Dear Load Distributor,
Great question. If you want to save as much energy as possible, you’ll want to run your heat pumps at their most efficient point, and that point isn’t necessarily at full load. We measure that efficiency with the coefficient of performance (COP): the ratio of useful heat delivered to electricity consumed, so the higher the better. The key fact, which we can summarize in a single sentence, is that a heat pump’s maximum COP is not at full load, so distributing the demand across more units can give you a better overall COP. Running cost isn’t the only thing that matters, of course, upfront investment plays a role too (more on that later), but let’s focus on energy first. Don’t worry, we’ll dive into this in more detail.
First, let’s look at a single heat pump for heating. Its COP depends mainly on the following conditions: the temperature at the condenser (where heat is delivered), the temperature at the evaporator (where heat is extracted from the source), and the part-load ratio (PLR). The PLR represents the heat actually supplied by the unit relative to its available capacity at those operating temperatures. When we look more closely at how the COP evolves with the PLR, we find something perhaps counterintuitive: the maximum COP is not at full load, but at a lower one. Why? At lower loads, the heat exchangers are effectively oversized for the reduced demand, so the temperature lift the compressor must overcome shrinks and the COP climbs; only at very low loads do compressor and motor losses start to drag it back down (see the figure below).
Now that we know a single heat pump runs more efficiently at part load than at full load, delivering more heat per unit of electricity, let’s see how this plays out in a cascade. When several heat pumps work together, load distribution becomes key. Most conventional heat pump cascades in buildings operate in a straightforward way: they turn on a single unit and increase its modulation until it reaches full load, then bring on the second one, and so on. But based on what we just saw, it can be more efficient to run two heat pumps at once, keeping the first near its peak-COP load and letting the second pick up the rest, rather than driving the first to full load while the second barely ticks over. This also keeps the incoming unit out of the very low part-load region, where efficiency is worst (see the figure below). Think of it like driving on the motorway: your car sips less fuel per kilometre cruising at a steady, moderate speed than with your foot flat to the floor. Running several heat pumps each in their comfort zone beats pushing one to the limit while the others wait.
So, with this in mind, my colleagues and I developed a heuristic optimization to find the optimal thresholds for a heat pump cascade. In simple terms: we discretize the possible threshold values, simulate a full year of cascade operation for each combination, and pick the one with the lowest electricity consumption. We applied it to a real installation, first presented at SimBuild 2024: a building in Velenje (Slovenia) where three air-to-water heat pumps meet the heating demand. Comparing a conventional cascade (driving units to full load) against the optimized one at the simulation level, we found electricity savings of up to 13.8% over the year. And a real plus of this approach, one that saves you a few headaches, is that it needs no new hardware and no real-time actuation: you optimize the cascade once and program the new threshold values into the existing controller. Straightforward.
And now let’s take it one step further. Everything so far happens at the operation level, but imagine bringing this thinking into the design phase. Choosing how many heat pumps to install is usually decided on upfront capital expenditure (CAPEX) alone, where a single large unit looks cheapest. But when we add the operational expenditure(OPEX) over the system’s life, the picture changes. We explored this in more detail in a follow-on paper, where we found that two or three smaller units recover their higher initial cost in about 3.5 years once the optimized cascade is applied, making them the more cost-effective choice in the long run.
In short: don’t be afraid to share the load. Whether you’re operating an existing cascade or designing a new plant, giving each heat pump room to breathe pays off, in energy and in economic terms.
Laura Zabala Urrutia
Modelling & optimization engineer at R2M Solution Spain SL
PhD student at University of the Basque Country (EHU)
