Wind, Solar, Nuclear, and Electricity Storage
So far, actual commercial installations of electric storage for the grid have used pumped storage exclusively, insofar as I’m aware. Battery facilities, super capacitors, compressed air storage, and flywheels have all been proposed and some even put on line for a while but none have shown commercial promise worthy of private investment. One could presuppose a micro-level storage device that would work only within the photovoltaic cell, like science fiction author Robert Heinlein did in “The Roads Must Roll” or maybe windmills with big wind-up springs inside, but for our purposes, we can confine our discussion to pumped storage at the grid level.
As most readers will remember, pumped storage is a type of hydroelectric development but with upper and lower reservoirs and hydroelectric turbine/generators that can run in reverse and serve as motor/pumps. To store electricity, megawatt-hours are consumed by the motors to drive the pumps which raise water from the lower reservoir to the upper. Energy is stored as potential energy in the water’s elevation difference. To deliver electricity, water in the upper reservoir is released back down the pipes through the pump impellers, now working as turbines, thereby driving the generators which used to act as motors during the storage phase. The released water is typically stored in the lower reservoir until the next storage phase. The highest differential between high and low reservoirs in the U.S. is the Helms pumped storage facility. This 1,050 MW capacity installation, located in the Sierra Nevada Mountains in Northern California has a 1,630 foot elevation difference between reservoirs connected through an underground equipment hall carved out of solid granite.
The Economics of Storage
Let’s look at a couple of the universal characteristics of energy storage technologies, including pumped storage, and how they affect the economics of storage. First, these installations are not free. While the variable operating costs (non-electrical) may be rather low on a per unit throughput basis and can be ignored in any first order analysis, the fixed capital costs are non-trivial and have to be allocated against each unit of delivered energy. Carving a huge underground hall out of granite with huge penstocks between artificial lakes ain’t cheap. The mortgage has to be paid and revenues from operation must recover the capital investment, with interest and profit.
Since the electrical demand for most human customers follows their waking hours, the demand on the grid falls off substantially late at night. Given the standard workweek, the weekends have typically lower demand than weekdays. That suggests that the upper reservoir is filled at night, when electricity prices are lowest and the stored power delivered to the grid during the day when electricity prices/costs are highest. The more megawatt-hours that are generated for sale, the lower the cost per megawatt-hour.
This is a simple function:
Cost per unit for fixed costs = (number of units sold per year) / (annual fixed costs)
Let’s make it look really mathematical by using letters to stand for the phrases:
Cf = T / MWhere:
Cf = unit costs for fixed expenditures T = Output in units sold per year M = annual fixed costs, ie the mortgage.
Another certain feature of any storage method, including pumped storage, is that it is not perfectly efficient. One has to put more electricity in than one can draw out. The motor/generators lose energy through heat and internal friction, the pump/turbines swirl water rather than move it, the penstocks offer friction to water flow through them. The list goes on and on but is comparable from any industrial use of power to move vast quantities of water. Batteries lose heat from internal resistance or make hydrogen bubbles. One thing every engineer has to learn is that NOTHING is perfect and never works as well as it does in the introductory textbooks.
With pumped storage, a good rule of thumb is that 4 units of electricity go in but only 3 come out for sale for a 75% cycle efficiency. An exceptional facility might see 80% (5 in and 4 out) but we’ll use the typical efficiency in our example calculations.
Variable cost per unit output = (price per input) / (efficiency)
Again, to make it look mathematical:
Cv = P / eWhere:
Cv = unit cost for variable costsIf we combine the efficiency term and the fixed cost allocation term, our equation for the cost per unit output (Cp) looks like this:
P = price of electricity bought as input
e = efficiency of output to input
Cost of product = fixed cost per unit output + variable cost per unit output
Cp = Cf + CvExpanding:
Cp = (P / e) + (T / M)So what does this cost equation tell us? If one wants the lowest delivered cost to the grid, one wants the lowest cost input and the maximum annual throughput. For the lowest cost input, can one really believe that solar or wind would be the best source of low cost power AT NIGHT, when one wants to charge the storage? Solar not only isn’t available except for a few hours around noon on days with little cloud cover, it also produces when grid demand is high and grid prices are relatively high so solar electric output would go directly to the customer unless the installed solar capacity is truly huge, some large fraction or multiple of peak grid demand. That way, solar wouldn’t be burdened with the inefficiencies of the storage.
Wind has the advantage that it can work at night or other off-peak times. However, the historical performance record in the U.S. doesn’t suggest that it preferentially does so. The U.S. Energy Information Agency’s records show that installed wind capacity only works at about 26% of its nameplate. The wind industry trade group would claim a higher number, maybe 30% or so, but either way, the wind blows when it will, not when we’d prefer it.
To achieve the maximum throughput is to lower the unit cost of storage since we spread those fixed costs over more output. If a storage facility costs a billion dollars but only produces one megawatt-hour for sale, that megawatt-hour will cost more than $1 billion. We have a strong economic incentive to keep the storage investment working every weekday. That means charging the facility with electricity every Sunday through Thursday night. Another crude way of looking at a 26% capacity factor for wind is that it works one day in four or six hours in 24. If we believe the wind advocates, that might look like one day in three or eight hours in 24 but either way, to use wind, we are trying to fit a narrow production window into a narrow recharge window. Like solar, production during peak load hours would be preferentially consumed at those higher prices rather than put into storage. Like solar, installed wind capacity would have to be some multiple of peak load to be justified as the preferred source for storage all the time.
Let’s do some examples to get a feel for the numbers. We’ll use price/cost in dollars per megawatt-hour (MWh).
Let’s say PV costs $100/MWh, wind costs $75/MWh, nuclear $70/MWh, the facility cost $1 billion and is financed at 8% for 30 years. Let’s assume it can deliver 1,000 MWh for six hours every weekday (200 days per year) and has a cycle efficiency of 75%.
We can posit several questions and answer them by cranking the above inputs through a simple spreadsheet (available on email request) using our equation. We’ll assume that the power input source is completely from one of our choices. We can ask, what would be the selling price for power from our pumped storage unit if the unit was utilized 100% of the 200 days per year and then 50% and 25% of the days, given supply limitations. An even more telling question is, what would be the selling price if the storage unit had the same capacity factor as the input power source?
Here are the results:
|At source’s capacity factor||$575||$395||$192|
To give one a sense of current market reality, the early summer 2008 on-peak, “day ahead” prices for Houston, Texas are running about $120/MWh with off-peak “day ahead” costs lower at about $66/MWh. A baseload nuclear plant would sell into both time markets, hence covering a $70 levelized production cost and making a profit. The spot market peak there might run $300 to $450/MWh during the summer. Peaking power in East Texas is not from pumped storage but from natural gas-fired gas turbines with low capital costs but high fuel costs.
The conclusion is that economics of electricity storage favors not renewables but rather the cheapest and the most reliable input source. Since electric storage will never be 100% efficient and will never be free, the conclusions will differ only in degree. Building a pumped storage facility on a grid does not enhance the economics of renewables but decreases their attractiveness relative to more conventional technologies like large coal and nuclear. The only way to turn that around is for wind and solar to become both more reliable than nuclear and cheaper too.
In the real world, the analysis above is far too simplistic for investment decision making – call it a first order analysis. But for public policy thinking and for understanding the fundamental economics, it should disabuse even the most optimistic fan of renewables of any pipedreams that more storage would overturn the current economics. We can test our results by looking at existing pumped storage units. You’ll find that where someone has invested in a pumped storage facility, one will usually find a big coal plant or a nuke with good connections to it. I suspect it will be that way for a long time.