We know that the balancing of load and generation cannot be exactly achieved in a power system. This means that the swing equation cannot be in the steady-state conditions. So in such conditions are the frequencies of a small generating unit and a large generating unit equal?
Hi Farhad!
What is known as system frequency is an average of the frequency of all system synchronous generators. Frequency in different points of the system has not always the same value, however such values may not be show big differences otherwise the system will split. Regarding your question on the frequencies of a small and large generating units they may be a bit different at an specific instant but such a difference is not necessarily associated only with the size of the unit. Considering that the system is operating in steady state condition, the frequency in all system units, no matter its size" would be practically the same.
Thank you Dr. Calderon. But if the frequency is not the same, so smaller generating units (i mean the units with lower inertia) must rotate faster. Are you agree?
Hi Farhad, regarding your last comment *** But if the frequency is not the same, so smaller generating units (i mean the units with lower inertia) must rotate faster. Are you agree? **** Let's considering the following situations:
a) A 3FF occurs very close to unit 1, this unit unit will accelerate faster than the ones electrically located far away from the faulted point, no matter if unit 1 is the one with the higher inertia.
b)Should the 3FF occurs at the midpoint between unit 1 and unit 2, the unit with the lower inertia will accelerate faster than the heavier one.
In summary, at steady state all units in the system will have the same frequency (theoretically), in daily operation the system conditions are changing continuously (due to normal load fluctuations), that's a reason why the frequency measured in one point of the grid should be slightly different if compared against another measurement taken in a different point of the grid. However this difference will be small enough to be neglected and consider that in steady state the frequency is practically the same.
Thank you Mahdi. Do you have any comment or explanation in this regard?
As Dr. Calderon mentioned, in the SS conditions, the average frequency in all measured points is the same. what is important in this regard, is the determination of the system frequency in the transient/sub-transient conditions. This is a very important issue when designing the power electronics control systems, synchronization of renewable resources and microgrid (with power system or other microgrids), power quality issues etc.. This is due to existence of non-stationary short-time signals, stochastic renewable resources and loads, noise, harmonics, DC offset, and system unbalance etc. Therefore, many researches have been done in the field of frequency and phase estimation, for example, based on the scalar samples, vector-valued methods, the Wiener filtering approach and etc.
Yes, while operating large system, as experienced with proper time stamping measurements done, though average frequency for an integrated synchronous system has been found to be more or less same at each bus under 'so-called' steady-state operating condition (as inherently load changes from time-to-time and so the generation to match) due to sub-transient / transient condition (resulting from disturbances, faults, etc.) variations are not uncommon with coherency and inertia playing significant role.
More information related this question can be obtained from R&D and related development in Phasor Measurement Unit (PMU) technology.
This is relatively a new technology and is now generally embedded in digital/numerical protection relays. It has GPS time stamping - thus very accurate and synchronous records from geographical different parts of the power systems.
I do not have anything specific to share but I do suggest you Google search or any other search engines to get to PMU information.
Responses on your question so far has been interesting. At first glance, your question came across as an enquery on frequency of the power system in a steady state operating condition. However some responses were related to situations which were not steady state. Of course when any system which moves away from a steady state to another state, than all variables are subjected to various transient changes - some very fast and others relatively slower changes (voltage, current and frequency). During a transient period, one should not expect to observe pre-transient nor post-transient behaviour of the power system. For instance, after 3-phase fault at a zone substation, you can end up with a power system network state with zero voltage, zero current and zero frequency on some parts of the network and a new steady state in other parts of the netpork i.e. a black out of some parts of the network because protection system sensed the fault and cleared it by tripping the circuit breakers thus isolating the faulted network. However between onset of the fault and final clearing of the fault, the power system would had gone through a transient period for the duration of the fault where voltage and currents magnitudes were going thorugh very rapid changes (based on R-L-C and inertia of the pwoer system).
It's not exactly new technology so far as synchronously running system having constant frequency, if I have understood the intrinsic meaning, In fact that is the fundamental theory. However, I am inclined to agree for the possibility of accurate measurement of frequency wide-area-network wise for a large system simultaneously (due to time-stamping for comparison) now-a-days on account of deployment of PMUs collecting, transmitting, & storing data in fractions of a second. This is based on my experience of operating large Regional Grids in India earlier that are of course interconnected (with variation in degree of integration due to geographic and / or smooth ideal connective conditions) now forming pan-Indian National Grid with extensive use of PMUs at various locations.
Even though there will be very very minor variations in the system frequency at two ends of a large power system because of continuous load fluctuations and the time taken by the governors to adjust to the varying load conditions for all practical purposes a stable power system is taken to be operating at a constant frequency.
I agree with Mahdi Zolfaghari .
The frequency is constant (considering the percent of tolerance) in steady-state. But it is different in dynamic-states. Based on this issue, some times the frequency difference is used for some applications in power systems such as input signal of damping controllers and PSSs.
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