Power System Simulation - Optimal Power Flow

Optimal Power Flow

Electricity flows through an AC network according to Kirchhoff's Laws. Transmission lines are subject to thermal limits (simple megawatt limits on flow), as well as voltage and electrical stability constraints.

The simulator must calculate the flows in the AC network that result from any given combination of unit commitment and generator megawatt dispatch, and ensure that AC line flows are within both the thermal limits and the voltage and stability constraints. This may include contingencies such as the loss of any one transmission or generation element - a so-called security-constrained optimal power flow (SCOPF), and if the unit commitment is optimized inside this framework we have a security-constrained unit commitment (SCUC).

In Optimal Power Flow (OPF) the generalised scalar objective to be minimised is given by:

f(u0,x0))

where u is a set of the control variables, x is a set of independent variables, and the subscript 0 indicates that the variable refers to the pre-contingency power system.

The SCOPF is bound by equality and inequality constraint limits. The equality constraint limits are given by the pre and post contingency power flow equations, where k refers to the k’th contingency case:

gk(uk,xk)=0 for k=0,1…n

The equipment and operating limits are given by the following inequalities:

Uk_min≤Uk≤Uk_max - Represent hard constraints on controls

Xk_min≤Xk≤Xk_max - Represents hard/soft constraints on variables

hk(uk,xk)≤0 for k=0,1....n - Represents other constraints such as reactive reserve limits

The objective function in OPF can take on different forms relating to active or reactive power quantities that we wish to either minimise or maximise. For example we may wish to minmise transmission losses or minimise real power generation costs on a power network.