Dear Prof. Ray, Thank you very much for your clarification. I have one final inquiry regarding the first question of my previous mail.
1- Since the objective function does not include the non-served load, the OPF minimizes only the cost of the served load. Therefore, the cost of curtailing load is not included in the optimization decisions taken. Then why does it not curtail more load? Is there somewhere in the formulation where the curtailed load is minimized? I thought that it is included in the objective function since the objective function value is negative. Thank you for your time and efforts. Regards, Ibtihal From: [email protected] [mailto:[email protected]] On Behalf Of Ray Zimmerman Sent: miércoles, 22 de junio de 2016 17:27 To: MATPOWER discussion forum Subject: Re: LMP Calculation during Voltage Congestion I’m sorry. The link I sent the first time was definitely the wrong one … and the title I sent was wrong both times (copy-paste error). The correct link and title should be … MATPOWER Tech Note 1 "Uniform Price Auctions and Optimal Power Flow<http://www.pserc.cornell.edu/matpower/TN1-OPF-Auctions.pdf>” Now, to your questions … 1. The objective function actually contains the load *served*, not the load *shed*, so increasing the size of the load does not change the objective function value. 2. Presumably load is curtailed because the price per MW of the bundled load is higher than the curtailment price. That is the bundled LMP (without dispatchable loads) is higher than the highest generator cost. Note that it is possible for nodal prices to go higher (much higher under certain constrained conditions) than the highest generator cost. Ray On Jun 22, 2016, at 10:28 AM, Ibtihal Abdelmotteleb <[email protected]<mailto:[email protected]>> wrote: Dear Prof. Ray, Thank you very much for your reply, it is very useful. I now understand why the LMP for active power does not reach 100€/MWh. Actually the link (document) you sent in your first reply is different from the one you sent in your last reply. I am following up on the same topic, and I have 2 more questions: 1- I increased the load, therefore the load curtailed increased. The LMPs are the same (which makes sense), but the objective function value is the also the same. Shouldn’t it be different? Since more load is curtailed and it is included in the objective function? 2- I tried load curtailment in another case study with different loads. Without introducing the load curtailment option, the OPF converges. With the load curtailment option, it curtails load. Since the load curtailment cost is higher than the cost of generation, why is there load curtailment? Thank you very much for your efforts. Regards, Ibtihal From: [email protected]<mailto:[email protected]> [mailto:[email protected]] On Behalf Of Ray Zimmerman Sent: miércoles, 22 de junio de 2016 15:28 To: MATPOWER discussion forum Subject: Re: LMP Calculation during Voltage Congestion Since real and reactive power are bundled (by virtue of the constant power factor constraint), it is the bundled quantity whose price should equal 100€/MWh. If Pd and Qd are the real and reactive powers of the load, and lamP and lamQ are the nodal prices of real and reactive power at the load, and if the load is set to curtail at 100€/MWh and you are actually seeing curtailment in the solution, then you should observe the following relationship … lamP + Qd/Pd * lamQ = 100€/MWh In other words, it is the per-MWh price of curtailing the bundled commodity (that is, both the real power and the reactive power, both of which have value) that should equal 100€/MWh. This is exactly what I’ve attempted to describe in section 4.1 in the MATPOWER Tech Note 2 on AC Power Flows, Generalized OPF Costs and their Derivatives using Complex Matrix Notation<http://www.pserc.cornell.edu/matpower/TN1-OPF-Auctions.pdf>. In your case, does that relationship hold? What are Pd, Qd, lamP and lamQ in your case? Ray On Jun 21, 2016, at 11:36 AM, Ibtihal Abdelmotteleb <[email protected]<mailto:[email protected]>> wrote: Dear Prof. Ray, Thank you very much for your reply. But I still do not understand why the LMP at the node of load curtailed does not reach 100€/MWh. I tried increasing the load (both active and reactive with constant power factor) and my results were each time the same. The LMPs are the same (82€/MWh) and the objective function is the same. May you please explain why the value never reaches 100 €/MWh? Thank you. From: [email protected]<mailto:[email protected]> [mailto:[email protected]] On Behalf Of Ray Zimmerman Sent: lunes, 23 de mayo de 2016 15:50 To: MATPOWER discussion forum Subject: Re: LMP Calculation during Voltage Congestion I think what you are seeing is the effect of the constant power factor constraint on the curtailable load. This constraint essentially bundles the real and reactive power together into a single bundled commodity that is being curtailed at 100€/MWh. Some of that due to the nodal price of real power and some to the nodal price of reactive power, which is likely to be high in a voltage congestion case. See section 4.1 in the MATPOWER Tech Note 2 on AC Power Flows, Generalized OPF Costs and their Derivatives using Complex Matrix Notation<http://www.pserc.cornell.edu/matpower/TN2-OPF-Derivatives.pdf> for more details on this effect. Ray On May 20, 2016, at 9:30 AM, Ibtihal Abdelmotteleb <[email protected]<mailto:[email protected]>> wrote: Dear Prof. Ray, I have a question regarding LMP calculation during congestion. I ran OPF on the 34-node feeder distribution network, feeding from a single infinite generator of price 50€/ MWh. It did not converge due to voltage congestion, not thermal congestion (there is no line congestion). Then, I introduced load curtailment with a price of 100€/MWh. The OPF converged, and at the bus of load curtailment the price was 82€/MWh, although I was expecting it to be at least 100€/MWh. Do you think I have done something wrong? or is there an explanation why thermal congestion is different from voltage congestion? Thank you very much. Ibtihal Abdelmotteleb PhD Student IIT, Comillias University Madrid, Spain
