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MATPOWER – steady state power flow simulation and optimization for MATLAB and Octave
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How to get particular jacobians and sensitivity matrix #197

Closed akhtar3100 closed 1 year ago

akhtar3100 commented 1 year ago

I have two questions:

  1. if I use makeJac(mpc) I can get the jacobian matrix. Is it possible to get for example J4=dQ/dVm directly with some command rather than finding exact location/indices of these submatrices.
  2. My second question is related to first one, how to do sensitivity analysis using matpower. If we need to find for example dploss/dq or dqloss/dq how we can find it using matpower?
rdzman commented 1 year ago

These are good questions.

  1. If you are working with a system that has been converted to internal numbering via ext2int() and you have the complex bus voltage vector V, you can use dSbus_dV() to compute the parts of the Jacobian separately as ...

    [Ybus, Yf, Yt] = makeYbus(mpc);
[dSbus_dVa, dSbus_dVm] = dSbus_dV(Ybus, V);
dQ_dVm = imag(dSbus_dVm);

  2. You could use dSbr_dV() to get the sensitives of line flows (losses equal sum of Sf and St) w.r.t the voltages, but that's not w.r.t. q.

akhtar3100 commented 1 year ago

Ok. Thanks for your answer, I still need more clarity.

  1. What is the use of ext2int function? what if I don't use it. I see no difference between using it or not?
  2. Here we are calculating dQ/dVm, if I want to calculated dVm/dQ will I need to take inverse of the matrix?
  3. One more thing, where i can find details of the functions like dSbus_dv() and dSbr_dv()? do you have function for dVm_dQ?
  4. Regarding losses, if I want to calculate losses caused by reactive power flow and loss sensitivity to reactive power, how should I calculate it.
akhtar3100 commented 1 year ago

@rdzmanWhat is the use of ext2int function? what if I don't use it. I see no difference between using it or not? Here we are calculating dQ/dVm, if I want to calculated dVm/dQ will I need to take inverse of the matrix? One more thing, where i can find details of the functions like dSbus_dv() and dSbr_dv()? do you have function for dVm_dQ? Regarding losses, if I want to calculate losses caused by reactive power flow and loss sensitivity to reactive power, how should I calculate it.

rdzman commented 1 year ago

(Sorry for the delay in responding. I was out for several days.)

  1. It removes offline equipment (generators, branches) and renumbers buses consecutively. If all buses are already numbered consecutively and there is no offline equipment, it will not make a difference.
  2. Yes.
  3. You can use MATLAB's help command for basic help. The details of the formulae used for the calculations can be found in “AC Power Flows, Generalized OPF Costs and their Derivatives using Complex Matrix Notation”.
  4. Not sure what you mean by "losses caused by reactive power flow"? The total active power loss in the system is a function of all of the variables (bus voltages and bus complex power injections. In any case, you can use get_losses() to compute the losses for a given operating point, along with sensitivities w.r.t bus voltages. However, to get sensitivities w.r.t reactive power injections, you will need to make some assumptions about how other variables are constrained when Q is perturbed. I have a function that computes AC shift factors at a given operating point, with certain assumptions about slacks and fixed voltages that I've attached here. As mentioned previously, the sensitivity of losses in a branch should simply be the sum of the sensitivities of flows at the two ends. You may find makePTDFac.m.txt useful as is, or at least find the code illuminating for your application (remember to strip the .txt extension).