R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder

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1 R. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder

2 Introduction to Inverters Robert W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder Single-Phase Inverter Approaches The Solar Application Single-Phase Solar Inverters Microinverters

3 A Basic Single-Phase Inverter Circuit DC power source H-bridge inverter circuit AC load L-C filter may or may not be present Simple resistive load illustrated; actual AC loads are more complex Even in the single-phase case, there are multiple ways to control the switches Applications: Uninterruptable power supply (UPS) AC motor drive Fluorescent lamp driver Solar power inverter Automobile AC power inverter Some three-phase applications: AC motor drives Inverters for wind and solar Electric vehicles DC transmission line stations

4 The Modified Sine Wave Inverter H-bridge switches at the output frequency Waveform is highly nonsinusoidal, with significant harmonics Some ac loads can tolerate this waveform, others cannot Inexpensive, efficient v ac + V HVDC V HVDC DT/2 T/2 Control of ac rms voltage by control of duty cycle D: Standalone inverter: inverter drives a passive load, and regulates the voltage supplied to the load

5 The True Sine Wave Inverter Use of PWM with high frequency switching to produce a sinusoidal ac voltage having low harmonic content. Typically an L-C filter is included to meet EMI requirements Switches 1a and 1b are driven by the same gate drive signal, and conduct during d interval Switches 2a and 2b are driven by the complement and conduct during d interval v ac Two-level waveform v = (2d 1) V g For positive half cycle, switch 1b is on. Switches 1a and 2a operate with PWM For negative half cycle, switch 2a is on. Switches 2b and 1b operate with PWM 6 Three-level waveform t v = ± d V g Alternate: b switches switch at the line frequency, and a switches operate with PWM Three-level exhibits reduced switching loss

6 Standalone vs. grid-tied applications Standalone inverter: Inverter regulates ac voltage Grid-tied inverter: Inverter regulates its ac current Inverter Inverter V dc + AC load V dc + v ac d inv PWM v ac d inv PWM i ac v ac Phase-locked loop G c3 (s) H 3 G c3 (s) H 3 v ref + Sinusoidal reference V control i ref + Sinusoid unit amplitude phase-locked to v ac

7 Reactive power For a standalone application, the inverter must be capable of supplying whatever current waveform is demanded by the ac load Reactive load, in which current is phase-shifted relative to voltage Distorted current In most grid-tied applications, the inverter supplies a low-thd current waveform to the grid, with power factor very close to unity. Improved efficiency This opens the possibility of simpler converter topologies using singlequadrant switches

8 The grid-tied solar inverter application AC voltage is determined by the utility system ( infinite bus ) Power is determined by the solar array Inverter produces ac current synchronized to the utility, with amplitude dependent on array power A residential solar array system

9 Functions performed by the inverter Maximum power point tracking: operate the solar array at the voltage that maximizes generated power 120 Hz energy storage: the difference between the constant power supplied by the array and the 120 Hz pulsating power flowing into the utility is supplied/stored in the capacitor AC current control: ac line current must meet harmonic requirements (THD < 5%), with unity power factor p ac P pv Array voltage, capacitor voltage, and ac line voltage are independent System resembles PWM rectifier system, but with power flow reversed v c t

10 An Inverter System v pv DC-DC v bus Inverter EMI PV v ac v pv H 1 d PWM d inv PWM i ac v ac Phase-locked loop G c3 (s) i bus v bus G c3 (s) H 3 MPPT + V ref-pv V ref-bus + H 2 G c2 (s) i ref + Sinusoid unit amplitude phase-locked to v ac

11 Standards IEEE 1547: standard for connecting a renewable energy source to the utility grid Current harmonic limit (THD < 5%) Anti-islanding (detect loss of grid, shut down within 1 sec) Disconnection when grid frequency or grid voltage is out of bounds National Electric Code UL 1741 Weighted Efficiency standards: California Energy Commission (CEC) Power level, % of rated Weight 100% % % % 0.12 Provides a way to compare products of different companies Weightings reflect typical distribution of array power experienced in California 20% % 0.04

12 Microinverters One inverter per panel Mounted on or near the panel on roof MPPT on per-panel basis Conventional AC wiring reduces Balance-of-system cost Straightforward expandability Reliability? Efficiency? Rated temperature? Ascension Tech. microinverter, 1998 Enphase microinverter, 2008

13 Elements of a Microinverter System v i PV Cells i v i + v DC-DC Converter P dc P dc P ac Energy storage + v cap v ac i ac P ac DC-AC Inverter i ac + v ac t Microinverter power train: DC-DC converter (high boost ratio) Energy storage capacitor Inverter Central box Rooftop system Microinverter Power stage MPPT Current control Anti-islanding Microinverter Power stage MPPT Current control Anti-islanding Roof AC Transient protection Communications AC disconnect AC utility Microinverters include most or all of grid interface control Central box Computer Smart grid

14 Microinverter Approaches H-bridge inverter Buck converter plus unfolder Unfolder: similar to bridge rectifier, but power flows in reverse direction. Implemented using transistors that switch at ac line frequency

15 Inverter sinewave synthesis approaches We can employ any of the approaches we have already discussed for PWM rectifier systems: Average current control Peak current control Boundary conduction mode Hysteretic control Discontinuous conduction mode control Cycle-by-cycle control (and there are a few we didn t discuss, most notably harmonic elimination, that could be employed for either rectifiers or inverters)

16 Synthesizing a Sinusoidal Current: Boundary Conduction Mode (BCM) Inductor current waveform, BCM Loss components at different solar irradiance levels, BCM (300 W, 240 Vac example)

17 Discontinuous conduction mode (DCM) Higher conduction loss Lower switching loss A net improvement in CEC efficiency CEC efficiency [%] inductance [µh] constant peak current BCM Weighted efficiency vs. inductor size, DCM vs. BCM 300 W, 240 Vac example

18 Measured Results: 300 W Microinverter Prototype AC line voltage Current reference Filtered inverter current Instantaneous inductor current CEC power level weight CEC Efficiency average AC power P ac Average loss over AC cycle average AC efficiency 100 % W 2.6 W % 75 % W 1.97 W % 50 % W 1.26 W % 30 % W 0.7 W % 20 % W 0.45 W % 10 % W 0.24 W 99.2 % Overall weighted CEC efficiency = %

19 Development of Electrical Model of the Photovoltaic Cell, slide 1 Photogeneration Semiconductor material absorbs photons and converts into hole-electron pairs if Photon energy h > E gap (*) Energy in excess of E gap is converted to heat Photo-generated current I 0 is proportional to number of absorbed photons satisfying (*) + photon Charge separation Electric field created by diode structure separates holes and electrons Open circuit voltage V oc depends on diode characteristic, V oc < E gap /q

20 Development of Electrical Model of the Photovoltaic Cell, slide 2 Current source I 0 models photo-generated current I 0 is proportional to the solar irradiance, also called the insolation : I 0 = k (solar irradiance) Solar irradiance is measured in W/m^2

21 Development of Electrical Model of the Photovoltaic Cell, slide 3 Diode models p n junction Diode i v characteristic follows classical exponential diode equation: I d = I dss (e V d 1) The diode current I d causes the terminal current I pv to be less than or equal to the photo-generated current I 0.

22 Development of Electrical Model of the Photovoltaic Cell, slide 4 Modeling nonidealities: R 1 : defects and other leakage current mechanisms R 2 : contact resistance and other series resistances

23 Cell characteristic Cell output power is P pv = I pv V pv At the maximum power point (MPP): V pv = V mp I pv = I mp At the short circuit point: I pv = I sc = I 0 P pv = 0 At the open circuit point: V pv = V oc P pv = 0

24 Maximum Power Point Tracking Automatically operate the PV panel at its maximum power point Some possible MPPT algorithms: Perturb and observe Periodic scan I-V curve with partial shading Newton s method, or related hillclimbing algorithms What is the control variable? Where is the power measured? Power vs. voltage

25 Example MPPT: Perturb and Observe A well-known approach" Works well if properly tuned" When not well tuned, maximum power point tracker (MPPT) is slow and can get confused by rapid changes in operating point" A common choice: control is switch duty cycle" Basic algorithm!! Measure power" Loop:" Perturb the operating point in some direction" Wait for system to settle" Measure power" Did the power increase?" Repeat" Yes: retain direction for next perturbation" N: reverse direction for next perturbation"!

26 Control Issues: MPPT by Perturb-and-Observe,, Key elements of digital controller Measured power vs. commanded PV voltage Find PV voltage that maximizes power output Switching converter is high noise environment This noise is partly correlated to the control, and hence isn t entirely random The highly-filtered dc control characteristic exhibits many small peaks ( traps ), where P&O algorithm gets stuck Magnified view More noise makes P&O work better!

27 Typical experimental data () α () α Perturb-and-observe step time of 15 msec Perturb-and-observe algorithm may take minutes to find max power Weather can change in seconds Improved algorithm achieves max power in seconds Adaptive algorithm finds max power quickly, then reduces jitter size to improve equilibrium MPPT accuracy

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