Old Engineers Formula for kWh to kVA

[GSEng01]

I wonder if anyone out that can help me translate a formula I inherited from a now retired engineer. He was considered one of the best engineer our utility has ever had and he created a lot of spreadsheet that our people use daily. Now however, I've got the task of maintaining them. I've been puzzling over several formulas he used in various spreadsheets, one of which I've included below. To save anyone the trouble - yes, I've asked the engineer directly, but all he could tell me was that he doesn't remember where he got the information.

1. One such spreadsheet was used to kVA load on a 1? transformer based on the known kWh from multiple customers.
The formula to determine kVA from a given customers kWh is:

kVA load = (SQRT(kWH)*0.326)+1.51

I may be showing my relative "youth" in the engineering field, but I can't find this formula anywhere nor do the factors make sense to me. Can anyone on the forum shed some light on this one?

 

[mivey]

I wonder if anyone out that can help me translate a formula I inherited from a now retired engineer. He was considered one of the best engineer our utility has ever had and he created a lot of spreadsheet that our people use daily. Now however, I've got the task of maintaining them. I've been puzzling over several formulas he used in various spreadsheets, one of which I've included below. To save anyone the trouble - yes, I've asked the engineer directly, but all he could tell me was that he doesn't remember where he got the information.

1. One such spreadsheet was used to kVA load on a 1? transformer based on the known kWh from multiple customers.
The formula to determine kVA from a given customers kWh is:

kVA load = (SQRT(kWH)*0.326)+1.51

I may be showing my relative "youth" in the engineering field, but I can't find this formula anywhere nor do the factors make sense to me. Can anyone on the forum shed some light on this one?

It is based on empirical data, like the RUS A-B factors with a power factor assumption. It may or may not give you the correct answer for a particular customer, and more than likely won't.

 

[charlie b]

The formula to determine kVA from a given customers kWh is:

What it is is utterly absurd to even attempt to create a formula for this. Either you are not stating the situation correctly :happyno:, or the entire situation is nonsense:happyyes:. Come on, think about it.

Try it this way: I tell you that three friends and I took our four cars out for drives around the town this past weekend, and the total distance we drove was 256 miles. That is all I will tell you. Now, I want you to tell me (1) What was the maximum speed any of us drove at any given time? and (2) What was the average speed we drove for the entire weekend?

KW is a measure of power, or the rate at which energy is being used. KWH is a measure of the total amount of energy that has been used. How can you calculate the rate from the total? You can't.

 

[mivey]

What it is is utterly absurd to even attempt to create a formula for this.

Utilities use formulas like these for sizing transformers, making work plan studies, etc. so they do serve a purpose. The user just needs to make sure to use them for the intended purpose while accounting for the underlying assumptions.

 

[GSEng01]

What it is is utterly absurd to even attempt to create a formula for this. Either you are not stating the situation correctly :happyno:, or the entire situation is nonsense:happyyes:. Come on, think about it.

KW is a measure of power, or the rate at which energy is being used. KWH is a measure of the total amount of energy that has been used. How can you calculate the rate from the total? You can't.

Wow. Thanks for the sarcasm and the academic answer. "Utterly absurd" and yet it has to be done practically every day at every electrical utility.

 

[GSEng01]

It is based on empirical data, like the RUS A-B factors with a power factor assumption. It may or may not give you the correct answer for a particular customer, and more than likely won't.

Thanks mivey. I suspected it was based on empirical data, but wanted to get a few other opinions, just in case there was something out there I had missed.

 

[charlie b]

Thanks for the sarcasm. . . .

I wasn?t being sarcastic. I was giving my honest opinion. I apologize if I came across as being unprofessional in my response.

"Utterly absurd" and yet it has to be done practically every day at every electrical utility.

Then, as I said before, you are not describing the situation correctly. What is not clear to me is the input data and the output you are trying to calculate. What is clear to me is that one cannot infer a maximum rate of using energy based solely on the total amount of energy used. This may well be an empirical formula, but did you notice mivey?s comment to the effect that it is not likely to accurate for a particular customer?

 

[pfalcon]

Considering that it's old enough the original guy doesn't remember where the assumptions came from - I'd guess it now underestimates peak usage based on the increased use of electronics today. More things get turned on when people get home.

 

[GSEng01]

I wasn?t being sarcastic. I was giving my honest opinion. I apologize if I came across as being unprofessional in my response.
Then, as I said before, you are not describing the situation correctly. What is not clear to me is the input data and the output you are trying to calculate. What is clear to me is that one cannot infer a maximum rate of using energy based solely on the total amount of energy used. This may well be an empirical formula, but did you notice mivey?s comment to the effect that it is not likely to accurate for a particular customer?

Agreed. Sarcasm is easily inferred on text when none was implied. Likewise, I apologize if I misread your comments.

To be more specific - The formula is used to determine the approximate maximum load on an in-service transformer, based on the only data we have available - the kWh readings from the connected consumers. We are not attempting to determine the kVA for a particular customer, just whether or not the combined load of all consumers is still within the safe operating range of the transformer. I had misgivings about the formula from the start, but was giving it some credit due to the reputation of the engineer who developed it. I had previously concluded that the constants in the formula were likely based on empirical data - but the SQRT(kWh) was puzzling, as I couldn't think of any formula where that particular function is used. I am skeptical of the formula's results, hence my posting on this forum. The responses I've received have reinforced that skepticism. Now the difficult part will be developing a replacement formula that will have some hope of approximating the load on the transformer.

 

[K8MHZ]

Agreed. Sarcasm is easily inferred on text when none was implied. Likewise, I apologize if I misread your comments.

To be more specific - The formula is used to determine the approximate maximum load on an in-service transformer, based on the only data we have available - the kWh readings from the connected consumers. We are not attempting to determine the kVA for a particular customer, just whether or not the combined load of all consumers is still within the safe operating range of the transformer. I had misgivings about the formula from the start, but was giving it some credit due to the reputation of the engineer who developed it. I had previously concluded that the constants in the formula were likely based on empirical data - but the SQRT(kWh) was puzzling, as I couldn't think of any formula where that particular function is used. I am skeptical of the formula's results, hence my posting on this forum. The responses I've received have reinforced that skepticism. Now the difficult part will be developing a replacement formula that will have some hope of approximating the load on the transformer.

kWh for what period? A month? A day? An hour??????

 

[steve66]

kWh for what period? A month? A day? An hour??????

Its hard to evaluate this formula without knowing that. But I tried a few examples using KWH/day, and KWH per month.

For KWH per day, it way underestimated the load I used. For KWH per month, it way overestimated. You could say that my examples I used weren't real life, but I don't think that's the problem.

The formula given takes the square root of the KWH used. It calculates 1/4 the demand for 1/2 of the power used. That doesn't make any sense to me. It should be a straight multiplication of KWH to get some estimate of demand. If someone uses twice as much KWH as his neighbor, he will probably have twice the demand.

Also, if you look at the term on the end:
+ 1.51

that doesn't make any sense either. Assuming the utility is using this equation to size something like a transformer, they probably aren't going to use anything smaller than a 25 KVA transformer. Adding an extra 1.5 KVA doesn't seem like its enough to worry about. For a rough estimate like this, I could see adding maybe a 5 or 10 KVA spare capacity buffer onto the end of the equation. But 1.51? We aren't doing anything accurate enough to worry about the 3 decimal place.

I'm thinking this equation isn't right at all.

 

[ggunn]

Its hard to evaluate this formula without knowing that. But I tried a few examples using KWH/day, and KWH per month.

For KWH per day, it way underestimated the load I used. For KWH per month, it way overestimated. You could say that my examples I used weren't real life, but I don't think that's the problem.

The formula given takes the square root of the KWH used. It calculates 1/4 the demand for 1/2 of the power used. That doesn't make any sense to me. It should be a straight multiplication of KWH to get some estimate of demand. If someone uses twice as much KWH as his neighbor, he will probably have twice the demand.

Also, if you look at the term on the end:
+ 1.51

that doesn't make any sense either. Assuming the utility is using this equation to size something like a transformer, they probably aren't going to use anything smaller than a 25 KVA transformer. Adding an extra 1.5 KVA doesn't seem like its enough to worry about. For a rough estimate like this, I could see adding maybe a 5 or 10 KVA spare capacity buffer onto the end of the equation. But 1.51? We aren't doing anything accurate enough to worry about the 3 decimal place.

I'm thinking this equation isn't right at all.

If nothing else, from a dimensional standpoint the square root of kilowatt hours doesn't make any sense. That's the problem with "rule of thumb" equations that play fast and loose with dimensional units. It's impossible to tell how (or if) they were mathematically derived.

 

[GSEng01]

kWh for what period? A month? A day? An hour??????

Sorry. I suppose that's something we take for granted in the utility industry. Billing periods for electric utilities may vary based on several factors, but MOST will assume a 30-day period or one typical month in order to simplify calculations.

 

[al hildenbrand]

Billing periods for electric utilities may vary based on several factors, but MOST will assume a 30-day period or one typical month in order to simplify calculations.

I'd ask an additional clarification: Is the type of "multiple customers on a transformer" restricted to transformers in residential neighborhoods? Mixed light commercial and residential? Etc.

 

[K8MHZ]

Sorry. I suppose that's something we take for granted in the utility industry. Billing periods for electric utilities may vary based on several factors, but MOST will assume a 30-day period or one typical month in order to simplify calculations.

OK.

So, let's say we have two shops. One is a retail store that has lots of lights and no machinery. The other is a welding shop with a big air compressor. Both use the same amount of kWh each month. According to the formula, both shops would have the same peak demand because they both use the same amount of kWh each month.

As such, I don't see how ANY formula can convert from kWh to peak demand.

 

[rcwilson]

Curve Fitting Data

Curve Fitting Data

My guess is that the original equation is a curve fitting routine based on a lot of historical data.

For example, maybe the original data came from a graph of monthly peak demand on a feeder versus the sum of the kWh use for that month of all the customers fed by that feeder. A feeder from a substation probably has a peak load meter but individual transformers typically won't. Graph the data points for many, many feeders and customers in the utility service territory and we get a chart of peak load versus total monthly kWH.

The graph would have a bunch of dots all over that might show a trend. A curve fitting program or visual estimation could draw a curve approximating the average data. The program could come up with an equation that best describes the relationship between sum of customer's KWH and peak demand.

The original data analysis gave a curve with a minimum value. The curve increases in a non-linear fashion as the KWH goes up. ( 0.3 times 1/2 power of kWH).

The equation doesn't have to make sense directly to still be useful. It tells the planners that the utility's historical average peak for their customer mix can be estimated from the combined kWH of the customers. The equation empirically accounts for monthly kWH to peak KVA unit conversions, load diversity, demand factors, peak loads, average loads, customer mix etc. It won't be correct for any one customer, but it will match the utility's history close enough to size the transformers based on data from thousands of observations.

The trick is to figure out how to update the curve for the present customer load characteristics. With all the smart metering coming on line, the curve fitting may not be necessary, because utilities will be able to track actual peaks.

 

[jghrist]

Another old formula, from REA Bulleting 45-2, June, 1963, Demand Tables:

Demand = (Factor "A")?(Factor "B")
Factor "A" = C?[1 - 0.4?C + 0.4?(C? + 40)^0.5]
where C = # of consumers
Factor "B" = 0.005925?(kWh/Mo/Consumer)^0.885

Using 200 consumers at 400 kWh/Mo/Consumer gives

Factor "A" = 208
Factor "B" = 1.19
Demand = 247.5 kW

With your formula, you would get:

(SQRT(200?400)*0.326)+1.51 = 93.7

 

[pfalcon]

... kVA load = (SQRT(kWH)*0.326)+1.51 ...?

A lot of guestimates like this are reduced equations that someone thought made sense based on assumptions.

Since Power = Amps^2 * R = Volts^2 / R the term "SQRT(kWH)" is likely to represent Volts or Amps.
The constants are scaling and offset.

The original equation this was reduced from probably operated in the opposite direction using kVA to estimate kWH.
I'm assuming this since the voltage is one of the few knowns. And frankly it's what the equation looks like to me.

 

[steve66]

If nothing else, from a dimensional standpoint the square root of kilowatt hours doesn't make any sense. That's the problem with "rule of thumb" equations that play fast and loose with dimensional units. It's impossible to tell how (or if) they were mathematically derived.

Good point - the square root of KWH doesn't sound like the right dimensional units.

Another old formula, from REA Bulleting 45-2, June, 1963, Demand Tables:

Demand = (Factor "A")?(Factor "B")
Factor "A" = C?[1 - 0.4?C + 0.4?(C? + 40)^0.5]
where C = # of consumers
Factor "B" = 0.005925?(kWh/Mo/Consumer)^0.885

Using 200 consumers at 400 kWh/Mo/Consumer gives

Factor "A" = 208
Factor "B" = 1.19
Demand = 247.5 kW

With your formula, you would get:

(SQRT(200?400)*0.326)+1.51 = 93.7

Again, the square root just doesn't make sense to me. Assume you have the exact same situation with 400 houses. Now the peak demand only goes up to about 130kW. Doesn't make sense to me. Especially if everyone has air conditioning, and its a hot, humid 110 degree Saturday.

 

[Besoeker]

I wonder if anyone out that can help me translate a formula I inherited from a now retired engineer. He was considered one of the best engineer our utility has ever had and he created a lot of spreadsheet that our people use daily. Now however, I've got the task of maintaining them. I've been puzzling over several formulas he used in various spreadsheets, one of which I've included below. To save anyone the trouble - yes, I've asked the engineer directly, but all he could tell me was that he doesn't remember where he got the information.

1. One such spreadsheet was used to kVA load on a 1? transformer based on the known kWh from multiple customers.
The formula to determine kVA from a given customers kWh is:

kVA load = (SQRT(kWH)*0.326)+1.51

I may be showing my relative "youth" in the engineering field, but I can't find this formula anywhere nor do the factors make sense to me. Can anyone on the forum shed some light on this one?

That it's in a spreadsheet infers that, while it may be old, it isn't ancient. I can't remember when I first started using spread sheets but probably post 1980.