# Solar power and power loss over distance

• jimmylegss
In summary: Swedish coast. and during peak demand in Brazil, over 60% of the power comes from hydro installations more than 6000 kilometers from the population centers.In summary, solar power is not sustainable if you also need fossil fuel plants to run in the background.
jimmylegss
I was having a discussion with a friend, and my side of the argument was that for solar to work you also need a lot of fossil fuel running in the back ground just during the day, making it very expensive. Let's take New york as an example.

Let's assume they have enough solar panels to produce 150% of the power needed on average during a sunny day. But when it gets cloudy , you could have a lot of power outages if the sun suddenly goes away, meaning you need fossil plants in the back ground, wasting a lot of energy. Because it takes time to fire up power plants.

Now the question is, could you set up a network between all cities with a range of a 2-3k miles where if it becomes cloudy and rainy in one city (so solar can only sustain about 20-30% of power needs), other cities within a range of hundreds, or possibly a several thousand mile can jump in? Assuming ofcourse every city in this network has power left over during sunny days.

How much would be lost per mile? Or would we really need batteries to make this sustainable.

Could it be possible to set up massive solar farms in the desert in california? And power all of the US?

Edit: my understanding is that A = V/ Ohms

So if you generate a certain amount of Amps (that is electrons per second right?), and you want to push a lot of them over large distances, you need to send a lot of them at once? Meaning Voltage is high? So if differences would be small, and only small amounts of power would be sent at the time, more energy would be lost due to resistance? Or am i misreading that formula?

Last edited:
You could use the same methods that power distribution companies use. To send a lot of power over long distances with low loss, the power company steps up the voltage to very high voltages using transformers and then steps it back down at the site where the power would be used.
power lost = I^2 * R
Because P and r are fixed values, less power will be lost if high voltages are used.

jimmylegss said:
could you set up a network between all cities with a range of a 2-3k miles where if it becomes cloudy and rainy in one city (so solar can only sustain about 20-30% of power needs), other cities within a range of hundreds, or possibly a several thousand mile can jump in? Assuming ofcourse every city in this network has power left over during sunny days.

such a network exists, called "The Power Grid" .
All generators connected to the grid are in synchronism,
regions with surplus power pull ahead by a small fraction of a turn which pushes power into regions with a power shortfall.

Ypu can watch that almost realtime here
http://fnetpublic.utk.edu/anglecontour.html

See the swath of yellow along Mississippi river? It's ahead of most of the rest of the country.
I'd say at that moment Mississippi Valley was exporting power in all directions. Not a surprise, there's lots of coal plants there and in mild weather less efficient plants are shut off. Nukes are refueled in mild weather too, so as to be able to replace their generation with inexpensive fossil.

old jim

Way back in my power class they said as a rule of thumb 50% of power is lost every 500 miles. I don't know how true that is, but it's a number.

Higher voltages do mean less current. But higher voltages don't mean more power flows. For technical reasons power flows by phase shift instead. And there's a limit to phase shifts and power flows.

There's a type of power plant called a peaking plant. These can be turned on and off quickly. Mostly these are gas plants, but sometimes hydro plants are used (I think).

Utilities seem to like a mix of plant types. It's not so much a question of whether a particular type will be used, but how much it will be used.

Jeff Rosenbury said:
Way back in my power class they said as a rule of thumb 50% of power is lost every 500 miles. I don't know how true that is, but it's a number.

That is a widely quoted number. I don't know under what circumstances it is true but it is wildly misleading.

The world bank lists electric power losses for many countries here. http://data.worldbank.org/indicator/EG.ELC.LOSS.ZS In the USA it is 6%. Instructive are Sweden (7%) and Brazil (16%). In both of those countries their hydro power resources are located thousands of miles away from population centers where the power is consumed. During July, nearly all of Sweden's power generation is located 1500 miles from the loads. If what they said in your power class was true, their losses would be 87.5% instead of 7%.

Back to the OP's question. California to NY no. But there are proposals to sell midwest wind power to NY and New England. But the extra power transmission capacity would cost billions. Wind generators in the midwest want to sell the energy "on our loading dock" and have the easterners to pay to transmit it. The easterners say that the westerners should pay transmission costs and to sell their energy "delivered to my door." The easterners also prefer the better deal they can get buying hydro power from James Bay in northwest Quebec, 2000 km away.

Finance, not power losses are the important limitations.

anorlunda said:
Wind generators in the midwest want to sell the energy "on our loading dock" and have the easterners to pay to transmit it. The easterners say that the westerners should pay transmission costs and to sell their energy "delivered to my door."
either way, the owners of the transmission lines get their transport fee.

jim hardy said:
either way, the owners of the transmission lines get their transport fee.

That would be true, but in this case the lines never got built and midwest wind power is not sold in the northeast. It is very difficult to get investors to invest in power transmission nowadays instead of (for example) buying Apple stock.

It's a growing sector.

http://www.eia.gov/todayinenergy/detail.cfm?id=17811one driving force is
http://www.ferc.gov/industries/electric/indus-act/trans-invest.asp
The Commission has established rules to bolster investment in the nation's transmission infrastructure, and to promote electric power reliability and lower costs for consumers, by reducing transmission congestion. The rule identifies specific incentives the Commission would allow based on a case-by-case analysis of individual transmission proposals.

The Energy Policy Act of 2005 directed the Commission to develop incentive-based rate treatments for transmission of electric energy in interstate commerce, adding a new section 219 to the Federal Power Act. The rule implemented this new statutory directive through the following incentive-based rate treatments:

• Incentive rates of return on equity for new investment by public utilities (both traditional utilities and stand-alone transmission companies, or transcos);
• Full recovery of prudently incurred construction work in progress;
• Full recovery of prudently incurred pre-operations costs;
• Full recovery of prudently incurred costs of abandoned facilities;
• Use of hypothetical capital structures;
• Accumulated deferred income taxes for transcos;
• Adjustments to book value for transco sales/purchases;
• Accelerated depreciation;
• Deferred cost recovery for utilities with retail rate freezes; and
• A higher rate of return on equity for utilities that join and/or continue to be members of transmission organizations, such as (but not limited to) regional transmission organizations and independent system operators.

It's attracting European capital.

anorlunda
Thanks for that Jim. Glad to hear that it's moving in the right direction.

anorlunda said:
That is a widely quoted number. I don't know under what circumstances it is true but it is wildly misleading.

Finance, not power losses are the important limitations.

Do you know a number? I don't. The class I got the number in was a transmission line design class (undergraduate, balanced lines only). While 50%/500 miles seems excessive, 7% over 1500 miles seems way low.

Finance isn't the big problem for new transmission lines. Regulation is. Few land owners want a new transmission line run anywhere near their property. That is the sort of thing that turns nice neighborhoods into slums. Since running such a line involves a serious decline in property values of thousands of registered voters, it is almost impossible to get right of ways approved.

This in turn causes finance problems. Building a line involves buying up land. So a company starts buying land, then tries to get approval, then get bogged down in litigation for some number of decades. Finally, a corridor might get approved. But probably not, at least historically. So the finance company has spent perhaps a billion dollars, then carried that money for decades. In the end they have nothing to show for it.

Yes, finance is a problem. But it's a problem because democracy is three wolves and a sheep deciding what's for dinner.

So in theory you could put enourmous solar farms in the midwest then? And sell it to large surrounding cities within a 1-2k mile radius? If those panels become cheap enough.

jimmylegss said:
So in theory you could put enourmous solar farms in the midwest then? And sell it to large surrounding cities within a 1-2k mile radius? If those panels become cheap enough.

Yes in theory, but it makes no sense economically. The reason that we have the big grid in the first place is to support areas that are temporarily short of power by importing power from neighboring regions.

Each of the corner dots is an inverter - my estimate 1 to 1.5 MW each...

As for long haul HV transmission -- wikipedia... LINK or basically at 765KV 0.5 to 1.1% per 100 Miles... the 50% maybe should have been 5%?

As for long haul HV transmission -- wikipedia... LINK or basically at 765KV 0.5 to 1.1% per 100 Miles... the 50% maybe should have been 5%?
That sounds like a much better number. 17% at 1500 miles. That's not an unreasonable loss for shipping power. It could be lowered by about half if there were a dedicated (DC) line over long distances.

So large non-photovoltaic collectors in the South West could power East Coast areas -- given the political will.

BTW, 2013 overnight costs (pg. 10): Coal $2,934/kW; Clean Coal$4724/kW; Natural Gas $917/kW; Nuclear$5530/kW; Wind (on shore) $2,213; Photovoltaic$3,873.

Gas costs 3.6¢/kWh in fuel, while the sun and wind are free (ish).

Gas is the clear winner here. Those who wish to change our reliance on fossil fuels need to change those numbers through tax incentives, etc.

There are unaccounted costs such as environmental damage. But which is worth more, the large footprint of a solar plant, dead birds, or climate change? These are questions we need to decide on a political level.

One disadvantage of a solar-wind-fossil fuel power grid is the increased startup cost of fossil fuel generators. Peak power demand occurs at about 5 pm when solar generators are under far reduced output. This prompts fossil fuel sourced power suppliers to ramp up standby generators at increased cost to consumers. It also means there must be more generators dedicated standby status at further increased cost.

A very "hot" topic now is large scale energy storage for just this reason - to maximize energy harvest from these sources and to locally level the demand better. The industry is changing - and many consumers are willing to pay more for cleaner as well, so the cost needs to be competitive but does not need to beat.

People are willing to pay more for clean until their electric bill goes up 400%. Then they make laws giving themselves subsidies. When these get large enough utilities start to lose money. Then they stop investing, rolling blackouts occur, and economic growth ceases for the region they serve.

Perhaps that is the correct solution. That is a political question and this is not the forum for politics. Still, engineers need to be aware of the costs of their designs, and not just in dollars.

jim hardy
The 50% energy loss quoted is the probably the maximum loss over the whole system from generator to wall socket.

Loss to 50% of the generated energy will be a drop to 70.71% of the voltage.
The maximum acceptable voltage drop is usually considered to be 5% on any section of the system.
For n sections we then have; 0.95n = 0.7071 ; then, n * Log(0.95) = Log(0.7071) ; so, n = 6.75 sections.

An efficiency audit of those possible sections, each with a maximum of 5% voltage drop due to I2R could be:
1. Generator, transformer and switch yard.
2. First EHV Transmission line section.
3. Middle section of EHV line.
4. Last section of EHV line.
5. Substation, local 6kV or 11kV distribution to final transformer.
6. Final transformer and power line from street to structure.
7. Meters, CB protection and within the structure.

Baluncore said:
The 50% energy loss quoted is the probably the maximum loss over the whole system from generator to wall socket.

No, the losses I cited and linked in post #5 were end to end losses including pilferage. They are much less than 50%.

Jeff Rosenbury said:
Way back in my power class they said as a rule of thumb 50% of power is lost every 500 miles. I don't know how true that is, but it's a number.
That was the 50% I referred to.
anorlunda said:
No, the losses I cited and linked in post #5 were end to end losses including pilferage. They are much less than 50%.
From "End to End" of what? I suggest the losses on the EHV line are a maximum of 1 - 0.953 = 14.25%
And, what has pilferage got to do with the physics of power transmission?

Baluncore said:
That was the 50% I referred to.

From "End to End" of what? I suggest the losses on the EHV line are a maximum of 1 - 0.953 = 14.25%
And, what has pilferage got to do with the physics of power transmission?

end to end means from generator, through transmission, through distribution, to the end user. In other words, all losses, not just transmission.

National numbers I quoted in post five (6% USA, 7% Sewden, 16% Brazil) are inflated by pilferage losses rampant in some third world countries. That means that physics losses are lower than those numbers.

The 50% number from Jeff's power class doesn't hold up, it sounds like you agree, so I don't see were we disagree.

I certainly don't stand by the 50% number. It was a one off comment 25 years ago.

I do have a problem of total system efficiency of 94% (100 less 6%). Transformer losses alone are 1-3% per transformer. There should be 3-5 transformers between the generator and the consumer. That doesn't leave any for power factor mismatch or line losses. Synchronous machines top out at about 94% efficiency, so there's another 6% loss.

I suspect bankers define efficiency a bit differently than engineers.

Jeff Rosenbury said:
Transformer losses alone are 1-3% per transformer.
that's about right for small transformers like the one behind your house probably 10 kva.

Bigger than about 50kva and oil cooled they beat 99%
see http://www1.eere.energy.gov/buildings/appliance_standards/product.aspx/productid/66

## 1. What is solar power and how is it generated?

Solar power is a renewable energy source that is generated by converting sunlight into electricity. This is done through the use of solar panels, which contain photovoltaic cells that convert the sun's energy into direct current (DC) electricity.

## 2. How does power loss occur over distance in solar power?

Power loss over distance in solar power is due to the resistance in the wires that transport the electricity from the solar panels to the location where it is used. The longer the distance, the greater the resistance, resulting in a lower amount of electricity reaching its destination.

## 3. What are the factors that affect power loss over distance in solar power?

The main factors that affect power loss over distance in solar power are the length of the wire, the thickness of the wire, and the amount of electricity being transmitted. Other factors such as temperature and weather conditions can also play a role in power loss.

## 4. How can power loss be minimized in solar power systems?

One way to minimize power loss in solar power systems is by using thicker wires with lower resistance. This reduces the amount of energy lost during transmission. Additionally, installing solar panels closer to the location where the electricity is needed can also help minimize power loss.

## 5. Can power loss be completely eliminated in solar power?

Unfortunately, it is impossible to completely eliminate power loss in solar power systems. However, with proper design and installation, power loss can be minimized to ensure maximum efficiency. As technology advances, there are also ongoing efforts to improve the efficiency of solar power systems and reduce power loss.

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