# Spin-Up Sample Exam Problems Discussion



## Insaf (Jan 30, 2012)

Please ask for explanation of Spin-up sample exam problems. Hope forum members will help to understand the problems and their solutions.

Thanks,


----------



## Insaf (Feb 1, 2012)

Q. 1-56: In electrical engineering, average value of sine wave is not zero rather it is 63.7% of peak value. Its always averaged over half cycle (not over full cycle).

Here is the math:Vavg=(1/pi) [(Integrate over 0 to pi (sinө dө)]=0.637Vm.


----------



## cali78 (Feb 1, 2012)

Insaf said:


> Q. 1-56: In electrical engineering, average value of sine wave is not zero rather it is 63.7% of peak value. Its always averaged over half cycle (not over full cycle).
> 
> Here is the math:Vavg=(1/pi) [(Integrate over 0 to pi (sinө dө)]=0.637Vm.


In Camara's reference book in Table 27.2 , it says the average of a Sine Wave is 0. Half wave is .637


----------



## Power12 (Feb 1, 2012)

The integral of a sine wave over a full period (360 degrees) is = 0


----------



## mauldinite (Feb 2, 2012)

I noticed that question last night. The question states "the sine wave shown," which is a full cycle. For the full period shown in the diagram, the average is 0.


----------



## Insaf (Feb 2, 2012)

In electrical engineering, we used to have “Form Factor” of sine wave which is defined as ratio of RMS value to average value. If average is zero, what will happen?

My understanding as we learned from college:

In case of symmetrical alternating signal, the average value is zero. Hence in that case, the average value is obtained by adding or integrating the instantaneous values of signal over one half –cycle only.

Additional:

In the same book, problem 2-10, answer described as “The average magnitude of sine wave is the peak *(2/pi) (i.e., 63.7% of peak value). What is the difference between average value and average magnitude?


----------



## DK PE (Feb 2, 2012)

Insaf said:


> IWhat is the difference between average value and average magnitude?


The average value takes into account that for half the period the value is negative and it therefore subtracts. The magnitude is always positive and would therefore be the output of a full wave rectifier.


----------



## Insaf (Feb 2, 2012)

Spin-up prob 2-14:

Slack or swing bus where voltage magnitude and angle are specified (generally angle set to zero). Normally there can only be one slack or swing bus in the system and it is generally chosen from among the voltage controlled buses.

In this problem slack and swing buses are described as different, but its not. It looks voltage controlled buses referred as generator’s bus (major types of buses: Load Buses, Voltage Controlled buses and Swing / Slack bus). According to the definition of the buses, slack or swing bus (one of the voltage controlled bus chosen as slack or swing bus) keeps voltage constant.

Any explanation from Spin-up or forum members will be appreciated.


----------



## Insaf (Feb 2, 2012)

Spin-up problem 2-15: In solution MVAL=6, from where it is coming?

Thanks,


----------



## Ivory (Feb 2, 2012)

Insaf said:


> Spin-up prob 2-14:
> 
> Slack or swing bus where voltage magnitude and angle are specified (generally angle set to zero). Normally there can only be one slack or swing bus in the system and it is generally chosen from among the voltage controlled buses.
> 
> ...


The generator bus is the answer. It is known as the voltage controlled bus. My book does not say the slack and swing buses are described differently. I see the slack bus as a possible answer or swing bus as another possible answer. I think the answers are just trying to confuse you.


----------



## Ivory (Feb 2, 2012)

Insaf said:


> Spin-up problem 2-15: In solution MVAL=6, from where it is coming?
> 
> Thanks,


For these type of problems I use the trial and error method. I multiply the generator MVA by the other generators impedance.

SA = 2 times 3 = 6

SB = 3 times 4 = 12

Then I see SA is equal to half of SB

Since Gen B has a max load of 4MVA, therefore Gen A is half of 4 MVA which equals 2MVA

So MVAL = SA + SB = 2MVA + 4 MVA = 6MVA


----------



## bethy (Feb 3, 2012)

I like this solution better. The solution from the test takes more more time to calculate. I tried to use this method to solve one of the sample from the NCEES and the answer is easier to understand.

Thanks Ivory.

There is a couple problems calculating the fault current by using MVA method. Usually, we need to choose the base MVA, base Voltage, then calc the total fault Z and fault MVA. Then using fault MVA and fault Z to calc the fault current. But Spinup using different way to solve it. It confuse me since I use SpinUp method to solve one of the problem from NCEES (from 500 series - the one with 100MVA base, 20mile transmisstion line, 7.5KVA Transf) and it did not work. Any idea??


----------



## EEVA PE (Feb 3, 2012)

bethy said:


> I like this solution better. The solution from the test takes more more time to calculate. I tried to use this method to solve one of the sample from the NCEES and the answer is easier to understand.
> 
> Thanks Ivory.
> 
> There is a couple problems calculating the fault current by using MVA method. Usually, we need to choose the base MVA, base Voltage, then calc the total fault Z and fault MVA. Then using fault MVA and fault Z to calc the fault current. But Spinup using different way to solve it. It confuse me since I use SpinUp method to solve one of the problem from NCEES (from 500 series - the one with 100MVA base, 20mile transmisstion line, 7.5KVA Transf) and it did not work. Any idea??


There is two ways to solve these questions, either PU or MVA. Show us the way you solved it with your calculations. We could then point out where you went wrong. Both methods will give the same answer.


----------



## Power12 (Feb 3, 2012)

EEVA PE said:


> bethy said:
> 
> 
> > I like this solution better. The solution from the test takes more more time to calculate. I tried to use this method to solve one of the sample from the NCEES and the answer is easier to understand.
> ...



I agree with EEVA, both methods should get the same answer. During the exam if I have enough time I will do it both ways to check myself, to make sure I solved the fault problem correctly.

Bethy, you must be talking about NCEES prob # 513. The way to solve this problem using the method from spinup is

S short circuit for the transformer is = S/Z = 7.5 X 106 /.075 = 100 MVA

S short circuit for the conductors is = V2 / Z = (12 X103)2/ 15.312 = 9.4 MVA

The total short circuit is calculated with Trans and conductors similiar to series capacitors so = ((100 X 106) (9.4 X 106))/((100X106) +(9.4 X 106)) = 8.6MVA

Isc = Ssc/(sqroot 3 X V) = (8.6 x10 6) /((1.73)(12 x 103) = 414 A which is the same answer that is in the NCEES


----------



## forest (Feb 4, 2012)

Spin-up Problem 3-4:

Should the answer is d? Would you let me know why the answer is c?

Thank you


----------



## bethy (Feb 4, 2012)

I used the same method.

SA = 3x4 = 12

SB = 4x3 = 12

So Gen A should equal to Gen B.

SA = SB = 3MVA (can not choose 4MVA since it's overload Gen A).

ST = 6MVA (answer C)

Thanks to EEVA and Power12 for the MVA fault method. I did the calc wrong on the series capacitors. But I have another question and need your help to understand problem with power factor correction (lagging and leading reactive power). I got confuse every time I try to solve it. I used the formula below to calc the KVAR added

Qc = P [(tan(cos-1PF1) - tan(cos-1PF2)]

For NCEES sample # 502: From the formula above Qc = 8.4KVAR. To improve the PF to .9 lagging we need to add capacitor in (Q&lt;0). It means the reactive power Qc = -8.4KVAR (negative).

Then from #503: With my understanding the answer should have the negative sign (-) 3370KVAR. But the answer is positive KVAR (Q&gt;0).

Am I missing something here?? The equestion asking "the total reactive power supplied by a 3 phase capacitor....Do we need to find the magnitude of the reactive power? What is the key point here??

Any easy way (rule of thumb) to recognize when it should be negative or positive KVAR??

spin-up proble 3-27 and 4-07, I got the correct answer, but the NCEES 503 confused me.

Thanks.


----------



## Insaf (Feb 4, 2012)

Regarding problem 503:

You calculated perfectly (-) 3370 KVAR. The var supplied by capacitor is always negative and this question asking only to find the magnitude of KVAR required.

Please note that in question # 502, you have to decide what type of var (capacitive or inductive) is required to correct the power factor.

Thanks,


----------



## mauldinite (Feb 8, 2012)

I'm having some trouble understanding the solution for problem 3-02:

The diagram shows 2 gens in parallel, G1 is 175KVA, 2%; and G2 is 275KVA, 4%. These are tied to a transformer that is 400KVA, 5%, with a fault on the low side of the transformer. The question is as follows:

"Using the provided diagram, the three-phase distribution system has a voltage of 480V on the secondary side. Use the MVA method to find the short-circuit current at the fault."

The method used in the solution is to calculate the MVA fault contribution for each generator and add them. This value is taken in parallel with the transformer fault MVA (Srated/Zpu). In other words,

(Ssc-Gens * Ssc-TX)/(Ssc-Gens + Ssc-TX)

From there, total fault current is calculated as (Ssc-Tot)/(Vrated*sqrt(3)). Their answer is 6,375 A.

That goes against the method I've known as the MVA method (from the Camara PPI book). With that method, I would select a base-S (I used 400KVA). With that base I would calculate the new Zpu values for each generator and the transformer. Since the gens are in parallel, I then have

(Zpu-Gen1 * Zpu-Gen2)/(Zpu-Gen1 + Zpu-Gen2) + Zpu-TX = Ztotal

With this I calculate S-FC = Sbase/Ztotal = 7.062 MVA.

From there, I get Isc = Ssc/(Vrated * sqrt(3)) = 8495 A.

My biggest hangup is that the Spinup solution takes the generator power contributions in series and then it takes the total contribution in parallel with the max of the transformer. Can anyone steer me in the right direction here?


----------



## Power12 (Feb 8, 2012)

mauldinite said:


> I'm having some trouble understanding the solution for problem 3-02:
> 
> The diagram shows 2 gens in parallel, G1 is 175KVA, 2%; and G2 is 275KVA, 4%. These are tied to a transformer that is 400KVA, 5%, with a fault on the low side of the transformer. The question is as follows:
> 
> ...



Mauldinite,

You are looking at it backwards. You handle the parallel power sources as additive and the series as capacitors.


----------



## Power12 (Feb 8, 2012)

Power12 said:


> mauldinite said:
> 
> 
> > I'm having some trouble understanding the solution for problem 3-02:
> ...


The MVA method does not include converting to per unit. There must be an error in Camara's book.


----------



## Power12 (Feb 8, 2012)

hmmm..... I get the same answer as Maulinite when doing it the PU method.


----------



## mauldinite (Feb 9, 2012)

Ok, further reading clarified that you treat the S-values as you would capacitors. Thanks for helping me out everyone!

I've always used the per-unit method since most of the time, they throw in some impedance in the line. Also, the Camera book describes looks like it describes the per-unit process well enough, but then in the example problem (36.8), the solution uses the per-unit method! That's where I got confused.

Still, using the per-unit method I would think I should be getting the same answer. If anyone has any more input, please let me know!


----------



## mauldinite (Feb 9, 2012)

Woops. Wrote that last post a little too fast. I meant that the Camera book describes the MVA method well enough.


----------



## spinup (Feb 11, 2012)

mauldinite said:


> I'm having some trouble understanding the solution for problem 3-02:
> 
> The diagram shows 2 gens in parallel, G1 is 175KVA, 2%; and G2 is 275KVA, 4%. These are tied to a transformer that is 400KVA, 5%, with a fault on the low side of the transformer. The question is as follows:
> 
> ...


It is important that everyone understand that the answer should be the same no matter which method is used to come up with the solution. You should use the method that you are most comfortable with on the exam. Spin-Up will be providing this question as the "Question for the Week" with the solution done both ways. The question and both solution methods will be posted tomorrow (Sunday).

www.spinupexams.com

Joan


----------



## spinup (Feb 12, 2012)

spinup said:


> mauldinite said:
> 
> 
> > I'm having some trouble understanding the solution for problem 3-02:
> ...


QFTW has been uploaded.

www.spinupexams.com

Joan


----------



## mauldinite (Feb 13, 2012)

Ahhhhh, was swapping Sbase new and Sbase old the whole time! Thanks Spin-Up!


----------



## Insaf (Feb 25, 2012)

Spin up problem 2-65:

I believe for calculating "daily load factor" 24 hours should be used instead of 6 hours. Any comments about the spin-up solution will be appreciated.

Note: This answer could be right if there is any "quarter day load factor".

Thanks,


----------



## cali78 (Feb 25, 2012)

Insaf said:


> Spin up problem 2-65:
> 
> I believe for calculating "daily load factor" 24 hours should be used instead of 6 hours. Any comments about the spin-up solution will be appreciated.
> 
> ...


Load Factor is also a function of availability. Since the generation was only avail for 6 hours for a given day and used at half capacity for 5 hours and zero capacity for the other hour than the Load Factor is

((.5 hrs use )(5 hr avail) + (0)(1 hr avail))/ ( 6 hrs of Max Capacity) = 42%

The load factor for the generator is a measure of the output of the generator compared to the maximum output the generator could *"produce"*. Since the generator is only avail for use to produce power for 6 hrs daily, then one needs to use 6 hrs. If the generator was avail for 24 hours then 24 hrs would of been used. The problem was a little tricky.


----------



## Insaf (Feb 25, 2012)

Thanks Cali78!!


----------



## Insaf (Feb 25, 2012)

Spin up problem 2-69 and 3-01:

Why the solutions methodologies are different ?

Thanks,


----------



## Ivory (Feb 26, 2012)

Insaf said:


> Spin up problem 2-69 and 3-01:
> 
> Why the solutions methodologies are different ?
> 
> Thanks,


Careful on those. They are different type of questions, therefore different solution methodologies. The sawtooths are the same in the picture, but one of them are asking for average and the other average "magnitude". They are different questions. I used to mix them up and not pay attention to that word "magnitude" which changes things.

On the real exam I am going to read all the questions slowly, to make sure I do not get misled and provide the wrong answer.


----------



## EEmarcus (Mar 5, 2012)

Back to question 2-65 the question asks for load factor. My formula for this is LF=(Avg Load)/(Peak Load). But the answer provided is a formula for capacity factor. CF= (Avg Load for a period)/(Output Capacity of Plant). This is according to my reference book. Aren't these two things different?

The peak load is 500KW and the avg is 2500MW/(6hrs) = 416.67KW

My solution thus is 416.67/500= 83%.


----------



## Insaf (Mar 17, 2012)

Spin-up prob 3-78: Why MVAL= 12, any feedback will be appreciated ?

Thanks,


----------



## Ivory (Mar 18, 2012)

Insaf said:


> Spin-up prob 3-78: Why MVAL= 12, any feedback will be appreciated ?
> 
> Thanks,


SA = 6 X 2 = 12

SB = 8 X 3 = 24

When in parallel, SB = 2SA

The max load of Trans B is 8MVA which limits Trans A to 4MVA. Therefore the total Max load is 4MVA + 8MVA = 12 MVA


----------



## BH_Cubed (Mar 29, 2012)

Problem 5-53

I'm not quite sure how where the -38.25&lt;-27.8 is coming from in the second line of the solution. It seems like they multiplied the current 100&lt;-36.9 by the impedance 0.51&lt;9.1 then by the 750/1000 for the length of the cable. Shouldn't you multiply the impedance by the 750/1000 first because the impedance is per unit length? When I do this, I get a different answer. I calculated Z=(.51&lt;9.1)*(750/1000) = 0.38&lt;9.1 . Then IZ = (100&lt;-36.9)*(0.38&lt;9.1) = 37.98&lt;-27.8. If you subtract that from 480 you get 442V at the load not 422V. I think the solution may be incorrect. or maybe I'm doing something wrong? 442V is answer C


----------



## BH_Cubed (Mar 29, 2012)

oh way nevermind, i'm missing the root 3. duh

:beat:


----------



## GreenNGold (Mar 1, 2014)

I had a few questions:

1) Spin Ups Problem 1-80: When a generator is overloaded, the frequency will drop...but when will a generator trip offline?

2) Spin Ups Problem 2-4: Can anyone help explain how to differentiate between buck and boost autotransformers?

3) Spin Ups Problem 2-15: Are the equations for parallel transformers &amp; parallel generators the same?

KVA1 = ((KVA1/Z1%) / ((KVA1/Z1%) + (KVA2/Z2%))) * KVAL

KVA2 = ((KVA2/Z2%) / ((KVA1/Z1%) + (KVA2/Z2%))) * KVAL

I used the two above equations and solved for MVAL for each case. I got MVAL = 9 for case 1 and MVAL = 6 for case 2. Then I used 6MVA as my load because anything higher would overload generator B, plugged it back into this equation KVA2 = ((KVA2/Z2%) / ((KVA1/Z1%) + (KVA2/Z2%))) * KVAL and got MVA2 = 4 MVA. Does the way I did this make sense?

4) What are the ranges for low voltage, medium voltage, and high voltage? I googled it and it says Low voltage is 0-1000V, medium voltage is 1kV to 36kV, and anything higher is high voltage.

Thank you.


----------



## Ship Wreck PE (Mar 3, 2014)

A generator is normally protected with a overcurrent breaker located on the generator, and when the current exceeds the set amount for a given time, it will trip out the circuit.
Most newer generators are programmable and they will not transfer until the frequency, voltage, and phases are all correct, They can be programmed to drop out at low voltage, high voltage, low frequency, high frequency, Phase loss, or an overcurrent condition, But they can be programmed to not do all of this also.

A buck transformer lowers the voltage and the boost transformer raises the voltage, and in the spinup workbook the buck transformer is noted by the transformer diagram being wider than the boost..


LV = Voltage levels that are less than or equal to 1 kV

MV = Voltage levels that are greater than 1 kV, but less than or equal to 69 kV

HV = Voltage levels that are greater than 69 kV, but less than or equal to 230 kV

EHV = Voltage levels that are greater than 230 kV, but less than or equal to 800 kV

UHV = Voltage levels that are greater than 800 kV


----------



## GreenNGold (Mar 3, 2014)

For problem 2-4, isn't it a buck because of the location of the dots? I don't think I completely understand what you mean by the buck transformer being wider than the boost. I always thought step-up and boost were the same and step-down and buck were the same but the answer for this problem is step-up, buck.

I assume the transformer is a step up because the load is connected across the series and common winding, and it is a buck because the currents will cancel due to the dot convention?


----------



## Ship Wreck PE (Mar 4, 2014)

I sold my spinup book so I really don't recall the problems.


----------



## GreenNGold (Apr 5, 2014)

For problem 19 in exam 5, why is 2 x 10^-2 used rather than 4 x 10^ -7?

I have seen two equations for inductance per phase, (2 x 10^-7) ln (GMD/GMR) and (4 x 10^-7) ln (GMD/GMR). Can anyone clarify when each should be used? Thank you.


----------



## GreenNGold (Apr 6, 2014)

Is (2 x 10^-7) ln (GMD/GMR) used when per phase inductance is asked for? And (4 x 10^-7) ln (GMD/GMR) for total inductance?


----------



## Electron (Apr 6, 2014)

Do some searching on 3 Phase Inductance vs Single Phase Inductance Calculations.


----------

