The previous article described the relationship between power imbalance and rate of frequency change for the first few seconds after a disturbance in power balance. Important as those few seconds are, the few seconds of energy being provided by the spinning angular momentum of the synchronous machines, if something isn’t done to correct the power imbalance within those few seconds, collapse will certainly follow in only a few more seconds. Feedback control is the key to this response. The machine governor is the all important device providing the control … and if there is insufficient governor response the backstop is load shedding triggered by under frequency relays.
The diagram below shows how a governor fits in the system as a feedback controller. The governor’s purpose is to sense the shaft rotational speed, and the rate of speed increase /decrease, and to adjust machine input via a gate control.
Remember that shaft rotational speed w is directly aligned with frequency, and that frequency has to be kept within about +/- 0.5 Hz of nominal, and that power imbalance, angular momentum and rate of frequency change is described by Pm – Pe = M * dw/dt.
Starting with an initial condition where the machine running a constant speed w, Pm = Pe and dw/dt =0. When more electrical load Pe is taken from the generator (Pe>Pm), rotational energy will be extracted from the machine and it will slow (dw/dt<0). Of course the opposite would happen if less electrical load was taken from the generator.
The governor’s job is to continuously monitor the rotational speed w of the shaft and the rate of change of shaft speed dw/dt and to control the gate(s) to the prime mover. In the example below, a hydro turbine, the control applied is to adjust the flow of water into the turbine, and increasing or reducing the the mechanical power Pm compensate for the increase or reduction in electrical load, ie: to approach equilibrium.
It should be pointed out that while the control systems aim for equilibrium, true equilibrium is never actually achieved. Disturbances are always happening and they have to compensated for continuously, every second of every minute of every hour, 24 hours a day, 365 days a year, year after year.
The discussion has been for a single synchronous generator, whereas of course the grid has hundreds of generators. In order for each governor controlled generator to respond fairly and proportionately to a network power imbalance, governor control is implemented with what is called a ‘droop characteristic’. Without a droop characteristic, governor controlled generators would fight each other each trying to control the frequency to its own setting. A droop characteristic provides a controlled increase in generator output, in inverse proportion to a small drop in frequency. Refer to the graph below.
The governor senses system frequency and it controls it’s generator’s prime mover to increase the generator’s output according to the droop characteristic. The droop slope is typically referred to in percentage terms. It is typically about 4%. This equates to 2 Hz drop in a 50Hz system for a 0% to 100% change in generator output.
In New Zealand the normal operational frequency band is 49.8 to 50.2 Hz. An under frequency event is an event where the frequency drops to 49.25 Hz. It is the generators controlled by governors with a droop characteristic that pick up the load increase and thereby maintain stability. If it happens that the event is large and the governor response is insufficient to arrest the falling frequency, under frequency load shedding relays turn off load.
Here is a record of an under frequency event earlier this month, where a power station tripped.
The generator tripped at point A which started the frequency drop. The rate of drop dw/dt is determined by size of the power imbalance divided by the synchronous angular momentum (Pm – Pe)/M. In only 6 seconds the frequency drop was arrested at point B by other governor controlled generators and under frequency load shedding, and in about 6 further seconds additional power is generated, once again under the control of governors, and the frequency was restored to normal at point C. The whole event lasting merely 12 seconds.
So why would we care about a mere 12 second dip in frequency of less than 1 Hz. The reason is that without governor action and under frequency load shedding, a mere 12 second dip would instead be a complete power blackout of the North Island of New Zealand.
The next article will look more closely at this event.
[Article updated 9 Jul 17 following comments from chrism56. Thanks Chris]