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This is a document on inverter design with references to DC AC inverters made by Nova Electric at http://www.novaelectric.com
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UNIVERSITY OF GUYANA
ELE 4209 ASSIGNMENT#1
Inverter Design
Jeremy Rathanum - 11/0935/2381
28/04/2014 submission Faculty of Technology
Introduction
Electrical power is usually transmitted and used in the form of alternating current. However, some kinds of electrical generation and storage devices produce direct current, examples being PV modules and batteries. An inverter is a power electronic apparatus which converts DC to AC, allowing the DC power from these generators to be used with ordinary AC appliances, and/or mixed with the existing electrical grid. The World demand for electrical energy is constantly increasing and conventional energy resources are diminishing and even threatened to be depleted. With the increasing popularity of alternative power sources, such as solar and wind, the need for static inverters to convert dc energy stored in batteries to conventional ac form has increased substantially. This conversion can either be achieved by transistors or by SCRs (silicon controlled rectifiers). For lower and medium power outputs, transistorised inverters are suitable but for high power outputs, SCRs should be used.
This design assignment can be said to be divided into two parts: - a. DC-DC Converter b. DC-AC Inverter
In designing the DC-DC converter, the following was considered: -
Figure showing Boost converter schematic diagram
The output to the input voltage gain of the inverter is given by
๐ฃ๐ฃ๐๐๐๐๐๐๐ฃ๐ฃ๐๐๐๐
= 1
1 โ ๐ท๐ท
and ๐๐๐๐๐๐๐๐๐๐๐๐๐๐
= 1
1 โ ๐ท๐ท
where D, is the duty cycle of switching converter that is
๐ท๐ท = ๐ก๐ก๐๐๐๐๐๐
Where ๐ก๐ก๐๐๐๐ = switched on time for the transistor T = switching period of the transistor which is defined by the following relation
๐๐ = ๐ฟ๐ฟโ๐ผ๐ผ๐๐๐๐๐๐๐๐
๐๐๐๐๐๐(๐๐๐๐๐๐๐๐ โ ๐๐๐๐๐๐)
However, with 555-timer ICโs an inexpensive regulated SMPS is constructed, feedback
and pulse width modulation are shown below. If the desired inverter frequency and the voltage are known, the power consumed by the switching on and off of the converter can be estimated by the following equation
๐๐๐๐๐๐๐๐ = ๐๐๐๐๐๐๐๐๐ถ๐ถ๐๐๐๐๐๐๐๐๐๐๐๐๐๐2
Figure showing DC-DC Boost Converter
Neglecting switch resistance, inductor losses, and other parasitic, the relationship between these parameters can be approximated by the following
๐๐๐๐๐๐๐๐ = (๐ท๐ท๐๐๐๐๐๐)2
2๐๐๐๐๐ฟ๐ฟ
Selection of a converter frequency is very important, since many applications require
certain frequencies for EMI reasons. Higher switching frequencies allow the use of smaller inductors but lead to high switching losses. Conversely, lower frequencies can reduce switching losses but require large inductors. Converter in the range of 20 kHz-100 kHz are generally suitable. Duty cycle is calculated as follows.
๐ท๐ท = 2๐๐๐๐๐ฟ๐ฟ๐๐๐๐๐๐๐๐
๐๐๐๐๐๐
The equation above yield duty cycles greater than 100%. For the inductor rating, peak inductor current can be approximated using the following equation
๐ผ๐ผ๐ฟ๐ฟ(๐๐๐๐) = 2๐๐๐๐๐๐๐๐๐๐๐๐๐ฟ๐ฟ
For switching transistor Qsw, the most important parameters are break down voltage, on
resistance, peak current, and power dissipation. For the diode, the important parameters are reverse break down voltage, peak repetitive current, and average forward current and reverse recovery time. Since peak inductor current also flows through the switch and the diode, it may be used to rate these components as well.
๐ผ๐ผ๐๐๐๐(๐๐๐๐) = ๐ผ๐ผ๐๐(๐๐๐๐) = ๐ผ๐ผ๐ฟ๐ฟ(๐๐๐๐)
Maximum average current will occur at minimum input voltage
๐ผ๐ผ๐๐๐๐ = ๐๐๐๐๐๐๐๐๐๐๐๐๐๐
Average power dissipation in the switch can be estimated from the following equation.
๐๐๐๐๐๐ = ๐ ๐ ๐๐๐๐(2๐๐๐๐๐๐๐๐)๐๐๐๐๐๐๐๐๐๐๐ฟ๐ฟ
Where ๐ ๐ ๐๐๐๐ = switch on resistance
Input capacitance Cin functions as an input bypass capacitor to reduce the effective source impedance and also EMI by restricting high frequency current paths to short loops.. For the best performance Cin impedance should be less than 1ฮฉ.
๐ถ๐ถ๐๐๐๐ โฅ 1
2๐๐๐๐๐๐๐๐๐๐๐๐
Where ๐๐๐๐๐๐ = ๐ถ๐ถ๐๐๐๐ impedance
Output capacitance ๐ถ๐ถ๐๐๐๐๐๐ stores high voltage energy and also reduces EMI by restricting high frequency current paths to stop short loops. The value of ๐ถ๐ถ๐๐๐๐๐๐ must largely dependent on the desired ripple voltage on Vout. Generally, ripple (as a fraction of output voltage) of about 10% is adequate.
๐ถ๐ถ๐๐๐๐๐๐ โฅ Iout
๐๐๐๐๐๐๐๐๐๐๐๐ โ ๐๐๐๐๐๐๐๐Vout
Where Iout = output current to the inverter,
๐ ๐ ๐๐๐๐๐๐๐๐๐๐ = Vripple(pโp)
Vout
And ๐๐๐๐๐๐๐๐= inverter frequency, both ๐ถ๐ถ๐๐๐๐ and ๐ถ๐ถ๐๐๐๐๐๐ should be high frequency types
In designing the DC-AC inverter, the following was considered: -
However, in this part H-bridge inverter topology was adopted. The half bridge inverter in the simplest form is shown is in the figure below. H-bridge inverter topology has lower number of switches and simple control. The duration of the dead band should be large enough to allow the switch that is turned off to close before the other switch, to start conducting. The advantage of H-bridge inverter topology has lower number of switches and simple control. The differential equation for the current from 0 = t to t = T/2 governing the current and voltage flows of half-bridge inverter may be written as
๐ฟ๐ฟ๐๐๐๐(๐ก๐ก)๐๐๐ก๐ก
+ ๐ ๐ ๐๐(๐ก๐ก) = ๐๐๐ ๐ Its general solution is of the form
๐๐(๐ก๐ก) = ๐๐๐ ๐ ๐ ๐
+ ๐ด๐ด๐๐โ๐๐ ๐๐
Where ๐๐, the time constant for R-L Load, is ๐๐ = ๐ฟ๐ฟ๐ ๐ , Applying the initial condition, that is
๐๐(0) = ๐ผ๐ผ๐๐๐๐๐๐ = โ๐ผ๐ผ๐๐๐๐๐๐ when t = 0, we get
๐ด๐ด = โ๐๐๐ ๐ ๐ ๐ โ๐ผ๐ผ๐๐๐๐๐๐
Hence, the expression for the current in the circuit during t = 0 and ๐๐ = T/2 is
๐๐(๐ก๐ก) = ๐๐๐ ๐ ๐ ๐ 1 โ ๐๐โ๐๐ ๐๐ โ๐ผ๐ผ๐๐๐๐๐๐๐๐
โ๐๐ ๐๐ The current attains its maximum value at t = T/2 and is obtained from the above equation as
๐ผ๐ผ๐๐๐๐๐๐ = ๐๐๐ ๐ ๐ ๐ 1 โ ๐๐โ๐๐ 2๐๐ โ๐ผ๐ผ๐๐๐๐๐๐๐๐
โ๐๐2๐๐
Rearranging the term we get
๐ผ๐ผ๐๐๐๐๐๐ = ๐๐๐ ๐ ๐ ๐
1 โ ๐๐โ๐๐ 2๐๐
1 + ๐๐โ๐๐ 2๐๐
Hence the current in the circuit during t = 0 and t = T/2 is
๐๐(๐ก๐ก) = ๐๐๐ ๐ ๐ ๐ 1 โ ๐๐โ๐๐ ๐๐ โ
๐๐๐ ๐ ๐ ๐
1 โ ๐๐โ๐๐ 2๐๐
1 + ๐๐โ๐๐ 2๐๐ ๐๐โ๐๐ ๐๐
Figure showing Half-bridge inverter with dual supply and single supply
The design topology which was adopted is shown below, with two stages; boost converter and half-bridge inverter, and their controls.
Figure showing DC-AC inverter circuit design
Figure showing comparison of other converters compared to the boost converter
Figure showing the grapf of the gain to the duty cycle from the simulation results
Figure Showing a DC-DC then to a DC-AC configuration
Figure showing Converter output from simulation
Figure showing output wave from the two AND-gate
Figure showing inverter output voltage from the simulation
Protective Measures Reverse Polarity
A lot of electronic equipment designed to be operated from a battery is fitted with an internal diode in series with one battery lead, to protect the equipment from damage if the connections to the battery are accidentally reversed. But this type of reverse polarity is generally not fitted to DC-AC inverters, because of the heavy current drain involved. The additional voltage drop introduced by a diode would degrade the inverterโs regulation too much, quite apart from wasting power and hence reducing the overall efficiency.
If reverse polarity protection is provided, this is usually in the form of a protective fuse or circuit breaker in series with the battery leads, plus a reversed-polarity power diode connected across the inverterโs DC input. This means that when the battery leads are connected with the correct polarity, the diode is reverse biased and remains dormant. But if the battery connections are accidentally reversed, the diode is forward biased and suddenly conducts, blowing the fuse and hopefully protecting the inverter itself.
This system generally does provide protection against reversed-polarity damage to most of the inverter circuitry, without degrading its efficiency or output regulation. However the price you pay is that an accidental reversal of the battery connections still blows a fairly expensive high-current fuse, and sometimes also destroys the protective shunt diode as well.
Overload Protection
Considering the inverter protection, the designers usually employ special protection devices and control circuits. The most common form of overcurrent protection is fusing but this method is not always effective because fuses have relatively slow response-time, so additional protective equipment is required, such as crowbar circuits or a di/dt limiting inductance.
The DC supply and load-side transients can be suppressed with filters, which have the disadvantage of increasing the inverter power losses, cost and weight.
Current source inverters (CSI) have an inherent over-current protection capability, since proper design of the DC link inductance can provide protection against overload conditions.
Voltage source inverters (VSI) include an L-C filter at the output stage thus, in case of an output short-circuit condition, the filter inductance limits the output current rising rate. In both preceding cases, the high inductance value leads to inverter size and power losses increase. The inverter output current, load voltage and filter capacitor current are sensed and compared to preset limits. If any of the above quantities exceeds the preset limits, an inhibit signal shuts off the DC power supply.
Figure showing an inverter protection circuit
Low Battery Cutoff Plus Integrated Overload Protection The figure below shows a very simple circuit set up which performs the function of an overload sensor and also as an under voltage detector. In both the cases the circuit trips the relay for protecting the output under the above conditions. Transistor T1 is wired as a current sensor, where the resistor R1 forms the current to voltage converter. The battery voltage has to pass through R1 before reaching the load at the output and therefore the current passing through it is proportionately transformed into voltage across it.
This voltage when crosses the 0.6V mark, triggers T1 into conduction. The conduction of T1 grounds the base of T2 which gets immediately switched Off. The relay is also consequently switched OFF and so is the load. T1 thus takes care of the over load and short circuit conditions. Transistor T2 has been introduced for responding to T1's actions and also for detecting low voltage conditions. When the battery voltage falls beyond a certain low voltage threshold, the base current of T2 becomes sufficiently low such that it's no longer able to hold the relay into conduction and switches it OFF and also the load.
Grounding
The rules for grounding electrical systems have evolved over time. Boat builders, installers, and electricians continue to recognize hazards and increase safety measures. Battery chargers were originally treated like any other small appliance, first without having any safety ground as was common through the 1950's, and then by adding a safety ground to reduce shock hazards during faults.
It was found that faults in the DC wiring or the DC side of chargers could generate fires because high current could flow back from the batteries, so a fuse was added between inverters or chargers and the battery system. As the capacity of chargers increased, and with the introduction of inverters, these DC fuses became quite large. It was then determined that a fire hazard exists when a DC fault in a charger or inverter can pass DC current into the AC safety ground wire. The AC safety ground was not sized for the high DC currents, so a high capacity DC grounding wire is now required by standards A-20 and A-25.
Now three critical grounding wires for these systems have been identified. This may seem excessive, but this combination of grounding conductors has been shown to give protection against a wide variety of faults.
Reference http://www.bluesea.com/support/articles/DC_and_AC_Circuit_Wiring http://homemadecircuitsandschematics.blogspot.com/2013/03/how-to-design-inverter-basic-circuit.html http://www.ti.com/solution/solar_power_inverters http://www.scribd.com/doc/7378809/Power-Inverter-Hard-Ware-Design http://www.allaboutcircuits.com/worksheets/proj_inv.html http://www.novaelectric.com/ http://www.wiringcircuit.com/powerinverter/Basic_Theory_of_DC_to_AC_Inverters_1238.html
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