Reynolds-Calder Cost Of Power Response(WEB EXTRA)

Retired control systems engineer, John Reynolds has a few thoughts on marine power stemming from a close read of Nigel Calder's COST OF POWER from our July/August 2014 issue.
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Reynolds' Comments On Calder’s "Cost of Power" Article:

The author presents a lot of technical data using assumptions and operating scenarios to support his conclusion. Based on my own experience, the real world does not operate as per his assumptions.

In the second section, charging while at anchor is discussed, using the main engine to charge the batteries. A set of unrealistic assumptions is made which result in highly skewed data. The data is taken with the engine at 1,200 RPM, well below the RPM at which the alternators develop their rated output. While the data might be valid for the 1,200 RPM condition, the prudent mariner would not operate his main engine at that RPM. Rather, the engine would be operated such that the alternators would make close to rated output, probably around 2,200 engine RPM.

The assumed life of the engine is 5,000 hours, which is unrealistically low. The installation cost is assumed to be $20,000, equating to an assumed fixed cost of $4 per hour. This assumption is not valid, as not all the engine hours are allocated to power generation only. The purpose of the main engine is to push the boat around. Most of the operate hours are consumed while underway, mostly propulsion with some added load due to power generation. An hour driving the boat at hull speed produces substantially more wear and tear on the engine than an hour of lightly loaded operation while charging the batteries. At most, the main engine is probably used no more than 10% of the time to charge batteries. Thus, the allocated fixed cost should be $.40 per hour, which obviously negate the conclusions of the author.

In Figure 1, the dominate cost is the fixed cost of the engine divided by the assumed life, i.e. $4 per hour. However, on a day-to-day basis, the only thing the boat captain sees is fuel cost. The total amount of fuel consumed for this charge curve, improbable as it is, seems to be about three gallons. Thus, the cost of electricity is down in the noise for most boat captains, unless the boat is anchored forever.

Although the author states that Figure 1 was derived from real world testing, he does not state how the fuel consumption was measured. If he used the engine manufacturer’s data for fuel consumption, specifically the fuel consumption per hour vs. crankshaft speed, then the data could be severely skewed, since this data assumes that a propeller is connected to the engine, i.e. the load on the engine follows a propeller power curve. If the engine is more lightly loaded, i.e. a lower load is applied than assumed for the fuel curve, then the fuel consumption is also less, again negating the conclusion of the author.

The author states that the area of the graph within the dotted lines represents the typical region in which battery charging at anchor takes place. Based on my experience, this statement is incorrect. When anchored, I don’t charge the batteries until they have

discharged to at least 60%, in which case the entire curve is utilized. It takes about four hours to charge my 1,380 Amp-Hr. battery bank to 100% using the 8 kW generator set. I suspect other mariners follow the same practice.

In Figure 1, the author uses the acronym SFC, with the SFC units being g/kWh, with the g being grams of fuel burned per kWh of energy output is used. Nobody burns or buys diesel fuel by the gram. We buy it, and burn it, by the liter or gallon. The author should use conventional units.

Figure 2, while interesting to a point, is non-relevant to flooded cell, AGM, or Gel batteries, as no one would intentionally discharge them to 80%. At a SOC of 20%, the available output power would essentially be useless, incapable of powering a VHF radio or an inverter. Although not stated here, the expected life of lithium-ion batteries is more than 2,000 cycles when discharged to 80%. Thus, he appears to be laying the ground work for the “Lithium-Ion Batteries Are the Answer” argument in his next article.

In the section titled “Generating Underway”, the author discusses the effects of imposing a 10 kW load on the propulsion engine, while acknowledging that a 10kW alternator is not a practical reality at the present time, and is not likely to be available anytime in the near future, thus begging the question: Why make this assumption? In Figure 3 he presents the effects of 2 kW and 10 kW alternator loads added to the propeller load at various speeds. Aside from this being impractical, as previously acknowledged, these curves are incorrect since the alternator output varies as a function of engine speed, as the author previously stated. The alternator output curve vs. RPM should be taken into account when plotting these curves. When this is done, the author’s conclusions stated in Figure 3 are not valid.

In the section on batteries, the author states that the higher purchase price and reduction in life cycle associated with AGM batteries will pale in comparison to the reduced overall cost of energy. If one is to take advantage of the AGM battery higher CAR, there are additional costs such as upgrading alternators and battery chargers. Based on the errors and omissions previously mentioned, this statement is not supported by the data.

If the only objective is to minimize the total through cost, and a charge curve of Figure 1 is assumed, then the lowest cost approach would be to purchase a Honda 2 kW portable generator and Charles 50 amp battery charger for $2,000.00, and be done with it.

A Response From Nigel Calder

I appreciate the detailed comments. There are a number of overlapping issues here which I will address in the order they are raised.

  1. ‘The battery charging at anchor data is based on an unrealistic engine rpm’. This depends on how the alternators are wound internally and the pulley ratios used. In the case of my example, the two alternators start out at 2.5 kW which, if this were a 12-volt system bulk charging at ~14.0 volts would be ~180 amps which is already higher than the output of the alternator(s) on most boats. I could increase the rpm as suggested but the alternator output in most applications would be no higher and the fuel consumption and amortization rates would hardly change so the result would be pretty much the same.
  2. ‘Engine life and amortization costs are incorrect’. Engine life is extremely variable in marine use depending on such things as the application, load profiles and maintenance. In some ‘industrial’ applications (e.g. commercial use) it can exceed 25,000 hours while in many sailboats it is often less than 5,000 hours. The 5,000 hours I used is based on the manufacturer’s rated life of the engine in pleasure boat applications. The assumed installation cost of $20,000 is on the low side.
  3. ‘An hour driving at hull speed produces substantially more wear and tear on the engine than an hour of lightly loaded operation while charging batteries, and as such the amortization cost when lightly loaded is overstated’. This is not the case. In fact, one of the reasons why engines in ‘industrial’ applications have longer lives is because they are run well loaded much of the time. Most of us still have mechanically injected engines on which the fuel injection process is not well managed at low loads and speeds, resulting in accelerated engine degradation (it is not so much wear as carbon fouling of the engine). This is one of the reasons why sailboat engines, and many marine generators, have relatively short life expectancies. If anything, the amortization cost goes up and not down at light loads. This will change in the future as ever tightening emissions legislation forces high pressure common rail injection systems onto smaller engines. Common rail maintains very tight fuel injection control down to very low loads and engine speeds, eliminating much of the carbon fouling issue (and also substantially improving fuel economy at these speeds and loads).
  4. ‘The author does not state how fuel consumption was measured’. It was measured using a very expensive, absolute fuel flow meter (as opposed to the more common differential meters, which are not that accurate) with a level of accuracy (which was checked down to very low flow rates using calibrated laboratory flasks) of 0.1%. The fuel temperature and fuel grade (the fuel was analyzed in a laboratory) were consistent throughout numerous tests (fuel temperature and ‘weight’ are two other significant factors in this kind of testing).
  5. ‘The area of the graph within the dotted line is not the typical region of battery charging at anchor’. I would argue it is. Only what I would call hard-core cruising boats have battery banks of over 1,000 Ah (at any voltage) or alternators rated at over 100 amps. With a smaller battery bank, the charge acceptance rate of batteries rapidly drops into the dotted region on the graph.
  6. ‘The author should use conventional units such as liters or gallons rather than specific fuel consumption (SFC) and grams per kilowatt hour (g/kWh)’. Specific fuel consumption and fuel measured by weight and not volume are the conventional units used in this kind of testing. The reason for using weight and not volume is because fuel weight per volume varies widely. This is also one of the reasons why we had our fuel analyzed in a laboratory. The typical assumption is 840 grams per liter whereas our fuel was 817 grams per liter. For SFC, in the USA you might see ‘lbs per hp-hour’ as opposed to g/kWh, but it is still weight that is being used.
  7. ‘Using an 80% battery discharge level is irrelevant to lead-acid batteries as no one would intentionally discharge them to this level’. The reason for selecting the 80% level of discharge is because there is a lot of cycling data from battery manufacturers based on this level of discharge.
  8. ’10 kW alternator loads should not be used as an example and the 2kW and 10kW loads need to be adjusted for engine speeds’. First, it needs to be remembered that conventional alternators typically have a peak mechanical-to-electrical efficiency that is not much above 50% so a 2kW engine load translates to a 1kW electrical output and a 10kW load to a 5kW electrical output. One kW at 14.0 volts (bulk charging a battery) is 70 amps, so this level of output is readily available with today’s technology. Five kW is 360 amps at a nominal 12 volts, and 180 amps at a nominal 24 volts. These power levels are available but rarely seen on boats (you can buy off-the-shelf 12-volt and 24-volt alternators rated to as high as 400 amps; I have a Balmar 24-volt alternator on my boat that is rated at 195 amps – i.e. 5kW). However, the principal reason for introducing the notion of 10kW alternator loads is because I believe within a year or two this kind of equipment will be readily available. It is correct that I should have adjusted the alternator curves for engine speed. However, this only applies to the bottom end of the curves. These higher output alternators tend to be wound such that they reach their rated output at considerably lower speeds than most other alternators; the devices under development will carry this further.
  9. ‘The lowest cost approach is to buy a portable 2kW Honda generator’. For many cruisers battery charging at anchor, or currently using a conventional inboard generator to charge batteries, this is definitely true, and in fact the system will be optimized if charging is done two times a day rather than once a day because this gives the batteries a chance to equalize internally between charges and increases the average charge acceptance rate of the batteries (and therefore the load on the generator) for a given amount of total generator run time. However, there are safety issues associated with using a portable generator, both on the electrical side and also in terms of potential carbon monoxide poisoning from the exhaust, that need to be thought through.

In conclusion, once again, thanks for the detailed comments. My purpose with this article was not to generate cost-of-energy numbers that can be blindly applied to any application, but to (1) illustrate a methodology for determining these things; (2) highlight the extraordinary high cost of generating onboard energy when battery charging at anchor or using a generator to charge batteries; and (3) illustrate mechanisms to reduce this cost. The assumptions and cost numbers will need to be adjusted for any given application, but one thing I can guarantee is that using conventional approaches to generate onboard energy the cost will typically still be shockingly high.

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