The cost of energy on boats
Ways to increase electrical system efficiency and get more power for the money
One important area for any voyager is understanding, and improving, the efficiency of the electrical systems on his or her boat. To do this requires knowledge of real-world performance. I have made an attempt to gather this data by testing the efficiency of DC systems and participating in extensive testing of AC generators. I’ve learned that when boat electrical systems are powered by a fossil-fueled engine, they are not efficient. In order to compare efficiency between different systems, and between different approaches to generating power on a boat, we need standardized units of measurement. In what follows I will use kilowatt-hours (kWh) and specific fuel consumption (SFC).
Kilowatt-hours are familiar to most people. They are what you see on your electricity bill each month. A kWh is a measure of how much electricity you have consumed. In our testing, we derive kWh by measuring volts, amps and time. Volts x amps = watts. Watts/1,000 = kilowatts (kW). One kW sustained for 1 hour = 1 kWh.
Specific fuel consumption (SFC, also known as ‘brake specific fuel consumption,’ or BSFC) will be new to most readers. It is the quantity of fuel that is burned to produce 1 kWh of energy. It is typically expressed as grams per kilowatt-hour (g/kWh). Let’s say we have a diesel-powered generator, or an engine-driven alternator, that is producing 2.5 kW of electrical output with the engine burning a liter of fuel every hour. A liter of diesel weighs 840 grams. Over the course of an hour we create 2.5 kWh of electricity and burn 840 grams of diesel for an SFC of 840/2.5 = 336 g/kWh.
To put this in perspective, if our equipment was 100 percent efficient at converting the heat content of diesel fuel into electrical power we would have an SFC of around 78 g/kWh. However, a small diesel engine is lucky to attain a peak efficiency of even 30 percent, which puts us at 260 g/kWh or higher, to which we must add the losses through the alternator (which can be the alternator on the boat’s propulsion engine, or the electrical end of an AC generator). As we shall soon see, in the real world our imagined 336 g/kWh is actually quite good.
Battery charging at anchor
To see how good it is, I measured the SFC when battery charging at anchor. The test engine was a Volvo Penta D2-75, rated at 75 hp (55 kW). It came with the standard 80-amp, 12-volt alternator, and an optional additional 120-amp, 24-volt alternator. Charging on a 12-volt system takes place at an average of around 14 volts, and on a 24-volt system at an average of around 28 volts, so our maximum nominal output is [(80A x 14v) = 1,120 watts] + [(120A x 28v) = 3,360 watts] for a total of 4,480 watts = 4.48 kW.
Alternator output is directly related to speed. Most alternators don’t reach their rated output until up to 4,000-plus rpm. Typically, they have a 2:1 pulley ratio with the engine, which means the engine must run at 2,000-plus rpm. No one wants to run this fast when battery charging at anchor. We ran the engine at 1,200 rpm which gave us a peak output from the two alternators combined of 2.5 kW. This reduced output over the maximum rated output is typically not an issue with conventional lead-acid batteries (wet cell, gel cell and AGM) because their ability to soak up large amounts of charging current (their charge acceptance rate, or CAR) diminishes rapidly as the state of charge (SOC) rises above the 50 percent charged level. However, any reduction in output is an issue with the high CAR batteries now coming on the market (thin plate pure lead (TPPL) and lithium-ion) as these have the ability to soak up astonishing amounts of power.
The declining battery CAR as batteries come to charge is clearly visible in Figure 1. The graph shows SFC plotted against kW. It is read from right to left. At right, the batteries are well discharged and both alternators go to their full output for that engine speed (1,200 rpm). As the batteries come to charge (we are moving from right to left on the graph) the CAR declines, alternator output falls (the kilowatts decrease), and SFC rises (the charging process is increasingly inefficient).
Look at those SFC numbers! At the beginning of the charging process they are around 800 g/kWh, increasing to 4,000 g/kWh at the end of the process. In absolute terms (the efficiency of converting diesel fuel into electrical power) we start around 10 percent efficiency and end at 2 percent efficiency. And this isn’t the last of the bad news. The losses in charging and discharging conventional lead-acid batteries are about 15 percent in each direction, so in terms of producing the electrical power that gets to our appliances via the batteries we are now down to an absolute efficiency of between 7 and 1.4 percent.
Why so bad?
To understand what is gong on here, we have to look at losses at the engine and at the alternators. An engine operates at its peak efficiency (lowest SFC) over a narrow speed and power range. Any deviation from this narrow band results in increasing inefficiency (the SFC goes up). This relationship between speed, power and efficiency is expressed in something called a fuel map. Figure 2 is a fuel map for a 4-cylinder Steyr diesel engine with similar performance to our test engine. Note that the peak efficiency of 240 g/kWh occurs at around 1,800 rpm and 22 kW (this is almost identical to the D2-75 test engine). At 2.5 kW and 1,200 rpm the SFC has risen to 360 g/kWh. As the load decreases (the battery CAR declines), the SFC rises fairly rapidly.
These SFC numbers are measured at the flywheel in a test laboratory. In the real world, they will be higher. It’s reasonable to assume that at 1,200 rpm and 2.5 kW in the test boat, we are already at 400 g/kWh.
Alternators have a peak efficiency of not much above 50 percent and this too is over a relatively narrow speed and power range. Outside of this narrow band, efficiency declines. If we assume 50 percent efficiency at 2.5 kW, with 400 g/kWh fuel consumption, we arrive at our measured peak efficiency number of 800 g/kWh, with a rapidly increasing SFC (i.e., decreasing efficiency) as the output of the alternators declines (both the engine and alternators are becoming less efficient).
Let’s look at AC generators. In 2007, I participated in extensive testing by Victron Energy, a Dutch company, of 19 off-the-shelf AC generators. The full test report can be viewed at www.victronenergy.com.
Most AC generators have to be run at a fixed speed in order to maintain the correct output frequency (60 Hz in North America; 50 Hz in much of the world). So instead of developing a fuel map, Victron tested the generators over the full power range at the required operating speed, deriving SFC numbers from no load to full load. Figure 3 illustrates the results for the ‘medium’ sized generators (4-7 kW).
AC generators have to be sized to handle the peak load they will encounter. This is typically at least four times the average running load, and frequently much higher. In point of fact, there is often no load on a generator. For example, it is powering an air conditioner which has temporarily cycled to ‘off’ because the room has cooled to the temperature set point. The net result is that most AC generators on boats spend most of their time operating at between 0 percent load and 25 percent load.
We end up with SFC numbers in the region of 550 g/kWh to 2,000 g/kWh (actually, if the load is 0, the SFC is infinite). The end result is an absolute efficiency of 14 percent down to 4 percent or less as measured at the output from the generator. If the generator is being used to power a battery charger which is charging conventional batteries, the total additional losses through the charger and batteries can easily be another 40 percent, bringing us down to an absolute efficiency of between 8.5 and 2.4 percent — not dissimilar to using the boat’s engine for battery charging at anchor.
The cost of power
Here’s another calculation I have taken to doing. I make a guesstimate for the replacement cost of the boat’s engine or an AC generator. This is the purchase price plus installation cost. For the D2-75 it will be more than $20,000; for a 4-7 kW diesel-powered AC generator, probably around $10,000. I then make a guesstimate of lifetime operating hours. For inboard engines in sailboats, 5,000 hours seems reasonable. For small AC generators let’s use 3,000 hours. With these numbers in hand, we can crudely calculate the amortized hourly cost of running the equipment before we add any fuel or maintenance. In the case of the D2-75 it is $20,000/5,000 hours = $4.00; in the case of the AC generator, it is $10,000/3,000 hours = $3.33.
When battery charging at anchor, by the time we factor in the declining CAR as a battery comes to charge, the average power output on most boats is less than 1 kW. If we include the losses in feeding the energy in and out of the batteries on the way to our DC loads, the effective output is more like 0.75 kW. This gives us a cost of from $4.00 to $5.33 per kWh of electricity before paying for fuel and maintenance. The same kind of calculation based on average generator outputs frequently results in similar cost numbers. In comparison, power from the utility company at home costs 10 to 20 cents per kWh.
Once again, this isn’t the end of the story on boats. For all the power that is fed through the batteries to our DC system, we need to factor in not just the efficiency losses of charging and discharging batteries, but also the cost of the batteries themselves. To do this, I make another guesstimate of the depth of discharge and state of recharge of the batteries at each use cycle, and the number of cycles before they fail. With these numbers in hand, I can calculate a lifetime kWh energy “throughput” for the batteries. This is divided into the replacement cost of the batteries to derive a kWh “throughput” cost, which is an overhead that must be added into the DC system for every kWh of energy that gets stored in the batteries prior to use. With conventional batteries, this cost is typically between 50 cents and $1.00 per kWh.
The real cost of electricity on boats can get as high as $6.00 a kWh. What can we do to reduce this?
First and foremost is the importance of optimizing the efficiency of onboard electrical equipment by using LED lights, adding insulation to iceboxes, turning things off when they are not needed, etc. Next, we need to improve the efficiency of electricity-producing machines, and here the future lies with highly efficient, purpose-built, DC generators (such as those from Polar Power Inc – www.polarpowerinc.com). The best of these are 90+ percent efficient at converting mechanical power into electricity over a broad power range.
Given the high amortization costs associated with running engines, we need to reduce engine run hours. There are two ways to do this:
1. Get energy from other sources, notably shorepower, solar, and wind.
2. Increase the average load on fossil-fueled power generating equipment so that the amortized hourly running cost gets spread over a higher energy output.
Let’s say the amortized cost of battery charging at anchor is $4.00 an hour, plus fuel and maintenance. If my power output is 1 kW and I run the engine for an hour, the amortized cost is $4.00 per kWh, but if my power output is 20 kW the amortized cost drops to 20 cents per kWh. Increasing the average load is the greatest cost reducer if a fossil-fueled engine is used for energy production.
This is where the high-CAR batteries come in. These batteries, combined with powerful charging devices, are the enabling technology for maintaining high average loads on energy producing machinery. The key to optimizing efficiency is to maintain high loads that correlate with peak efficiency.
How would this would work with our D2-75 engine battery charging at anchor. The peak efficiency on this engine occurs at around 22 kW and 1,800 rpm, at which point the published SFC is 240 g/kWh. This is laboratory data. If we build in a 10 percent “fudge” factor for real world losses, and assume a 90-percent efficiency at converting mechanical power into electrical power, we end up with an SFC of [(240/0.9)/0.9] = 296 g/kWh. These are real, attainable numbers that can be verified by existing generators. If we had a powerful-enough generating device, and a management strategy that ensures the engine only runs at, or close to, this peak efficiency, fuel consumption will be less than a third of what we are seeing in the conventional battery charging at anchor mode, or when charging via an AC generator and battery charger. The amortized cost of power will be one-twentieth of what we are seeing in those same examples. Engine run times will be substantially reduced.
The technology exists
These are truly radical improvements in the cost of producing energy. The technology exists to make these gains. Once again, the key enabling technology is the new high-CAR batteries that can be used as a ‘buffer’ to achieve high average power levels with engines running close to peak efficiency.
However, even if energy production is optimized, the cost of energy will still be high. It’s hard to get the total cost below 50 cents/kWh. Still, it’ll be a fraction of what we pay now.
Contributing editor Nigel Calder is the author of The Boatowner’s Mechanical and Electrical Manual and Marine Diesel Engines.
The true cost of solar power
On my boat I have four 85-watt Kyocera panels for a total of 340 watts. Because my panels are installed flat, and there is some shading from the boom, performance is far from optimal. In this kind of situation, I like to work on the relatively conservative assumption that on average I will get the equivalent of four hours of full-rated output a day, i.e. 4 x 340 = 1,360 watt-hours, or 1.36 kilowatt-hours (kWh).
The total cost of the panels, regulator and installation was around $2,000. If I had these panels installed on the roof of my house, I would be paying somewhere around 15 cents/kWh for electricity from the grid, so at 1.36-kWh a day, I would be getting 20.4 cents in electrical output, and my payback period would be 2,000/0.204 = 9,804 days = 27 years. This doesn’t look too good.
With the panels installed on my boat, however, the equation changes dramatically. If we assume that the cost of generating electricity with a fossil-fueled engine is $4/kWh, at 1.36-kWh a day, the payback period on my solar panels becomes 368 days, or just a fraction over a year! This assumes the boat is used year-round. For a weekend sailor, the calculation gets more complicated. If the solar output can be stored during the week and used on weekends, and the boat is kept on a mooring without access to shore power for battery charging, then the calculation is similar to that for the full-time liveaboard cruiser, but if the boat has access to shore power then the solar output during these periods is only worth what the shore power costs.