Reactive Capability Curve 1

[coolfish]

Does anyone know how to draw a generator reactive capability curve as a function of the cooling air (for an air cooled machine)? The centers of the circles are fixed but the radii of the circles will vary as a function of temperature (assuming constant voltage and frequency). Both stator and rotor have Class 155 insulation.

 

[cuky2000]

The manufacturer of the generator should be able to provide the performance of the unit for different cooling gas temperature. In absence of better information the following could help to obtain an approx. adjusted generator reactive capability performance.

Let’s use the following as example to describe an approximate procedure:
Ex. 250 MVA air-cooled generator, 15oC inlet air and 85% PF lagging. Determine the reactive capability curve for 40oC at rated power factor.

1- From the Generator MW vs. Gas Temperature curve, determine the normalized MW increment factor, K.
Ex. K= 1- MW40oC/Rate MW15oC = 0.80.

_{NOTE: In absence of any data for K, use the following approximation:
MW(T) = 180-1.44. T. T = Ambient Temp (oC)}

2- Maintain fix the under excited point witch is the point (MW=0, -MVAR). This point does not set by thermal limits because is determined by the minimum excitation and stability limits requirements.

MVAR40oC @ 0 MW = MVAR15oC @ 0 MW.

3- Determine a set of points Adjust set of points

For MW: MW40oC = K . MW15oC.

For MVAR: MVAR40oC = [K+(1+K).(1-MW15oC/Tarted max MW15oC)].MVAR15oC.

4- Draw the new reactive capability curve for 40 oC with the new values determined in 2 & 3 above.

References:
1- IEEE 67-1990, “IEEE Guide for Operation & Maintenance of Turbine Generator”
2- Siemens/Westinghouse: Technical Appendix, “Adjustment of Generator Capability Curves-General Guideline”.

 

[electricpete]

I vote another well-deserved star to cuky

 

[jbartos]

Suggestion: What kind of generator is under consideration?
1. A synchronous generator capability curve has approximate equations for circles:
1a. For the armature heating limit (circle)
Apparent power = (P**2 x Q**2)**(.5)=Vta x Ia
where
Vta x Ia is the circle radius from the power coordinates center will vary as temperature and Ia change
Assume the operation under conditions of constant terminal voltage and armature current (at the maximum value permitted by heating limitations.)
1b. For field heating limit (circle)
P**2 + (Q + (Vta**2)/Xs)**2 = (Vta x Eaf / Xs)**2
The circle is centered on Qc=-(Vta**2/Xs)
Assume Terminal Voltage constant
Eaf is limited to a maximum value as determined by heat limitations. Eaf (and Iaf) will vary as temperature changes.

 

[coolfish]

Thank you very much for the information. Is the Siemens/Westinghouse paper, Adjustment of Generator Capability Curve available? I've checked their websites and did a search but I can't find any reference to the article/paper.

 

[jbartos]

Suggestion/Correction:
1. Correction (I beg your pardon):
Apparent power = (P**2 + Q**2)**(.5)=Vta x Ia
2. Check with

http://www.beckwithelectric.com/infoctr/upgrading.pdf

since they upgrade generator protection for the coming digital technology.

 

[jbartos]

Suggestion: The Siemens advertizes

http://www.siemenstd.com/PA/10GenAppPage.html

relays that track the actual generator capability curve.

 

[jbartos]

Suggestion: Try the Siemens Product Line Engineering

http://www.siemenswestinghouse.com/en/steamservice/steamonsite/geservice/index.cfm

 

[coolfish]

Thanks again. What we are trying to do is to monitor the operation of our generator relative to its capability curve. If the operating point is within the curve, nothing further is required. If the operating point is outside the curve, the difference is recorded as well as the time it operated outside the limits. The intent is to knwo how much and how long we're exceeding the curve and hopefully compare this with some vlaues from the manufacturer. We're assuming constant terminal voltage and frequency. However, the radii of the circles varies with the incoming cooling air temperature.
Any thoughts? Any alternative way of achieving the same results? The machine is 30 years old.

 

[jbartos]

Suggestion: The Vta, Ia can be measured and Eaf measured or calculated if Xs is known.

 

[cuky2000]

Check the enclose site for Mathcad Application File no 173 for a sample of calculation of generator reactive capability curve.
If you do not have this program use the mathcad browser to see this work. I believe the browser is free download software.

MATHCAD APPLICATION PROGRAMS:

http://www.mathsoft.com/appsindex.html

 

[electricpete]

From what I can tell the files cannot be accessed without mathcad. The browser plug-in viewer requires the user to own mathcad. There are a small subset of files (not including the generator reactive capability) that do not reqruire mathcad which are accessible by clicking the link in the 2nd paragraph of your linked page.

 

[jbartos]

Suggestion: The mathcad file is ok. It can be cut and pasted into MS Word.