By small, I meant, say, less than 100 buses. And my conjecture is just a gut feeling based on the difficulty of being able to find multiple local optima. There is certainly no proof that this is true (in which case it wouldn't be a conjecture).
-- Ray Zimmerman Senior Research Associate B30 Warren Hall, Cornell University, Ithaca, NY 14853 phone: (607) 255-9645 On Jul 29, 2013, at 3:50 PM, spyros gian <[email protected]> wrote: > Dr Zimmerman , you wrote that your conjecture is that in most cases, > especially for relatively small systems, the solution found by MATPOWER is > likely the global optimum or else something extremely close to it. > - First of all, what is a 'small system' for you ? e.g. less than 10 buses? > - Secondly, where do you base your conjecture that in most cases the interior > point method finds the global - or sth very close to it- optimum ? Is there a > proof that the interior point method solves the non-linear problems to the > global optimum or very close to it? > > Thank you > > Date: Wed, 24 Jul 2013 08:56:51 +0200 > From: [email protected] > To: [email protected]; [email protected] > Subject: Re: OPF on matpower > > Dear Dr. Zimmerman, > > the "Bus types play no role" confused me a bit, so I tried declaring some > previous generator nodes as PQ buses. > It seems to me the only effect is, that the voltage now is not longer fixed > to the generator set point during a normal Power Flow calculation. > > Do you know if that's correct or has it any further consequences? > > thanks in advance > Simon > > > > >>> Ray Zimmerman <[email protected]> 23.07.2013 19:44 >>> > Shri is correct with some *very* minor tweaks the only bus type that matters > is the REF bus which determines the voltage reference for the system, and the > voltage angle at that bus is set to the corresponding value in the bus > matrix, which is usually set to 0, but need not be. > > And, yes, the OPF solvers in MATPOWER do find locally optimal solutions that > are not guaranteed to be globally optimal. Theoretically, MATPOWER could find > different solutions depending on the algorithm, starting point, algorithm > parameters, etc. However, in my experience, it has been very difficult to > find multiple local optima. The one example I have been able to confirm has > nearly identical objective values and active power dispatches, with some > differences in voltage profile and reactive dispatch in a few buses. > > My conjecture is that in most cases, especially for relatively small systems, > the solution found by MATPOWER is likely the global optimum or else something > extremely close to it. I hope to include in an upcoming version some > contributed code that will be able to confirm in some cases that a solution > is a indeed a global optimum. > > -- > Ray Zimmerman > Senior Research Associate > B30 Warren Hall, Cornell University, Ithaca, NY 14853 > phone: (607) 255-9645 > > > > > > On Jul 23, 2013, at 1:05 PM, Shri <[email protected]> wrote: > > > > On Jul 23, 2013, at 9:42 AM, spyros gian <[email protected]> wrote: > > Dear Dr Zimmerman, > > Running an OPF in matpower means that > > 1. Bus types play no role (eg slack, PV, PQ etc) > Yes. > 2. All values for Real Power generation and reactive power generation are > unknown > Yes. > 3. All values for bus_voltages and voltage phase angles in buses, are unknown > as well > The voltage angle of the reference bus is fixed and set to 0. > 4. As a result, all values for real and reactive power flows are unknown. > Yes. > 5. Losses are unknown. > Yes. > > What is known : > 1. The resistance, reactance, admittance per unit / per conductor > 2. Values for Real and Reactive demand at each bus > 3. Limits on voltage magnitude , limits on real and reactive power generation > 4. MVA limits on each line > 5. Fuel cost for each generator. > Yes for all > > So my question is > a. Are the above correct for matpower ? > b. Since matpower uses a non-linear optimisation, is the result a local > minimum or a global minimum? > (for the case of a cost-minimization OPF) ? i.e. the values for voltages, > reactive powers etc, are > globally optimum or perhaps other optimum values for all the unknown > quantities exist ? > I believe most of the optimization tools, such as fmincon in Matlab, find a > local minimum. > > Shri > > Thank you, > Spyros Gian > > > >
