You can do it by using simple switching, provided you adhere to a
number of constraints. I'm assuming that all of your heating elements
have the same wattage. (For heating elements, watts of power input is
virtually identical to watts of heat output, by the way.)
Consider the basic design to use just one heating element, shown here as VVV:
You can then use a combined series/parallel arrangement of four
heating elements to achieve the same heat output:
In this arrangement, each heating element has half the voltage across
it, and also half the current flowing through it (because each
series-group of two has twice the resistance). Therefore, each heating
elements consumes and dissipates one-quarter of the power that it
would if if were directly connected to the input voltage.
In a similar way, you could use nine heating elements arranged as
three parallel groups, each group comprising three series heating
But, as I mentioned in the request for clarification, this is only
going to work if the resistance of the heating elements does not
change much as they heat up, and that's unlikely to be true.
Certainly, it won't be true for tungsten heating elements.
You have not stated your reason for wanting to maintain the same power
output whilst changing the number of heating elements, but I'm
guessing it may be because you want to radiate the same amount of heat
from a larger or smaller area. If that is the case, perhaps an
alternative method of achieving this goal will be more practical. You
could use a fixed number of heating elements and move them closer or
further apart, or you could swap between different-sized rear
reflectors that would distribute the same amount of heat over a larger
or smaller area. You could conceivably even use one flexible rear
reflector that could be stretched out or curved up.
If you want to go beyond these designs, you would need to consider
active control of the electrical input. If you will allow the user to
re-balance the heat output, then you can just put all the elements in
parallel and let the user operate a simple SCR-based controller
(effectively the same as a lamp dimmer, but able to handle higher
If the power control must be automatic, you can put all the elements
in parallel and use a constant-power control device. The principles
are explained here:
"SCR Control of Electric Heaters"
An example industrial product that performs SCR power control with a
constant-power facility is this one:
"PCI Series SCR Power Controllers"
I trust this provides the information that you are seeking. If not,
please request clarification.