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

𝑣𝑣𝑜𝑜𝑜𝑜𝑜𝑜𝑣𝑣𝑖𝑖𝑖𝑖

= 1

1 − 𝐷𝐷

and 𝑖𝑖𝑜𝑜𝑜𝑜𝑜𝑜𝑖𝑖𝑖𝑖𝑖𝑖

= 1

1 − 𝐷𝐷

where D, is the duty cycle of switching converter that is

𝐷𝐷 = 𝑡𝑡𝑜𝑜𝑖𝑖𝑇𝑇

Where 𝑡𝑡𝑜𝑜𝑖𝑖 = switched on time for the transistor T = switching period of the transistor which is defined by the following relation

𝑇𝑇 = 𝐿𝐿∆𝐼𝐼𝑉𝑉𝑜𝑜𝑜𝑜𝑜𝑜

𝑉𝑉𝑖𝑖𝑖𝑖(𝑉𝑉𝑜𝑜𝑜𝑜𝑜𝑜 − 𝑉𝑉𝑖𝑖𝑖𝑖)

However, with 555-timer IC’s 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

𝑃𝑃𝑜𝑜𝑜𝑜𝑜𝑜 = 𝑓𝑓𝑜𝑜𝑜𝑜𝑜𝑜𝐶𝐶𝑜𝑜𝑜𝑜𝑜𝑜𝑉𝑉𝑜𝑜𝑜𝑜𝑜𝑜2

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

𝑃𝑃𝑜𝑜𝑜𝑜𝑜𝑜 = (𝐷𝐷𝑉𝑉𝑖𝑖𝑖𝑖)2

2𝑓𝑓𝑐𝑐𝐿𝐿

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.

𝐷𝐷 = 2𝑓𝑓𝑐𝑐𝐿𝐿𝑃𝑃𝑜𝑜𝑜𝑜𝑜𝑜

𝑉𝑉𝑖𝑖𝑖𝑖

The equation above yield duty cycles greater than 100%. For the inductor rating, peak inductor current can be approximated using the following equation

𝐼𝐼𝐿𝐿(𝑝𝑝𝑝𝑝) = 2𝑃𝑃𝑜𝑜𝑜𝑜𝑜𝑜𝑓𝑓𝑐𝑐𝐿𝐿

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.

𝐼𝐼𝑆𝑆𝑆𝑆(𝑝𝑝𝑝𝑝) = 𝐼𝐼𝑃𝑃(𝑝𝑝𝑝𝑝) = 𝐼𝐼𝐿𝐿(𝑝𝑝𝑝𝑝)

Maximum average current will occur at minimum input voltage

𝐼𝐼𝑆𝑆𝑆𝑆 = 𝑃𝑃𝑜𝑜𝑜𝑜𝑜𝑜𝑉𝑉𝑖𝑖𝑖𝑖

Average power dissipation in the switch can be estimated from the following equation.

𝑃𝑃𝑆𝑆𝑆𝑆 = 𝑅𝑅𝑆𝑆𝑆𝑆(2𝑃𝑃𝑜𝑜𝑜𝑜𝑜𝑜)𝑉𝑉𝑖𝑖𝑖𝑖𝑓𝑓𝑐𝑐𝐿𝐿

Where 𝑅𝑅𝑆𝑆𝑆𝑆 = 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 1Ω.

𝐶𝐶𝑖𝑖𝑖𝑖 ≥ 1

2𝜋𝜋𝑓𝑓𝑐𝑐𝑍𝑍𝑖𝑖𝑖𝑖

Where 𝑍𝑍𝑖𝑖𝑖𝑖 = 𝐶𝐶𝑖𝑖𝑖𝑖 impedance

Output capacitance 𝐶𝐶𝑜𝑜𝑜𝑜𝑜𝑜 stores high voltage energy and also reduces EMI by restricting high frequency current paths to stop short loops. The value of 𝐶𝐶𝑜𝑜𝑜𝑜𝑜𝑜 must largely dependent on the desired ripple voltage on Vout. Generally, ripple (as a fraction of output voltage) of about 10% is adequate.

𝐶𝐶𝑜𝑜𝑜𝑜𝑜𝑜 ≥ Iout

𝑟𝑟𝑖𝑖𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 ∗ 𝑓𝑓𝑖𝑖𝑖𝑖𝑖𝑖Vout

Where Iout = output current to the inverter,

𝑅𝑅𝑖𝑖𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = Vripple(p−p)

Vout

And 𝑓𝑓𝑖𝑖𝑖𝑖𝑖𝑖= inverter frequency, both 𝐶𝐶𝑖𝑖𝑖𝑖 and 𝐶𝐶𝑜𝑜𝑜𝑜𝑜𝑜 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

𝐿𝐿𝑑𝑑𝑖𝑖(𝑡𝑡)𝑑𝑑𝑡𝑡

+ 𝑅𝑅𝑖𝑖(𝑡𝑡) = 𝑉𝑉𝑠𝑠 Its general solution is of the form

𝑖𝑖(𝑡𝑡) = 𝑉𝑉𝑠𝑠𝑅𝑅

+ 𝐴𝐴𝑟𝑟−𝑜𝑜 𝜏𝜏

Where 𝜏𝜏, the time constant for R-L Load, is 𝜏𝜏 = 𝐿𝐿𝑅𝑅, Applying the initial condition, that is

𝑖𝑖(0) = 𝐼𝐼𝑚𝑚𝑖𝑖𝑖𝑖 = −𝐼𝐼𝑚𝑚𝑚𝑚𝑚𝑚 when t = 0, we get

𝐴𝐴 = −𝑉𝑉𝑠𝑠𝑅𝑅−𝐼𝐼𝑚𝑚𝑚𝑚𝑚𝑚

Hence, the expression for the current in the circuit during t = 0 and 𝜏𝜏 = T/2 is

𝑖𝑖(𝑡𝑡) = 𝑉𝑉𝑠𝑠𝑅𝑅1 − 𝑟𝑟−𝑜𝑜 𝜏𝜏 −𝐼𝐼𝑚𝑚𝑚𝑚𝑚𝑚𝑟𝑟

−𝑜𝑜 𝜏𝜏 The current attains its maximum value at t = T/2 and is obtained from the above equation as

𝐼𝐼𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑉𝑉𝑠𝑠𝑅𝑅1 − 𝑟𝑟−𝑇𝑇 2𝜏𝜏 −𝐼𝐼𝑚𝑚𝑚𝑚𝑚𝑚𝑟𝑟

−𝑇𝑇2𝜏𝜏

Rearranging the term we get

𝐼𝐼𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑉𝑉𝑠𝑠𝑅𝑅

1 − 𝑟𝑟−𝑇𝑇 2𝜏𝜏

1 + 𝑟𝑟−𝑇𝑇 2𝜏𝜏

Hence the current in the circuit during t = 0 and t = T/2 is

𝑖𝑖(𝑡𝑡) = 𝑉𝑉𝑠𝑠𝑅𝑅1 − 𝑟𝑟−𝑜𝑜 𝜏𝜏 −

𝑉𝑉𝑠𝑠𝑅𝑅

1 − 𝑟𝑟−𝑇𝑇 2𝜏𝜏

1 + 𝑟𝑟−𝑇𝑇 2𝜏𝜏 𝑟𝑟−𝑜𝑜 𝜏𝜏

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 inverter’s 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 inverter’s 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