Revisiting the idea of a thermostat with no deadband

Back in 2015 I worked with Jakob Stoustrup, Ned Djilali, and Panajotis Agathoklis on a question that had been rolling about in my head for some time: “Do thermostats require a deadband when a discrete-time control model is used?” In our paper on the subject, we showed that unequivocally the answer for thermostats was “no, deadbands are not necessary, provided certain conditions are met”.

The reasoning was essentially as follows. Analog thermostats had a deadband because the bimetal used to measure temperature experiences hysteresis, i.e., the state of the sensor is different depending on whether the bimetal is experiencing a rising or a declining temperature. When a bimetal is used for the feedback signal in a system that integrates its output (something which all temperature control systems do), it tends to require the output to change by non-trivial amount before changing the input state. This resulted in delay which is akin to a lock-out time, i.e., a minimum time during which the device state cannot change. Although lock-out behavior is not technically required for all systems, it is necessary for systems that use hardware that degrades more quickly when fast-cycling such compressors or where fast-cycling is annoying to the users, such as when chattering occurs or noisy fans start and stop often.

When digital thermostats began to replace analog thermostats, hysteresis was no longer implicit in the sensing technology itself. As a result, digital thermostats had to implement hysteresis synthetically using a temperature deadband. In addition, a lock-out time was needed to ensure the thermostat ignores changes in set-point and mode coming from the user of the thermostat.

During the early development of transactive energy systems demonstrations used existing sensing technology, including thermostats that had deadbands built-in to protect compressors from damage resulting from fast-cycling behavior. Strategies had to be devised for the bidding agents to accomodate the hysteresis behavior of these thermostats. Although it was not difficult to do, it turned out to be unnecessary from the device perspective because under auction mechanisms, the discrete-time behavior of the market limits how often the price signal can be updated. Provided this update rate is longer than the minimum cycling time of the devices, no damage will result. The only reason compensation was necessary was to ensure that device responses to price signals were accurate relative to the original bid.

It turns out that unless the response strategy overrides the device state directly it is nearly impossible to compensate in the bidding strategies for early state changes in the response; auction-based mechanisms inevitably experience an accrual of dispatch errors during each market clearing interval. Merely adjusting the setpoint is not sufficient if the deadband is too small or the current temperature is too close to the critical temperature. This shortcoming, combined with the fact that using a periodic auction inherently limits to time-constant of the response to roughly 10 times the auction period led to a search for an alternative to the transactive energy auction mechanism for price-based distributed energy resource dispatch.

In our latest transactive energy research, we have proposed using an orderbook to dispatch power using an energy prices. The difference between an auction and orderbook is that the periodic update of the auction is no longer a constraint on how often the agents can update the state of devices. In orderbooks a device may bid as often as it wishes. Consequently orderbooks can create the conditions for fast-cycling. We have concluded that when an orderbook is used, a minimum lockout time will be necessary for many devices. This lockout time may vary, and based on past experience with these devices, we suggest that agents use a default lock-out time based on that widely used when no price-based dispatch is present, i.e., 1-2 minutes.

As for devices that do not have a requirement for a lock-out, an incentive to minimize the number of bids submitted will be necessary, but that will have to be the subject of another post.