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Frontiers in Energy

Front. Energy    2015, Vol. 9 Issue (4) : 472-485     https://doi.org/10.1007/s11708-015-0373-7
RESEARCH ARTICLE |
Estimation of composite load model with aggregate induction motor dynamic load for an isolated hybrid power system
Nitin Kumar SAXENA(),Ashwani Kumar SHARMA
Deptment of Electrical Engineering, NIT Kurukshetra, Haryana 136119, India
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Abstract

It is well recognized that the voltage stability of a power system is affected by the load model and hence, to effectively analyze the reactive power compensation of an isolated hybrid wind-diesel based power system, the loads need to be considered along with the generators in a transient analysis. This paper gives a detailed mathematical modeling to compute the reactive power response with small voltage perturbation for composite load. The composite load is a combination of the static and dynamic load model. To develop this composite load model, the exponential load is used as a static load model and induction motors (IMs) are used as a dynamic load model. To analyze the dynamics of IM load, the fifth, third and first order model of IM are formulated and compared using differential equations solver in Matlab coding. Since the decentralized areas have many small consumers which may consist large numbers of IMs of small rating, it is not realistic to model either a single large rating unit or all small rating IMs together that are placed in the system. In place of using a single large rating IM, a group of motors are considered and then the aggregate model of IM is developed using the law of energy conservation. This aggregate model is used as a dynamic load model. For different simulation studies, especially in the area of voltage stability with reactive power compensation of an isolated hybrid power system, the transfer function ΔQ/ΔV of the composite load is required. The transfer function of the composite load is derived in this paper by successive derivation for the exponential model of static load and for the fifth and third order IM dynamic load model using state space model.

Keywords isolated hybrid power system (IHPS)      composite load model      static load      dynamic load      induction motor load model      aggregate load     
Corresponding Authors: Nitin Kumar SAXENA   
Online First Date: 31 August 2015    Issue Date: 04 November 2015
 Cite this article:   
Nitin Kumar SAXENA,Ashwani Kumar SHARMA. Estimation of composite load model with aggregate induction motor dynamic load for an isolated hybrid power system[J]. Front. Energy, 2015, 9(4): 472-485.
 URL:  
http://journal.hep.com.cn/fie/EN/10.1007/s11708-015-0373-7
http://journal.hep.com.cn/fie/EN/Y2015/V9/I4/472
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Nitin Kumar SAXENA
Ashwani Kumar SHARMA
Fig.1  Structure of composite load in power system
Fig.2  Equivalent circuit of induction motor
Fig.3  State space model representation for induction motor
S. No. Order of IM model Matrix notation Order of matrix Number of elements
1 5th Aq5 5 × 5 25
2 Bq5 5 × 1 05
3 Cq5 1 × 5 05
4 Dq5 1 × 1 01
5 3rd Aq3 3 × 3 09
6 Bq3 3 × 1 03
7 Cq3 1 × 3 03
8 Dq3 1 × 1 01
9 1st Aq1 1 × 1 01
10 Bq1 1 × 1 01
11 Cq1 1 × 1 01
12 Dq1 1 × 1 01
Tab.1  Summary of state space model for different orders of induction motor load
Motor specification Single unit of IM Group of IMs for aggregate model
(IM1) (IM2) (IM3) (IM4) (IM5) (IM6)
Induction motor rating /kW 50 1.5 3.5 4.0 7.5 18.5 15
Supply voltage/V 400 400 400 400 400 400 400
Supply frequency/Hz 50 50 50 50 50 50 50
Power factor at full load (lag) (lagging) 0.9 0.9 0.9 0.9 0.9 0.9 0.9
Efficiency at full load 0.9 0.9 0.9 0.9 0.9 0.9 0.9
Slip at full load /% 4 4 4 4 4 4 4
Pole pair 1 1 1 1 1 1 1
Tab.2  Manufacturer data for induction motors
Fig.4  Rotor speed characteristics for 50 kW induction motor
Fig.5  Electro-magnetic torque characteristics for 50 kW induction motor
Fig.6  Active power characteristics for 50 kW induction motor
Fig.7  Reactive power characteristics for 50 kW induction motor
Fig.8  Step response comparison for evaluated transfer function ( D v = Δ Q / Δ V ) of single unit 50 kW IM load model
Fig.9  Bode plot of evaluated transfer function ( D v = Δ Q / Δ V ) for fifth order IM load model
Fig.10  Bode plot of evaluated transfer function ( D v = Δ Q / Δ V ) for third order IM load model
Rating/kW Rs Rr Xs Xr Xm J/(kg·m2) B/(N·m·s)
IM1 1.5 9.584 2.916 5.943 5.944 376.42 0.0006 0.0172
IM2 3.5 4.108 1.250 2.547 2.547 161.32 0.0014 0.0403
IM3 4.0 3.594 1.094 2.229 2.229 141.16 0.0016 0.0460
IM4 7.5 1.917 0.583 1.189 1.189 75.28 0.0030 0.0863
IM5 15 0.958 0.292 0.594 0.594 37.64 0.0060 0.1725
IM6 18.5 0.777 0.236 0.482 0.482 30.52 0.0074 0.2128
Single unit of IM 50 0.288 0.088 0.178 0.178 11.29 0.0200 0.5750
Aggregate Model for IM1-IM6 50 0.288 0.088 0.178 0.178 11.29 0.0181 0.1504
Tab.3  Evaluated parameters of induction motors
Fig.11  Bode plots for fifth order 50 kW dynamic load model
Fig.12  Bode plots for third order 50 kW dynamic load model
S. No. Transfer function of load
1 Static load model of 200 kW ( D v ) SLM = 0.5479
2 5th order aggregate dynamic load model of 50 kW ( D v ) DLM = 0.1586 s 5 + 105.6 s 4 + 3.904 × 10 5 s 3 + 2.999 × 10 7 s 2 + 4.171 × 10 8 s + 1.493 × 10 8 s 5 + 665.7 s 4 + 2.114 × 10 5 s 3 + 1.599 × 10 7 s 2 + 8.223 × 10 8 s + 3.573 × 10 9
3 3rd order aggregate dynamic load of 50 kW ( D v ) DLM = 2.337 s 3 + 189.7 s 2 + 2586 s + 911 s 3 + 95.55 s 2 + 5019 s + 2.181 × 10 4
4 Composite load of 250 kW for 5th order model ( D v ) CLM = 0.4996   s 5 + 332.6 s 4 + 3.579 × 10 5 s 3 + 2.741 × 10 7 s 2 + 6.135 × 10 8 s + 1.49 × 10 9 0.7071   s 5 + 470.7   s 4 + 1.495 × 10 5 s 3 + 1.131 × 10 7 s 2 + 5.814 × 10 8 s + 2.526 × 10 9
5 Composite load of 250 kW for 3rd order model ( D v ) CLM = 2.04 s 3 + 171.2 s 2 + 3773 s + 9095 0.7071 s 3 + 67.52 s 2 + 3549 s + 1.542 × 10 4
Tab.4  Evaluated transfer functions for composite load model
Fig.13  Step response for transfer function ( D v = Δ Q / Δ V ) of composite load (third order DLM+ exponential SLM)
Fig.14  Step response for transfer function ( D v = Δ Q / Δ V ) of composite load (fifth order DLM+ exponential SLM)
V Load terminal voltage
Δ V Incremental change in load voltage due to load disturbances
D v Load transfer function of reactive power change to voltage change
R s , R r Stator and rotor resistance
L s , L r Stator and rotor leakage inductance
L ss , L rr Stator and rotor self inductance
  ω s , ω b   and ω r   Synchronous, base and rotor speed of induction motor
φ q s , φ d s , φ q r and φ d r Stator and rotor flux for direct and quadrature axis
I q s , I d s , I q r and I d r Stator and rotor current for direct and quadrature axis
V q s , V d s , V q r and   V d r Stator and rotor voltage for direct and quadrature axis
T e , T L Electromagnetic and load torque
B ,   H and   J Torque-damping factor, machine inertia and moment of inertia
Tab.5  Notations
1 Sharma  P, Kumar Saxena  N, Ramakrishna  K S S, Bhatti  T S. Reactive power compensation of isolated wind-diesel hybrid power systems with STATCOM and SVC. International Journal on Electrical Engineering and Informatics, 2010, 2(3): 192–203
https://doi.org/10.15676/ijeei.2010.2.3.3
2 Hunter  R, Elliot  G. Wind-diesel systems, a guide to the technology and its implementation. Cambridge: Cambridge University Press, 1994
3 Cardenas  R, Pena  R, Perez  M, Clare  J, Asher  G, Vargas  F. Vector control of frond end converters for variable speed wind-diesel systems. IEEE Transactions on Industrial Electronics, 2006, 53(4): 1127–1136
https://doi.org/10.1109/TIE.2006.878321
4 Bansal  R C, Bhatti  T S, Kumar  V. Reactive power control of autonomous wind diesel hybrid power systems using ANN. In: Proceedings of the International Power Engineering Conference, Singapore, 2007, 982–987
5 Bansal  R C. Automatic reactive power control of autonomous hybrid power system. Dissertation for the Doctoral Degree. Delhi: Indian Institute of Technology, 2002
6 Sharma  P, Saxena  N K, Bhatti  T S. Study of autonomous hybrid power system using SVC and STATCOM. In: Proceedings of International Conference on Power Systems. Kharagpur, India, 2009, 27–29
7 Stojanović  D P, Korunović  L M, Milanović  J V. Dynamic load modelling based on measurements in medium voltage distribution network. Electric Power Systems Research, 2008, 78(2): 228–238
https://doi.org/10.1016/j.epsr.2007.02.003
8 Kim  B H, Kim  H, Lee  B, 0. Kim  H, Lee  B. Parameter estimation for the composite load model. Journal of International Council on Electrical Engineering, 2012, 2(2): 215–218
https://doi.org/10.5370/JICEE.2012.2.2.215
9 Parveen  T. Composite load model decomposition: induction motor contribution. Dissertation for the Doctoral Degree. Brisbane: Queensland University of Technology, 2009
10 Choi  B K, Chiang  H D, Li  Y, Chen  Y T, Huang  D H, Lauby  M G. Development of composite load models of power systems using on-line measurement data. Journal of Electrical Engineering & Technology, 2006, 1(2): 161–169
https://doi.org/10.5370/JEET.2006.1.2.161
11 Aree  P. Aggregating method of induction motor group using energy conservation law. ECTI Transactions on Electrical & Computer Engineering, 2014, 12(1): 1–6
12 Muriuki  J K, Muriithi  C M. Comparison of aggregation of small and large induction motors for power system stability study. Global Engineers & Technologists Review, 2013, 3(2): 9–13
13 Sharma  P, Bhatti  T S. Performance investigation of isolated wind-diesel hybrid power systems with WECS having PMIG. IEEE Transactions on Industrial Electronics, 2013, 60(4): 1630–1637
https://doi.org/10.1109/TIE.2011.2175672
14 Bansal  R C, Bhatti  T S, Kothari  D P. A novel mathematical modelling of induction generator for reactive power control of isolated hybrid power systems. International Journal of Modelling and Simulation, 2004, 24(1): 1–7
https://doi.org/10.2316/Journal.205.2004.1.205-4068
15 Sharma  P, Sulkowski  W, Hoff  B. Dynamic stability study of an isolated wind-diesel hybrid power system with wind power generation using IG, PMIG and PMSG: a comparison. International Journal of Electrical Power and Energy Systems, 2013, 53: 857–866
https://doi.org/10.1016/j.ijepes.2013.06.014
16 Vachirasricirikul  S, Ngamroo  I, Kaitwanidvilai  S. Coordinated SVC and AVR for robust voltage control in a hybrid wind-diesel system. Energy Conversion and Management, 2010, 51(12): 2383–2393
https://doi.org/10.1016/j.enconman.2010.05.001
17 Saxena  N, Kumar  A. Load modeling interaction on hybrid power system using STATCOM. In: Proceedings of Annual IEEE India Conference. Kolkata, India, 2010.
18 Kosterev  D, Meklin  A. Load modelling in WECC. Power Systems Conference and Exposition (PSCE’06), 2006, 576–581
19 Fahmy  O M, Attia  A S, Badr  M A L. A novel analytical model for electrical loads comprising static and dynamic components. Electric Power Systems Research, 2007, 77(10): 1249–1256
https://doi.org/10.1016/j.epsr.2006.09.018
20 Hiskens  I A, Milanovic  J V. Load modelling in studies of power system damping. IEEE Transactions on Power Systems, 1995, 10(4): 1781–1788
https://doi.org/10.1109/59.476041
21 Krause  P C, Wasynczuk  O, Sudhoff  S D. Analysis of Electric Machinery and Drive Systems, 2nd Ed. New York: John Wiley & Sons Publication-IEEE Press, 2002
22 Lehtla  T. Parameter identification of an induction motor using fuzzy logic controller. 2014−10, http://www.ene.ttu.ee/elektriajamid/teadus/artiklid/Ungar965/
23 Sandhu  K S, Pahwa  V. A novel approach to incorporate the main flux saturation effect in a three-phase induction machine during motoring and plugging. International Journal of Computer and Electrical Engineering, 2011, 3(3): 443–448
https://doi.org/10.7763/IJCEE.2011.V3.358
24 Kundur  P. Power System Stability and Control. India: Tata-Mcgraw-Hill, 2006
25 Boldea  I, Nasar  S A. The Induction Machine Handbook. New York, USA: CRC Press LLC, 2001, Chapter 13
26 Wang  K, Chiasson  J, Bodson  M, Tolbert  L M. A nonlinear least-squares approach for identification of the induction motor parameters. In: Proceedings of the 43rd IEEE Conference on Decision and Control. Atlantis, Paradise Island, Bahamas, 2004, 14–17
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