Does household energy conservation have diminishing returns?

[Habeed]

A little mental experiment. I’ve been reading up on more efficient ways to heat hot water for your house.

Suppose you start with an electric tank model hot water heater. That’s just about the most expensive way to do it. It costs you X dollars per year to provide the hot water you need.

So you upgrade to a natural gas fired hot water heater. You pay a few hundred bucks for the heater and a bunch of money to install new gas lines and vents.

Calculator located heresays that if you need 50 gallons of hot water/day, at 11 cents per kWh, it’s gonna run you $408/year.

Gas is going to cost $115/year, or 28% of the original cost, X.

You save $293/year, so you’ll definitely get a return on investment, even if it cost $1500 to install the gas lines and vents.

Ok, well, what about solar hot water? A quick estimate from the graph shown here, and it looks like a solar hot water system reduces your costs to 40% of what it was before.

This means that if you started with electric, you save 408*.6 = $244/year, but if you started with gas, you save only $69/year. A solar hot water system costs you $721, so you’ll definitely make the money back if you have an electric heater, but it’s a marginal proposition if you have gas.

Well, let’s do even more. Let’s purchase (either when the house was built or when it’s time to replace it anyway) a geothermal A/C system that happens to include a heat-pump heated hot water supply. You only run it during the summer when the heat from it is “free”, and it provides half your hot water heat needs.

So if you had a natural gas + solar heater, your bills are already down to .4*109 = 43/year. This system now only has to do half the work, so now you save $21 more per year - you’ll definitely not make back the money it cost to install this thing.

Why stop here? Why not include an energy reclaiming heat exchanger. The cold water supply to your showers will loop around this heat exchanger on their way to the shower taps. This means you use even less energy when taking a shower.

Those cost about $500, and let’s say they reduce your water heating needs in half again. Totally not worth it if you already have taken other conservation measures.

Working through this problem mentally, it brings up another point. There must be a theorem to this. If you have several alternatives, each one of which will cost a certain amount of money, X, and save you a certain amount of money, Y. Do you want to always pick the alternative that has the best ratio between cost and money saved (even if it has a small absolute effect), or do you want to pick the alternative that saves the most total money, regardless of cost?

Or do you have to run a computer program to consider all possible combinations of alternatives until you find the one that provides the maximum net present value?

Finally, I’ve read this a few times. People talk about installing solar on their roofs to reduce electric bills. Frequently, the response is “fix your insulation first”. As a matter of fact, since solar scales linearly - 2 solar panels give you double the power of one - past a certain level of efficiency, it will always make more sense to install more solar than to try to conserve more energy.

The same argument has been made more broadly, that the U.S. as a whole doesn’t need more sources of energy (fracking/nuclear/solar/wind), it just needs to conserve the energy it already has more effectively.

[Habeed]

Regarding my last point : what I mean is, since each energy conserving measure has diminishing returns, since it is operating upon a lower initial cost, this means that many tricks for, say, fuel efficient cars aren’t worth it past a certain point.

If a car already has a certain level of efficiency, the cost of a complex and expensive system on the car to save fuel will exceed the cost of fuel saved over the car’s lifetime. Also, there’s system lifecycle costs, you can’t just compare up front costs, you have to include maintenance.

Some of the complex systems I mentioned above would have a hugely negative ROI because they only save a little energy but require maintenance and eventual replacement.

[dracoi]

In a nutshell, yes.

There’s no way to get hot water without some energy input; reducing losses can make sure you don’t lose more energy maintaining the temperature, but can’t change the minimum heat. Even looking at the process of heating the water in the first place - even if you have a 100% efficient system of heat transfer, the laws of physics still state a minimum energy to heat the water.

Of course, it’s also true that most houses leak like a sieve, especially older and cheaper buildings. Many people get the best bang for their buck in improving efficiency.

The calculation of what actually gets you the best result could be calculated using an NPV-style calculation. The disadvantage is that a lot of assumptions go into - what’s the future cost of money and the future cost of power? A tax credit can be introduced or expire at any time; a new tax on “dirty” energy could be introduced at any time. So the calculations can be done, but two different people could both use reasonable assumptions and arrive at totally different answers.

[md2000]

I think you seriously underestimate just how much energy a household uses.
the amount of electricity required to run an electric car, for example, is huge. A few solar panels on the roof won’t cut it.

the biggest problem is that the sun doesn’t always shine nice and warm when you often need hot water the most - in the early morning or late after sundown. It’s worse in the winter. Also solar electric panels are fairly inefficient. probably heating water in a solar heating panel is more efficient than creating electricity to heat water. The, factor in how much energy you use doing simple tasks like cooking. (I do wonder, though, whether it’s necessary to use so much energy baking the dishes once the dishwasher has done its wash cycle.)

I wonder if there are more efficient ways - for example, is it faster to heat a bowl of water in the microwave, then pour it into a pot on the stove to continue cooking?

Yes, of course, the first few pounds are the easiest to lose in any diet. At a certain point the law of diminishing returns sets in. Buy a Smart car or a Prius for your commute- something like 80% of commuters travel one person per vehicle, an SUV is a total waste. Better yet, cycle or take transit - but modern north American cities don’t have the layout or roads for cycling, nor any efficient transit infrastructure. That change will cost more than replacing your hot water heater.

look at your expenditures. A hot water tank costs you, at worst, $408/year you say. If you fill up your car $40 every week for a year, that’s about $2,000 in gas. Cut that in half saves a lot more. CFL lighting saves a lot of electricity, new LED lighting even more. Smart thermostats save a lot of the heating or air conditioning costs by turning services down while nobody’s home.

[beowulff]

Does household energy conservation have diminishing returns?
Absolutely. The only way to do this rationally is to do a Pareto analysis of your energy usage, and pick the low-hanging fruit first. For example, there’s no way that replacing a 13W CFL with a $10 9.5W LED in a closet which is used for 1hr/month will pay back the cost of the LED.

Similarly, increasing your insulation from R-4 to R-32 might be worth it, but it’s unlikely to be economically justifiable to increase from R-32 to R-64.

Even items with huge energy impacts - like HVAC systems - need to be looked at closely. It almost always makes sense to replace a broken HVAC with a much more efficient model, but it rarely makes economic sense to upgrade a working unit just on the basis of energy efficiency.

[KneadToKnow]

Does anything not have diminishing returns?

[Carl_Pham]

Don’t forget also your opportunity costs – what *else * you could be doing with the money, time, ingenuity, et cetera. This is arguably a more potent issue at the state and national level. For example, a nation that spent $5 billion on “clean coal” initiatives could instead spend $5 billion on developing a much safer nuclear reactor, or make a breakthrough on fusion. You only get to spend the money once.

The advantage of something like reducing demand is that you know what its payoff will be. But that is also its disadvantage – there is no room for serendipity, discovery, ingenuity, which is what you can get when you focus on new supply and growth. I think which you choose reflects the zeitgeist: in optimistic times, nations try to discover new ways of doing things. In pessimistic times, nations focus on reducing the cost of doing things the way they’ve always been done.

[Carl_Pham]

@KneadToKnow

Does anything not have diminishing returns?

No process that can be defined as reducing entropy fails to exhibit the phenomenon, courtesy of the Second Law of Thermodynamics. Conversely, any process that increases entropy – roughly speaking, any destructive process, like a wildfire, avalanche or riot, can and often does display the opposite effect, whereby the size of the return grows with the size and duration of the investment.

There are a few odd cases of phase transitions, e.g. crystallization, were apparent order can actually be entropically driven, and therefore which can snowball in the same way. In the realm of social affairs, this would be like a preference cascade or (successful) revolution.

[Habeed]

@beowulff

Does household energy conservation have diminishing returns?
Absolutely. The only way to do this rationally is to do a Pareto analysis of your energy usage, and pick the low-hanging fruit first. For example, there’s no way that replacing a 13W CFL with a $10 9.5W LED in a closet which is used for 1hr/month will pay back the cost of the LED.

What if it’s a 60 watt lightbulb. You can choose to either spend $10 on that Cree LED bulb, or about $2 for a CFL. To inject some numbers, the LED takes 10 W and the CFL takes 13 watts, and electricity is at 11 cents/kWH. Which alternative is superior, and how do you compute this?

Both have positive NPV, but the rate of return on investment is higher for the $2 CFL (since $2 gets you 60 minus 13 watts in energy savings). I mean, I “want” the LED because it lasts longer, doesn’t have the mercury problem if you break it, and turning it off and on won’t shorten it’s life. But how do I figure out which alternative is better from the math?

[Habeed]

@Carl_Pham

No process that can be defined as reducing entropy fails to exhibit the phenomenon, courtesy of the Second Law of Thermodynamics. Conversely, any process that increases entropy – roughly speaking, any destructive process, like a wildfire, avalanche or riot, can and often does display the opposite effect, whereby the size of the return grows with the size and duration of the investment.

Strictly speaking, doesn’t a solar panel increase entropy (because it converts lower entropy rays of sunlight into higher entropy heat) and insulation decrease it (since it prevents the spread of heat)?

I mean, I know that “the size of the return grows with the size and duration of the investment” is factually true with regards to solar, as larger arrays for longer time periods produce more return, at a rate slightly larger than 1. More insulation scales with a rate less than 1.

[KneadToKnow]

@Carl_Pham

No process that can be defined as reducing entropy fails to exhibit the phenomenon, courtesy of the Second Law of Thermodynamics. Conversely, any process that increases entropy – roughly speaking, any destructive process, like a wildfire, avalanche or riot, can and often does display the opposite effect, whereby the size of the return grows with the size and duration of the investment.

There are a few odd cases of phase transitions, e.g. crystallization, were apparent order can actually be entropically driven, and therefore which can snowball in the same way. In the realm of social affairs, this would be like a preference cascade or (successful) revolution.

Good to know! Thanks!

[beowulff]

@Habeed

What if it’s a 60 watt lightbulb. You can choose to either spend $10 on that Cree LED bulb, or about $2 for a CFL. To inject some numbers, the LED takes 10 W and the CFL takes 13 watts, and electricity is at 11 cents/kWH. Which alternative is superior, and how do you compute this?

Both have positive NPV, but the rate of return on investment is higher for the $2 CFL (since $2 gets you 60 minus 13 watts in energy savings). I mean, I “want” the LED because it lasts longer, doesn’t have the mercury problem if you break it, and turning it off and on won’t shorten it’s life. But how do I figure out which alternative is better from the math?

This ends up being an economics problem, not an engineering one.

The rule-of-thumb is: an efficiency investment is worthwhile if the payback is two years or less. Of course, this is a judgement call, and being able to call yourself “green” may mean that you are willing to extend the payback time to as much as 5 years. But, beyond that, there’s no way to justify the upgrade for purely economic reasons (i.e. - there are better ways to invest your money).

So, for your example, at 10¢/KWH, your 60W IC bulb is costing you $6 every 1,000 hours, while your 13W CFL would only cost $1.30. So, the playback is pretty quick (under 500 hours), if you use it a lot (and, this doesn’t include the savings due to the much better longevity of the CFL).
But, if this same 60W bulb is in a place where it is only used a few hours/month, then the numbers say it’s not a good idea to replace it.

[dracoi]

@Habeed

Strictly speaking, doesn’t a solar panel increase entropy (because it converts lower entropy rays of sunlight into higher entropy heat) and insulation decrease it (since it prevents the spread of heat)?

I mean, I know that “the size of the return grows with the size and duration of the investment” is factually true with regards to solar, as larger arrays for longer time periods produce more return, at a rate slightly larger than 1. More insulation scales with a rate less than 1.

If the question is “does x increase entropy?” the answer is going to be “yes” - it’s just one those things that sucks about real life.

I wouldn’t say that insulation decreases entropy. Probably better to say that it slows the change of entropy.

[Habeed]

@beowulff

This ends up being an economics problem, not an engineering one.

The rule-of-thumb is: an efficiency investment is worthwhile if the payback is two years or less.

So, for your example, at 10¢/KWH, your 60W IC bulb is costing you $6 every 1,000 hours, while your 13W CFL would only cost $1.30. So, the playback is pretty quick (under 500 hours), if you use it a lot (and, this doesn’t include the savings due to the much better longevity of the CFL).
But, if this same 60W bulb is in a place where it is only used a few hours/month, then the numbers say it’s not a good idea to replace it.

Why 2 years and where does this come from? That’s expecting something like a 66% interest rate. What alternative investment do you have that provides a better return?

[johnpost]

as long as the payback is well within the lifetime of new system it is worth it.

[beowulff]

@Habeed

Why 2 years and where does this come from? That’s expecting something like a 66% interest rate. What alternative investment do you have that provides a better return?

Two years is considered the “no-brainer” payback period. Payback times of 3-5 years is probably worth doing. But, you need to make these decisions yourself, based on your risk aversion.

Here’s a very detailed analysis.

[bob_2]

Many people, when doing these cost/benefit calculations forget the cost of borrowing or the lost opportunity from using capital.

A $10,000 loan over 5 years would cost at least $300 in interest and quite possibly twice that. Selling stock to raise the cash would cost less, but $300 would still be a good rule-of-thumb.

[Habeed]

@bob_2

Many people, when doing these cost/benefit calculations forget the cost of borrowing or the lost opportunity from using capital.

A $10,000 loan over 5 years would cost at least $300 in interest and quite possibly twice that. Selling stock to raise the cash would cost less, but $300 would still be a good rule-of-thumb.

Yes, but when you do borrowing/opportunity costs, you assume an interest rate of 10% or so (that’s the average RoI you get with the stock market, historically). The efficiency device does not need to pay for itself within 2 years to give you an effective interest rate of at least 10%.

[Habeed]

@beowulff

Two years is considered the “no-brainer” payback period. Payback times of 3-5 years is probably worth doing. But, you need to make these decisions yourself, based on your risk aversion.

Here’s a very detailed analysis.

I see nothing about “2 years”. I see the method I’m familiar with, where you do a cash flow table and then compute NPV, using the MARR that is appropriate for the situation. In some cases, you can borrow money for home improvements at a lower interest rate than you can get money for any other purpose. In these situations, it makes a lot of efficiency improvements viable that would not other be viable, because essentially the bank (backed by the government) is giving you very cheap money.

As a matter of fact, using reasonable interest rates, 7-10 years is an acceptable payback period for an efficiency improvement.

[PastTense]

Actually a big problem in these calculations is that a lot of people will move and thus won’t be able to capture efficiency savings for more than a very few years.