Regarding the using a perturbation to analyze a negative active power price, I
simply meant that if you increase the active load by a small amount, you should
expect to see a corresponding increase in active generation, which has a cost.
You will also see a re-dispatch of reactive power. Since your reactive power
has non-zero costs, this redispatch affects the objective function cost as
well. If the active power price is negative, you will expect a decrease in
reactive cost that is greater in magnitude that the increase in active
generation cost. That is, the objective function value will decrease over all.
In fact, the total change in objective function value divided by the magnitude
of the load perturbation should roughly equal the active power nodal price.
Regarding your non-convergence issue, it’s hard to say. I suspect that it’s
just a numerically more difficult problem due to the addition of the reactive
costs, possibly less convex. Adding those costs should not have any impact on
the feasibility of the problem. If you have access to other optional solvers, I
suggest trying a different solver to see if one is more robust for this
problem. I don’t have a lot of experience with problems that include reactive
power costs, but I seem to remember that it can make the problem harder for
some solvers.
Ray
> On Mar 17, 2016, at 11:29 AM, Mirish Thakur <[email protected]> wrote:
>
> Dear Prof. Ray,
>
> I have performed the test of perturbation of active power demand on one
> particular bus on my model. I plotted graph of both LMP_P and LPM_Q and also
> observed how the dispatch pattern of active power and reactive power changes.
> In fact I already fixed active power dispatch for all generators except one
> generator and Qg is free variable for all generators, so it is easy to see
> the changes in dispatch pattern while change in demand on one particular
> bus. But I'm confused while interpreting the results after increasing the
> active power demand by small amount as you said "increasing the active demand
> will allow for a redispatch of reactive power whose cost decreases by more
> than the cost of the required increase in active power ". So could you
> please elaborate it little bit more about it.
>
> Another query I would like to share with you. I performed OPF by mpc=
> load2disp(myfile) successfully on same model for every hour in a day and
> extract active power dispatch pattern and load pattern for 24 hour data and
> use it again to perform OPF with fixed active power and Qg as free variable
> and it converge successfully. But when I impose reactive power cost to model
> it fails to converge. So to improve the solution by adding extra virtual
> generator for flexibility which can supply Pg (with cost higher than all
> generators) and no Qg and solution converges successfully for some time
> hours. So my question is why without addition of virtual power plant and
> addition of cost on Qg solution fails to converge? Is it due to fact that in
> load2disp function reactive power cost is not considered in OPF operation and
> I'm imposing Qg cost later. And how to improve the solution without addition
> of such extra generator? Thank you very much for your time.
>
> Regards
> Mirish
>
> On Fri, Mar 11, 2016 at 9:41 PM, Ray Zimmerman <[email protected]
> <mailto:[email protected]>> wrote:
> Because of the coupling between active and reactive power, costs on one
> affect the nodal prices for the other. For example, even with zero cost on
> reactive power, the price of reactive power at a particular bus may be
> positive or negative, depending on the sensitivity of the real power dispatch
> to reactive demand at that bus. So, yes, they are coupled and when you put a
> cost on one it affects prices of both.
>
> If you want to see exactly *how* the negative prices on active power arises
> in your case, I suggest perturbing the active power demand at the bus of
> interest by a small amount and observing how all of the active and reactive
> dispatches change. Presumably, increasing the active demand will allow for a
> redispatch of reactive power whose cost decreases by more than the cost of
> the required increase in active power. I’ve found that doing an explicit
> perturbation and sensitivity analysis like this can shed light on these sorts
> of things. I once used it to understand a case in which a nodal price was
> much higher than any of the generator costs in the system, which can
> legitimately happen.
>
> Ray
>
>
>> On Mar 11, 2016, at 9:54 AM, Mirish Thakur <[email protected]
>> <mailto:[email protected]>> wrote:
>>
>> Dear Prof. Ray,
>>
>> With reference to the same thread, I want to clear one doubt.
>> I have imposed reactive power cost on conventional generators into my model,
>> renewable generators delivers only active power with zero active power cost.
>> Owing to this fact when I perform runopf successfully with active and
>> reactive power demands, LAM_P and LAM_Q values for some buses goes negative.
>> I know that LMP prices comprised of congestion, energy cost and losses
>> together. But when I compare my case with other cases like case89pegase or
>> case1354pegase, I noticed that in both cases susceptance values are zero and
>> LMP_P values are always positive in opf results. Also without implementing
>> reactive power cost in my model it also give all positive values for LMP_P.
>> So in my case, lines susceptance which generates reactive power and to
>> compensate such reactive power, generators absorb it and this is why few
>> generators delivers negative (means absorbs) reactive power (in QG column).
>> And due to implementation of reactive power cost into the model this
>> negative generation of reactive power by generators causes LMP_P values
>> negative or is there any other technical reason? For your information i have
>> used linear cost function for active power generation and exponential cost
>> for reactive power. Also I have attached diagram showing reactive power
>> losses (Qf+Qt) in branches in pure reactive power grid model concern to our
>> last discussion.
>>
>> Regards
>> Mirish.
>>
>> On Wed, Mar 2, 2016 at 12:48 AM, Mirish Thakur <[email protected]
>> <mailto:[email protected]>> wrote:
>> Thank you very much Dr. Ray and Dirk.
>> Regards
>> Mirish
>>
>> On Mon, Feb 29, 2016 at 4:14 PM, Ray Zimmerman <[email protected]
>> <mailto:[email protected]>> wrote:
>> Hi Mirish and Dirk,
>>
>> I believe Dirk is close, but the signs are incorrect. It is in fact the line
>> charging capacitance (like a any other shunt capacitor used for voltage
>> support) that produces reactive power (negative reactive losses) rather than
>> consuming it. And the series component always consumes reactive power rather
>> than generating it. If you look at Fig 3-1 and do the math carefully, the
>> series reactive losses are:
>>
>> series_Q_losses = |Vf – Vt|^2 * 1/x
>> shunt_Q_losses = – (|Vf|^2 + |Vt|^2) * b/2
>>
>> The total reactive losses in the line including both components can always
>> be found by adding Qf + Qt.
>>
>> So, yes, the reason for the overall negative reactive losses in the second
>> line is that the shunt components are generating more reactive power than
>> the series element is consuming. As Dirk said, it’s important to realize
>> that reactive power is generated by network elements such as transmission
>> lines and shunt capacitors, not just generators.
>>
>> Ray
>>
>>
>>
>>> On Feb 28, 2016, at 1:03 PM, Dirk Toewe <[email protected]
>>> <mailto:[email protected]>> wrote:
>>>
>>> Hello Mirish,
>>>
>>> A branch can have negative reactive power losses
>>> The shunt charging susceptance is positive so it cannot produce reactive
>>> power but it will always consume reactive power:
>>>
>>> 0 < Q_branch_shunt_loss = b/2 * |Vf|² + b/2 * |Vt|² = b/2 * (
>>> (V_magnitude_f)² + (V_magnitude_t)² )
>>>
>>> so it can only be the inductance that produced reactive power. And indeed:
>>> The series element susceptance is -1/X ( since 1/j = -j )
>>>
>>> 0 > Q_series_loss = -1/x * | Vf - Vt |²
>>>
>>> so the series element actually generates reactive power (negative loss).
>>> The second Line has a slightly higher X in relation to B (0.91% against
>>> 0.87%) and therefore has a net reactive power production which is even
>>> positive. Impedances can produce reactive power if their suscepance is
>>> negative. Why can't they produce real power? Because the resistance R is
>>> usally positive (There is few exceptions to that as well though:
>>> https://en.wikipedia.org/wiki/Negative_resistance
>>> <https://en.wikipedia.org/wiki/Negative_resistance>). You must free
>>> yourself from the idea that reactive power is something only a generator
>>> produces.
>>>
>>> I believe what also confuses you, is power flow and current flow. Current
>>> flow and power flow must not have the same direction. If you for example
>>> have the:
>>> complex voltages Uf = -Ut
>>> and the complex currents If = -It
>>> (see Figure 3-1, http://www.pserc.cornell.edu//matpower/manual.pdf
>>> <http://www.pserc.cornell.edu//matpower/manual.pdf>)
>>> Then the currents If = -It point in the same direction but the power flows:
>>>
>>> Pf = Uf * conj(If) = -Ut * conj(-It) = Ut * conj(It) = Pt
>>>
>>> point in opposite directions.
>>>
>>> How to calculate branch losses
>>> There seems to be a little bit of a difference of opinions here. I a agree
>>> with your approach: To me, the loss of a branch is:
>>>
>>> P_loss = Pf+Pt
>>> Q_loss = Qf+Qt.
>>>
>>> The to equations a simple conservation of energy. And yes the conservation
>>> of energy fortunately also extends to reactive powers.
>>>
>>> You have to be careful though: In the pretty printed output of the runpf()
>>> method, the branch losses are only the series element losses (I^2 * Z).
>>> That might cause some confusion.
>>>
>>>
>>> I hope this helps and i hope my statements are correct, since I only work
>>> on power grids for 5 months now.
>>>
>>> P.S.: Next time please also include the 'from' and 'to' bus entry. That
>>> would make it easier for me to give you a practical example.
>>>
>>> Best regards
>>> Dirk
>>>
>>>
>>> On 28.02.2016 02:36, Mirish Thakur wrote:
>>>> Hello Matpower friends,
>>>>
>>>> I have a question over similar sign of flows at both nodes of a branch. I
>>>> have performed PF with PG=0, PD=0 BRANCH_R=0; means total reactive power
>>>> model (reactive power generation and reactive demand exist) and I got
>>>> successful convergence. When I observed reactive power flows in branches
>>>> I got some surprising results in branch field which I would like to share-
>>>> [ 2 44 0 0.00103 0.1179
>>>> 501.0822 0 0 0 0 1
>>>> -360 360 0 2.53088 0 -14.8590]
>>>>
>>>>
>>>> [ 2 44 0 0.001491 0.16406
>>>> 501.0822 0 0 0 0 1
>>>> -360 360 0 -2.53088 0 -14.6211]
>>>>
>>>>
>>>> So in above two branches (2 to 44) I can understand first branch flow, but
>>>> in second one both flows (QF and QT) have same negative sign. I didn’t
>>>> understand why this happened? Is this due to more charging susceptance of
>>>> second line or what? Another question is how can I estimate MVAr losses in
>>>> these scenarios? By simply adding both flows in first transmission line
>>>> gives Q loss = -12.3281 MVAr or by using average power formula
>>>> From = sqrt(result.branch(:, 14).^2 + result.branch(:, 15).^2);
>>>> To = sqrt(result.branch(:, 16).^2 + result.branch(:, 17).^2);
>>>> Losses = (To + from)./2 = 8.6949 MVAr; ?
>>>> From my point of view simple addition will give me MVAr loss value but I’m
>>>> confused how to calculate MVAr loss in second line? Thanks in advance.
>>>>
>>>> Regards
>>>> Mirish.
>>>
>>
>>
>>
>> <reactivepowerloss.jpg>
>
>
