In modern power systems, shiftable loads contribute to the flexibility needed to increase robustness and ensure security. Thermal loads are among the most promising candidates for providing such service due to the large thermal storage time constants. This study demonstrates the use of variable-speed refrigeration (VSR) technology, based on brushless DC motors, for the fast-frequency response. First, the authors derive a detailed dynamic model of a single-phase VSR unit suitable for time-domain and small-signal stability analysis in low-inertia systems. For analysing dynamic interactions with the grid, they consider the aggregated response of multiple devices. However, the high computational cost involved in analysing large-scale systems leads to the need for reduced-order models. Thus, a set of reduced-order models is derived through transfer function fitting of data obtained from time-domain simulations of the detailed model. The modelling requirements and the accuracy versus computational complexity trade-off are discussed. Finally, the time-domain performance and frequency-domain analyses reveal substantial equivalence between the full- and suitable reduced-order models, allowing the application of simplified models in large-scale system studies.

References

1. 1)
  - 33. Xiao, F., Dong, L., Li, L., et al: ‘A frequency-fixed SOGI-based PLL for single-phase grid-connected converters’, IEEE Trans. Power Electron., 2017, 32, (3), pp. 1713–1719.
2. 2)
  - 36. Weckesser, T., Van Cutsem, T.: ‘Equivalent to represent inertial and primary frequency control effects of an external system’, Transm. Distrib. IET Gener., 2017, 11, pp. 3467–3474.
3. 3)
  - 22. Rasmussen, C.B., Ritchie, E.: ‘Variable speed brushless DC motor drive for household refrigerator compressor’. 8th Int. Conf. on Electrical Machines and Drives, Cambridge, UK, January 1997, pp. 128–132.
4. 4)
  - 20. Li, H., Jeong, S.-K., You, S.-S.: ‘Feedforward control of capacity and superheat for a variable speed refrigeration system’, Appl. Therm. Eng., 2009, 29, (5), pp. 1067–1074.
5. 5)
  - 24. Kim, S.-H.: ‘Chapter 2 - control of direct current motors’, in Kim, S.-H. (Ed.): ‘Electric motor control’ (Elsevier, Netherlands, 2017), pp. 39–93.
6. 6)
  - 11. Malekpour, M., Azizipanah-Abarghooee, R., Teng, F., et al: ‘Fast frequency response from smart induction motor variable speed drives’, IEEE Trans. Power Syst., 2020, 35, (2), pp. 997–1008.
7. 7)
  - 10. Azizipanah-Abarghooee, R., Malekpour, M.: ‘Smart induction motor variable frequency drives for primary frequency regulation’, IEEE Trans. Energy Convers., 2020, 35, (1), pp. 1–10.
8. 8)
  - 4. Fernandez-Munoz, D., Perez-Diaz, J.I., Guisandez, I., et al: ‘Fast frequency control ancillary services: an international review’, Renew. Sust. Energy Rev., 2020, 120, p. 109662.
9. 9)
  - 31. Yang, Y., Zhou, K.: ‘Modeling and control of single-phase AC/DC converters’, in Blaabjerg, F. (Ed.): ‘Control of power electronic converters and systems’ (Academic Press, USA, 2018), pp. 93–115.
10. 10)
  - 35. Rocabert, J., Luna, A., Blaabjerg, F., et al: ‘Control of power converters in AC microgrids’, IEEE Trans. Power Electron., 2012, 27, (11), pp. 4734–4749.
11. 11)
  - 15. Gils, H.C.: ‘Assessment of the theoretical demand response potential in Europe’, Energy, 2014, 67, pp. 1–18.
12. 12)
  - 13. EnergieSchweiz: Bundesamt für Energie BFE: ‘Energieetikette für Kühl- und Gefriergeräte’, (2020).
13. 13)
  - 37. Misyris, G.S., Chatzivasileiadis, S., Mermet Guyennet, J.A., et al: ‘Grid supporting VSCs in power systems with varying inertia and short-circuit capacity’. Proc. of IEEE PES PowerTech 2019, Milan, Italy, 2019.
14. 14)
  - 41. Kundur, P.: ‘Chapter 12: small-signal stability’, in Balu, N.J., Lauby, M.G. (Eds.): ‘Power system stability and control’ (McGraw-Hill, New York, 1994), pp. 699–827.
15. 15)
  - 5. Vrettos, E., Ziras, C., Andersson, G.: ‘Fast and reliable primary frequency reserves from refrigerators with decentralized stochastic control’, IEEE Trans. Power Syst., 2017, 32, (4), pp. 2924–2941.
16. 16)
  - 7. Hui, H., Ding, Y., Zheng, M.: ‘Equivalent modeling of inverter air conditioners for providing frequency regulation service’, IEEE Trans. Ind. Electron., 2019, 66, (2), pp. 1413–1423.
17. 17)
  - 39. Markovic, U., Vorwerk, J., Aristidou, P., et al: ‘Stability analysis of converter control modes in low-inertia power systems’. IEEE PES ISGT Europe 2018, Sarajevo, Bosnia and HerzegovinaOctober 2018.
18. 18)
  - 12. Ibrahim, I., O'Loughlin, C., O'Donnell, T.: ‘Virtual inertia control of variable speed heat pumps for the provision of frequency support’, Energies, 2020, 13, (8), p. 1863.
19. 19)
  - 27. Xia, C.-l.: ‘Permanent magnet brushless DC motor drives and controls’ (Wiley, Hoboken, NJ, 2012).
20. 20)
  - 19. Verhelst, C.: ‘Model predictive control of ground coupled heat pump systems for office buildings’. PhD dissertation, KU Leuven, 2012.
21. 21)
  - 23. Samsung: ‘How the digital inverter compressor has transformed the modern refrigerator’. Available at www.news.samsung.com.
22. 22)
  - 29. Bacha, S., Munteanu, I., Bratcu, A.I.: ‘Power electronic converters modeling and control’, ser. Advanced Textbooks in Control and Signal Processing (Springer London, London, 2014).
23. 23)
  - 34. Golestan, S., Monfared, M., Freijedo, F.D., et al: ‘Dynamics assessment of advanced single-phase PLL structures’, IEEE Trans. Ind. Electron., 2013, 60, (6), pp. 2167–2177.
24. 24)
  - 9. Che, Y., Yang, J., Zhou, Y., et al: ‘Demand response from the control of aggregated inverter air conditioners’, IEEE Access, 2019, 7, pp. 88163–88173.
25. 25)
  - 16. Grein, A., Pehnt, M.: ‘Load management for refrigeration systems: potentials and barriers’, Energy Policy, 2011, 39, (9), pp. 5598–5608.
26. 26)
  - 26. Kim, S.-H.: ‘Chapter 10 - brushless direct current motors’, in Kim, S. -H. (Ed.): ‘Electric motor control’ (Elsevier, Netherlands, 2017), pp. 389–416.
27. 27)
  - 18. Koury, R., Machado, L., Ismail, K.: ‘Numerical simulation of a variable speed refrigeration system’, Int. J. Refrig., 2001, 24, (2), pp. 192–200.
28. 28)
  - 17. UCTE: ‘Appendix 1: load-frequency control and performance’, (final policy 2.2 E, 20.07.2004).
29. 29)
  - 38. Mahdavi, N., Braslavsky, J.H.: ‘Modelling and control of ensembles of variable-speed air conditioning loads for demand response’, IEEE Trans. Smart Grid, 2020, PP, (99), pp. 1–1.
30. 30)
  - 32. Ciobotaru, M., Teodorescu, R., Blaabjerg, F.: ‘A new single-phase PLL structure based on second order generalized integrator’. Proc. of IEEE PESC 2006, Jeju, Republic of Korea, June 2006.
31. 31)
  - 14. FEA Fachverband Elektroapparate für Haushalt und Gewerbe Schweiz: ‘Schweizer Verkaufsstatistik Geräte 2004–2016’. Tech. Rep., 2018.
32. 32)
  - 1. Milano, F., Dörfler, F., Hug, G., et al: ‘Foundations and challenges of low-inertia systems (invited paper)’. 2018 Power Systems Computation Conf. (PSCC), Dublin, Ireland, 2018.
33. 33)
  - 30. Hackl, C.M.: ‘On the equivalence of proportional-integral and proportional-resonant controllers with anti-windup’, Systems and Control, arXiv:1610.07133v1, p. 10.
34. 34)
  - 28. Song, H.-S., Keil, R., Mutschler, P., et al: ‘Advanced control scheme for a single-phase PWM rectifier in traction applications’. 38th IAS Annual Meeting on Conf. Record of the Industry Applications Conf., 2003, Salt Lake City, UT, USA, 2003, vol. 3.
35. 35)
  - 25. Krishnan, R.: ‘Permanent magnet synchronous and brushless DC motor drives’ (CRC Press, USA, 2017, 1st edn.).
36. 36)
  - 21. SECOP: Variable Speed Drive Compressor R600a, (May 2017).
37. 37)
  - 6. Kim, Y.-J., Norford, L.K., Kirtley, J.L.: ‘Modeling and analysis of a variable speed heat pump for frequency regulation through direct load control’, IEEE Trans. Power Syst., 2015, 30, (1), pp. 397–408.
38. 38)
  - 8. Chakravorty, D., Chaudhuri, B., Hui, S.Y.R.: ‘Rapid frequency response from smart loads in Great Britain power system’, IEEE Trans. Smart Grid, 2017, 8, (5), pp. 2160–2169.
39. 39)
  - 40. Kemmler, A., Spillmann, T., Koziel, S.: ‘Der Energieverbrauch der Privaten Haushalte 2000–2017: Auswertung nach Verwendungszwecken und Ursachen der Veränderungen’. Tech. Rep., Prognos AG, 2018.
40. 40)
  - 2. Fang, J., Li, H., Tang, Y., et al: ‘On the inertia of future more-electronics power systems’, IEEE Trans. Emerg. Sel. Top. Power Electron., 2019, 7, (4), pp. 2130–2146.
41. 41)
  - 3. Markovic, U., Stanojev, O., Vrettos, E., et al: ‘Understanding stability of low-inertia systems’, February 2019. Available at engrxiv.org/jwzrq.

Modelling of variable-speed refrigeration for fast-frequency control in low-inertia systems

References

Related content