_{1}

This paper presents the perturbation and observation (P & O) algorithm as maximum power point tracking (MPPT) method for the dynamical analysis of DC shunt motor fed by photovoltaic generator at different solar irradiance levels. At each solar intensity, the maximum power point of current/voltage (I/V) characteristic of the PV generator is achieved by perturbation and observation algorithm. The nonlinear behavior of (I/V) characteristics of the PV generator at various solar intensities and the magnetization curve of the ferromagnetic material of the DC shunt motor are described by high order polynomial mathematical expression. The dynamical analysis of the DC shunt motor fed by PV generator at different solar intensity has been carried out, also the dynamical analysis of DC shunt motor is investigated at a step change in solar intensity levels with fixed load at motor.

As the world population is increasing dramatically, the demand for electricity became one of the world’s largest concerns. So many researchers have focused recently on this aspect. Moreover, the environment problems and other related issues have boosted the attention for the use of renewable energy resources such as wind, solar, fuel cells, water power and many others as solutions for expected critical crisis in many countries.

The Perturbation and Observation (P & O) as Maximum Power Point Tracking (MPPT) technique for PV generator integrator to the grid is investigated [

The dynamical analysis of PV-powered DC shunt, series and permanent- magnet motors is studied [

The simulation study of PI controller for boost converter in a standalone photovoltaic energy is presented [

The dynamical and the steady-state behavior of hybrid powered DC series motor through PV and DC shunt generators are presented [

The modeling, simulations and operational performance characteristics of a hybrid-powered permanent-magnet DC (PMDC) motor for pumping applications are investigated [

The analysis of a standalone PV generator with MPPT utilized by P & O technique is presented [

In this paper, the proposed system is a stand-alone PV generator feeding DC shunt motor. In this work a perturbation and observation P & O technique is used to track the maximum power point of the PV generator. P & O technique is used for changing the duty cycle of the DC-DC buck-boost converter to keep the output voltage of DC-DC buck boost converter equal to the value of voltage at maximum power point of the I/V characteristic of PV generator. This paper is structured in the following manner: Section 2 describes the configuration of the system under study. The dynamical mathematical model of DC shunt motor also the design of the PV generator is outlined in Section 3. Section 4 presents the perturbation and observation technique which is used to track the MPP of the designed PV generator. The numerical simulations and discussions are addressed in Section 5 and finally conclusions are presented in Section 6.

Appendix A presents the physical explanations for all parameters in this paper. Appendix B presents the values of the numerical parameters of the system and presents the constants of the polynomials which approximate the output characteristics of the PV generator at three solar intensities levels.

DC shunt motor. The PV generator is designed by connecting many modules in series and parallel combination in order to achieve the rated values for DC shunt motor. DC-DC buck-boost converter is used as a common stage between PV generator and DC shunt motor to change the output voltage that apply on DC shunt motor for tracking way. The DC-DC converter is used to inject the voltage at MPP of current-voltage characteristic of the PV generator by adjusting its duty cycle

This section presents some design aspects of the PV generator along with its output characteristics which are the terminal voltage of the PV generator as function of the output current and the corresponding output power at various solar irradiance levels. The mathematical equations representing the dynamics of the DC shunt motor is also summarized.

PV cells are assembled from modules which are interconnected in series-parallel arrangement to produce arrays. The mathematical model of PV array is given by the following Equation [

where

As can be noted from ^{th} order polynomial function using MATLAB as [

In DC shunt motor, the field and armature circuits are connected in parallel. The nonlinear dynamical mathematical model of DC shunt motor is [

^{th} order degree for ferromagnetic material in the DC shunt motor using MATLAB software.

Perturbation and observation (P & O) algorithm works by detecting the operating point on the V-I characteristics of the PV array and compare it with the pre-

vious operating point. The controller calculate the Power

The DC-DC buck boost converter is a power electronic device used to change the average value of the input voltage into higher, equal or lower value. They are used in regulated power supplies, electrical motor drive systems and renewable energy resources as an intermediate stage for controlling purposes. The output voltage of buck boost converter is controlled by changing the duty cycle

−∆D) and if the operating point at the left side of MPP the duty cycle is greater than 0.5 boost mode (positive perturbation + ∆D).

This section presents the numerical simulations of the nonlinear dynamical model of the system after step changes in the mechanical load coupled to the motor when the PV generator is fully and partially intensified and the response of the system with a fixed motor load while the solar intensity levels of the PV generator are step changed.

_{L}) has stepped changed from 5 Nm to 10 Nm. Initially at 5 Nm, the motor rotates at a speed of 1582 rpm with a DC-DC converter duty cycle of 0.4613. As the load coupled to the motor becomes 10 Nm, the steady- state motor rotational speed becomes 1465 rpm with a converter duty cycle of 0.4763. The duty cycle of the converter has changed to achieve the target of tracking the maximum power point of PV generator which equal the motor rated terminal voltage 125 V. During these numerical simulations, it is found that the armature currents of DC shunt motor are changed from 5.84 A to 11.62 A. Correspondingly, field currents are 1.789 A to 1.684 A. The steady state PV output currents are 7.634 A & 13.3 A. The PV output terminal voltages are 143.1 V and 134.8 after step change in load torque from 5 Nm to 10 Nm, respectively.

_{L}) has stepped changed from 8 Nm to 4 Nm. Initially at 8 Nm, the motor rotates at a speed of 1346 rpm with a DC-DC converter duty cycle of 0.4847. As the load coupled to the motor becomes 4 Nm, the steady-state motor rotational speed becomes 1464 rpm with a converter duty cycle of 0.4647. The duty cycle of the converter has changed to achieve the target of tracking the maximum power point of PV generator at 75% of full solar intensity which equal 115.4 V. During these numerical simulations, it is found that the armature currents of DC shunt motor are changed from 9.354 A to 4.65 A. Correspondingly, field currents are 1.534 A to 1.662 A. The steady state PV output currents are 10.89 A & 6.314 A. The PV output terminal voltages are 122.8 V and 133 V after step change in load torque from 8 Nm to 4 Nm, respectively.

by tracking the MPP of the PV generator which equal the motor rated terminal voltage. The duty cycle of buck-boost converter has changed in the following manner 0.4613, 0.4815 and 0.523. The load torque is kept fixed; the armature and field currents are not changed.

As a summery for the steady-state system parameters for all running conditions,

Parameter | Full Solar Irradiance | 75% of Full Solar Irradiance | ||
---|---|---|---|---|

Field current I_{F} (A) | 1.789 | 1.684 | 1.534 | 1.662 |

Armature current I_{A} (A) | 5.84 | 11.62 | 9.354 | 4.65 |

Motor rotational speed, | 1582 | 1465 | 1346 | 1464 |

Duty cycle of the DC-DC Converter, | 0.4613 | 0.4763 | 0.4847 | 0.4647 |

PV output terminal voltage (V) | 143.1 | 134.8 | 122.8 | 133 |

PV output terminal current (A) | 7.634 | 13.3 | 10.89 | 6.314 |

Motor terminal voltage that equal to value at MPP (V) | 122.5 | 122.5 | 115.4 | 115.4 |

The dynamical performance of a DC shunt motor fed from PV generator is investigated. The PV generator is designed at full solar intensity to give the maximum power at the motor rated conditions. The nonlinearity of the output characteristics I/V of the photovoltaic generator at different solar irradiance levels is included in all simulations by polynomial curve fitting. The perturbation and observation algorithm is employed in the simulation to track the MPP of the PV

generator by adjusting the duty cycle of the DC-DC converter. The study comprises the response of DC shunt motor when after step changes in the load coupled with the motor at 100% and 75% of full solar irradiance level and after successive step changes in the solar intensity with constant motor loading conditions. It is concluded that P & O technique always changes the value of duty cycle of the DC-DC buck boost converter to track the MPP of the PV generator which is close to the motor rated voltage. Basically, as the mechanical load coupled to the motor increases, the rotational speed of the motor decreases and the armature current of the motor are increased too. As a general conclusion, the proposed PV generator can withstand step changes in the load coupled to the motor and step changes in the solar irradiance levels, which indicates the robustness and proves the reliability of the integration between PV system and DC shunt motor.

Sweidan, T.O. (2017) Dynamical Analysis of DC Shunt Motor Powered by PV Generator Using Perturbation and Observation as MPPT Technique. Energy and Power Engineering, 9, 55-69. http://dx.doi.org/10.4236/epe.2017.91005

The following are the physical explanations for all parameters in this paper.

DC: Direct current

PV: Photovoltaic

V_{PV}: PV output terminal voltage.

I_{PV}: PV output current.

D: Duty cycle of the DC-DC buck-boost converter.

V_{d}: Output voltage of DC-DC buck-boost converter.

L_{A}: Armature winding inductance:

R_{A}: Armature winding resistance

R_{F}: Field winding resistance

L_{F}: Field winding inductance

i_{F}: Motor field current.

i_{A}: Motor armature current.

i_{m} :Motor load current.

J: Rotor and load moment of inertia.

ω: Rotational speed of the rotor.

K: Constants depends of the design of the machine.

Φ: Flux per pole

T_{L}: Load Torque

The following are the values of the numerical parameters of the system:

L_{F} = 10 mH, R_{F} _{adj} = 80 − 120 Ω, V =120 V, L_{A} =18 mH, R_{A} = 0.24 Ω, J = 0.5 kg・m^{2}

Full Solar Irradiance | 75% of Full Irradiance | 50% of Full Irradiance | |
---|---|---|---|

α_{1} | −0.0000002448 | −0.00000409564 | −0.00021566167 |

α_{2} | 0.000020221518 | 0.00025368261 | 0.0089053426 |

α_{3} | −0.00071025735 | −0.0066827305 | −0.15639491 |

α_{4} | 0.013832714 | 0.097612823 | 1.5229452 |

α_{5} | −0.16327544 | −0.86413501 | −8.9880971 |

α_{6} | 1.1990814 | 4.7596023 | 33.003923 |

α_{7} | −5.4118479 | −16.111235 | 74.478767- |

α_{8} | 14.277315 | 31.878 | 98.243414 |

α_{9} | −19.834429 | −33.214329 | −68.241193 |

α_{10} | 10.88503 | 13.670886 | 18.725203 |

α_{11} | 147.89258 | 139.30756 | 127.20767 |

Magnetization Curve Constants | |
---|---|

α_{1} | −2.5423194e−15 |

α_{2} | 1.0763872e−14 |

α_{3} | −1.5528838e−14 |

α_{4} | −0.3084 |

α_{5} | 1.0272 |

α_{6} | 0.0049 |