I have a feeling that concentration on the development and fine-tuning of financial mechanisms in order to stabilise grid voltages is missing the point. The transfer functions between prices and voltage are too complex. As Dr Holmberg suggests, a more simple mechanism such as a feeder level dynamic price might be the answer. But there has to be a dominant time lag in the system otherwise it will become unconditionally unstable.

The situation is highly dependent on the local policies in each country and the scale of the prosumer's production. The following discussion provides some surprising answers.

https://www.researchgate.net/post/Does_the_Rooftop_solar_consumer_have_to_pay_self_consumption_charges_in_any_country

I think that the goals of your research may be conflicting - why should maximising profit have anything to do with stabilising a grid? I suspect the reverse would be closer to the truth. In an interconnected system the overall performance measured on some axis may not be maximised by maximising the performance of each individual connected unit, especially when the degree of connectedness is high. While it sounds a good idea to maximise profit, don't you mean maximising system stability and remunerating prosumers for doing this? This might not mean each prosumer's profit is maximised, only that the overall remuneration across all prosumers is maximised.

Exactly, I'm interested in maximizing the overall remuneration across all prosumers while maintaining the stability of the grid. It's like a contract between the DSO and the prosumers. The prosumers in one control area has to regulate the voltage within the limits, and the DSO has to pay for this service. I'm wondering how the prosumers could be remunerated (euros/kWh, euros/kvar).

Any renumeration to prosumers paid by the DSO has to be paid for by all the other DSO consumers. Maximumizing the renumeration for the few at the expense of the many is unpopular so it is discouraged by regulators and governments. It would be better to have an objective that minimises the overall costs.

My take on the way things are going in the U.S. is that provision of reactive power (by PV and battery inverters) will be mandated as part of an interconnection agreement. This provides some voltage support. On the other hand, it is tricky to reward loads for adjusting in response to real voltage. Real voltage varies on the distribution system with flow direction, with passing clouds (due to PV systems) and with load changes. How can we signal to devices that they should use more or less power, and how to reward for responding? I believe we need a real-time price that is specific to each meter. But this is both complex (formulating the price based on DS modeling) and also too simplistic (customers need a price forecast, and we need to also consider frequency regulation and energy market price at the same time as voltage fluctuations). I think where we may end up is a feeder-level dynamic price that the DSO manages so that customer load/DER response is effective for voltage support as well as regulation and capacity and wind ramps (and whatever other variables might drive energy markets). That is, the DSO provides a single dynamic price to the customers on a feeder to incentivize use of energy that aligns the load with needed capacity and regulation. Then on top of this, inverters will supply reactive power to help manage voltage.

I have a feeling that concentration on the development and fine-tuning of financial mechanisms in order to stabilise grid voltages is missing the point. The transfer functions between prices and voltage are too complex. As Dr Holmberg suggests, a more simple mechanism such as a feeder level dynamic price might be the answer. But there has to be a dominant time lag in the system otherwise it will become unconditionally unstable.