Efficient algorithm to reduce peak power from multiple pwm output?

Question

I have multiple power mosfet pwm controlled and connected to a single main power supply. Thee pwm signals operate all at the same frequency and their duty factor is determined otherwise and can change frequently. It can can vary between 0 and 100%. My PWM controller allows me to choose On time and off time independently for each signal.

I am looking for an efficient algorithm to determine the on time of each channel in order to minimize the peak power drawn from the power supply.

A trivial example: With 10 mosfet each one with a 10% duty factor the optimal solution will be to turn on each mosfet one at a time in sequence.

Any ideas out there on how to address this problem? Thanks

Answer 1

Let the pulse width fractions (between 0 and 1) be p₁, ..., p_n. Let s₀ = 0 and s_n = s_n−1 + p_n be the prefix sums. Signal i should turn on at times s_i−1 mod 1 and end at times s_i mod 1.

This algorithm does what you want on the trivial example, since s₀, s₁, ..., s_n−1, s_n = 0, 1/10, ..., 9/10, 0.

For a less trivial example, suppose that we have signals at 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%. Then the pulses look like

1---------1---------
-22--------22-------
---333-------333----
------4444------4444
55555-----55555-----
6----666666----66666
-7777777---7777777--
888888--88888888--88
99999-999999999-9999