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Novel Analytical Approaches for Induction Machine Direct Start-up Speed–Time Curve Modeling under Fan Load

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Abstract

In the ship's electrical power system, the largest percentage of a load powered by an induction machine (IM) can be represented through the fan load characteristics. Likewise, it is well known that, from the point of view of the current load, the “most problematic” way of starting the induction machine is the direct start. This paper deals with a novel analytical modeling of the IM direct start-up speed–time curve under fan load. The derived analytical expressions have been used for modeling the start of induction machines of different powers and voltage levels. Also, the obtained results have been compared with the corresponding results provided by using the realized MATLAB/Simulink model of the induction machine coupled with fan load. Moreover, the results obtained have been compared with the methods presented in the literature as regards the modeling of start-up characteristics. The experimental validation of the proposed analytical expressions for modeling the direct start of IM driving fan load has also been carried out on a 300 W machine in a laboratory environment. Both the simulations and experimental verification have demonstrated an exceptional accuracy of the derived analytical expressions. The paper also provides the implemented MATLAB code for determining the speed–time curve of IM during direct start under fan-type load.

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Abbreviations

B :

Fan load coefficient

dt :

Time increment

J :

Moment of inertia

M :

IM torque

M br :

Maximum machine torque

M em :

Electromagnetic torque

ω :

Speed of rotation

ω s :

Synchronous speed

p :

Number of pole pairs

P 0 :

Losses from the no-load test

P cus :

Losses in the stator copper

R T :

Thevenin equivalent resistance

R 1 :

Stator resistance

R 2 :

Rotor resistance referred to the stator side

s :

Slip of the machine

s br :

Corresponding slip at the maximum machine torque

t :

Time to represent the IM speed–time curve during direct start-up

U T :

Thevenin equivalent voltage

U :

Supply line-to-line voltage

X T :

Thevenin equivalent reactance

X 1 :

Stator leakage reactance

X 2 :

Rotor leakage reactance referred to the stator side

X m :

Magnetizing reactance

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Author information

Authors and Affiliations

  1. Faculty of Maritime Studies Kotor, University of Montenegro, Put I Bokeljske Brigade 44, 85330, Kotor, Montenegro

    Ilija Knežević & Tatijana Dlabač

  2. Faculty of Electrical Engineering, University of Montenegro, Dzordža Vašingtona Bb, 81000, Podgorica, Montenegro

    Martin Ćalasan

Authors
  1. Ilija Knežević
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  2. Martin Ćalasan
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  3. Tatijana Dlabač
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Contributions

IK: Writing—Original draft; Formal analysis; Conceptualization; MĆ: Writing—Original draft; Formal analysis; Conceptualization; Validation; TD: Validation, Methodology, Writing—review & editing.

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Correspondence to Martin Ćalasan.

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Appendix

Appendix

UT = Xm/(X1 + Xm)*U.

RT = R1*Xm^2/( R1^2 + (X1 + Xm)^2).

XT = (Xm*R1^2 + X1^2*Xm + X1*Xm^2)/(R1^2 + (X1 + Xm)^2).

Mpr = 3/ws*(UT/sqrt(3))^2*(XT + X2)/((RT + XT + X2)^2 + (XT + X2)^2).

spr = R2/(sqrt(RT^2 + (XT + X2)^2)).

A = − B*(ws)^2;

B1 = 2*B*(ws)^2;

C = − B*(ws)^2 − (spr)^2*B*(ws)^2;

D = 2*B*(ws)^2*(spr)^2 + 2*Mpr*spr;

E = − B*(ws)^2*(spr)^2;

F = J*ws;

G = 0;

H = (spr)^2*J*ws;

karakteristicna = [A B1 C D E];

korijeni = roots([A B1 C D E]).

indeks_real = find(imag(korijeni) =  = 0).

real_root = korijeni(indeks_real);

s1 = korijeni(indeks_real(1)).

s2 = korijeni(indeks_real(2)).

[R Q] = deconv(karakteristicna, [1 − s1 − s2 s1*s2]);

R1 = R(1)

R2 = R(2)

R3 = R(3)

Matrica = [R1 R1 1 0; R2 − s2*R1 R2 − s1*R1 − s2 − s1 1; R3 − s2*R2 R3 − s1*R2 s1*s2 − s1 − s2; − R3*s2 − s1*R3 0 s1*s2];

spolja = [0; F; G; H];

resenje = inv(matrica)*spolja;

k1 = resenje(1).

k2 = resenje(2).

k3 = resenje(3).

k4 = resenje(4).

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Knežević, I., Ćalasan, M. & Dlabač, T. Novel Analytical Approaches for Induction Machine Direct Start-up Speed–Time Curve Modeling under Fan Load. Electr Eng 106, 1925–1938 (2024). https://doi.org/10.1007/s00202-023-02039-3

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