Transient and steady-state performance analysis of hybrid powered DC series motor via DC shunt and PV generators with maximum power point tracking

Abstract

This paper presents a comprehensive transient and steady-state analysis of hybrid powered DC series motor through DC shunt and PV generators. The solar cell generator is interfaced with the system through a DC–DC buck–boost switch mode converter. At full solar irradiance, the PV generator can completely run the DC series motor as its maximum power point is placed at the rated conditions of the DC series motor. As the solar intensity decreases, the shortage of power demanded by the series motor is compensated by the fuel-driven DC generator. To fully utilize the pollution-free PV generator at various solar intensities and, therefore, to reduce the total fuel consumption by the prime mover of the DC shunt generator, the operating point of the solar cells in case of hybridization is adjusted at its maximum power point by automatically calibrating the terminal voltage at the common coupling point of the two generators. The transient analysis comprises step changes in the load coupled to the motor at different solar irradiances and after successive step changes on the solar illuminations for some given fixed loading conditions. The nonlinearities of the PV generator are taken into account along with that of the ferromagnetic material of the two DC machines. The effect of changing the field resistance of the DC generator on the performance of the system is addressed. The steady-state output characteristics of the DC series motor when powered by only PV generator at full solar illumination, in case of hybridization at 0.85 and 0.70 of full solar intensity are outlined and compared.

Appendices

Appendix A

The following are the physical explanations of system mathematical model parameters:

$L_\mathrm{m}$ :

DC series motor armature and field circuits self inductances

$i_\mathrm{PV}$ :

PV generator output current

$V_\mathrm{PV}$ :

PV generator terminal voltage

$R_\mathrm{m}$ :

DC series motor armature and field circuits resistances

$K_\mathrm{m}$ :

DC series motor design constant

$\phi _\mathrm{m}$ :

DC series motor flux

$\omega _\mathrm{m}$ :

DC series motor rotational speed

$J_\mathrm{m}$ :

DC series motor and load moment of inertia

$T_\mathrm{L}$ :

Mechanical load coupled to the motor

$\beta _1 , \beta _2$ and $\beta _3$ :

Polynomial constants representing the magnetizing curve of the DC series motor

$L_\mathrm{g}$ :

DC shunt generator armature circuit self inductance

$i_\mathrm{g}$ :

DC shunt generator armature current

$R_\mathrm{g}$ :

DC shunt generator armature circuit resistance

$\omega _\mathrm{g}$ :

DC shunt generator rotational speed

$L_\mathrm{f}$ :

DC shunt generator field circuit self inductance

$i_\mathrm{f}$ :

DC shunt generator field circuit current

$R_\mathrm{f}$ :

DC shunt generator field circuit resistance

$R_\mathrm{adj}$ :

DC shunt generator field circuit adjustable resistance

$J_\mathrm{g}$ :

DC shunt generator and prime mover moment of inertia

$\alpha _1 , \alpha _2$ and $\alpha _3$ :

Polynomial constants representing the magnetizing curve of the DC shunt generator

$T_\mathrm{V}$ :

Time constant of the voltage controller

$T_\mathrm{m}$ :

Mechanical torque output from the prime mover

$V_\mathrm{ref}$ :

Reference voltage of the voltage controller

$V_\mathrm{g}$ :

Terminal voltage of the DC shunt generator

$K_\mathrm{V}$ :

Gain of the voltage controller

Appendix B

The following are the values of the constants of the system mathematical model:

$L_\mathrm{m} =62\,\hbox {mH},\,R_\mathrm{m} =0.44\,\Omega ,\,J_\mathrm{m} =0.5\,\hbox {kg m}^{2},\,\beta _1 =-0.0017\, \mathrm{Wb/A}^{2},\,\beta _2 =0.0938\,\hbox {Wb/A},\,\beta _3 =0.0062\,\hbox {Wb}, L_\mathrm{g} =18\,\hbox {mH}, R_\mathrm{g} =0.24\,\Omega ,\,\alpha _1 =-0.3084\,\hbox {Wb/A}^{2},\,\alpha _2 =1.0272\, \hbox {Wb/A},\,\alpha _3 =0.0049\,\hbox {Wb},\,L_\mathrm{f} =10\,\hbox {H},\,R_\mathrm{f} +R_\mathrm{adj} =100\,\Omega , J_\mathrm{g} =0.5\,\hbox {kg m}^{2},\,T_\mathrm{V} =0.5\,\hbox {s}, V_\mathrm{ref} =130\,V,\,K_\mathrm{V} =10\,\mathrm{Nm/V}$.

Appendix C

The values of the 10th order polynomial curve of the output characteristics of the PV generator at the three solar intensities are:

Constant	Full solar illumination	0.85 of full solar illumination	0.70 of full solar illumination
$\gamma _1 \quad (\mathrm{V/A}^{10})$	-0.0000001946676	-0.0000009393512	-0.0000060645127
$\gamma _2 \quad (\mathrm{V/A}^{9})$	0.0000173750718	0.0000712655896	0.0003789020201
$\gamma _3 \quad (\mathrm{V/A}^{8})$	-0.0006612144493	-0.0023052314457	-0.0100934744372
$\gamma _4 \quad (\mathrm{V/A}^{7})$	0.0139854557681	0.0414445806261	0.1494421186619
$\gamma _5 \quad (\mathrm{V/A}^{6})$	-0.1796699014675	-0.4525696026617	-1.3439086881053
$\gamma _6 \quad (\mathrm{V/A}^{5})$	1.4387276827434	3.0804032776748	7.5330538490437
$\gamma _7 \quad (\mathrm{V/A}^{4})$	-7.0882339219053	-12.8998881292824	-25.9793663015432
$\gamma _8 \quad (\mathrm{V/A}^{3})$	20.4035579282125	31.5625972539290	52.3473206103495
$\gamma _9 \quad (\mathrm{V/A}^{2})$	-30.7877840811318	-40.4822074593410	-55.2923468949142
$\gamma _{10} \quad (\mathrm{V/A})$	17.5214040234632	19.5827456844042	22.0269079020039
$\gamma _{11} \quad (\mathrm{V})$	172.9875813716187	164.3382023014351	152.2290716084487