System loss calculations due to voltage imbalance

[saford42]

I work for a local municipality that owns the typical 69kV Sub-transmission system that is stepped down to 12.47kV. For several years our transmission provider has provided us with imbalanced voltage. At the stations without regulation we have consistently measured C-phase being 2 volts higher on a 120V scale. I have been asked by the transmission provider to calculate the losses to a dollar amount per year because of this issue. Does anyone have any suggestions or knowledge of how to go about doing this? Any help will be very much appreciated.

 

[Desrod2]

It could be done using simulations. Most power system software provides you with a losses calculation. If you have a detailed load profile (by the hour for example), you can run multiple load-flows with balanced and unbalanced voltage supply and then compare the resulting losses.
You will need to obtain/calculate a kW and kWh cost to translate into $. If you don't have a working simulation model, a simplified one could be build. Associated results will depend on how precise you want to estimate those costs.

 

[dpc]

Not sure how a voltage imbalance translates directly to increased losses. Many power system software programs are not going to be able to do this, since they assume a balanced three-phase system and their loss calculations are pretty rudimentary. This would required a PSSE type simulation with complex transformer and load modeling.

 

[Desrod2]

Dpc, saford42 will need to use a distribution type software supporting unbalanced LF since I believe PSSE does not support it. A Google search with the following will find some good references for such products: "distribution network analysis"
In North America we use single and multiphase supply for distribution load thus the need to correctly estimate phase voltage and current. Since losses are a function of I2, unbalanced load could result in losses increases but it will be significant for severe load unbalance. Just to illustrate the principle, let's assume that instead of having a perfectly balanced network (1.0 p.u. on each phase), we have 0.9 pu on phase A, 1.0 p.u. on phase B and 1.1 p.u. on phase C we will see losses at 0.81 on phase A, 1.0 p.u on phase B and 1.21 p.u. on phase C giving us 3.02 p.u of losses instead of 3.0 p.u....it's not much but it is there in theory. I am not considering the current in the ground carrying the unbalanced current.
Naturally, there are some assumptions that we have to validate if we want to find out how a voltage unbalance translate into a current unbalance. Is the load constant impedance, constant power, mixed?
Hope this will help
Daniel

 

[MKFPE]

I note that you work for a municipal system.

I do as well, and in my case this means a limited budget available for engineering tools.

If you are in the US, APPA DEED has an inexpensive book covering manual calculations as well as inexpensive software.

I have used their TRANSPAC program for many years (DOS version!).

WinIGS is another program that handles unbalanced circuits, is relatively inexpensive to license, and does a lot of other useful things, including fault calculations and especially grounding design and GPR.

Any of these tools will provide a calculated cost at a particular load but your load varies every hour of the year.

You will need to apply load factor/loss factor techniques to your calculated peak loss similar to transformer loss evaluations to arrive at your annual cost.

There is a lot of material available on-line covering this subject. The old REA Bulletin 61-16 is an example.

 

[jghrist]

There will be a loss increase from unbalanced voltage because of the unbalanced load current that result. A small unbalanced voltage on motors will cause a large unbalanced current.

Distribution analysis programs will handle unbalanced loads, but you have to enter the load per phase in some manner. Typically, you would enter the feeder load by phase from measurements and allocate this by customer kWh, connected transformer kVA, or some other method. I doubt that the programs will calculate the increased unbalanced current from the unbalanced voltage - the current per phase is an entered value. You will have to estimate how much the voltage unbalance will affect the load. The unbalanced voltage input will only have a minor effect on the load, and will depend on the type of load model used (constant impedance, constant power, constant current). Motor current unbalance will be higher than the typical load model will predict.