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## Inverter Circuits

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Inverter Circuits

- Provide a variable voltage, variable frequency AC output from a DC input
- Very important class of circuits. Extensively used in variable speed AC motor drives for example (see H5CEDR)
- We have already seen how the fully controlled thyristor converter can operate in the inverting mode ( > 90O) - however that is limited:
- Can only invert into an existing AC supply
- Voltages must already be present to provide natural commutation of thyristors
- The circuits we will look at here are much more versatile and can provide an AC output into just about any kind of load
- Three phase and single phase versions are possible - principles are the same

D1

E/2

IAC

DC Supply (E)

O

X

Don’t worry about where

current goes yet

E/2

D2

Q2

Basic Inverter Leg (1)- Basic building block is the “2-level inverter leg”

- Capacitor does not have to be split - O provides a convenient place to reference voltages to for understanding
- Obviously never gate Q1 and Q2 at the same time! - “shoot through” causes destruction
- Normal mode is to use complementary gating for Q1 and Q2
- In practice a small delay must be introduced between turning Q1 off and Q2 on (and vice versa) to avoid “shoot through” due to finite switching times
- We will ignore the effect of this and assume perfect switching

Basic Inverter Leg (2)

- Output voltage depends on gated device only and not on current direction
- Circuit produces 2 voltage levels
- Equivalent circuit:

- Not often used on its own - but provides basic building block for other circuits

DC LINK

D1

D3

E/2

Q1

Q3

IAC

DC Supply (E)

X

O

VAC

load

Y

Q2

Q4

E/2

D2

D4

Single Phase Inverter H-bridge (1)- Uses 2 inverter legs

- Energy flow in both directions possible - circuit can be used as a rectifier - see later

Single Phase Inverter H-bridge (2)

- VXO, VYO are 2-level waveforms (E), VXY can be a 3-level waveform
- Note: this is called a “2-level” circuit since each leg is a 2-level leg
- Circuit can produce +E, 0 and -E in response to gating commands, regardless of current direction
- We can synthesize (on average) any waveform we like by switching for varying amounts of time between +E, 0, -E
- For example, for variable DC we could use:
- Q1, Q4 gated 0 < t < dT, Q2, Q3 gated dT < t < T

- Average (DC) output = Ed - E(1-d) = E(2d-1)
- Used like this (or similarly) circuit is called a “Chopper” - see H5CEDR for application to DC motor drives

Single Phase Inverter H-bridge (3)

- To get AC output, we could operate like described previously, but dynamically vary the duty cycle (d) to follow an AC demand
- This is called Pulse-Width Modulation (PWM) - see lhandout for what the waveform looks like
- For this to be effective, the switching frequency has to be an order of magnitude greater than the demand frequency
- PWM produces an output waveform with a spectrum consisting of the wanted component + distortion components clustered (sidebands) around the switching frequency and its multiples

Single Phase Inverter H-bridge (4)

- Some sort of filtering action is required to extract the desired component and eliminate the distortion
- To produce an AC voltage we could use:

- For an inductive load that requires a smooth current (eg an electrical machine), the machine inductance provides the filtering:

Single Phase Inverter Square wave operation

- Return to PWM later - simplest method of voltage/frequency control is “quasi-squarewave”
- Used to be very popular when power devices were slow and high switching frequencies were not possible
- Gate each side of the bridge with a squarewave at the desired output frequency
- Adjust phase shift between the two sides to get voltage control

- See handout for waveforms
- See handout on relationship between AC side and DC side harmonics

PWM Techniques

- 2 Basic forms for single phase (H-bridge) inverter
- 2-level PWM.
- Each diagonal pair of switches is operated together.
- Output is either +E or –E (hence name 2-level).
- Gating pattern is Q1Q4 Q2Q3 Q1Q4.
- 3-level PWM
- All possible (allowable) gating patterns are used.
- Output can be +E, 0 or –E.
- Generation of PWM gating pattern.
- Easiest method to understand is Natural Sampling (analogue method not often used now)
- Most applications now use a microprocessor, microcontroller or DSP to generate the PWM pattern using a digital modulation technique.

Natural Sampling 1

- See handout for detail of comparison process
- Definitions:

Natural Sampling 2

- Frequency ratio (FR) can be integer (synchronous PWM) or non-integer (asynchronous PWM).
- It is normal now to keep the carrier frequency fixed as the modulating frequency is varied – hence most PWM today is asynchronous.
- Modulation Index (MI) tells us how large the modulating frequency component at the inverter output will be for a given DC link voltage.
- Modulation Depth (MD) tells us how much we have modulated the pulses by (compared to an unmodulated 50% duty cycle carrier frequency squarewave).
- For Natural Sampling MI = MD (provided MD < 1)
- Hence control of amplitude and frequency of the modulating wave, provides direct frequency and voltage control at the inverter output.
- Spectrum of 2-level PWM: Modulating component + sidebands around carrier frequency + sidebands around 2 times carrier frequency etc – see Handout

Natural Sampling 3

- 3-level use the same carrier for both sides of the H-bridge, but invert the modulating wave (180O shift).
- VXO and VYO are 2-level, VXY is 3-level.
- Components clustered as sidebands around odd multiples of the carrier frequency are in-phase in VXO and VYO and therefore cancel in VXY
- Other components are in anti-phase in VXO and VYO and therefore add in VXY
- 3-level produces less distortion for given carrier (switching) frequency – see Handout

Digital PWM

- Natural sampling is not suitable for a microprocessor implementation.
- Switching instants occur at the natural intersection between a triangle wave and a sinewave.
- Equation determining the switching instants has no analytical solution (transcendental equation) and can only be solved by iteration – no good for real time calculation.
- Microprocessor implementation uses the Regular Sampling method (or something similar).
- There are no continuous modulating or carrier waves.
- Time is divided into a sequence of carrier periods of width TC.
- The modulating wave exists as a series of samples, sampled either every TC (symmetric PWM) or every TC/2 (asymmetric PWM).
- One pulse is produced within each carrier period.
- Pulsewidth depends on either one sample of the modulating wave (symmetric PWM) or two samples of the modulating wave (asymmetric PWM).

Regular SamplingSymmetric PWM

- Let SK-1, SK, SK+1 etc be the samples of the modulating wave sampled at rate (1/TC).
- Assume the modulating wave is scaled so that its peak amplitude is unity.

- Simple equations define the pulsewidths – OK for real time digital implementation.
- MD MI for regular sampling

Regular Samplingasymmetric PWM

- Let SAK-1, SBK-1, SAK, SBK, SAK+1, SBK+1 etc. be the samples of the modulating wave sampled at rate (2/TC).
- Assume the modulating wave is scaled so that its peak amplitude is unity.

- Asymmetric PWM produces less distortion than symmetric PWM for a given carrier (switching frequency)
- MD MI as for symmetric sampling

PWM Miscellaneous

- Choice of carrier frequency
- Compromise depending on switching losses in the inverter and output waveform distortion.
- Also depends on the switching device technology used.
- Typical values: 16kHz (1kW), 5kHz (100kW), 1kHz (1MW) – assuming IGBT devices.
- Other types of PWM (not a complete list)
- Space Vector PWM
- Similar to regular sampling, but derived from the “space-phasor” representation of 3-phase quantities. Popular in “Vector controlled” induction motor drives (see H54IMD)
- “Optimised PWM”
- Spectrum of PWM is defined mathematically in terms of the pulsewidths. Numerical techniques are then used to calculate the pulsewidths to meet a particular performance target.
- For example: eliminate certain harmonics, minimise weighted sum of harmonics etc.
- Not popular except in some special applications

DC Supply (E)

O

A

B

C

3-phase load

3-phase Inverter- VAO etc are 2-level (±E/2), VAB etc are 3-level (±E and 0).
- Each leg is modulated using the same carrier, but with modulating waves 120o apart (3-phase).
- The large carrier frequency component in VAO etc cancels in VAB etc.
- PWM control of inverter gives variable voltage and variable frequency output.
- Average power flow can be bidirectional if the DC source can accept power input.

3-phase AC to AC(rectifier - inverter)

RECTIFIER

DC LINK

INVERTER

3-PHASE

SUPPLY

3-Phase

AC Load

- Industry “workhorse” - made from a few kW to MW - particularly for Induction Motor drives.
- Unidirectional power flow since diode rectifier can't accept power reversal.
- Energy can only be extracted from motor (braking) if some form of resistor is connected across the DC link during this mode. Common practice in industrial drives - known as dynamic braking.
- AC supply current waveforms are poor because of diode rectifier.

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