ELEC 5564 Electric Power Generation - PV Power Generation System Structure

Structure of Solar PV Systems

  • Overview of the structure of solar PV systems.
    • Solar PV Array.
    • Power inverters in solar PV systems.
    • Power converters in solar PV systems.
  • State-space analysis will be performed.

Solar PV Generator and Converter

  • Solar PV generator characteristics are represented by V-I curves for different irradiation levels (600W/m², 800W/m², 1000W/m²), illustrating the Maximum Power Point (MPP).
  • Current (I) ranges from 0.1 to 0.7 A.
  • Voltage (V) ranges from 1.5 to 3.5 V.

System Components and Power Flow

  • The system includes:
    • A solar PV generator.
    • A DC-DC converter.
    • A DC load.
  • Key parameters:
    • V_{PV(MPP)} (Voltage at Maximum Power Point)
    • P_{PV} (Power from PV array)
    • P_{Out} (Output Power)
    • V_L (Load Voltage - Rated power)
  • Equations:
    • P{PV} = V{PV} \times I_{PV}
    • P{Out} = V{Out} \times I_{Out}
  • Function of DC-DC converters:
    • Step-Down (Buck) converter.
    • Step-Up (Boost) converter.
    • Buck-Boost, Cuk-converter.
  • DC-AC Converters:
    • PWM DC-AC inverter.

Step-Down Converter (Buck Converter)

  • A solar PV module connects to a buck converter (step-down DC-DC converter).
  • Components:
    • Inductor (L).
    • Diode.
    • Switch.
    • Input Capacitor (C_{In}).
    • Output Capacitor (C_{Out}).
    • Load resistor (R_L).
  • Variables:
    • I_{PV} (PV current).
    • I_L (Inductor current).
    • V_O (Output voltage).
    • I_D (Diode current).
    • I_O (Output current).
    • V_{PV} (PV voltage).
    • I_I (Input current).
    • I_C (Capacitor current).
  • Switching period (T) is the sum of the switch-on time (T{on}) and switch-off time (T{off}).
    • T = T{on} + T{off}
  • Duty cycle (D) is defined as the ratio of switch-on time to the total period.
    • D = \frac{T_{on}}{T}
    • T_{on} = DT
    • T_{off} = (1-D)T

Step-Down Converter - Steady State Mode

  • Mode 1 (Switch is ON):
    • Inductor voltage during switching ON mode: VL = VI - V_O
    • VI is input voltage and VO Vo is output voltage.
    • V_L = L \frac{\Delta I}{\Delta t}
    • \frac{\Delta I}{\Delta t} = \frac{VI - VO}{L}
    • \Delta I = \frac{(VI - VO) T_{on}}{L}
    • \Delta I = \frac{(VI - VO) DT}{L}
  • Mode 2 (Switch is OFF):
    • Inductor voltage during switching OFF mode: VL = -VO
    • V_L = L \frac{\Delta I}{\Delta t}
    • \frac{\Delta I}{\Delta t} = \frac{-V_O}{L}
    • \Delta I = \frac{-VO T{off}}{L}
    • \Delta I = \frac{-V_O (1-D)T}{L}
  • The change in current, \Delta i, has the same magnitude in both modes.

Lossless System

  • For a lossless system, input power equals output power: P{in} = Po
  • Output power: Po = Io V_o
  • Input power: P{in} = VI \times (\text{average of } iI) = VI i_{IAV}
  • VI i{IAV} = Io Vo
  • \frac{Vo}{VI} = \frac{i{IAV}}{Io} = k

Ripple Current

  • With load R and without output capacitor C_O, current expressions are derived.
  • During on time: Ton
  • During off time: Toff
  • \tau = \frac{L}{R_L} (time constant)
  • The equation to solve for Imin requires substituting Imax to find the recursive relationship between the minimum current in successive chopper cycles.

Ripple Current Analysis

  • At steady state, the maximum and minimum output currents are defined.
  • The peak-to-peak current is defined.
  • When k = 0.5, the peak-to-peak current is at its maximum and represents the worst-case condition for determining smoothing inductance.

Ripple Current Reduction

  • For k = 0.5, the maximum peak-to-peak current is given as
  • This is used to determine the filter inductance L value and/or converter switching frequency f to limit the ripple current.

Simplified Inductor Calculations

  • In practice, the switching frequency f = \frac{1}{T_P} is high.
  • Current variations during the on and off periods are assumed to be linearly changing rather than exponential.
  • The net current changes from on to off and vice versa are the same.

Capacitor on the PV Terminal

  • Assuming load current I_O has negligible ripple.
  • A small input inductor L1 is used, and a capacitor C_{in} is necessary to reduce PV terminal voltage ripples.
  • When the switch is ON, the current to the converter is supplied by the capacitor which discharges during the on-time, causing V_I to drop.
  • When the switch is OFF, the capacitor is charged, and V_I will increase causing the converter input voltage to fluctuate around the PV terminal voltage.
  • \Delta V_I represents the change in input voltage.
    • V_I (converter input voltage ).
    • I_{PV} (PV current).
    • I_{CI} (Capacitor current).
    • I_O (Output current).