Last lesson's bill had one line: kilowatt-hours times a rate. A house is billed that way. A plant, a school or a supermarket is not. A commercial invoice carries a second line that often rivals the first, and almost nobody is taught to read it: the demand charge. The utility has to build wires and transformers big enough for your worst moment, so it bills you for that moment.

$C_d = P_d \, r_d$, read aloud C-d equals P-d times r-d. $C_d$ is the demand charge in dollars, and it is what you are usually solving for. $P_d$ is the billed peak demand in kilowatts: the meter averages the site's power over each demand interval, fifteen minutes on most tariffs, and keeps the single highest average it sees all month. $r_d$ is the demand rate in dollars per kilowatt, printed on the rate schedule. The subscript d is for demand on all three, which keeps them apart from last lesson's $C_e$ and $p_e$, where e was for energy. The whole bill is the two lines added: $E\,p_e + P_d\,r_d$.

Two traps live here. The first is the unit: demand is kW, not kW·h. It is a rate, the height of the peak, and the energy inside that quarter-hour is trivial. The second follows from it: a demand charge is never divided by time. A chiller and a compressor that start together at 09:15 one Tuesday set the peak, and that one interval is paid for in full, exactly as if it had happened every interval of the month. Note the size of the rate, too. Energy is priced in cents per kilowatt-hour; demand is priced in whole dollars per kilowatt, often ten to twenty of them.

That is why demand is managed by sequencing, not efficiency. Stagger the starts, interlock the electric heat against the chiller, shed a non-critical load for four minutes, and the line shrinks without a single unit of production lost. Read the relation backwards, $P_d = \dfrac{C_d}{r_d}$, and an invoice tells you the peak the utility billed. Read it the other way, $r_d = \dfrac{C_d}{P_d}$, and it gives the effective rate for comparing tariffs. Units guide, they do not confess: kilowatts times dollars per kilowatt is dollars, but the units will never tell you that you prorated a charge that is not prorated.