Generation Loss on May 12, 2012
Frequency Responses > Frequency Events Analysis > Eastern Interconnection Disturbances
1.0 Incident data
On May 12, 2012 at 3:30 in the afternoon 1711 MW of generation were lost in the Eastern Interconnection. The incident data is provided in Figure 1 below. This figure was obtained from NERC report titled "Frequency Response Initiative Report " dated October 2012.
1.1.0 Calculation of System Inertia
1.1.1 Calculation of ∆PNo information could be found on the system total load just before the disturbance. Without this information the generation left in service (GLS) just after the disturbance cannot be calculated. As the GLS is required as the base value for calculating the pu value of the generation loss ∆P and the pu values of Frequency Response(FR), for the purpose of this discussion the GLS was estimated by assuming that the FR, given in Figure 1 as -2369 MW/0.1 Hz, was 1% of the total system load. Based on this assumption, the GLS was calculated to be 235,189 MW. Accordingly, the pu value of the generation loss was calculated as:∆P=-1711/235189=-0.007275 pu1.1.2 Calculation of ∆f’0As noted in Figure 1, the slope of frequency decay curve at time zero is about:∆f’0 = ((59.94-60.021)/60)/3.8 = -0.0003553 pu /secThis slope was obtained by "guessing" graphically the line tangent to the frequency excursion curve at time zero. This calculation can be improved significantly by capturing the frequency excursion curve data in a digital format. This would permit developing a mathematical formula for the curve using regression techniques. The formula could then be differentiated and evaluated at time zero to obtain the required slope.1.1.3 Calculation of System Inertia MAccording to Equation (5) in the Background page the pu value of M is given by:M=∆P/∆f’0 = -0.007275/-0.0003553 = 20.48 sec
1.2.0 Calculation of Equipment Frequency Response D
Assuming that the governor dead band was 0.036 Hz, from the frequency decay curve it is established that governor response started at 4.25 seconds. Therefore, there was no governor response at 4 seconds, this point (t=4 sec, f=59.969 Hz) can be used to calculate the equipment frequency response (D) using Equation (1) from the "Background" page, namely:
The calculations results in D=5.41 pu. Now that the M and D are known, the effective governor response can be established using the FREDEV program with different values of effective droops and various governors vs time response curves.
The results of the duplication shown in Figure G2 above lead to the conclusion that at the time of the incident the system exhibited the following parameters:
Inertia = 24 secSelf Regulation D= 5.4 puGovernor droop = 111 %Governor Response arrives at 8 sec
As a further consistency check, according to Equation 4 in the "Background" page, the frequency rate of change at time t=0 should be ∆P/M Hz/sec in pu, namely, (-0.007275/24)*60 = 0.0182 Hz/sec. This looks pretty close to what the graph in Figure G1 shows and confirms the 24 sec Inertia.
The 111% governor droop in essence means almost no governor response. More simulations would need to be done to establish if this is always the case. If it were, Figure G2 shows that the "L" shape of the frequency excursion following loss of generation in the Eastern Interconnection is due to lack of governor response.
The parameters to start the trial and error simulation wer obtained as follows.
Estimating the ∆P and D Parameters
From the data provided in Figure G1, it is known that the Frequency response was, in absolute value, 2369 MW/0.1 Hz or 23690 MW/Hz. As prior studies have shown that frequency response on the Eastern Interconnection are about 1% of the load, the generation at the time of the incident is estimated to be 23690/0.01 or 236,900 MW. As the frequency at the time of the incident was a bit above 60 Hz, the generation was actually a bit higher but this refinement is neglected here. Now that the generation at the time of the incident is known, the generation remaining after the disturbance can be calculated as G=236900-1711=235189. With this information, the pu value of ∆P=1711/235189=0.007275, and the per unit value of β =(23690/235189)*60 = 6.04. Based on this, the values for starting the trial and error simulation are:
∆P = -1711/235189 = -0.007275 puD = 5 pu (as β=D+Governor Response)
From Figure G1 the frequency rate of change at time t=0 is estimated to be about 0.02 Hz/sec. In pu this value is (0.02/60) equal to 0.000333 pu Hz/sec. Using Equation 5 in the "Background" page, M is given by:
M = 0.007275/0.000333 =21.85 sec
Estimating Time of Arrival of Governor Response
From Figure G1, we notice that the frequency curve suddenly flattens at about 8 sec. We interpret this to signal the arrival of Governor Response.
Based on the above the trial and error simulation was started with the following parameters:
∆P = - 0.007275 (this value remains constant throughout the trial and error process))M = 22 secD = 5Governor response injected at 8 sec starting with a 5% droop.
Starting with above parameters we converge rather quickly on the solution illustrated in Figure G2 above.
From Figure G2 above it is evident that governor control is much less than expected. It is of interest to check what was the Governor response compared to the Self Regulation response. The two curves in Figure G3 below were calculated to estimate the impact of Governor response. From the two curves we conclude that, in terms of the lowest frequency attained, a D of 5.1 pu plus a Frequency Response from an effective Governor Droop of 111% is equivalent to a D = β = 6.04365. From this point of view, in this incident, governor response was equivalent to an additional D of 0.94365 pu. From Figure G1 the maximum frequency deviation is estimated to be 0.052 Hz or 0.000867 pu (This needs further scrutiny as Figure states that frquency deviation was 0.0722). In terms of MW, Governors contributed (0.94365 * 0.000867)*235,189 = 192 MW while Self Regulation contributed (5.1 * 0.000867)*235,189 = 1040 MW. This highlights the importance of Self Regulation.
The black dotted line in Figure G4 below illustrates the fact that things would have been much worse if there had been no Self Regulation. And Figure G5 illustrates that if the Governor response had been consistent with a 5 % Droop, the frequency would have recovered to just above 60 Hz.
