Electric Power Principles, 2nd Edition

13System Dynamics and Energy Storage

13.1 Load–Frequency Relationship

In a power system consisting of one synchronous generator and a limited set of loads, control of frequency is simply that of controlling the speed of the generator shaft, but in most cases there are multiple generators and a mix of generator types. Rotating electric machines, including generators and motors, store energy in their moving masses. An unbalance between input energy in the form of generation and output energy in the form of load would induce an increase or decrease of rotational speed of the generators and with it the electrical frequency of the system. Maintaining a constant frequency therefore is maintaining a balance between load and generation. In this chapter we consider how one might go about controlling a system with a mix of generators, including rotating machines and inverters.

13.2 Energy Balance

To start, consider an isolated system that has some rotating inertia. In Figure 13.1 the generator(s) will have a rotational moment of inertia. The load might or might not also contribute some inertia. A battery‐based energy storage system might be present, capable of inserting power into the system. Each shaft can be characterized as having rotational energy as:

where J is the rotational moment of inertia of the shaft and Ω is the speed at which the shaft is rotating. If all of the shafts ...