In addition, since the system is
geographically spread out, the transmission losses are dependent on
the generation pattern and must be considered in obtaining the
optimum pattern. Certain other factors have to be considered when
obtaining the optimum generation pattern.

One is that the generation pattern
provide adequate reserve margins. This is often done by constraining
the generation level to a lower boundary than the generating
capability. A more difficult set of constraints to consider are the
transmission limits.

Under certain real-time conditions it
is possible that the most economic pattern may not be feasible
because of unacceptable line flows or voltage conditions. The
present-day economic dispatch (ED) algorithm cannot handle these
security constraints.

However, alternative methods based on
optimal power flows have been suggested but have not yet been used
for real-time dispatch. The minimum cost dispatch occurs when the
incremental cost of all the generators is equal.

The cost functions of the generators
are nonlinear and discontinuous. For the equal marginal cost
algorithm to work, it is necessary for them to be convex. These
incremental cost curves are often represented as monotonically
increasing piecewise-linear functions.

A binary search for the optimal
marginal cost is conducted by summing all the generation at a certain
marginal cost and comparing it with the total power demand. If the
demand is higher, a higher marginal cost is needed, and vice versa.

This algorithm produces the ideal
setpoints for all the generators for that particular demand, and this
calculation is done every few minutes as the demand changes.

The losses in the power system are a
function of the generation pattern, and they are taken into account
by multiplying the generator incremental costs by the appropriate
penalty factors. The penalty factor for each generator is a
reflection of the sensitivity of that generator to system losses, and
these sensitivities can be obtained from the transmission loss
factors.

This ED algorithm generally applies to
only thermal generation units that have cost characteristics of the
type discussed here. The hydro units have to be dispatched with
different considerations. Although there is no cost for the water,
the amount of water available is limited over a period, and the
displacement of fossil fuel by this water determines its worth.

Thus, if the water usage limitation
over a period is known, say from a previously computed hydro
optimization, the water worth can be used to dispatch the hydro
units. LFC and the ED functions both operate automatically in
realtime but with vastly different time periods.

Both adjust generation levels, but LFC
does it every few seconds to follow the load variation, while ED does
it every few minutes to assure minimal cost. Conflicting control
action is avoided by coordinating the control errors.

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