Cycle Stealing Dimmer Algorithm

This document details the cycle stealing algorithm used in MycilaDimmerCycleStealing. It employs a First-Order Delta-Sigma Modulator (related to Bresenham's algorithm) to achieve precise power control while strictly mitigating DC offsets in the AC load.

Overview

Cycle stealing (or integral cycle control) varies power by delivering complete half-cycles of the AC sine wave to the load.

• 100% Power: The solid-state relay (SSR) is ON for every half-cycle.
• 50% Power: The SSR is ON every other half-cycle.
• 1% Power: The SSR is ON for 1 half-cycle out of every 100.

Unlike phase control, which chops the sine wave (generating high EMF noise), cycle stealing switches only at zero-crossing points, generating virtually zero noise. This makes it ideal for resistive loads like heaters.

The Algorithm: Delta-Sigma Modulation

Instead of using a fixed time window (e.g., "count 20 cycles and turn on for 5 of them"), this implementation uses a continuous accumulator approach. This allows it to adapt instantly to changes in the target duty cycle without waiting for a window to reset.

1. The Accumulator (density_error)

We maintain a running float value called density_error. This represents the "energy debt" — the amount of power the load should have received but hasn't yet.

Every Zero-Crossing (Half-Cycle):

1. We add the target dutyCycle (0.0 to 1.0) to density_error.
   • Example: If the target is 30% (0.3), we look at the debt. If we don't fire providing 0 power, the debt grows by 0.3.
2. We check if density_error >= 1.0.
   • 1.0 represents the energy of one full half-cycle.
   • If the debt is greater than a full cycle, it means we "owe" the load at least one pulse.

2. Decision Logic

If density_error >= 1.0, we attempt to fire the TRIAC/SSR.

• If we fire: We subtract 1.0 from density_error. This pays off the debt.
• If we don't fire: The density_error keeps growing until the next cycle.

3. DC Component Balancing (Critical)

AC loads (like transformers or even heating elements) perform best when the current is symmetric. If we blindly fired pulses based only on the accumulator, we might accidentally fire only on positive half-cycles (rectification), causing a massive DC current component that can saturate transformers or trip breakers.

To solve this, we track the DC Balance:

• Positive Half-Cycle: counts as +1 balance.
• Negative Half-Cycle: counts as -1 balance.

We maintain a counter dc_balance.

• We only allow a pulse to fire if it helps return the balance to zero.
• If dc_balance is positive (too many positive pulses), we wait for a negative half-cycle to fire.

// Simplified logic:
phase_val = current_is_positive ? 1 : -1;

bool helps_balance = (balance == 0) ||
                     (balance > 0 && phase_val < 0) ||
                     (balance < 0 && phase_val > 0);

if (density_error >= 1.0 && helps_balance) {
    fire();
    balance += phase_val;
    density_error -= 1.0;
}

Why This Works

1. Instant Response: If you change the duty cycle from 10% to 90%, the density_error accumulation rate changes immediately. No waiting for a "1-second window" to finish.
2. Frequency Independence: It works identically on 50Hz or 60Hz grids without configuration. 50% power is simply "50 pulses out of 100" or "60 pulses out of 120".
3. Perfect Symmetry: The DC guard ensures that over time, the net DC offset is exactly zero.

Example Trace (30% Power)

Cycle	Type	Accumulator (+0.3)	Action	New Accumulator	Balance	Note
1	Pos	0.3	OFF	0.3	0	Not enough debt
2	Neg	0.6	OFF	0.6	0
3	Pos	0.9	OFF	0.9	0
4	Neg	1.2	ON	0.2	-1	Fire (Neg)! Balance becomes -1
5	Pos	0.5	ON	-0.5*	0	Fire (Pos)! Restore balance to 0
6	Neg	...	...	...	...

(Note: In the simplified view, if debt remained high, we might fire back-to-back if polarity allows).