ENFUSE Experiment: Energy/Environment: Power Inverter
Module: Energy/Environment: DC-AC Power Inversion
Example Problem: Energy Efficiency
Name:
Score: ____________ / 100
Computing power: DC and AC cases
How much power does a load with resistance R dissipate? If both the voltage
across the load and current through the load are constant (as when dealing with
DC), the answer is straightforward:
𝑃𝐷𝐶 = 𝐼𝑉 = 𝐼 2 𝑅 =
𝑉2
𝑅
Because the power at every time instant is the same, the average power and the
instantaneous power are equal.
If the voltage and current are sinusoidal with the same frequency (as in AC) then
we can measure their RMS (root mean-square) values 𝐼𝑅𝑀𝑆 and 𝑉𝑅𝑀𝑆 using a
multimeter. Because the instantaneous power varies over the AC cycle, we
compute the average power
2
𝑃𝐴𝐶 = 𝐼𝑅𝑀𝑆 𝑉𝑅𝑀𝑆 = 𝐼𝑅𝑀𝑆
𝑅=
Power Efficiency
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𝑉𝑅𝑀𝑆
𝑅
ENFUSE Experiment: Energy/Environment: Power Inverter
A car’s fuel economy (e.g, in miles/gallon) is one measure of energy efficiency.
However, the way to speak of efficiency for inverters is the power efficiency: the
ratio of the output power to the input power. The best possible efficiency is one, or
100%. But if the inverter dissipates (or loses) power such that only half is
delivered to the load, the efficiency is 0.5 or 50%. To summarize, the power
efficiency is
𝜂=
𝑂𝑢𝑡𝑝𝑢𝑡 𝑃𝑜𝑤𝑒𝑟
𝐼𝑛𝑝𝑢𝑡 𝑃𝑜𝑤𝑒𝑟
Energy efficiency and power efficiency
Energy is power integrated over time. In units, we have
𝑤𝑎𝑡𝑡𝑠 × 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 = 𝑗𝑜𝑢𝑙𝑒𝑠
This relationship is true if the power is constant over a time interval. Thus for DC,
the average power is identical to the instantaneous power.
But AC power fluctuates over a cycle. Consider multiple cycles. If the average
power over each of those cycles is the same, then the above equation is also true
for average AC power.
Thus, in both DC and AC cases, the energy is the average power integrated over
time. Thus the time can be divided out of both, and so the power efficiency is equal
to the energy efficiency. Thus for our DC-AC inverter, the energy efficiency is the
ratio of the (AC) output power and the (DC) input power.
Problems
1. If a DC power source delivers 1 KW to an inverter, but the inverter delivers 750
W to the load, what is the efficiency of the inverter?
2. A DC-AC inverter takes in 100 W from a solar panel, but dissipates 32 W in
heat. The rest of the power is delivered to the load. What is this inverter’s energy
efficiency?
3. A poorly-designed DC-AC inverter has an efficiency of 42%. The load requires
100 W of AC power. How much DC power must be delivered by the power source
to the inverter?
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