Editing Power inverter (section)

==Circuit description==
[[File:Inverter ckt 01cjc.png|thumb|''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.]]
[[File:Squarewave01CJC.png|thumb|Square waveform with fundamental sine wave component, 3rd harmonic, and 5th harmonic]]

===Basic design===
In one simple inverter circuit, DC power is connected to a [[transformer]] through the center tap of the primary winding. A [[relay]] 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 (electronic)|vibrator]] or buzzer, was once used in [[vacuum tube]] automobile radios. A similar mechanism has been used in door bells, buzzers, and [[tattoo machine]]s.

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

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 [[Sine wave|sinusoidal]] waveform that is the usual waveform of an AC power supply. Using [[Fourier analysis]], [[periodic function|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.

Fourier analysis can be used 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:

: <math>\text{THD} = {\sqrt{V_2^2 + V_3^2 + V_4^2 + \cdots + V_n^2} \over V_1}</math>

===Advanced designs===
[[File:H-bridge inverter cjc.png|thumb|upright=0.5|[[H-bridge]] inverter circuit with transistor switches and antiparallel diodes]]
There are many different power [[circuit topology (electrical)|circuit topologies]] and [[control system|control strategies]] used in inverter designs.<ref>{{cite conference |last1=Unruh |first1=Roland |title=Evaluation of MMCs for High-Power Low-Voltage DC-Applications in Combination with the Module LLC-Design |book-title=22nd European Conference on Power Electronics and Applications (EPE'20 ECCE Europe) |date=Oct 2020 |pages=1–10 |isbn=978-9-0758-1536-8 |s2cid=222223518 |doi=10.23919/EPE20ECCEEurope43536.2020.9215687 |url=https://ieeexplore.ieee.org/document/9215687 |url-access=subscription}}</ref> 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. For example, an electric motor in a car that is moving can turn into a source of energy and can, with the right inverter topology (full H-bridge) charge the car battery when decelerating or braking. In a similar manner, the right topology (full H-bridge) can invert the roles of "source" and "load", that is, if for example the voltage is higher on the AC "load" side (by adding a solar inverter, similar to a gen-set, but solid state), energy can flow back into the DC "source" or battery.

Based on the basic [[H-bridge]] topology, there are two different fundamental control strategies called basic frequency-variable bridge converter and PWM control.<ref>{{cite book |title=Principles of Power Electronics |date=1991 |isbn=978-0201096897 |pages=169–193 |last1=Kassakian |first1=John G. |publisher=Addison-Wesley}}</ref> Here, in the left image of H-bridge circuit, the top left switch is named as "S1", and others are named as "S2, S3, S4" in counterclockwise order.

For the basic frequency-variable bridge converter, the switches can be operated at the same frequency as the AC in the electric grid. However, it is the rate at which the switches open and close that determines the AC frequency. When S1 and S4 are on and the other two are off, the load is provided with positive voltage and vice versa. We could control the on-off states of the switches to adjust the AC magnitude and phase. We could also control the switches to eliminate certain harmonics. This includes controlling the switches to create notches, or 0-state regions, in the output waveform or adding the outputs of two or more converters in parallel that are phase shifted in respect to one another.

Another method that can be used is PWM. Unlike the basic frequency-variable bridge converter, in the PWM controlling strategy, only two switches S3, S4 can operate at the frequency of the AC side or at any low frequency. The other two would switch much faster (typically 100&nbsp;kHz) to create square voltages of the same magnitude but for different time duration, which behaves like a voltage with changing magnitude in a larger time-scale.

These two strategies create different harmonics. For the first one, through Fourier Analysis, the magnitude of harmonics would be 4/(pi*k) (k is the order of harmonics). So the majority of the harmonics energy is concentrated in the lower order harmonics. Meanwhile, for the PWM strategy, the energy of the harmonics lie in higher-frequencies because of the fast switching. Their different characteristics of harmonics leads to different THD and harmonics elimination requirements. Similar to "THD", the conception "waveform quality" represents the level of distortion caused by harmonics. The waveform quality of AC produced directly by H-bridge mentioned above would be not as good as we want.

The issue of waveform quality can be addressed in many ways. [[Capacitor]]s and [[inductor]]s can be used to [[electronic filter|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 filter]]s 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 [[resonance|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 [[rectifier]]s or [[antiparallel (electronics)|antiparallel]] [[diode]]s 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 ''[[flyback diode|freewheeling diodes]]'' used in AC/DC converter circuits.

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{| class="wikitable" style="float:right; width:100px;"
|-
! Waveform
! Signal<br>transitions<br>per period
! Harmonics<br>eliminated
! Harmonics<br>amplified
! System<br>description
! [[Total harmonic distortion|THD]]
|-
| [[File:Square wave.PNG|160px]]
|  2 ||	 	            ||            || 2-level<br>square wave        || ~45%<ref name=Hahn/>
|-
| [[File:Sqarish wave, 3 level.PNG|160px]]
|  4 || 3, 9, 27, ...	||            || 3-level<br>modified sine wave || >23.8%<ref name=Hahn/> 
|-
| [[File:Sqarish wave, 5 level.png|160px]]
|  8 ||                 ||            || 5-level<br>modified sine wave || >6.5%<ref name=Hahn/>
|-
| [[File:Pwm 3rd and 5th harmonic removed, 2 level.PNG|160px]]
| 10 || 3, 5, 9, 27	    || 7, 11, ... || 2-level<br>very slow PWM      ||
|-
| [[File:Pwm 3rd and 5th harmonic removed, 3 level.PNG|160px]]
| 12 || 3, 5, 9, 27	    || 7, 11, ... || 3-level<br>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, 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.<ref>{{cite web |title=MIT open-courseware, Power Electronics, Spring 2007 |website=mit.edu |url=https://ocw.mit.edu/courses/6-334-power-electronics-spring-2007/resources/ch9/}}</ref>

Changing the square wave as described above is an example of pulse-width modulation. 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 (electricity)|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.<ref>{{cite journal |last=Rodriguez |first=Jose |title=Multilevel Inverters: A Survey of Topologies, Controls, and Applications |journal=IEEE Transactions on Industrial Electronics |volume=49 |issue=4 |pages=724–738 |date=August 2002 |display-authors=etal |hdl=10533/173647 |hdl-access=free |doi=10.1109/TIE.2002.801052|url=http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3239971 }}</ref>

===More on achieving a sine wave===
[[Electrical resonance|Resonant]] inverters produce sine waves with [[LC circuit]]s 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 supply|uninterruptible power supplies]] in data centers that run the inverter continuously in an "online" mode to avoid any switchover transient when power is lost.
(See related: [[Resonant inverter]])

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 [[uninterruptible power supply#Offline/standby|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.

====Enhanced quantization====
A proposal suggested in ''Power Electronics'' magazine utilizes two voltages as an improvement over the common commercialized technology, which can only apply DC bus voltage in either direction or turn it off. The proposal adds intermediate voltages to the common design. Each cycle sees the following sequence of delivered voltages: v1, v2, v1, 0, −v1, −v2, −v1, 0.<ref name="Hahn">{{cite web |last=Hahn |first=James H |title=Modified Sine-Wave Inverter Enhanced |date=August 2006 |publisher=Electronic Design |url=https://www.electronicdesign.com/technologies/power/power-supply/discrete-power-semis/article/21189030/modified-sine-wave-inverter-enhanced}}</ref>

===Three-phase inverters===
[[File:3-phase inverter cjc.png|thumb|upright=0.6|Three-phase inverter with wye connected load]]

[[Three-phase electric power|Three-phase]] inverters are used for [[variable-frequency drive]] applications and for high power applications such as [[high-voltage direct current|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.

[[File:6-step waveform CJC.png|thumb|left|upright=2|3-phase inverter switching circuit showing 6-step switching sequence and waveform of voltage between terminals A and C (2<sup>3</sup> − 2 states)]]
{{Clear}}

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.