# What does “mod 2” mean in these multi-level inverter switching equations?

I am working through a paper that discusses the design of a multi-level inverter to connect photovoltaic arrays to the grid. It uses 4 PV modules (only two are shown in the design image below, but it is expandable) along with an H-bridge to produce 31 voltage levels. These are used to produce a modified sine wave with low THD:

The scheme for switching Q1 - Q4 uses a reference voltage: V_ref(t) = V_max*sin(wt + delta_ref)

The authors given equations for calculating the switch signals, which include "mod 2":

I am aware of the usual meaning of "m mod n" as "the remainder left over when m is divided by n". This doesn't seem to work here at all!

Can anybody tell me how the given equations are able to generate the switching signals?:

• Modulo 2 is the remainder when an integer is divide by 2. For example 7 modulo 2 = 1, since 7/2 = 3 remainder 1. Modulo 2 is used in digital systems because dividing any positive integer by 2 will give a remainder of either 1 or zero – Chu May 7 '15 at 7:35
• Can you give a link to the paper, so we can get a bit more context around the equations? (In particular what the function $$V_{ref}$$ does.) – Li-aung Yip May 7 '15 at 8:14
• Here is the paper, but it is behind a pay wall (perhaps available through your own institution): link. V_ref is a reference sine wave with the same frequency as the desired output AC voltage. I understand the usual remainder usage of modulus, but in this case V_ref is not an integer. It also may never get above 1, depending on the chosen value of V_max. – DFisher May 7 '15 at 15:31