Duty Cycle: Why Run Hours, Not Clock Hours, Set the Cost
Why this matters
The fastest way to lose a customer's trust on a bill call is to tell them their air conditioner costs several times what it really does. It happens constantly, and it happens the same way: somebody takes a running wattage, or worse a breaker size, multiplies by 24 hours, and announces a number. The customer compares it with their bill, sees it cannot be true, and stops listening. Equipment that cycles is paid for by the hours it actually runs, and getting that one idea right is what makes every other operating-cost figure you give believable.
Plugged in is not running
Duty cycle is the fraction of time a piece of cycling equipment is actually running. A compressor that runs 36 minutes out of 60 has a 60 percent duty cycle for that hour. The other 24 minutes it is plugged in, energized at its controls, and drawing next to nothing.
Most of the big energy users in a house cycle: air conditioners and heat pumps, furnaces and boilers, refrigerators and freezers, dehumidifiers, water heaters, well pumps, sump pumps. Each one runs until a thermostat, humidistat or pressure switch is satisfied, shuts off, and waits for the condition to drift back.
So the energy formula for a cycling load is:
kWh = running kW x hours actually running
and the clock hours only enter through the duty cycle:
hours actually running = clock hours x duty cycle
What one hour looks like
A single-stage central air conditioner on a warm afternoon, running at a measured 3.7 kW (compressor and outdoor fan 3.2 kW, indoor blower 0.5 kW):
ONE HOUR, ONE CHARACTER = ONE MINUTE, # = RUNNING
0 10 20 30 40 50
############........############........############........
ON 12 OFF 8 ON 12 OFF 8 ON 12 OFF 8
RUN 12 + 12 + 12 = 36 MIN OF 60 = 60 PCT DUTY CYCLE
THIS HOUR = 3.7 KW X 36 / 60 H = 2.22 KWH
24 X 3.7 KW WOULD CLAIM 3.7 KWH FOR THIS SAME HOUR
The line is the whole idea. For this hour the equipment used 2.22 kWh, not 3.7, even though it was "on" the entire hour in the sense the customer means.
How duty cycle moves with the weather
Duty cycle is set by the ratio of the load to the equipment's capacity at that moment. Both halves move.
- The load rises as the weather gets more extreme. The hotter it is outside, the faster heat comes into the house, and the more of each hour the air conditioner has to run to remove it. In heating, the colder it is, the faster heat leaves.
- The capacity falls at the same time. An air conditioner removes less heat per hour on a 100 F afternoon than on an 85 F one, because it has to reject heat into hotter outdoor air. A heat pump in heating mode delivers less heat per hour as the outdoor air gets colder. So the duty cycle climbs faster than the load does.
At some point the duty cycle reaches 100 percent: the equipment runs continuously and still cannot keep up. For a heat pump that point is called the balance point, the outdoor temperature at which its capacity just equals the house's heat loss. Below it, the thermostat brings on backup heat to make up the difference, and the cost per hour changes completely. See related: COP, AFUE and Delivered Heat: Putting Every Fuel on One Scale.
The running kW also moves with conditions. A compressor draws more current on a hot afternoon than on a mild evening because it is working against higher pressure. So a wattage measured at 75 F is not the wattage at 98 F. Measure under the conditions you are estimating, or say which conditions your figure came from.
Variable-speed equipment changes the shape
Single-stage equipment has one speed: full output or off. Two-stage equipment has a low and a high stage. Variable-speed or inverter equipment can run anywhere across a range, and in mild weather it slows down to match the load instead of cycling.
That means a variable-speed system often runs nearly all the time, which alarms customers who were used to the old unit shutting off. Long run hours are not the cost. Running at part speed draws far less power, and at part load these units commonly move more heat per kWh than they do at full speed. For variable-speed equipment the duty-cycle idea is replaced by an average power over the hour, and the only honest way to get it is to measure energy over time, not to time on-off cycles.
Worked example: one hot day, three estimates
A customer with a 3-ton single-stage system asks what their air conditioning costs them on a hot day. The thermostat's runtime history for a recent 96 F day shows 9.5 hours of cooling. A clamp reading the service tech took at the condenser that afternoon gave the 3.7 kW running figure above.
Estimate 1, running power for 24 hours. 3.7 kW x 24 h = 88.8 kWh.
Estimate 2, from the breaker. The condenser is on a 30 A breaker at 240 V. 30 A x 240 V = 7,200 W = 7.2 kW. 7.2 kW x 24 h = 172.8 kWh. This number is meaningless twice over: a breaker is sized above the running current so that starting current and code margins fit, and the equipment never draws the breaker's rating while running normally.
Estimate 3, run hours. 3.7 kW x 9.5 h = 35.15 kWh.
Check it from the other side. 35.15 kWh across 24 hours is an average of 35.15 / 24 = 1.46 kW, and 1.46 / 3.7 = 0.396, a 39.6 percent duty cycle across the day, which matches 9.5 / 24 = 0.396. Both directions agree.
Now compare:
- Estimate 1 overstates the real figure by 88.8 / 35.15 = 2.5 times.
- Estimate 2 overstates it by 172.8 / 35.15 = 4.9 times.
The cost of that hot day is 35.15 kWh x the rate per kWh on the bill. A mild day with 3 hours of runtime is 3.7 x 3 = 11.1 kWh, under a third of the hot day (11.1 / 35.15 = 0.32). The monthly cooling cost depends on how many of each kind of day the month had, which is exactly why you give the customer a per-day figure tied to a temperature rather than a monthly promise.
What a variable-speed replacement might look like on the same day. The single-stage unit removed 3 tons x 9.5 h = 28.5 ton-hours of heat. A variable-speed unit could remove those same 28.5 ton-hours by running, say, 20 hours at an average of 28.5 / 20 = 1.43 tons. If its average draw over those hours measured 1.4 kW, the day would be 1.4 x 20 = 28 kWh, against 35.15. Treat those two figures as illustrative of the shape, not as a promise for any particular unit: the actual part-load draw comes from the manufacturer's performance data or a measurement on the installed system. See related: Savings Claims Without Overpromising: The Honest Language.
Where to get run hours
In rough order of how much you can trust them:
- A logged energy measurement. A plug-in meter on a refrigerator or dehumidifier, or a logging power meter on a hard-wired load installed by someone qualified to work in the panel, totals kWh directly. This skips the duty cycle entirely, which is why it is the best figure available.
- Thermostat runtime history. Most connected thermostats report cooling, heating and auxiliary heat hours per day. It is the call for heat or cooling, which is close to equipment runtime on single-stage systems and less precise on staged or variable systems.
- Interval data from the smart meter. Shows when the house drew more, which brackets when the big cycling loads ran. See related: Smart Meter Interval Data: What the Hourly Record Shows.
- An observed sample. Timing on and off cycles for an hour. Useful for spotting short cycling, poor for estimating a day, because one hour at 3:00 pm says nothing about 3:00 am.
The nameplate trap beyond air conditioners
The same error shows up on every cycling appliance. A refrigerator's nameplate current includes the defrost heater, which runs only briefly, so nameplate volts x amps x 24 overstates it badly. A dehumidifier's rated watts apply while the compressor runs; on a humidistat in a dry month it may run a small fraction of the day. A water heater's elements are rated for full output, but they only run while recovering from a draw. See related: How to Measure Real Watts Instead of Trusting the Nameplate.
Put illustrative numbers on the refrigerator. Say the nameplate reads 115 V and 6.0 A. Volts x amps gives 690 W, and 690 W x 24 h is 16.56 kWh a day. A plug-in meter left on the same refrigerator for three days totals, say, 4.2 kWh, which is 1.4 kWh a day. The nameplate method claimed 16.56 / 1.4 = 11.8 times what the appliance used. Nobody would believe that figure on a bill call, and they would be right not to.
The rule of thumb: nameplate figures are a ceiling for the running state. They are not the running power, and they are never the average.
When the duty cycle is itself the finding
A duty cycle that does not fit the weather is information. An air conditioner running nearly continuously on an 80 F day, a freezer whose compressor never seems to stop, a well pump that starts every few minutes with no water being used: each one is running far more than its load requires. That is a fault to diagnose, not a cost to estimate, and it goes to the technician who works on that equipment. See related: Why a Bill Rises: The Causes That Are Not the New Equipment.
Short cycling, where equipment starts and stops many times an hour, is a different symptom. It can leave the duty cycle near normal while wearing the equipment and losing efficiency at every start. Do not read a normal duty cycle as proof that the equipment is healthy.
References
- See related: How to Estimate an Appliance's Operating Cost by Hand
- See related: How to Confirm Backup Heat Runtime From the Thermostat and a Clamp
- See related: What a BTU Actually Is
- See related: Reading Energy Data Without Misleading the Customer
- Manufacturer expanded performance data for capacity and power at each outdoor temperature