Introduction |
DC to AC Conversion |
There are three types of inverter. An inverter circuit which creates an ac voltage (and current) from a dc voltage source is called a voltage source inverter (VSI). Similarly, the current source inverter (CSI) creates an ac current (and voltage) from a dc current source. A third converter type is called a resonant inverter. The load is a series resonant circuit that produces a high frequency sine-wave ac voltage. The dc voltage supplying the inverters is obtained from batteries or by rectifying the line voltage. Thus energy conversion sometimes takes place twice, from ac to dc then from dc to ac. |
Voltage Source Inverters |
Voltage source inverters are used in ac motor drives and uninterruptible supply systems. They can be divided into two main categories. 1. Pulse-Width-Modulated (PWM) inverters. The input dc supply voltage is constant. The inverter controls the magnitude and the frequency of the ac output voltage from the inverter. The synthesized output PWM voltage simplifies filtering and obtains a pure sine-wave curve. 2. Square-wave inverters. The inverter has to control only the frequency of the output voltage. Therefore, the input dc voltage is controlled in order to control the magnitude of the ac output voltage. |
Harmonics |
Let us assume that a voltage signal is formed from the voltage sum of a set of sine waves. The first term in this sum is u_{1} = U_{m}.sinωt. The second term is u_{3} = (U_{m}/3).sin3ωt. The next term is u_{5} = (U_{m}/5).sin5ωt and so on. The result is a rectangular wave. Conversely, a rectangular wave could be described as the sum of odd sine-wave components. The most important is the wave u_{1} called the first harmonic or fundamental. The other components are higher harmonics. Their number and amplitude depends on the shape of the rectangular curve. |
Principles of Operation |
The voltage source inverter (VSI) is supplied from a dc voltage source. A capacitor is included in parallel to the dc supply to ensure a low internal resistance for the dc source. The output voltage is obtained by alternately closing the switch pairs S_{1}, S_{3} and S_{2}, S_{4}. When S_{1}, S_{3} are closed, the upper output terminal is positive with respect to the lower and vice-versa when S_{2}, S_{4} are closed. Thus the inverter produces an ac voltage. The output voltage formed has a rectangular (square-wave) shape. Its amplitude is equal to the supply voltage U_{d}. The output inverter current depends on the load. |
Resistive Load |
If the dc supply source is symmetrical about "0", the voltage at point "a" - u_{ao} depends on switches S_{1} and S_{4}. If S_{1} is closed the voltage at "a" is + 0.5U_{d}. Alternatively, when S_{4} is closed (S_{1} is opened), the voltage at "a" is - 0.5U_{d}. It is not permissible to simultaneously close S_{1} and S_{4}. S_{2} and S_{3} switch on and off in a similar way. The output voltage is obtained from the voltage difference u_{out} = u_{ao} - u_{bo}. The output voltage u_{out} is a square-wave with amplitude equal to U_{d}. The first harmonic (fundamental) is shown in the diagram. It may be obtained by filtering the square wave voltage (the filter is not shown in the diagram). |
Inductive Load |
The positive half wave of the output voltage is created when the switches S_{1} and S_{3} are closed. Current flows from the source +U_{d} through S_{1}, load (L and R_{L}) and S_{3} to -U_{d}. The negative half wave is formed when switches S_{2} and S_{4} are closed. Due to the energy stored in the inductor L_{L} the current through the load continues to flow in the positive direction. Thus it flows from -U_{d} through S_{4}, load and S_{2} to +U_{d}. When the inductor's energy is dissipated, the load current falls to zero and changes the direction. Now it flows from +U_{d } through S_{2}, load (L and R_{L}) and S_{4} to -U_{d}. Hence, an inductor in the load imposes a very important requirement for bi-directionally conducting switches in a VSI. |
Real Circuit |
In a real VSI the switches are implemented using power semiconductor devices - old-fashioned thyristors or transistors. An anti-parallel diode is connected to the devices. With a purely resistive load only the transistors provide power. If a load is resistive-inductive, after switching off the transistors (for example T_{1} and T_{3} ), the diodes D_{2} and D_{4} conduct. Thus the inductor feeds the stored energy back into the dc source at the beginning of the negative half period. After dissipating the stored inductor energy, T_{2} and T_{4} begin conducting. The voltage across the transistors is approximately equal to the supply voltage U_{d}. |
VSI Circuits |
Three VSI circuit topologies are primarily used: bridge, half-bridge and push-pull. The first operates with four power devices, the others with two devices. Half bridge circuits use one half of the dc supply voltage. Hence, its output voltage and power are half that of the other circuits. Push-pull circuits allow easy driving of transistors but require a transformer and the transistor voltage is twice as high. The output voltage depends on the transformer ratio. The bridge circuit is the most powerful circuit. The voltage across the transistors is equal to supply voltage U_{d}. The load could be supplied with ac via a transformer. |
Voltage Regulation |
The VSI may be controlled in more flexible way. Two legs of the bridge (T_{1}, T_{4} and T_{2}, T_{3}) can be driven by phase-shifted pulses. Then the voltages at points "a" and "b" have the shapes shown in the illustration. The output voltage consists of three different states. The third, zero state, is due to simultaneously turning on the transistors T_{1} and T_{2} or T_{3} and T_{4}. The phase shift Ψ determines the zero state duration and the amplitude (rms value) of the output voltage u_{out}. |
Three-Phase Inverter |
A three-phase VSI feeding a Y-connected load from a center-tapped dc source is shown in the illustration. It consists of three legs, each with two switches - S_{1}/S_{4}, S_{3}/S_{6}, S_{5}/S_{2}. Every leg is driven such that the next is delayed by 120°(2π/3). Each switch conducts for 180°. The voltages u_{ao}, u_{bo} and u_{co} are square-waves as shown. It may be seen that during the operating period the circuit has six different states. Three switches conduct in each state. When a switch is turned on, another switch turns off. This determines a new current path and a new circuit state. |
Waveforms |
The three-phase VSI produces a three-phase voltage system with respect to the neutral point (N) of the Y connection. The output line voltages are u_{A}, u_{B}, u_{C}. The line voltage u_{A }is positive, for example, when S_{1} is closed. The voltage is 1/3U_{d} when two of the upper switches are closed. The voltage value is 2/3U_{d} if two lower switches are closed. The voltage u_{A} is negative when S_{4} is closed. The voltage value is (-1/3U_{d} ) when two of the lower switches are closed and (-2/3U_{d} ) if two upper switches are closed. The line voltages u_{B} and u_{C} are identical but phase-shifted by 120°. |
Delta Connection |
A three-phase VSI with Δ connected load is shown in the illustration. The switches operate in the same manner as with a Y-connected load. Three switches conduct during every time interval. The voltages u_{ao}, u_{bo} and u_{co} have the same square-wave shape. Line-to line voltage u_{ab} is given by the difference u_{ab} = u_{ao} - u_{bo}. The line-to-line voltages u_{bc} and u_{ca} are identical but phase shifted by 120°. Their first harmonics are pure sine waves and are shown in the illustration. |
Scalar Voltage Sum |
Let us assume two ac voltage sources u_{1} and u_{2} are connected in series. The voltage source u_{2} is phase shifted by an angle Ψ. The load voltage is the sum of both voltages - u_{L} = u_{1} + u_{2} = U_{m}.sinωt + U_{m}.sin(ωt + Ψ). Such a sum is known as a scalar sum. If the angle Ψ = 0, the load voltage is at its maximum value. When the angle Ψ = 180° (π), the load voltage drops to zero. Note that voltage u_{1} and u_{2} have unchanged amplitude U_{m} during this regulating operation. Therefore, the load voltage may be regulated from zero to a maximum value depending on the phase-shift angle Ψ. |
VSI Voltage Sum |
Two ac voltage sources u_{1} and u_{2 }connected in series may be implemented using two VSIs. The control circuit must produce gate pulses in such a way as to phase-shift the voltage u_{2}. It is only possible to sum voltages if the VSI outputs are electrically isolated. The sum is obtained using different dc voltage sources or incorporating the output transformers in the VSI. The load voltage is the sum of both output VSI voltages, electrically isolated. It is a square-wave. The load voltage is regulated from zero to its maximum by changing the angle Ψ. |
Voltage Shape Improving |
Pulse Width Modulation - Principles |
The voltage produced from a VSI has a rectangular form. However, a lot of practical applications need a sinusoidal voltage shape. A VSI can easily produce a sine-wave form based on a sequence of square wave pulses. For this purpose a low frequency sine-wave signal called a modulated signal is sliced into short time intervals. Their duration is T_{s}, which is called the carrier period. At the mid-point of any time interval T_{s} a square wave pulse is input, the width of which is modulated in accordance with the value of the low frequency sine-wave as shown in the illustration. The method described is known as Pulse Width Modulation (PWM). The value of output voltage is determined by the modulation ratio μ. |
PWM - Possibilities |
The amplitude of an output voltage depends on the modulation ratio μ and the supply voltage U_{d}. It is less than U_{d}. Using PWM allows the rms value of the output voltage to be changed by varying the modulation ratio. Therefore, a VSI can operate with constant supply voltage, which simplifies the power circuit. Usually the ratio of carrier frequency to modulating frequency f_{s}/F is not changeable and is very high. The synthesized pulse sequence consists of a fundamental harmonic and high frequency harmonics. The lowest high frequency harmonic occurs with carrier frequency f_{s} and is easily filtered. |
Application 1 |
Application 2 |
To control the flow rate of a water pump a valve may be used. The ac motor and pump operate at maximum power and energy consumption. A PWM VSI can control both the frequency and the amplitude of the output voltage. It is used as such in adjustable speed ac motor drives. The main requirement for such ac speed motor control is keeping the voltage/frequency ratio constant. Using variable speed ac drives conserves energy significantly. |
Current Source Inverters |
The current source inverter (CSI) requires that the dc supply system functions like a dc current source. This is implemented by placing a large inductor L in series with the dc system. The positive half wave of the ac output current is formed when the thyristors Th_{1} and Th_{3} turn on. The current flows through +U_{d}, L_{d}, Th_{1}, C_{L} - R_{L}, Th_{3}, -U_{d}. When Th_{2} and Th_{4} are conducting, the negative half-wave is formed. A square-wave ac current i_{L} is created that passes through a parallel load circuit C_{L} - R_{L}. This capacitance makes the load voltage lag behind the square-wave current. The shape and amplitude of the load voltage depends on variations in C_{L} (or R_{L}). |
Thyristor Voltage and Current |
The switches in a CSI are mostly implemented using thyristors. To guarantee that the thyristor can turn off, a capacitive load impedance is required. The simplest load consists of a load resistor R_{L} and an auxiliary capacitor C_{L}. At the end of a half-period when Th_{1} and Th_{3} are conducting, the capacitor voltage has the polarity shown in the illustration. When Th_{2} and Th_{4} turn on, Th_{1} and Th_{3} are switched off by the capacitor voltage. When Th_{2} is on, it connects the capacitor C_{L} to Th_{1} and reverse biases it. Th_{2} turns off reliably if the time t^{ -} that the thyristor voltage is negative is long enough - t^{ -}=t_{q}. The thyristor current is a square wave with high di /dt, which is one disadvantage of a CSI. |
CSI Characteristics |
The main disadvantage of a CSI is the large variation in load (and thyristor) voltage when the load is changed. The load parameters (R_{L}, C_{L}, frequency) have an equal influence over the operation of the inverter. The load (thyristor) voltage may rise by a factor of 5 due to a variation in load. The load variations have an effect on the time t^{ - }when the thyristor voltage is negative. To avoid this disadvantage of CSIs, a modified CSI circuit with additional series diodes is used as shown in the diagram. This modified CSI is used in ac power drives (especially in a three-phase implementation). |
Three-Phase CSI |
A three-phase CSI with Δ connected load is shown in the illustration. A three-phase voltage and current system is formed when the appropriate thyristor turns on. At any time only two thyristors conduct simultaneously. The current flow in the circuit for every single operating stage can be seen in the diagram. The load capacitors make the load voltage lag behind the square-wave current. They provide the negative voltage for thyristor commutation. |
Parallel Resonance |
In a parallel RLC circuit the currents in the inductive I_{L} and the capacitive I_{C} branches are always 180° out of phase with one another and the current I_{CL} = | I_{L} - I_{C} |. In such a parallel RLC circuit parallel resonance occurs when the inductive reactance X_{L} equals the capacitive reactance X_{C}. For a given RLC circuit this happens at only one specific frequency called the resonant frequency f_{r}. When X_{L} = X_{C} the two branch currents are equal in magnitude. Thus the current I_{CL} is zero and the impedance of the parallel LC circuit is infinitely large. The total impedance reaches a maximum at the resonant frequency f_{r} and decreases above and below f_{r}. |
Resonant Inverters |
In the voltage and current source inverters the inverter switches operate in switched mode. The switches are objected to high switching stresses and high switching power loss. These shortcomings are removed when the voltage across the switches or the current through them is zero at the switching instant. This requires changes in converter topology. The load is an LC series resonant circuit so that these inverters are classified as resonant inverters . Another significant result is the reduction in electro-magnetic influence (EMI). For proper operation resonant inverters require a dc voltage source. Widespread applications include induction heating and dc-to-dc converters. |
Series Resonance |
Resonance in an electrical circuit acts as the basis for frequency tuning. In series RLC circuits inductor voltage U_{L} and capacitor voltage U_{C} effectively subtract because they are always 180° out of phase with each other as illustrated by the waveforms. In a series RLC circuit series resonance occurs when the inductive reactance X_{L} equals the capacitive reactance X_{C}. For a given RLC circuit this only happens at one specific frequency called the resonant frequency f_{r}. Since X_{L} = X_{C} the reactances effectively cancel out and the total impedance Z is purely resistive. The total impedance is a minimum at resonance frequency f_{r, }but increases above and below f_{r}. |
Thyristor Circuit |
The most popular thyristor bridge circuit is shown in the diagram. The first (positive) half-wave of the ac output voltage is formed when thyristors Th_{1} and Th_{3} turn on. The current flows through +U_{d}, L_{o}_{1}, Th_{1}, L_{o}_{2}, C_{o}, R_{L}, Th_{3}, -U_{d}. It has a sinusoidal form, rises to its maximum value I_{m} and falls to zero. This causes the thyristors to turn off. No current flows and no changes occur in the circuit until the thyristor pair Th_{2} and Th_{4} switch on. Then the current flows through the load in the opposite direction. The negative half-period of the load voltage is generated. An ac output voltage is produced from a dc supply. Due to the resonance, the capacitor voltage U_{C}_{max} is greater than the supply voltage U_{d}. |
Thyristor Voltage and Current |
An important feature of resonant inverters is self-commutation; once the thyristor is turned on, it initiates a process which causes the thyristor to turn off. The anode-cathode thyristor voltage at the end of every half-period is defined by the difference (U_{d} - U_{C}_{max}). Because the capacitor voltage U_{C}_{max} > U_{d}, the thyristor voltage is negative and causes it to turn off. The time t^{ -}, when the thyristor voltage is negative, must be enough to ensure that the thyristor turns off reliably (t^{ }=t_{q}). The current through the thyristor has a sinusoidal form. |
Transistor Circuit 1 |
The circuit is shown in the diagram. Its mode of operation depends on the relation between the switching frequency f_{s} (respective period T_{s} ) and the series resonant frequency f_{o} (T_{o}). If T_{s} > 2T_{o} and T_{1}, T_{3} are on, the load current flows through +U_{d}, T_{1}, L_{o}, C_{o}, R_{L}, T_{3}, -U_{d}. It has a sinusoidal form, reaches maximum and falls to zero. At zero current the capacitor voltage reaches its maximum value, higher than the supply voltage. This creates the opportunity for current to flow in the opposite direction from the capacitor's positive terminal through L_{o}, D_{1}, U_{d}, D_{1}, R_{L}, to the capacitor's negative terminal. T_{2} and T_{4} operate in the same manner. |
Transistor Circuit 1 |
When T_{o} < T_{s} < 2T_{o} and T_{1}, T_{3} are on, the load current flows through +U_{d}, T_{1}, L_{o}, C_{o}, R_{L}, T_{3}, -U_{d}. It reaches maximum and falls to zero. Then current flows in the opposite direction - through C_{o}, L_{o}, D_{1}, U_{d}, D_{3}, R_{L}. At a certain instant the transistors T_{2} and T_{4} turn on. This occurs when the load current is non-zero. Hence, conditions when switching on the transistor are undesirable: voltage is high (U_{d} ) and current is non-zero. When switching off the transistor, conditions are ideal - current and voltage are both zero. Switching the transistor at zero current is known as ZCS (zero current switching). Similarly ZVS means zero voltage switching. |
Transistor Circuit 2 |
When the transistors T_{1} and T_{3} switch on, the current flows through +U_{d}, T_{1}, L_{o}, C_{o}, R_{L}, T_{3}, -U_{d}. The transistors turn off before the natural end of the resonant half-wave. Because of the energy stored in series inductance L_{s}, the current continues to flow in the same direction through -U_{d}, D_{4}, L_{o}, C_{o}, R_{L}, D_{2}, +U_{d}. Hence, conditions for switching on the transistor are ideal - current and voltage are both zero. Conditions for switching off the transistor are not ideal: voltage is high (U_{d} ) and current is non-zero. The main advantage of transistor resonant inverters is that the voltage across the transistors changes between 0 V and U_{d}. It is not dependent on the Q-factor of the resonant circuit. |
DC to DC Application |
Since transistor switching losses in resonant inverters are very small, they are used in high and very high frequency applications involving frequencies of tens or hundreds of kilohertz. A typical application is the use of resonant inverters in dc-to-dc converters. The circuit is shown in the diagram. The rectifier included in the inverter circuit rectifies the high frequency ac resonant current. Thus, the load current is a sequence of positive sinusoidal half-waves with very high frequency. This reduces the need for filtering and makes it very easy to produce an almost pure dc voltage. |