Load models
The key idea
A load model answers one question: when the voltage at a load changes, what does the load's power do? Constant impedance backs off. Constant current backs off half as much. Constant power does not back off at all — it fights back.
The idea
"A 100 kW load" sounds complete, but it hides an assumption. 100 kW at what voltage? When the feeder sags to 0.95 pu, real equipment reacts in different ways:
- Constant impedance (Z). The load is just a resistance — a heater, an incandescent lamp. Lower voltage pushes less current through the same ohms, and power falls with the square of the voltage: at 0.95 pu it draws about 90%.
- Constant current (I). The load holds its current wherever the voltage goes, so power falls in direct proportion: about 95% at 0.95 pu. A useful middle-ground model.
- Constant power (P). The load has electronics that regulate: a variable speed drive, a server power supply. Whatever the voltage does, it takes its full power — by drawing more current as the voltage falls.
Try it
Drag the voltage down and watch the three models separate.
Constant power (P)
draws 100%
motor drives, switched-mode supplies
Constant current (I)
draws 95%
a middle-ground model, some lighting
Constant impedance (Z)
draws 90%
heaters, incandescent lamps
When the voltage sags, a constant-impedance load backs off and partly heals the sag. A constant-power load does not back off — it draws more current instead, and makes the sag worse.
Why it matters
- Constant power is the pessimistic — and often honest — choice. A sag makes it draw more current, which deepens the sag. On a weak network, the model choice can be the difference between a converged case and a collapse the solver cannot find.
- Constant impedance is self-healing. The load backs off as the voltage falls, which cushions the sag. Assuming it where drives and electronics dominate flatters the network.
- The mix is the model. Real feeders are a blend. Study results quoted to a decimal place inherit the assumption — state it.
The math, if you want it
Relative to nominal voltage V₀ and nominal power P₀, with v = V/V₀: constant impedance gives P = P₀·v², constant current gives P = P₀·v, and constant power gives P = P₀. The general polynomial ("ZIP") model blends them: P = P₀(a·v² + b·v + c) with a + b + c = 1, and the same form applies to Q. The exponent form P = P₀·vⁿ covers all three with n = 2, 1, 0.
See it in Phasor
Every load element in Phasor carries its model — constant power, constant current or constant impedance — per scenario. Run the same case twice with different models and diff the voltage profiles: the gap is the size of the assumption.