Estimation of composite load model with aggregate induction motor dynamic load for an isolated hybrid power system

doi:10.1007/s11708-015-0373-7

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 $Δ Q / Δ V$ 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 Author(s): 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:

https://academic.hep.com.cn/fie/EN/10.1007/s11708-015-0373-7
https://academic.hep.com.cn/fie/EN/Y2015/V9/I4/472

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	5^th	Aq₅	$5 × 5$	25
2		Bq₅	$5 × 1$	05
3		Cq₅	$1 × 5$	05
4		Dq₅	$1 × 1$	01
5	3^rd	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

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

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 $(D v) DLM = 0.1586 s 5 + 105.6 s 4 + 3.904 × 105 s 3 + 2.999 × 107 s 2 + 4.171 × 108 s + 1.493 × 108 s 5 + 665.7 s 4 + 2.114 × 105 s 3 + 1.599 × 107 s 2 + 8.223 × 108 s + 3.573 × 109$
3	3rd order aggregate dynamic load of 50?kW $(D v) DLM = 2.337 s 3 + 189.7 s 2 + 2586 s + 911 s 3 + 95.55 s 2 + 5019 s + 2.181 × 104$
4	Composite load of 250?kW for 5th order model $(D v) CLM = 0.4996 s 5 + 332.6 s 4 + 3.579 × 105 s 3 + 2.741 × 107 s 2 + 6.135 × 108 s + 1.49 × 109 0.7071 s 5 + 470.7 s 4 + 1.495 × 105 s 3 + 1.131 × 107 s 2 + 5.814 × 108 s + 2.526 × 109$
5	Composite load of 250?kW for 3rd order model $(D v) CLM = 2.04 s 3 + 171.2 s 2 + 3773 s + 9095 0.7071 s 3 + 67.52 s 2 + 3549 s + 1.542 × 104$

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

Notations

1	P Sharma, N Kumar Saxena, K S S Ramakrishna, T S Bhatti. 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	R Hunter, G Elliot. Wind-diesel systems, a guide to the technology and its implementation. Cambridge: Cambridge University Press, 1994
3	R Cardenas, R Pena, M Perez, J Clare, G Asher, F Vargas. 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	R C Bansal, T S Bhatti, V Kumar. 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	R C Bansal. Automatic reactive power control of autonomous hybrid power system. Dissertation for the Doctoral Degree. Delhi: Indian Institute of Technology, 2002
6	P Sharma, N K Saxena, T S Bhatti. Study of autonomous hybrid power system using SVC and STATCOM. In: Proceedings of International Conference on Power Systems. Kharagpur, India, 2009, 27–29
7	D P Stojanović, L M Korunović, J V Milanović. 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	B H Kim, H Kim, B Lee, 0. H Kim, B Lee. 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	T Parveen. Composite load model decomposition: induction motor contribution. Dissertation for the Doctoral Degree. Brisbane: Queensland University of Technology, 2009
10	B K Choi, H D Chiang, Y Li, Y T Chen, D H Huang, M G Lauby. 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	P Aree. Aggregating method of induction motor group using energy conservation law. ECTI Transactions on Electrical & Computer Engineering, 2014, 12(1): 1–6
12	J K Muriuki, C M Muriithi. Comparison of aggregation of small and large induction motors for power system stability study. Global Engineers & Technologists Review, 2013, 3(2): 9–13
13	P Sharma, T S Bhatti. 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	R C Bansal, T S Bhatti, D P Kothari. 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	P Sharma, W Sulkowski, B Hoff. 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	S Vachirasricirikul, I Ngamroo, S Kaitwanidvilai. 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	N Saxena, A Kumar. Load modeling interaction on hybrid power system using STATCOM. In: Proceedings of Annual IEEE India Conference. Kolkata, India, 2010.
18	D Kosterev, A Meklin. Load modelling in WECC. Power Systems Conference and Exposition (PSCE’06), 2006, 576–581
19	O M Fahmy, A S Attia, M A L Badr. 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	I A Hiskens, J V Milanovic. 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	P C Krause, O Wasynczuk, S D Sudhoff. Analysis of Electric Machinery and Drive Systems, 2nd Ed. New York: John Wiley & Sons Publication-IEEE Press, 2002
22	T Lehtla. Parameter identification of an induction motor using fuzzy logic controller. 2014-10
23	K S Sandhu, V Pahwa. 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	P Kundur. Power System Stability and Control. India: Tata-Mcgraw-Hill, 2006
25	I Boldea, S A Nasar. The Induction Machine Handbook. New York, USA: CRC Press LLC, 2001, Chapter 13
26	K Wang, J Chiasson, M Bodson, L M Tolbert. 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
27	J Pedra, L Sainz, F Corcoles. Study of aggregate models for squirrel-cage induction motors. IEEE Transactions on Power Systems, 2005, 20(3): 1519–1527 https://doi.org/10.1109/TPWRS.2005.852073

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