Energy from a linear power ramp and plateau calculator

Integrate a stated linear real-power ramp by its endpoint mean, then add the steady-period energy. Endpoint power alone cannot represent the full logged period.

E = \frac{\left(P_{0} + P_{1}\right) \times h_{r}}{2} + P_{1} \times h_{s}

Calculator

Enter the values you know and leave one box empty. Calculate finds the empty one, the result or any input.

Worked example

Given

$P_{0}$ = 160 kW
$P_{1}$ = 80 kW
$h_{r}$ = 1.5 h
$h_{s}$ = 2.5 h

E = \frac{\left(160 + 80\right) \times 1.5}{2} + 80 \times 2.5 = 380

Symbols and units

Symbol	Meaning	Unit
$E$	energy over the observed ramp and steady period	kWh
$P_{0}$	power at the beginning of the linear ramp	kW
$P_{1}$	power at the end of the ramp and during the plateau	kW
$h_{r}$	linear ramp duration	h
$h_{s}$	steady plateau duration	h

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Results are estimates for study and screening. Check the inputs, units and assumptions before you use them for design, billing or contract decisions.