This may be off-topic for math-fun, but here goes. The standard 'maximum power transfer' theorem says that the maximum power is transferred from a source to a sink when the source and the sink have conjugate impedances. For resistive loads, this means equal (real) impedances. My question is what happens when one has a single sink, but *multiple* sources with a multiplicity of power capacities, possibly time-varying ? This problem is prompted by an array of solar panels, each with different characteristics -- e.g., orientation -- and shading, so the output power is time-varying among the different panels in the array. In the modern world, everything can be digitized, or at least sampled. Solar panels with 'microinverters' produce alternating current (AC), so it is useful to consider each 1/60 sec *cycle period* from a collection of solar panels separately. Consider using microinverters with enough power storage to store a few seconds worth of power; each microinverter will have the same optimal impedance for the time during which it is connected to the load. Then it is conceivable to use a *scheduling* algorithm to enable optimum power transfer from all of the micro- inverters. Thus, a 'round-robin' scheduling of the microinverters would have each microinverter dump a 'unit' amount of power for 1/60 sec at the optimum source impedance to the load, in sequence. If a micro-inverter doesn't have enough power to contribute when its 'turn' comes up, it 'passes', and zero power transfer takes place during that 1/60 sec. Does this scheme provide optimal power transfer from the sources to the sinks?? I considered the idea of simply tying the outputs of the sources together and skipping the round-robin idea, but if the sources are different, then such a scheme would end up transferring power among the sources instead of transferring it to the load.