Re: Constraint types and its effect on OPF convergence

[Ray Zimmerman]

I am not familiar with any specific papers on this topic. As Shri suggests, I 
suspect the answer is it is very dependent on operating point, solution 
algorithm and parameters of your network.

Whether or not there is anything that you can say that would apply in general 
sounds like a significant research project.

Ray


> On Sep 11, 2015, at 8:47 AM, Arun Shrestha  wrote:
> 
> Dear Ray,
> 
> I was wondering if you could shed some light on this topic. Do you recommend 
> any book or paper which might provide some insights?
> 
> Thank you,
> Arun S.
> 
> On Thu, Sep 10, 2015 at 10:05 AM, Abhyankar, Shrirang G.  > wrote:
> I am not sure there is a clear obvious way to tell which constraints pose the 
> most problem for the optimization. Perhaps doing some sensitivity analysis 
> might help, but with different operating conditions you will get different 
> sensitivities. There are a few papers published on convergence behavior of 
> interior point algorithms, I haven't read them yet, that may be of help. 
> 
> It is an interesting question. I hope some of the folks working on OPF and 
> related problems can shed some light.
> 
> Shri
> 
> Sent from my iPad
> 
> On Sep 9, 2015, at 8:25 AM, Arun Shrestha  > wrote:
> 
>> Hello MATPOWER Community,
>> 
>> I am trying to understand how various constraint types can affect OPF 
>> convergence. Are some constraints easy to satisfy than others? Is there a 
>> way to figure out the effect of constraints type (in terms of total number 
>> of loadflow iteration or convergence time)  on OPF convergence?
>> 
>> For Example:
>> Let's assume a small power system with four generating stations. The 
>> solution of an unconstrained OPF is shown below:
>> 
>> Gen Active Power: P1gen_0, P2gen_0, P3gen_0, P4gen_0
>> Gen Reactive Power: Q1gen_0, Q2gen_0, Q3gen_0, Q4gen_0
>> Gen voltage Magnitude:  V1gen_0, V2gen_0, V3gen_0, V4gen_0
>> Gen Voltage Angle: TH1gen_0, TH2gen_0, TH3gen_0, TH4gen_0
>> Next I add a user defined constraints as shown below, one at a time.
>> 
>> Constraint #1: P1gen + P2gen <= P_const OR
>> Constraint #2: Q1gen + Q2gen <= Q_constOR
>> Constraint #3: V1gen + V2gen <= V_const  OR
>> Constraint #4: TH1gen + TH2gen <= TH_const
>> 
>> I would like to know which constraint (out of 4) will result in the fastest 
>> OPF convergence.
>> 
>> Since runopf function uses Newton Method (by default), I think P and Q 
>> constraints will converge faster than V and TH constraints (based on how 
>> power flow is solved). Is there any mathematical derivation which shows the 
>> effect of the constraints on OPF convergence? Or the OPF convergence solely 
>> depends upon the power system model/cost function used?
>> 
>> Any help on this topic is highly appreciated.
>> Thank you,
>> Arun
>> 
> 

Re: Constraint types and its effect on OPF convergence

[Abhyankar, Shrirang G.]

I am not sure there is a clear obvious way to tell which constraints pose the 
most problem for the optimization. Perhaps doing some sensitivity analysis 
might help, but with different operating conditions you will get different 
sensitivities. There are a few papers published on convergence behavior of 
interior point algorithms, I haven't read them yet, that may be of help.

It is an interesting question. I hope some of the folks working on OPF and 
related problems can shed some light.

Shri

Sent from my iPad

On Sep 9, 2015, at 8:25 AM, Arun Shrestha 
> wrote:


Hello MATPOWER Community,

I am trying to understand how various constraint types can affect OPF 
convergence. Are some constraints easy to satisfy than others? Is there a way 
to figure out the effect of constraints type (in terms of total number of 
loadflow iteration or convergence time)  on OPF convergence?

For Example:
Let's assume a small power system with four generating stations. The solution 
of an unconstrained OPF is shown below:

Gen Active Power: P1gen_0, P2gen_0, P3gen_0, P4gen_0
Gen Reactive Power: Q1gen_0, Q2gen_0, Q3gen_0, Q4gen_0
Gen voltage Magnitude:  V1gen_0, V2gen_0, V3gen_0, V4gen_0
Gen Voltage Angle: TH1gen_0, TH2gen_0, TH3gen_0, TH4gen_0

Next I add a user defined constraints as shown below, one at a time.

Constraint #1: P1gen + P2gen <= P_const OR
Constraint #2: Q1gen + Q2gen <= Q_constOR
Constraint #3: V1gen + V2gen <= V_const  OR
Constraint #4: TH1gen + TH2gen <= TH_const

I would like to know which constraint (out of 4) will result in the fastest OPF 
convergence.

Since runopf function uses Newton Method (by default), I think P and Q 
constraints will converge faster than V and TH constraints (based on how power 
flow is solved). Is there any mathematical derivation which shows the effect of 
the constraints on OPF convergence? Or the OPF convergence solely depends upon 
the power system model/cost function used?

Any help on this topic is highly appreciated.

Thank you,
Arun