The Price of Power
As part of my hybrid propulsion research I have been looking carefully at large-capacity litihum-ion batteries as a possible energy source on modern cruising sailboats. Lithium-ion batteries are common in cell phones and laptops, but they are rarely used in higher capacity applications. This may rapidly change, because the hybrid automotive and electric vehicle markets are in desperate need of better battery technology.
The few high-capacity lithium-ion battery packs that are now available are shockingly expensive, with the cheapest running over $1,000 per kWh of capacity. To put this in perspective, at these prices a 100 amp-hour (Ah) 12-volt battery with a nominal capacity of 1.2 kWh (100 x 12 = 1,200 watt-hours) would cost over $1,200. In fact, the first lithium-ion battery offered on the marine market has recently been released by Mastervolt. It is rated at 160 Ah at 24 volts (i.e., 3.84 kWh) and retails for around 4,000 Euros (or over $5,000thats $1,300 per kWh). Torqueedo is another company making early moves into the marine market.
These astronomical prices set me wondering about the real cost of generating and storing DC energy on a boat. Its a complicated equation in which parameters will vary from boat to boat. When I began to work through some real-life examples, I came up with surprising results.
By far the cheapest conventional way of getting DC energy on to a boat is via a battery charger hooked up to a shorepower connection. Assuming the cost of the shorepower is $0.15 per kWh, and the battery charger is 80 percent efficient, the power coming out of the charger is costing $0.19 per kWh. In theory, renewable energy sources, such as solar and wind, could work out to be cheaper, but typically they do not.
Things get a little complicated when we factor a battery bank into the equation, because we have to account for losses going into and out of the battery, and we also have to factor in the cost of the battery. Well look at these in a moment. For now, lets just stick to the cost up to the point of connection to the battery.
For most sailors, once the shorepower cord is unplugged, the principal mechanism for creating DC power on board is an engine-driven alternator. Alternators are, at best, only 50 percent efficient. If the engine is run for battery charging alone, it is extremely lightly loaded, which puts it at a very poor point on its fuel efficiency curve. Overall efficiency in terms of converting the heat content of the fuel burned into electricity is probably below 10 percent.
On larger boats, theres likely to be a generator powering a battery charger. A generator itself is more efficient at creating electricity than an alternator, but there are losses through the battery charger. Also, because AC generators have to be sized for peak AC demand, most of the time they are running they are extremely lightly loaded, and as such, once again, the fuel use is inefficient. I dont have hard numbers, but I suspect there is little difference in overall efficiency between the alternator and the generator/battery-charger combination.
Lets assume our propulsion engine or generator has a life expectancy of 5,000 hours. The all-up replacement cost (including installation cost) will be between $15,000 and $25,000 (higher for larger engines and more complicated installations; lower for smaller generators, but the life expectancy will also most likely be reduced). The amortized running cost is therefore $3 to $5 an hour. Lets now assume that we are charging a conventional 12-volt battery bank at 100 amps (which is higher than in most situations). Over an hour, this translates to 1.2 kWh. Our amortization cost per kWh is between $2.50 ($3/1.2) and $4.17 ($5/1.2). If we are running the engine solely for battery charging, we will be lucky if the fuel efficiency is even as good as 0.1 gallons per kWh. If our fuel costs $2.50 a US gallon, the fuel cost per kWh is $0.25. Our total cost per kWh is therefore between $2.75 and $4.42. With lower charging rates, or higher fuel costs (in Europe, it will be three times higher) the cost is higher.
What makes these numbers so astonishingly high is the amortization cost. If we are running our main engine for propulsion purposes, or the generator for other purposes, the amortization cost does not go away, but it can be spread over the kilowatts of energy being absorbed by these other functions. For example, if the 55 kW (70 hp) engine on my boat is driving us at 7 knots in calm conditions, the propeller absorbs 14 kW, so now the total hourly energy production is 15.2 kWh, which drops the amortization part of the cost to between $0.20 and $0.33 per kWh, and the total cost (amortization + fuel) to between $0.45 and $0.58 cents per kWh.
Storing the Power
Unfortunately, most battery banks cannot absorb 200 amps of charging current, even if it is available. The notable exceptions are the new Thin Plate Pure Lead (TPPL) batteries from Odyssey, and just about any sort of lithium-ion battery. Both TPPL and lithium-ion batteries can easily soak up charge rates equal to their rated capacities, and do so up to high states of charge. For example, if we have a 300 amp-hour battery bank, we can charge at 300 amps. Of course, we need a 300-amp charging device.
For the experimental electric propulsion system from Electric Marine Propulsion on my new boat we have the equivalent of a 1200 amp-hour battery bank at 12 volts (what we actually have is 100 amp-hours at 144 volts). The batteries can easily soak up an astonishing 14.4 kW from our 22 kW generator. The amortization cost per kWh drops dramatically, plus the generator is optimally loaded from a fuel efficiency point of view. In spite of the fact that we have an expensive DC generator, the cost per kWh falls to around $0.50 (this is still over three times the cost of shorepower).
Battery Efficiency and Cyclic Capability
When you charge and discharge a battery, there are always energy losses. With lead-acid batteries, these losses vary with the state of charge and other factors. For the purposes of this article, I will make some wild generalizations and say that the total loss per charge/discharge cycle is 30 percent. This means the kWh cost numbers derived above have to be multiplied by 1.3 for any energy that passes through batteries. For TPPL batteries, the total loss is probably closer to 15 percent (this is something we are investigating right now), but for lithium-ion batteries it can be as low as 2 percent.
We also have to factor in the battery lifetime cost per kWh, which is a function of the purchase price, life cycles, and usable capacity (depth of discharge and level of recharge) during each cycle.
If deeply discharged, most lead-acid batteries will last, at best, a few hundred cycles, so discharges are typically limited to 50 percent, even on quality deep-cycle batteries. In contrast, TPPL batteries can support a 60 percent discharge during each cycle for well over 1,000 cycles. Most lithium-ion batteries will support an 80 percent discharge for over 2,000 cycles.
The already low charge-acceptance rate of conventional lead-acid batteries tapers off rapidly once they are 80 percent charged. As a result, in many applications only 30 percent of a batterys rated capacity (from 50 percent to 80 percent) can be used during each cycle. By comparison, the high charge-acceptance rate to high states of charge enable 60 percent of a TPPL batterys capacity to be used during each cycle. For a lithium-ion, battery usable capacity increases to 80 percent.