On Mar 22, 2007, at 4:32 PM, Prof. Jose Roberto Camacho wrote:
I didn't have the case9 here, but running a power-flow (a non-
linear set of equations) you can
leave your power generation at zero (active and reactive) in the
slack bus (reference bus), in
matpower you can have more than one. As an iterative process, on a
slack bus (reference
bus) you specify voltage (1 pu) and angle (zero), generator active
and reactive powers in the
slack bus will be function of the voltages obtained in other bars
and the losses. In agreement
with all the equations of your non-linear system describing the
system.
Run your case9 model, and look if the powers remains the same after
convergence (at the
end of the routine).
Just one small additional clarification. There are two separate
concepts here that are often combined, and in fact they are combined
in the MATPOWER implementation of the power flow.
(1) Voltage angle reference bus -- Since the power flow equations
essentially only deal with angle differences, a single arbitrary
reference is necessary in each "island" in the network to uniquely
solve for the remaining voltage angles. Normally, you would only want
to specify more than one angle reference if you have multiple
unconnected islands.
(2) Real power slack -- When computing the power flow for an N-bus
system, where Q is specified at all load buses and V is specified at
the remaining buses and a reference angle is specified at the
reference bus, specifying P at every bus would leave us with 2N
equations [a] and 2N-1 unknowns [b]. A simple approach to solve this
is to allow P at a single bus to be a variable that takes up the
"slack". Conceptually, this could be any generator bus. I does not
have to be the same bus used for (1). It is also possible to allow P
to be free at multiple buses if we include additional equations
defining how the slack is to be distributed. Again this is
independent of (1).
One more point, an optimal power flow formulation needs (1) but not
(2), and in MATPOWER's implementation the reference bus is exactly
that. The power flow problem, on the other hand needs both (1) and
(2), and in the MATPOWER implementation the reference bus serves as
both.
[a] P and Q balance at each bus
[b] V at load buses, Q at remaining buses and angle at all buses
except the reference
--
Ray Zimmerman
Senior Research Associate
428-B Phillips Hall, Cornell University, Ithaca, NY 14853
phone: (607) 255-9645
