Power-sector decarbonisation envisages extensive uptake of variable renewable energy (VRE) technologies. Although VRE output is intermittent, coupling between heat and power sectors via combined heat and power (CHP) plants could provide the requisite flexibility. However, strategic CHP plants could use the link between the two energy sectors to manipulate electricity prices. We use a bi-level model to investigate the incentives for the exercise of such market power. At the upper level, a firm with both heat-only and CHP plants is a Stackelberg leader when determining its heat output and is constrained by power-market operations at the lower level. Such a strategic firm produces more (less) heat from its CHP (heat-only) plant vis-à-vis the social optimum to constrain its power output, thereby boosting the electricity price. Additional market power at the lower level from power-only generation induces the strategic heat producer to reduce distortions to its operations as long as the electricity market is relatively large. In order to attenuate welfare losses from such strategic behaviour, we devise an incentive-based regulatory mechanism consisting of a subsidy to or a tax on CHP heat output. Numerical examples illustrate the properties of our analytical results, which can inform future negotiations over CHP cost allocations between regulators and producers.

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