Dynamic Simulation of Self-Excited Induction Generator Feeding Motor Load Using

Matlab/Simulink

Pichai Pichai Aree, Somboon Lhaksup Department of Electrical Engineering, Thammasat University,

Pathumthani, Thailand.

Abstract—Self-excited induction generators (SEIG) are mostly exploited in isolated areas to generate electrical energy. Analyzing of a stand-alone SEIG dynamic performance is largely limited application of the SEIG to static load. This paper presents dynamic simulation of small SEIG feeding induction motor (IM) load. Mathematical models of SEIG, IM, and wind turbine are clearly implemented into Matlab/Simulink environment. The study results reveal that a great dip in SEIG voltage occurs when the IM load is suddenly connected to the SEIG since the excitation capacitor cannot provide sufficient reactive power support. By applying an additional paralleled-motor capacitor, the SEIG voltage dip can be alleviated and a faster acceleration of the IM load can be obtained.

Keywords—Self-excited induction generator; induction motor load; dynamic performance; Matlab/Simulink

I. INTRODUCTION The concept of self-excited induction generator (SEIG) has

been known since the 30s of the last century. After the first signs of the global energetic crisis, scientists and researchers from all over the world have increased their interest in the SEIG for huge potentials for renewable energy resource. The SEIGs are increasingly considered for isolated applications micro-hydro and wind-turbine system. They are the most suitable for remote area application since reduced unit cost, simplicity in operation, ease in maintenance, and no extra excitation supply are the main advantage of using the SEIG for electricity production [1-3].

The stand-alone SEIG is basically an induction machine which is driven by a prime mover, while an external capacitor is connected across its stator terminals. The capacitor is required to build the air-gap flux, and to provide any lagging reactive power demand of the load. The majority of the SEIG load in remote area usually enriches with both static and dynamic loads. Although considerable research works have been reported on various aspects of the SEIG, it is largely limited to application of the SEIG feeding static loads [4-8]. Very few of them have focused on dynamic IM load. For example, an attempt to study the behavior of the SEIG with the IM load has first shown in [9] and later in [10, 11], but it was limited to steady-state analysis. The transient analysis of the stand-alone SEIG with the IM load has been recently

received attentions [12-15]. Because only few works have been reported, the transient interactions between the SEIG and IM have to be further investigated.

In this paper, dynamic simulations of the SEIG feeding IM load are carried out to investigate its performance when the particular IM load is suddenly switched on. The implementation of SEIG, IM load, and wind turbine models are demonstrated in the step-by-step manner through Matlab/Simulink environment. The effects of switching the IM load on SEIG voltage profiles are explored with various values of the excitation capacitor. The dynamic performances of SIEG and IM with an aid of the extra paralleled-motor capacitor are also discussed.

II. SEIG-IM SYSTEM AND MODELING This section gives mathematical modeling of SEIG-IM

system. The system is shown in Fig. 1. It mainly consists of one-mass wind turbine, SEIG, and IM load.

Fig. 1. SEIG-IM system

The SEIG feeds IM load through a short-lenght cable. An excitation capacitor cg is permanently connected with the SEIG to build up its terminal voltage. The extra capacitor cm is parallelly connected with the IM load to provide extra reactive power. It can be possibly switched off as desired.

A. Induction Machine Model In this subsection, mathematical model of induction

machine in motoring and generating operations are briefly discussed. The induction machines are commonly modeled in term of d- q-axis using park’s transformation. In order to simulate their dynamic behaviors in stand-alone mode, it is

&J Jw g

Sw lineR lineLWT SEIG−

cgcm

IMSw

S R

cgi SRi

cmi

system

978-1-4799-2993-1/14/$31.00 ©2014 IEEE

convenient to express the machine equivalent circuit using stationary frame of reference [1]. The stator and rotor flux linkages of induction machine in SI unit [16] can be re-arranged and re-written in term of column vector as,

( )sd

Rdt

=ss sv - I i

ψ (1)

( ) ( )rω rd Rdt

= +rr r rv J - I iψ

ψ (2)

Where,

sv ds

qs

vv⎡ ⎤

= ⎢ ⎥⎣ ⎦

,rv dr

qr

vv⎡ ⎤

= ⎢ ⎥⎣ ⎦

,si

ds

qs

ii⎡ ⎤

= ⎢ ⎥⎣ ⎦

,ri

dr

qr

ii⎡ ⎤

= ⎢ ⎥⎣ ⎦

ψψs

ds

qs

⎡ ⎤= ⎢ ⎥⎣ ⎦

ψ , ψψr

dr

qr

⎡ ⎤= ⎢ ⎥⎣ ⎦

ψ 1 00 1

I ⎡ ⎤= ⎢ ⎥⎣ ⎦

, 0 11 0

J−⎡ ⎤= ⎢ ⎥

⎣ ⎦

The subscript “s” and “r” indicate stator and rotor quantities, respectively. The stator and rotor currents in (1)-(2) can be expressed by,

=s R s M ri L - Lψ ψ (3) =r S r M si L - Lψ ψ (4)

Where,

( )ls m

m lr ls ls lr

L LL L L L L

⎛ ⎞+= ⎜ ⎟⎜ ⎟+ +⎝ ⎠SL I (5)

( )lr m

m lr ls ls lr

L LL L L L L

⎛ ⎞+= ⎜ ⎟⎜ ⎟+ +⎝ ⎠RL I (6)

( )m

m lr ls ls lr

LL L L L L

⎛ ⎞= ⎜ ⎟⎜ ⎟+ +⎝ ⎠

ML I (7)

Lls and Llr are stator and rotor leakage inductances, and Lm is mutual inductance, respectively. In order to operate induction machine as SEIG, it is important to include the saturation effect. The nonlinear characteristic between Lm and magnetizing current im is essentially determined from the test. Such nonlinear relationship can be fitted with quadratic function as,

2 30 1 2 3

nm m m m n mL a a i a i a i ... a i= + + + + + (8)

2 2( ) ( )m ds dr qs qri i i i i= + + + (9)

The electrical torques of induction machine in SI unit [16] can be re-arranged and re-written as follows,

32 2

Te

PT ⎛ ⎞= ⎜ ⎟⎝ ⎠

r ri (- J)ψ (10)

The mechanical torque characteristic of induction machine operating as motoring mode can be expressed by

( )0 2( / ) ( / )m mT T A B C= + +r s r sω ω ω ω (11)

Where, 0

mT is the torque at synchronous speed (ωs). The change in rotor speed (ωr) can be formulated as,

1 ( - )2 e m

m

d P T Tdt J

⎛ ⎞= ⎜ ⎟⎝ ⎠

rω (12)

Where P is number of poles, Jm is moment of inertia. The components of instantaneous phase voltages under balanced condition are sometimes needed. They can be written by,

1−=ABC sv P v (13) Where,

s

s

s

2 cos(ω )

2 cos(ω -2π/3)

2 cos(ω +2π/3)

sa

b s

c s

V tvv V tv V t

⎡ ⎤⎡ ⎤ ⎢ ⎥⎢ ⎥= = ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥⎣ ⎦ ⎢ ⎥⎣ ⎦

ABCv (14)

cos(0) cos( 2 / 3) cos(2 / 3)2sin(0) sin( 2 / 3) sin(2 / 3)3

− π π⎡ ⎤= ⎢ ⎥− − − π − π⎣ ⎦P (15)

B. Cable Model According to Fig. 1, it can be seen that the IM load is

directly connected to the SEIG via the short-length cable. The cable equivalent circuit consists of series resistive and inductive elements. From Fig. 1, the current sri flowing from sending- to receiving-end nodes (node S and R) can be written by,

1line

line

dR

dt Lsr

S R sri

= v -v - i (16)

The sending- and receiving-end voltages can be expressed by,

gd

cdt

=Ss sr cg

v=i - i i (17)

mdcdt

=Rsr mot cm

v =i - i i (18)

It is noted that the sending-end voltage accounts for the effect of excitation capacitor.

C. Wind Turbine and Drive Train Model The mechanical power converted from wind energy is represented by well-known static relations as [1],

2 30.5m w pP R v C= ρπ (19) Where ρ is the air density, R is the blade radius, wv is the wind speed upstream of the turbine rotor, Cp is the power coefficient. This coefficient is a function of the tip-speed ratio ( λ ) and the blade pitch angle ( β ), which can be defined as [1],

( ) - /5

1 2 3 4 6/ - - C ip iC C C C C e Cλ= λ β + λ (20)

31 1 0.035-

0.08 1i=

λ λ + β + β (21)

Where 1 0 5176C = . , 2 116C = , 3 0 4C = . , 4 5C = , 5 21C = , 6 0 0068C = . and the tip-speed ratio is defined by,

/tur wR vλ = ω (22)

According to Fig. 1, the mass of all rotating components of the drive train are lumped. For simplicity, one-mass model is considered in this paper [17]. The inertia of low-speed shaft is refereed to high-speed shaft using the gear box ratio (GR). The mechanical dynamics of SEIG can be further modified from (12) by including lumped mass model as,

2 21

2w

e mg w

Dd P T Tdt J J GR GR

⎛ ⎞⎛ ⎞= ⎜ ⎟ ⎜ ⎟⎝ ⎠ + ⎝ ⎠

- -/

rr

ω ω (23)

Where Jw is moment of inertia of wind turbine rotor, Dw is the rotating damping. The mechanical torque delivering from the wind turbine to the SEIG is given by,

2m

mP PT ⎛ ⎞= ⎜ ⎟

⎝ ⎠-

rω (24)

III. MATLAB/SIMULINK IMPLEMENTATION In this section, the mathematical equations of each

component describing in the previous section are implemented in Matlab/Simulink environment. The schematic overview of block-diagram describing the SEIG-IM system (Fig. 1) is shown in Fig. 2.

Fig. 2. Schematic block diagram of SEIG feeding induction motor load

The system is fully represented via interconnected blocks that contain multi-level sub-blocks. The top-level consists of well-constructed blocks of SEIG, IM, wind turbine, cable, and two capacitors. The top-level diagram also describes full interconnections between each component in the SEIG-IM system. From Fig. 2, the SEIG current (labeled with is) and cable current (labeled with isr) are regarded as input quantities of the excitation capacitor to produce the output voltage (VS). This voltage is negatively fed back to the SEIG since the voltage polarity due to the excitation capacitor is in opposite

with that of SEIG [4]. The SEIG feeds IM load through the switch (SW). According to Fig. 1, the parallel-motor capacitor cm may be additionally employed to provide reactive power support for improving the starting performance of IM load and voltage profile of SEIG. In order to visualize SEIG dynamic performance under influence of this capacitor, the way in which it is modeled through Simulink platform must be carefully considered. If the SEIG running voltage is considered as an input quantity of the capacitor cm and IM load, a rapid change in the SEIG voltage due to a sudden connecting of the IM load may lead to a large excursion in the capacitor state variable during the dynamic simulation, causing numerical instability. To avoid this problem, a short-length cable model with small fictitious resistance and inductance in series must be applied. Hence, the cable current is necessarily regarded as an input quantity of the capacitor cm so that its output voltage can directly fed into the IM load as shown in Fig. 2.

Next, the discussion is moved to explore the second-level Simulink block of individual component. Firstly, the block diagrams of SEIG and IM in stationary frame of reference are fully demonstrated in Fig. 3. They mainly compose a set of four blocks that describes stator flux linkage in (1), rotor flux linkage in (2), flux-current relations in (3)-(9), torque balance in (10-12) for IM, and torque balance in (10), (23) for SEIG. These mentioned blocks are illustrated in detail via the third-level models as shown in Fig. 4. The reader can identify them according to the corresponding name located under them. It is noted that the same differential equations (1) and (2) are applied for stator and rotor flux representations of both SEIG and IM. The saturation model is only considered into account for SEIG via the flux-current block by adding extra algebraic equations in (8)-(9). Moreover, the shaft dynamics of IM is represented by (10)-(12), and that of SEIG is described by (10), (23). The second-level blocks of wind turbine, cable, and capacitor are then shown in Fig. 5 and 6, respectively.

Fig. 3. Second-level Simulink blocks of SEIG and IM

Fig. 4. Thrid-level Simulink block of SEIG and IM load

Fig. 5. Second-level Simulink block of wind turbine model

Fig. 6. Second-level Simulink block of cable and capacitor

IV. RESULTS AND DISCUSSIONS In this section, the dynamic simulation of SEIG feeding IM

load (Fig.1) is studied. A small induction machine (2HP, 380V, 3.6A) is employed for working as SEIG. Its electrical parameter is found from laboratory test. The main concerned load is an induction motor, whose horse power is smaller than the SEIG four times (0.5HP, 380V) [18]. All parameters of the SEIG-IM system are given in Appendix. It is noted that all state variables of the SEIG-IM system is initially set to zero during starting the dynamic simulation, except the SEIG’s speed (ωr) where is set equal to synchronous speed (ωs).

The studies are at first conducted to investigate dynamic performances of the SEIG when the IM load is suddenly connected to its terminal. The IM itself is equipped with speed-squared shaft torque characteristic, which is directly set through the coefficients A=1, B=C=0 in (11). The motor’s torque ( 0

mT ) is given by 1.5Nm. The torque profile applied to the IM shaft is associated with an irrigation centrifugal pump, normally used in the remote area. Before conducting the investigation, the minimum permanent capacitor cg of 49μF that permits a successful starting of the IM load with the SEIG is first sought. Then, the bigger sizes than cg (54 and 59μF) are chosen to visualize an effect of this capacitor on SEIG dynamic performances.

Let us first explore a true nature of the IM during the starting interval. Fig. 7 shows both active and reactive power, electrical torque and speed responses of the IM load when it is fully started from a normal grid supply and from SEIG with three different values of cg at t=5sec.

Fig. 7. Power, torque, speed responses of IM load

It is found that the IM initially draws high amount of both active and reactive powers (dotted line in Fig. 7). The IM basically requires the active power along with the electrical

torque development. As the IM load is suddenly connected to the SEIG, both active and reactive power input of the IM is significantly dropped, causing a great delay in the induced torque and speed (Fig. 7). The effect of switching the IM load on SEIG can be further investigated from the SEIG’s voltage, current, electrical torque, and speed responses, which are fully displayed in Fig. 8.

Fig. 8. Voltage, current, torque, and speed responses of SEIG

As the IM load is suddenly applied at t=5sec, a sharp increase in the SEIG electrical transient torque from 2.1Nm to 8Nm (become more negative) is clearly noticed. The rapid increase at this moment is related to a great demand of the active power immediately drawn by the IM in order to produce its accelerating torque as observed through Fig. 7. The SEIG electrical torque is then quickly declined along the same line as the IM’s active and reactive power do. The greatest drops of IM input powers are corresponding to the case when the lowest capacitor of 49μF is used. Because the IM load initially draws most of reactive power only from the permanent excitation capacitor at the starting moment, less availability of the reactive power to support the SEIG built-up voltage process leads to a fast plunge of the SEIG voltage and currents as clearly noticed in Fig. 8. Because reactive power absorption of the IM load is greatly limited due to a small capacity of the excitation capacitor (cg), a great delay in the IM’s induced torque and speed is evident. Fig. 7 indicates that the starting time of IM with SEIG’s capacitor (49μF) is 4sec longer than that when it is started from a normal gird supply. As the bigger capacitors (54μF or 59μF) are applied, not only the motor starting time (Fig. 7) is greatly reduced but also the dips in SEIG voltage and current (Fig. 8) are alleviated. However, making use of the bigger permanent capacitor cg gives rise to over-current problem. It is illustrated from Fig. 8 that 59μF capacitor causes a larger flow of SEIG steady-state current, exceeding the rated value (3.6A). Although a greater value of the permanent excitation capacitor leads to an improvement of voltage profiles and a quicker starting of the IM load, it may introduce undesired over-current problem during steady-state conditions before and after the IM load is switched on. This problem is due to an excessive value of cg that causes the SEIG operating power factor to move further into the leading region.

In this paper, the over-current problem is solved by limiting the capacity of the permanent capacitor cg, and adding a suitable parallel capacitor (cm) instead to improve the IM and SEIG dynamic performances. To demonstrate effectiveness of the paralleled-motor capacitor cm, the extra 10μF formerly added to the permanent capacitor cg is now passed to cm. The plot of motor’s powers, torque and speed is shown in Fig. 9.

Fig. 9. Power, torque, speed responses of IM load

It is apparent from Fig. 9 that a combination of both capacitors (cg and cm) gives a better starting performance of IM. The active and reactive power inputs (dashed-dotted line) of IM are significantly increased as compared with the case when only the capacitor cg is employed. Hence, the capacitor cm helps to improve the induced torque and speed up the starting time of IM. In addition, Fig. 10 shows that the extra 10μF applied for cm is more effective to alleviate the SEIG voltage dip problem as compared to the case where the 10μF is lumped with cg (59μF in total). Moreover, the combination between two capacitors leads to a great reduction in the SEIG steady-state current particularly when the IM load is not yet switched on (Fig. 10).

Fig. 10. Voltage, current, torque, speed responses of SEIG with IM load

In order to reduce the current after a successful starting of the IM load, the authors suggest removing the parallel capacitor cm from the circuit. Fig. 10 indicates a sudden disconnection of cm at t=10sec. As expected, the SEIG steady-state current is greatly dropped and moved to a lower value. By applying the same technique, a bigger size of cm (20μF) is also tested. Fig. 10 (solid line) exhibits shallow dips of the SEIG voltage and current during acceleration of the IM load. After the IM speed is already settled, cutting off the capacitor cm surely reduces the SEIG current under steady-state condition without any change much in the IM operating condition as seen from Fig. 9.

CONCLUSIONS This paper presents dynamic simulation of small stand-

alone SEIG feeding the IM load. The mathematical models of SEIG, IM, and wind turbine are clearly implemented into Matlab/Simulink environment in step-by-step manner. The study results reveal an occurrence of the great dips in SEIG terminal voltage and current due to an insufficient reactive power support when the IM load is suddenly connected. Making use the paralleled-motor capacitor is an effective way in providing reactive power support to achieve a good voltage profile of the SEIG and a quick starting duration of the IM load.

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APPENDIX SEIG parameters 2HP, 380V, 3.6A, 50 Hz, 4Poles, Jg=0.04 kg.m2, Rs=4.4241Ω, Rr=3.5970Ω, Lls= Llr =16.1mH, a0=2.9718×10-1, a1=3.0172×10-1, a2=-2.5087×10-1, a3=8.8795×10-2, a4=-1.7285×10-2, a5=1.9659×10-3, a6=-1.2024×10-4, a7=3.0510×10-6 IM parameters 0.5Hp, 380V, 50Hz, 4Poles, Jm=0.02 kg.m2, Rs=25Ω, Rr=18.58Ω, Xls= Xlr =52.8Ω, Xm=636.96Ω Cable parameters Rline=0.5Ω, Lline=1×10-3H Wind turbine parameters Jw=2kg.m2, ρ=1.25kg/m3, vw=6.6m/sec, R=1.5m, GR=3, β=0ο, Dw =0