1. Synchronous Inertial Response
Julia Matevosyan

2. Synchronous Inertial Response
SIR is stored kinetic energy that is extracted from the rotating mass of synchronous machines following a disturbance in a power system
SIR can be provided by synchronous machines, whenever in operation.
SIR is independent of machine’s operating point
Quantity of inertia contribution is determined as kinetic energy that can be provided by a synchronous machine during system imbalance:
H·MVA
where H is machine inertia constant in seconds, MVA is machine’s rated power (RARF data)

3. Frequency Control and SIR Need
Provide sufficient time from Point A to Point C, for Fast Frequency Response and Primary Frequency Response

4. Why SIR is becoming a concern?
Significant share of non-synchronous generation (WGRs) leads to displacement of synchronous generation in unit commitment, during low load/high wind periods (night time in spring).
With low SIR, the rate of change of frequency (RoCoF) is high, leaving less time for PFR and/or FFR to deploy and arrest the system frequency excursion.

5. Wind Generation Current Status
Wind generation capacity is over 12.6 GW (Apr 2015)
Wind generation record 11,154 MW (Feb 2015),
Instantaneous wind penetration record is 40.58% (10.3 GW wind, 25.4 GW load Mar 29, 2015)
Previous Instantaneous wind penetration record was 39.84% (9.9 GW wind, 25 GW load, Nov 3, 2014)
Higher penetration levels of wind and solar generation capacity are expected in the future.

6. ERCOT Wind Capacity

7. Historic SIR and Future Projections
SIR, MWs
Each box represents one year of historic SIR data.
Red line is the median, the edges of the box are the 25th and 75th percentiles, the whiskers are +/- 2.7 sigma, red crosses are the outliers.
Blue dots show SIR during maximum wind penetration hour in each year.
Blue stars show projected SIR during maximum wind penetration hour in future years based on planned wind projects with SGIA and Financial Commitments. 7

8. Supporting data for maximum penetration hours
2010
2011
2012
2013
2014
2015
2016
2017
Installed Capacity, MW
9,116
9,452
10,034
10,570
11,066
16545
17849
18738
Max Pwind/Pload
25.5%
27.4%
29.8%
35.8%
39.4%
55.3%
59.7%
62.7%
Pwind, MW
6,483
6,772
7,247
8,773
9,699
13,732
14,838
18,738
Pwind/Pwind_inst
71%
72%
83%
88%
Pload, MW
25,427
24,745
24,328
24,488
24,617
24,800
SIR, GWs
161.7
147
133.7
120
119.6
96.4
91.1
87.6

9. SIR v.s. Net Load High load low wind High wind low load
Data from Jan, 2014 to May, 2014

10. Basis for minimum SIR need
NERC BAL-003, for the largest N-2 event, (ERCOT: 2,750 MW) prevent first step under frequency load shedding (at 59.3 Hz)
Load Resources with under frequency relays, providing RRS (or FFR2 in FAST), responding within 0.5 s of frequency being at or below 59.7 Hz.
Some minimal SIR is needed to keep frequency from reaching 59.4 Hz (assuming 0.1 Hz margin above 59.3 Hz) within fist 0.5 seconds of 2750 MW generation trip.

11. System frequency after 2750 MW trip (first 0.5 s)
Calculated frequency following 2750 MW trip at minimum SIR conditions

12. Basis for minimum SIR Requirement, cont.
There might be other considerations:
Potential need to maintain minimum FFR requirement at low SIR;
too frequent deployment FFR for a smaller generation trip;
insufficient synchronizing torque can be an issue if too many (or at critical locations) synchronous generators are de-committed in some areas;
RoCoF protection at the generators?

13. Real Time SIR Calculator
Based on earlier discussions at FAST meetings ERCOT set up a real time SIR calculator;
Calculates system SIR as sum of H*MVA for all online generators (with output above certain threshold);
As well as contributions by generation type;
The calculator simplifies the analysis of historic SIR data and trends.

14. Spring, 2014
System inertia is calculated as H*MVA for all online machines (i.e. independent of the machine output)

15. Inertia Provided by Resource Type (MW-s)
Spring, 2014
Inertia Provided by Resource Type (MW-s)
Min
Max
Average
Nuke
17,219
23,749
23,109
Coal
16,287
24,435
20,651
CT-CC
43,556
114,099
83,419
ST-CC
19,420
46,142
34,375
CT-SC
13,988
27,944
18,254
Gas ST
9,267
38,025
13,966
Hydro
200 29
Total
119,899
272,318
193,804

16. Summer, 2014
System inertia is calculated as H*MVA for all online machines (i.e. independent of the machine output)

17. Inertia Provided by Resource Type (MW-s)
Summer, 2014
Inertia Provided by Resource Type (MW-s)
Min
Max
Average
Nuke
23,749
Coal
27,807
34,974
33,377
CT-CC
73,164
130,737
106,306
ST-CC
26,438
52,873
43,383
CT-SC
12,280
37,024
18,977
Gas ST
22,862
64,441
37,792
Hydro
441 78
Total
190,458
343,693
263,663

18. Fall, 2014
System inertia is calculated as H*MVA for all online machines (i.e. independent of the machine output)

19. Inertia Provided by Resource Type (MW-s)
Fall, 2014
Inertia Provided by Resource Type (MW-s)
Min
Max
Average
Nuke
18,406
23,749
20,590
Coal
25,036
34,974
30,232
CT-CC
42,416
129,566
85,469
ST-CC
17,751
51,567
36,803
CT-SC
3,667
30,725
14,269
Gas ST
14,321
52,158
24,502
Hydro
406 37
Total
122,075
321,862
211,903

20. Appendix

21. Frequency deviation after unit loss
Frequency deviation after the loss of generation unit or load can be calculated as follows:
𝛥𝑓 𝑡 = −𝛥𝑃 𝐷 (1− 𝑒 −𝑡𝐷 2𝐻 )
where D is load damping, H is total system inertia, ΔP is generation lost, in pu on committed capacity MVA base, Pbase
Source: P. Kundur Power Systems Stability and Control

22. Frequency deviation after unit loss
Load damping ( 𝐷 𝐿𝐵 ) usually given as fraction of total load 𝑃 𝑙𝑜𝑎𝑑 per Hz.
Expressing in pu on committed capacity base, Pbase.
𝐷= 𝐷 𝐿𝐵 𝑃 𝑙𝑜𝑎𝑑 𝑃 𝑏𝑎𝑠𝑒
H, total system inertia on committed capacity base, Pbase is calculated as: 
𝐻= 𝑖 𝑃 𝑀𝑊,𝑖 𝐻 𝑖 𝑃 𝑏𝑎𝑠𝑒  
Substituting expressions for D and H in the equation for 𝛥𝑓 𝑡
𝛥𝑓 𝑡 = − 𝛥𝑃 𝑀𝑊 𝑃 𝑙𝑜𝑎𝑑 (1− 𝑒 −𝑡 𝐷 𝐿𝐵 𝑃 𝑙𝑜𝑎𝑑 2 𝑖 𝑃 𝑀𝑊,𝑖 𝐻 𝑖 )

23. System inertia need Expressing for system inertia:
𝑖 𝑃 𝑀𝑉𝐴,𝑖 𝐻 𝑖 = −𝑡 𝐷 𝐿𝐵 𝑃 𝑙𝑜𝑎𝑑 2 ln⁡(1+ Δ𝑓 𝑡 𝐷 𝐿𝐵 𝑃 𝑙𝑜𝑎𝑑 Δ 𝑃 𝑀𝑊 )
For given system load conditions, substituting criteria for unit loss, time and permissible frequency deviation (before other frequency control measures become effective), minimum inertia requirement can be estimated from the above expression.