# Power inverter

An inverter for a solar-mounted free-standing plant in Speyer, down the Rhine.
Overview of the solar inverters

A power inverter, or inverter, is an electrical power converter that changes direct current (DC) to alternating current (AC);[1] the converted AC can be at any required voltage and frequency with the use of appropriate transformers, switching, and control circuits.

Solid-state inverters have no moving parts and are used in a wide range of applications, from small switching power supplies in computers, to large electric utility high-voltage direct current applications that transport bulk power. Inverters are commonly used to supply AC power from DC sources such as solar panels or batteries.

The inverter performs the opposite function of a rectifier. The electrical inverter is a high-power electronic oscillator. It is so named because early mechanical AC to DC converters were made to work in reverse, and thus were "inverted", to convert DC to AC.[citation needed]

## Types

### Square wave

The earliest electronic inverters produced a square wave, which can be seen as a sine wave sampled twice per cycle, i.e., at the Nyquist limit.

A square wave has a very high harmonic content and a peak-to-RMS voltage ratio of 1. Because electronic loads are usually sensitive to peak voltage while resistive loads such as incandescent lamps respond to the RMS value, the square wave is unsuitable for general use.

### Modified sine wave

A "modified sine wave" (MSW) waveform spends equal time at each level in the sequence +,0,-,0,... A 240V 50 Hz inverter therefore generates +339V for 5 ms, 0V for 5 ms, -339V for 5 ms and 0V for 5 ms before repeating the cycle; the corresponding values for 120V 60 Hz are +/-170V and 4.167 ms. This can be seen as a sine wave sampled four times per cycle at the peaks and zero crossings.

The big advantage of the modified sine wave is that it has the same peak-to-RMS voltage ratio as a true sine wave, i.e., sqrt(2) = 1.414, while being as easy to generate as a square wave. This has made MSW inverters very popular. They are compatible with most loads except those unusually sensitive to the harmonic content, e.g., certain laser printers, fluorescent lighting, audio equipment, and clocks that count power line zero crossings.[2]Costs are typically ~\$0.10USD/Watt, much cheaper than true sine wave inverters.

Most AC motors will run on MSW inverters with an efficiency reduction of about 20% due to the harmonic content. [3]

### Multilevel

A multilevel inverter synthesizes a desired voltage from several levels of direct current voltage as inputs. The advantages of using multilevel topology include reduction of power ratings of power devices and lower cost. There are three topologies - diode clamped inverter, ﬂying capacitor inverter and cascaded inverter.

### Pure sine wave

A pure sine wave inverter produces a nearly perfect sine wave output (less than 3% total harmonic distortion) that is essentially the same as utility-supplied grid power. Thus it is compatible with all AC electronic devices. This is the type used in grid-tie inverters. Its design is more complex, and costs more per unit power.[4]

### Resonant

Resonant inverters produce sine waves with LC circuits to remove the harmonics from a simple square wave. Typically there are several series- and parallel-resonant LC circuits, each tuned to a different harmonic of the power line frequency. This simplifies the electronics but the inductors and capacitors tend to be large and heavy. Its high efficiency makes this approach popular in large uninterruptible power supplies in data centers that run the inverter continuously in an "online" mode to avoid any switchover transient when power is lost.

A closely related approach uses a ferroresonant transformer, also known as a constant voltage transformer, to remove harmonics and to store enough energy to sustain the load for a few AC cycles. This property makes them useful in standby power supplies to eliminate the switchover transient that otherwise occurs during a power failure while the normally idle inverter starts and the mechanical relays are switching to its output.

### Grid tie

A grid tie inverter transmits power into the electric power distribution system. Such inverters must synchronise with grid, produce little harmonic distortion and implement elaborate precautions to avoid "islanding", feeding power into an otherwise de-energized distribution line and endangering nearby linemen.

With the popularity of grid-tied photovoltaic (solar power) systems, many grid-tie inverters include built-in maximum power point tracking.

### Synchronous

A synchronous inverter connects to a grid and allows routing to or from the grid depending on need.

### Stand-alone

A stand-alone inverter is the opposite of a grid tie inverter. They are commonly used on vehicles and in remote renewable energy systems producing power from photovoltaic panels and small wind turbines.

To minimize cost, most stand-alone inverters are of the modified sine wave type except when a specific load cannot tolerate the high harmonic content.

### Solar

A solar inverter can be fed into a commercial electrical grid or used by an off-grid electrical network. Solar inverters have special functions adapted for use with photovoltaic arrays, including maximum power point tracking and anti-islanding protection.

### Solar micro

A solar micro-inverter converts direct current from a single solar panel. Micro-inverters contrast with conventional string or central inverter devices, which are connected to multiple solar panels.

### Air conditioner

An air conditioner inverter modulates the frequency of the alternating current to control the speed of the air conditioner motor to achieve continuous adjustment of temperature control.

### CCFL

A CCFL inverter powers a cold cathode fluorescent lamp.

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## Applications

### DC power source utilization

Inverter designed to provide 115 VAC from the 12 VDC source provided in an automobile. The unit shown provides up to 1.2 amperes of alternating current, or enough to power two sixty watt light bulbs.

An inverter converts the DC electricity from sources such as batteries, solar panels, or fuel cells to AC electricity. The electricity can be at any required voltage; in particular it can operate AC equipment designed for mains operation, or rectified to produce DC at any desired voltage.

Micro-inverters convert direct current from individual solar panels into alternating current for the electric grid. They are grid tie designs by default.

### Uninterruptible power supplies

An uninterruptible power supply (UPS) uses batteries and an inverter to supply AC power when main power is not available. When main power is restored, a rectifier supplies DC power to recharge the batteries.

### Induction heating

Inverters convert low frequency main AC power to higher frequency for use in induction heating. To do this, AC power is first rectified to provide DC power. The inverter then changes the DC power to high frequency AC power.

### HVDC power transmission

With HVDC power transmission, AC power is rectified and high voltage DC power is transmitted to another location. At the receiving location, an inverter in a static inverter plant converts the power back to AC. The inverter must be synchronized with grid frequency and phase and minimize harmonic generation.

### Variable-frequency drives

A variable-frequency drive controls the operating speed of an AC motor by controlling the frequency and voltage of the power supplied to the motor. An inverter provides the controlled power. In most cases, the variable-frequency drive includes a rectifier so that DC power for the inverter can be provided from main AC power. Since an inverter is the key component, variable-frequency drives are sometimes called inverter drives or just inverters.

VFDs that operate directly from an AC source without first converting it to DC are called cycloconverters. They are now commonly used on large ships to drive the propulsion motors.

### Electric vehicle drives

Adjustable speed motor control inverters are currently used to power the traction motors in some electric and diesel-electric rail vehicles as well as some battery electric vehicles and hybrid electric highway vehicles such as the Toyota Prius, BYD e6 and Fisker Karma. Various improvements in inverter technology are being developed specifically for electric vehicle applications.[5] In vehicles with regenerative braking, the inverter also takes power from the motor (now acting as a generator) and stores it in the batteries.

### Air conditioning

An inverter air conditioner uses a variable-frequency drive to control the speed of the motor and thus the compressor.

### Electroshock weapons

Electroshock weapons and tasers have a DC/AC inverter to generate several hundred V AC out of a small 9 V DC battery. The AC is doubled or quadrupled in a diode/capacitor voltage multiplier followed by an impulstransformer with an output of 2 - 10 kV. The principle is also used in electronic flash and bug zappers.

### The general case

A transformer allows AC voltage to be stepped up or down to a desired voltage at the same frequency. Inverters, plus rectifiers for DC, can be designed to convert from any voltage, AC or DC, to any other voltage, also AC or DC, at any desired frequency. The output power can never exceed the input power, but efficiencies can be high, with a small proportion of the power dissipated as waste heat.

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## Circuit description

Top: Simple inverter circuit shown with an electromechanical switch
and automatic equivalent
auto-switching device implemented with two transistors and split winding auto-transformer in place of the mechanical switch.
Square waveform with fundamental sine wave component, 3rd harmonic and 5th harmonic

### Basic designs

In one simple inverter circuit, DC power is connected to a transformer through the center tap of the primary winding. A switch is rapidly switched back and forth to allow current to flow back to the DC source following two alternate paths through one end of the primary winding and then the other. The alternation of the direction of current in the primary winding of the transformer produces alternating current (AC) in the secondary circuit.

The electromechanical version of the switching device includes two stationary contacts and a spring supported moving contact. The spring holds the movable contact against one of the stationary contacts and an electromagnet pulls the movable contact to the opposite stationary contact. The current in the electromagnet is interrupted by the action of the switch so that the switch continually switches rapidly back and forth. This type of electromechanical inverter switch, called a vibrator or buzzer, was once used in vacuum tube automobile radios. A similar mechanism has been used in door bells, buzzers and tattoo machines.

As they became available with adequate power ratings, transistors and various other types of semiconductor switches have been incorporated into inverter circuit designs. Certain ratings, especially for large systems (many kilowatts) use thyristors (SCR). SCRS provide large power handling capability in a semiconductor device, and can readily be controlled over a variable firing range.

### Output waveforms

The switch in the simple inverter described above, when not coupled to an output transformer, produces a square voltage waveform due to its simple off and on nature as opposed to the sinusoidal waveform that is the usual waveform of an AC power supply. Using Fourier analysis, periodic waveforms are represented as the sum of an infinite series of sine waves. The sine wave that has the same frequency as the original waveform is called the fundamental component. The other sine waves, called harmonics, that are included in the series have frequencies that are integral multiples of the fundamental frequency.

The quality of the inverter output waveform can be expressed by using the Fourier analysis data to calculate the total harmonic distortion (THD). The total harmonic distortion (THD) is the square root of the sum of the squares of the harmonic voltages divided by the fundamental voltage:

$\mbox{THD} = {\sqrt{V_2^2 + V_3^2 + V_4^2 + \cdots + V_n^2} \over V_1}$

The quality of output waveform that is needed from an inverter depends on the characteristics of the connected load. Some loads need a nearly perfect sine wave voltage supply to work properly. Other loads may work quite well with a square wave voltage.

H bridge inverter circuit with transistor switches and antiparallel diodes

There are many different power circuit topologies and control strategies used in inverter designs. Different design approaches address various issues that may be more or less important depending on the way that the inverter is intended to be used.

The issue of waveform quality can be addressed in many ways. Capacitors and inductors can be used to filter the waveform. If the design includes a transformer, filtering can be applied to the primary or the secondary side of the transformer or to both sides. Low-pass filters are applied to allow the fundamental component of the waveform to pass to the output while limiting the passage of the harmonic components. If the inverter is designed to provide power at a fixed frequency, a resonant filter can be used. For an adjustable frequency inverter, the filter must be tuned to a frequency that is above the maximum fundamental frequency.

Since most loads contain inductance, feedback rectifiers or antiparallel diodes are often connected across each semiconductor switch to provide a path for the peak inductive load current when the switch is turned off. The antiparallel diodes are somewhat similar to the freewheeling diodes used in AC/DC converter circuits.

waveform signal
transitions
per period
harmonics
eliminated
harmonics
amplified
System
Description
THD
2 - - 2-level
square wave
~45%[4]
4 3, 9, 27,... - 3-level
"modified square wave"
> 23.8%[4]
8 5-level
"modified square wave"
> 6.5%[4]
10 3, 5, 9, 27 7, 11,... 2-level
very slow PWM
12 3, 5, 9, 27 7, 11,... 3-level
very slow PWM

Fourier analysis reveals that a waveform, like a square wave, that is anti-symmetrical about the 180 degree point contains only odd harmonics, the 3rd, 5th, 7th, etc. Waveforms that have steps of certain widths and heights can attenuate certain lower harmonics at the expense of amplifying higher harmonics. For example, by inserting a zero-voltage step between the positive and negative sections of the square-wave, all of the harmonics that are divisible by three (3rd and 9th, etc.) can be eliminated. That leaves only the 5th, 7th, 11th, 13th etc. The required width of the steps is one third of the period for each of the positive and negative steps and one sixth of the period for each of the zero-voltage steps.[6]

Changing the square wave as described above is an example of pulse-width modulation (PWM). Modulating, or regulating the width of a square-wave pulse is often used as a method of regulating or adjusting an inverter's output voltage. When voltage control is not required, a fixed pulse width can be selected to reduce or eliminate selected harmonics. Harmonic elimination techniques are generally applied to the lowest harmonics because filtering is much more practical at high frequencies, where the filter components can be much smaller and less expensive. Multiple pulse-width or carrier based PWM control schemes produce waveforms that are composed of many narrow pulses. The frequency represented by the number of narrow pulses per second is called the switching frequency or carrier frequency. These control schemes are often used in variable-frequency motor control inverters because they allow a wide range of output voltage and frequency adjustment while also improving the quality of the waveform.

Multilevel inverters provide another approach to harmonic cancellation. Multilevel inverters provide an output waveform that exhibits multiple steps at several voltage levels. For example, it is possible to produce a more sinusoidal wave by having split-rail direct current inputs at two voltages, or positive and negative inputs with a central ground. By connecting the inverter output terminals in sequence between the positive rail and ground, the positive rail and the negative rail, the ground rail and the negative rail, then both to the ground rail, a stepped waveform is generated at the inverter output. This is an example of a three level inverter: the two voltages and ground.[7]

### Three phase inverters

3-phase inverter with wye connected load

Three-phase inverters are used for variable-frequency drive applications and for high power applications such as HVDC power transmission. A basic three-phase inverter consists of three single-phase inverter switches each connected to one of the three load terminals. For the most basic control scheme, the operation of the three switches is coordinated so that one switch operates at each 60 degree point of the fundamental output waveform. This creates a line-to-line output waveform that has six steps. The six-step waveform has a zero-voltage step between the positive and negative sections of the square-wave such that the harmonics that are multiples of three are eliminated as described above. When carrier-based PWM techniques are applied to six-step waveforms, the basic overall shape, or envelope, of the waveform is retained so that the 3rd harmonic and its multiples are cancelled.

3-phase inverter switching circuit showing 6-step switching sequence and waveform of voltage between terminals A and C (23-2 states)

To construct inverters with higher power ratings, two six-step three-phase inverters can be connected in parallel for a higher current rating or in series for a higher voltage rating. In either case, the output waveforms are phase shifted to obtain a 12-step waveform. If additional inverters are combined, an 18-step inverter is obtained with three inverters etc. Although inverters are usually combined for the purpose of achieving increased voltage or current ratings, the quality of the waveform is improved as well.

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## History

### Early inverters

From the late nineteenth century through the middle of the twentieth century, DC-to-AC power conversion was accomplished using rotary converters or motor-generator sets (M-G sets). In the early twentieth century, vacuum tubes and gas filled tubes began to be used as switches in inverter circuits. The most widely used type of tube was the thyratron.

The origins of electromechanical inverters explain the source of the term inverter. Early AC-to-DC converters used an induction or synchronous AC motor direct-connected to a generator (dynamo) so that the generator's commutator reversed its connections at exactly the right moments to produce DC. A later development is the synchronous converter, in which the motor and generator windings are combined into one armature, with slip rings at one end and a commutator at the other and only one field frame. The result with either is AC-in, DC-out. With an M-G set, the DC can be considered to be separately generated from the AC; with a synchronous converter, in a certain sense it can be considered to be "mechanically rectified AC". Given the right auxiliary and control equipment, an M-G set or rotary converter can be "run backwards", converting DC to AC. Hence an inverter is an inverted converter.[8][9]

### Controlled rectifier inverters

Since early transistors were not available with sufficient voltage and current ratings for most inverter applications, it was the 1957 introduction of the thyristor or silicon-controlled rectifier (SCR) that initiated the transition to solid state inverter circuits.

12-pulse line-commutated inverter circuit

The commutation requirements of SCRs are a key consideration in SCR circuit designs. SCRs do not turn off or commutate automatically when the gate control signal is shut off. They only turn off when the forward current is reduced to below the minimum holding current, which varies with each kind of SCR, through some external process. For SCRs connected to an AC power source, commutation occurs naturally every time the polarity of the source voltage reverses. SCRs connected to a DC power source usually require a means of forced commutation that forces the current to zero when commutation is required. The least complicated SCR circuits employ natural commutation rather than forced commutation. With the addition of forced commutation circuits, SCRs have been used in the types of inverter circuits described above.

In applications where inverters transfer power from a DC power source to an AC power source, it is possible to use AC-to-DC controlled rectifier circuits operating in the inversion mode. In the inversion mode, a controlled rectifier circuit operates as a line commutated inverter. This type of operation can be used in HVDC power transmission systems and in regenerative braking operation of motor control systems.

Another type of SCR inverter circuit is the current source input (CSI) inverter. A CSI inverter is the dual of a six-step voltage source inverter. With a current source inverter, the DC power supply is configured as a current source rather than a voltage source. The inverter SCRs are switched in a six-step sequence to direct the current to a three-phase AC load as a stepped current waveform. CSI inverter commutation methods include load commutation and parallel capacitor commutation. With both methods, the input current regulation assists the commutation. With load commutation, the load is a synchronous motor operated at a leading power factor.

As they have become available in higher voltage and current ratings, semiconductors such as transistors or IGBTs that can be turned off by means of control signals have become the preferred switching components for use in inverter circuits.

### Rectifier and inverter pulse numbers

Rectifier circuits are often classified by the number of current pulses that flow to the DC side of the rectifier per cycle of AC input voltage. A single-phase half-wave rectifier is a one-pulse circuit and a single-phase full-wave rectifier is a two-pulse circuit. A three-phase half-wave rectifier is a three-pulse circuit and a three-phase full-wave rectifier is a six-pulse circuit.[10]

With three-phase rectifiers, two or more rectifiers are sometimes connected in series or parallel to obtain higher voltage or current ratings. The rectifier inputs are supplied from special transformers that provide phase shifted outputs. This has the effect of phase multiplication. Six phases are obtained from two transformers, twelve phases from three transformers and so on. The associated rectifier circuits are 12-pulse rectifiers, 18-pulse rectifiers and so on...

When controlled rectifier circuits are operated in the inversion mode, they would be classified by pulse number also. Rectifier circuits that have a higher pulse number have reduced harmonic content in the AC input current and reduced ripple in the DC output voltage. In the inversion mode, circuits that have a higher pulse number have lower harmonic content in the AC output voltage waveform.

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## References

1. ^ The Authoritative Dictionary of IEEE Standards Terms, Seventh Edition, IEEE Press, 2000,ISBN 0-7381-2601-2, page 588
2. ^ "Modified Sine-Wave. Inverter Enhanced". Retrieved 2012-11-03.
3. ^ Inverter selection
4. ^ a b c d "Modified Sine-Wave Inverter Enhanced Page of". Powerelectronics.com. Retrieved 2011-01-10.
5. ^ "Power Electronics: Energy Manager for Hybrid Electric Vehicles". Oak Ridge National Laboratory Review (U.S. Department of Energy) 33 (3). 2000. Retrieved 2006-11-08.
6. ^ MIT open-courseware, Power Electronics, Spring 2007
7. ^ Rodriguez, Jose; et al. (August 2002). "Multilevel Inverters: A Survey of Topologies, Controls, and Applications". IEEE Transactions on Industrial Electronics (IEEE) 49 (4): 724–738. doi:10.1109/TIE.2002.801052.
8. ^ "Inverter FAQ". PowerStream. 2006. Retrieved 2006-11-08.
9. ^ Owen, Edward L. (January/February 1996). "Origins of the Inverter". IEEE Industry Applications Magazine: History Department (IEEE) 2 (1): 64–66. doi:10.1109/2943.476602.
10. ^ D. R. Grafham and J. C. Hey, editors, ed. (1972). SCR Manual (Fifth ed.). Syracuse, N.Y. USA: General Electric. pp. 236–239.

### General references

• Bedford, B. D.; Hoft, R. G. et al. (1964). Principles of Inverter Circuits. New York: John Wiley & Sons, Inc. ISBN 0-471-06134-4.
• Mazda, F. F. (1973). Thyristor Control. New York: Halsted Press Div. of John Wiley & Sons. ISBN 0-470-58116-6.
• Dr. Ulrich Nicolai, Dr. Tobias Reimann, Prof. Jürgen Petzoldt, Josef Lutz: Application Manual IGBT and MOSFET Power Modules, 1. Edition, ISLE Verlag, 1998, ISBN 3-932633-24-5 PDF-Version
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