Re: Power flow VM VA, CPF end point

[Elis Nycander]

I see, that's interesting. Thanks!

2017-05-22 10:00 GMT+02:00 Jose Luis Marín :

>
> 1. Yes, VM VA are used both for input and output. Note one subtle point,
> though: in runpf.m (Lines 177--183) the initial seed for the iteration is
> first set to the values [VM VA] provided as input, but for
> voltage-controlled buses (with active generators), the value of VM is
> replaced by the setpoint VG of their respective bus generator(s) (the value
> of VA is preserved). This makes sense because it guarantees that the seed
> will be closer to the solution.
>
> 2. What you see here is to be expected. Basically, what happens is that
> the basins of attraction of low-voltage volutions are usually smaller than
> those of the operating solution. Also, note that there are *many* (for N
> buses, somewhat of the order of 2^N) low voltage solutions, so chances are
> that the iteration will converge to a solution that's different from the
> one you followed by homotopy (CPF). Even homotopy methods can encounter
> this same problem if their step-size is not small enough.
>
>
> Here's some refs on the fractal nature of the problem:
>
> @INPROCEEDINGS{KlumpOverbye00b,
> author={Klump, R.P. and Overbye, T.J.},
> booktitle={Power Engineering Society Summer Meeting},
> title={A new method for finding low-voltage power flow solutions},
> publisher={IEEE},
> year={2000},
> volume={1},
> pages={593--597},
> doi={10.1109/PESS.2000.867653},
> ISSN={}
> }
>
> @INPROCEEDINGS{ThorpNaqavi89,
> author={Thorp, J.S. and Naqavi, S.A.},
> booktitle={Proceedings of the 28th IEEE Conference on Decision and
> Control},
> title={Load flow fractals},
> year={1989},
> volume={2},
> pages={1822--1827},
> doi={10.1109/CDC.1989.70472}
> }
>
> @INPROCEEDINGS{ThorpNaqaviChiang90,
> author={Thorp, J.S. and Naqavi, S.A. and Chiang, H.-D.},
> booktitle={Decision and Control, 1990., Proceedings of the 29th IEEE
> Conference on},
> title={More load flow fractals},
> year={1990},
> month={dec},
> volume={6},
> pages={3028--3030},
> doi={10.1109/CDC.1990.203339}
> }
>
> @ARTICLE{ThorpNaqavi97,
> author={Thorp, J.S. and Naqavi, S.A.},
> journal=IEEE_M_CAP,
> title={Load-flow fractals draw clues to erratic behaviour},
> year={1997},
> month={jan},
> volume={10},
> number={1},
> pages={59--62},
> doi={10.1109/67.560872},
> ISSN={0895-0156}
> }
>
> @INPROCEEDINGS{Mori00,
> author={Mori, H.},
> booktitle={IEEE International Symposium on Circuits and Systems (ISCAS)},
> title={Chaotic behavior of the Newton-Raphson method with the optimal
> multiplier for ill-conditioned power systems},
> year={2000},
> volume={4},
> pages={237--240},
> doi={10.1109/ISCAS.2000.858732}
> }
>
>
> --
> Jose L. Marin
> Grupo AIA
>
>
>
>
> 2017-05-19 11:30 GMT+02:00 Elis Nycander :
>
>> Hi all matpower users!
>>
>> I have two questions:
>>
>> 1. In the bus matrix, the columns VM and VA are used both for the initial
>> guess when solving the power flow, and to store the resulting voltages?
>>
>> 2. When solving a cpf, I get lam_max which corresponds to the nose point,
>> i.e. maximum load/generation increase before "voltage collapse" happens. I
>> can also find the power flow at the nose point just by running an ordinary
>> power flow with flat start and conditions corresponding to the maximum
>> load. However, I have tried to do the same thing for the lower part of the
>> PV curve but failed to reproduce the solutions from the cpf. Basically I
>> thought I could get the lower part of the PV curve by just solving a power
>> flow using initial conditions which are close to the "unstable"/lower
>> solutions from the cpf (instead of a flat start), but I get different
>> solutions.
>>
>> Thanks,
>> Elis
>>
>
>

Re: Power flow VM VA, CPF end point

[Jose Luis Marín]

1. Yes, VM VA are used both for input and output. Note one subtle point,
though: in runpf.m (Lines 177--183) the initial seed for the iteration is
first set to the values [VM VA] provided as input, but for
voltage-controlled buses (with active generators), the value of VM is
replaced by the setpoint VG of their respective bus generator(s) (the value
of VA is preserved). This makes sense because it guarantees that the seed
will be closer to the solution.

2. What you see here is to be expected. Basically, what happens is that the
basins of attraction of low-voltage volutions are usually smaller than
those of the operating solution. Also, note that there are *many* (for N
buses, somewhat of the order of 2^N) low voltage solutions, so chances are
that the iteration will converge to a solution that's different from the
one you followed by homotopy (CPF). Even homotopy methods can encounter
this same problem if their step-size is not small enough.


Here's some refs on the fractal nature of the problem:

@INPROCEEDINGS{KlumpOverbye00b,
author={Klump, R.P. and Overbye, T.J.},
booktitle={Power Engineering Society Summer Meeting},
title={A new method for finding low-voltage power flow solutions},
publisher={IEEE},
year={2000},
volume={1},
pages={593--597},
doi={10.1109/PESS.2000.867653},
ISSN={}
}

@INPROCEEDINGS{ThorpNaqavi89,
author={Thorp, J.S. and Naqavi, S.A.},
booktitle={Proceedings of the 28th IEEE Conference on Decision and Control},
title={Load flow fractals},
year={1989},
volume={2},
pages={1822--1827},
doi={10.1109/CDC.1989.70472}
}

@INPROCEEDINGS{ThorpNaqaviChiang90,
author={Thorp, J.S. and Naqavi, S.A. and Chiang, H.-D.},
booktitle={Decision and Control, 1990., Proceedings of the 29th IEEE
Conference on},
title={More load flow fractals},
year={1990},
month={dec},
volume={6},
pages={3028--3030},
doi={10.1109/CDC.1990.203339}
}

@ARTICLE{ThorpNaqavi97,
author={Thorp, J.S. and Naqavi, S.A.},
journal=IEEE_M_CAP,
title={Load-flow fractals draw clues to erratic behaviour},
year={1997},
month={jan},
volume={10},
number={1},
pages={59--62},
doi={10.1109/67.560872},
ISSN={0895-0156}
}

@INPROCEEDINGS{Mori00,
author={Mori, H.},
booktitle={IEEE International Symposium on Circuits and Systems (ISCAS)},
title={Chaotic behavior of the Newton-Raphson method with the optimal
multiplier for ill-conditioned power systems},
year={2000},
volume={4},
pages={237--240},
doi={10.1109/ISCAS.2000.858732}
}


-- 
Jose L. Marin
Grupo AIA




2017-05-19 11:30 GMT+02:00 Elis Nycander :

> Hi all matpower users!
>
> I have two questions:
>
> 1. In the bus matrix, the columns VM and VA are used both for the initial
> guess when solving the power flow, and to store the resulting voltages?
>
> 2. When solving a cpf, I get lam_max which corresponds to the nose point,
> i.e. maximum load/generation increase before "voltage collapse" happens. I
> can also find the power flow at the nose point just by running an ordinary
> power flow with flat start and conditions corresponding to the maximum
> load. However, I have tried to do the same thing for the lower part of the
> PV curve but failed to reproduce the solutions from the cpf. Basically I
> thought I could get the lower part of the PV curve by just solving a power
> flow using initial conditions which are close to the "unstable"/lower
> solutions from the cpf (instead of a flat start), but I get different
> solutions.
>
> Thanks,
> Elis
>

Power flow VM VA, CPF end point

[Elis Nycander]

Hi all matpower users!

I have two questions:

1. In the bus matrix, the columns VM and VA are used both for the initial
guess when solving the power flow, and to store the resulting voltages?

2. When solving a cpf, I get lam_max which corresponds to the nose point,
i.e. maximum load/generation increase before "voltage collapse" happens. I
can also find the power flow at the nose point just by running an ordinary
power flow with flat start and conditions corresponding to the maximum
load. However, I have tried to do the same thing for the lower part of the
PV curve but failed to reproduce the solutions from the cpf. Basically I
thought I could get the lower part of the PV curve by just solving a power
flow using initial conditions which are close to the "unstable"/lower
solutions from the cpf (instead of a flat start), but I get different
solutions.

Thanks,
Elis