Discrete sensing and actuation in a simulation of frequency responsive loads

Loads acting autonomously on a local frequency signal can improve the response of a power system to sudden changes in supply, demand, or both. In this paper we address the use of load for regulating frequency by using feedback control. We extend prior research that focused on continuous proportional control, whereby one assumes that the load responds instantaneously, continuously, and in direct proportion to the changing frequency. However, sensors employed in any practical system have a finite sensitivity which introduces quantization effects into the control. As a result, a critical factor in the design of such a control is the relationship between the sensitivity of the sensor and the gain of the actuator. To study this issue, our model is constructed in two parts. The continuous dynamics of the power system is coupled to discrete event models of the sensors by state events that describe the detection points available to them. The quantized signals from the sensors are transformed by the actuators into discrete changes of load which, in turn, change the frequency and thereby complete the control loop. We illustrate the model with a scenario that involves a sudden, unanticipated change in load and the combined response of the control and power system to recover from the event.