DEPARTMENT: ELECTRICAL AND POWER ENGINEERING
COURSE NAME: POWER ELECTRONICS CONVERTER
COURSE CODE: EE8403
TASK: GROUP ASSIGNMENT
GROUP : CARRY GROUP
THREE PHASE INVERTERS
A three-phase inverter is a power electronic device used to convert fixed
DC power to variable three phase AC power. Generally, these are used in
high power and variable frequency drive applications like HVDC power
transmission. A basic three-phase inverter includes three single phase
inverter switches where each switch can be connected to one of the three
load terminals as shown bellow;
T1
D1
T3
A
D3
T5
D5
B
C
VDC
T4
D4
A
T6
B
Z
C
Z
N
D6
Z
T2
D2
• Generally, the three arms of this inverter will be delayed with 120degree angle to generate a 3-phase AC supply. The switches used in the
inverter have 50% of ratio and switching can be occurred after every 60
degrees angle.
• In this, three inverters with single phase are placed across a similar DC
source. The pole voltages within the three-phase inverter are equivalent
to the pole voltages within the half-bridge inverter with a single phase.
• In three-phase inverter like single-phase inverter there are two
conduction mode, a 180-degree conduction mode and 120-degree
conduction mode. That is, in 180-degree conduction mode, each device
will be in conduction mode, every electronic device will be in
conduction state with 120-degree
MATHEMATICAL MODEL OF OPERATION.
Let us consider a three-phase inverter with star connected purely resistive
load as shown below;
T1
T3
A
T5
B
C
VDC
T4
T6
A
B
Z
C
Z
N
T2
Z
For 180° conduction mode;
The control scheme is;
T4
T1
T6
T5
0
T6
T3
T2
T5
240
300
360
In 180° conduction mode, three switches are conducting at the same time.
Waveforms of phase voltage and line voltage.
From 0° to 60°, T1, T6 and T5 are conducting.
Equivalent circuit diagram will be;
• VAN = VCN
Vdc
=
A
C
Z
×𝑍 2
3𝑍 2
• VNB = Vdc - VAN = Vdc 2
=
1
V
3 dc
1
V
3 dc
=
Z
VDC
N
Z
2
V
3 dc
B
• ⸫ VBN = - Vdc
3
From 60° to 120°, T1, T6 and T2 are conducting.
Equivalent circuit diagram will be;
• VAN
Vdc
=
×𝑍
2
= Vdc
3𝑍 2
3
2
1
• VNB = VNC = Vdc - VAN = Vdc - Vdc = Vdc
• ⸫ VBN = VCN = -
A
1
V
3 dc
3
Z
VDC
N
3
Z
B
Z
C
From 120° to 180°, T1, T3 and T2 are conducting.
Equivalent circuit diagram will be;
• VAN = VBN
Vdc
=
×𝑍 2
3𝑍 2
• VNC = Vdc - VAN = Vdc -
=
1
V
3 dc
1
V
3 dc
=
A
B
Z
Z
VDC
N
2
V
3 dc
Z
2
• ⸫ VCN = - Vdc
3
C
From 180° to 240°, T4, T3 and T2 are conducting.
Equivalent circuit diagram will be;
Vdc × 𝑍 2
• VBN =
= Vdc
3𝑍 2
3
• VNA = VNC = Vdc - VAN = Vdc • ⸫ VAN = VCN = -
1
V
3 dc
2
V
3 dc
=
1
V
3 dc
B
Z
VDC
N
Z
A
Z
C
From 240° to 300°, T4, T3 and T5 are conducting.
Equivalent circuit diagram will be;
Vdc × 𝑍 2 1
• VBN = VCN =
= Vdc
3𝑍 2
3
1
B
C
Z
Z
VDC
N
2
• VNA = Vdc – VBN = Vdc - Vdc = Vdc
3
3
• ⸫ VAN = -
Z
2
V
3 dc
A
From 300° to 360°, T4, T6 and T5 are conducting.
Equivalent circuit diagram will be;
Vdc × 𝑍 2
• VCN =
= Vdc
3𝑍 2
3
• VNA = VNB = Vdc – VCN = Vdc • ⸫ VAN = VBN = -
1
V
3 dc
2
V
3 dc
=
1
V
3 dc
C
Z
VDC
N
Z
A
Z
B
Phase voltage waveforms are;
2/3Vdc
1/3Vdc
-1/3Vdc
-2/3Vdc
VBN
2/3Vdc
1/3Vdc
-1/3Vdc
-2/3Vdc
VCN
2/3Vdc
1/3Vdc
-1/3Vdc
-2/3Vdc
60
120 180 240 300 360
Line voltages;
𝑉𝐴𝐵 = 𝑉𝐴𝑁 − 𝑉𝐵𝑁 , 𝑉𝐵𝐶 = 𝑉𝐵𝑁 − 𝑉𝐶𝑁 , and 𝑉𝐶𝐴 = 𝑉𝐶𝑁 − 𝑉𝐴𝑁
Then;
From 0° to 60°;
1
2
V = Vdc
3 dc
2
1
− Vdc − Vdc = −Vdc
3
3
1
2
V − Vdc = 0
3 dc
3
• 𝑉𝐴𝐵 = Vdc +
3
• 𝑉𝐵𝐶 =
• 𝑉𝐶𝐴 =
From 60° to 120°;
• 𝑉𝐴𝐵 =
• 𝑉𝐵𝐶 =
• 𝑉𝐶𝐴 =
2
1
V + Vdc = Vdc
3 dc
3
1
1
− Vdc + Vdc = 0
3
3
1
2
− Vdc − Vdc = −Vdc
3
3
From 120° to 180°;
• 𝑉𝐴𝐵 =
• 𝑉𝐵𝐶 =
• 𝑉𝐶𝐴 =
1
1
V − Vdc = 0
3 dc
3
1
2
Vdc + Vdc = Vdc
3
3
2
1
− Vdc − Vdc = −Vdc
3
3
From 180° to 240°;
• 𝑉𝐴𝐵 =
• 𝑉𝐵𝐶 =
• 𝑉𝐶𝐴 =
1
2
− Vdc − Vdc =
3
3
2
1
V − Vdc = Vdc
3 dc
3
1
1
− Vdc − Vdc = 0
3
3
−Vdc
From 240° to 300°;
• 𝑉𝐴𝐵 = −
• 𝑉𝐵𝐶 =
• 𝑉𝐶𝐴 =
2
V
3 dc
−
1
V
3 dc
1
1
Vdc − Vdc
3
3
1
2
Vdc + Vdc
3
3
= −Vdc
=0
= Vdc
From 300° to 360°;
• 𝑉𝐴𝐵 =
• 𝑉𝐵𝐶 =
• 𝑉𝐶𝐴 =
1
1
− Vdc + Vdc = 0
3
3
1
2
− Vdc − Vdc = −Vdc
3
3
2
1
Vdc + Vdc = Vdc
3
3
Line voltage waveforms are;
VAB
Vdc
60 120 180 240 300 360
-Vdc
VBC
Vdc
-Vdc
VCA
Vdc
-Vdc
Rms phase voltage (Vprms);
• Vprms =
2
1 𝑉𝑑𝑐
( (
𝜋 9
𝜋
3
× +
2
𝜋𝑉𝑑𝑐
27
+
2
𝑉𝑑𝑐
9
𝜋
3
× )) =
2
𝑉
3 𝑑𝑐
Rms line voltage (VLrms);
• VLrms =
2
1 2𝜋𝑉𝑑𝑐
(
)
𝜋
3
=
2
𝑉
3 𝑑𝑐
Fourier series of phase voltage (vp(t))
• vp(t) =
∞
2𝑉𝑑𝑐
sin(𝑛𝜔𝑜 𝑡)
𝑘=6𝑘±1 𝑛𝜋
Fourier series of line voltage (vL(t))
• vL(t) =
∞
4𝑉𝑑𝑐
𝑛𝜋
𝑠𝑖𝑛 s𝑖𝑛
𝑛𝜋
3
𝑘=6𝑘±1
(𝑛𝜔𝑜 𝑡 +
𝑛𝜋
)
6
For 120° conduction mode;
The control scheme is;
T1
T4
T6
T3
T6
T2
0
60
120
T5
180
240
300
360
In 120° conduction mode, two switches are on at the same time
From 0° to 60° T1 and T6 are on. The equivalent circuit is;
By using voltage divider rule
•
VAN = 12𝑉𝑑𝑐
VBN = − 12𝑉𝑑𝑐
•
• VCN = 0
A
Z
VDC
N
Z
B
From 60° to 120° T1 and T2 are on. The equivalent circuit is;
• VAN = 12𝑉𝑑𝑐
• VBN =0
• VCN = − 12𝑉𝑑𝑐
From 120° to 180° T3 and T2 are on. The equivalent circuit is;
• VAN = 0
• VBN = 12𝑉𝑑𝑐
• VCN = − 12𝑉𝑑𝑐
From 180° to 240° T3 and T2 are on. The equivalent circuit is;
• VAN = − 12𝑉𝑑𝑐
• VBN = 12𝑉𝑑𝑐
• VCN = 0
A
Z
VDC
N
Z
C
B
Z
VDC
N
Z
C
B
Z
VDC
N
Z
A
From 240° to 300° T3 and T2 are on. The equivalent circuit is;
• VAN = − 12𝑉𝑑𝑐
• VBN = 0
• VCN = 12𝑉𝑑𝑐
From 300° to 360° T3 and T2 are on. The equivalent circuit is;
• VAN = 0
• VBN = − 12𝑉𝑑𝑐
• VCN = 12𝑉𝑑𝑐
C
Z
VDC
N
Z
A
C
Z
VDC
N
Z
B
Line voltages
• 𝑉𝐴𝐵 = 𝑉𝐴𝑁 − 𝑉𝐵𝑁 , 𝑉𝐵𝐶 = 𝑉𝐵𝑁 − 𝑉𝐶𝑁 , and 𝑉𝐶𝐴 = 𝑉𝐶𝑁 − 𝑉𝐴𝑁
From 0° to 60°
• VAB =𝑉𝑑𝑐
• VBC = 12𝑉𝑑𝑐
• VCA = − 12𝑉𝑑𝑐
From 60° to 120°
• VAB = 12𝑉𝑑𝑐
• VBC = 12𝑉𝑑𝑐
• VCA = − 12𝑉𝑑𝑐
From 120° to 180°
• VAB = − 12𝑉𝑑𝑐
• VBC =𝑉𝑑𝑐
• VCA = − 12𝑉𝑑𝑐
From 180° to 240°
• VAB = −𝑉𝑑𝑐
• VBC = 12𝑉𝑑𝑐
• VCA = − 12𝑉𝑑𝑐
From 240° to 300°
• VAB =− 12𝑉𝑑𝑐
• VBC =− 12𝑉𝑑𝑐
• VCA = 𝑉𝑑𝑐
From 300° to 360°
• VAB = 12𝑉𝑑𝑐
• VBC = −𝑉𝑑𝑐
• VCA = 12𝑉𝑑𝑐
Phase voltage and line voltage waveforms
VAB
VAN
Vdc
1
1
60
-1
/2Vdc
/2Vdc
120
180
240
300
360
/2Vdc
60
- Vdc
-1
/2Vdc
VBC
VBN
Vdc
1
-1
1
/2Vdc
/2Vdc
/2Vdc
- Vdc
-1
/2Vdc
VCA
VCN
Vdc
1
1
-1
/2Vdc
/2Vdc
/2Vdc
- Vdc
-1
/2Vdc
120
180
240
300
360
Rms phase voltage
2
1 𝑉𝑑𝑐
(
𝜋 4
• Vprms =
×
2𝜋
)
3
𝑉𝑑𝑐
6
• Vprms =
• Rms line current
• VLrms =
• VLrms =
2
1 𝑉𝑑𝑐
( (
𝜋 4
𝑉𝑑𝑐
2
𝜋
3
× +
2
𝜋𝑉𝑑𝑐
3
+
2
𝑉𝑑𝑐
4
𝜋
3
× ))
= 3𝑉𝑝𝑟𝑚𝑠
Fourier series expression;
• Vp(𝑡) =
∞
2𝑉𝑑𝑐
𝑛𝜋
𝑠𝑖𝑛 sin(𝑛𝜔𝑜 𝑡
3
𝑘=6𝑘±1 𝑛𝜋
Since in delta connection Vp = VL
+
𝑛𝜋
)
6
Ways to make a three-phase inverter efficiency;
• Optimize Pulse Width Modulation (PWM) Technique:
Use advanced PWM techniques such as sinusoidal PWM (SPWM) or space vector modulation (SVM) to
generate the switching signals for the inverter. These techniques can minimize harmonic distortion and
reduce switching losses, resulting in improved efficiency.
• Reduce Switching Losses:
Minimize the switching losses of the power semiconductor devices (IGBTs or MOSFETs) by operating
them at lower frequencies or employing advanced switching techniques such as soft switching. This
reduces the power dissipated during the switching transitions and improves overall efficiency.
• Minimize Conduction Losses:
Reduce the conduction losses in the power semiconductor devices by selecting components with low onstate resistance (RDS(on)) and operating them within their specified safe operating area (SOA). This
ensures that power losses are minimized during the conduction period.
• Optimal Filtering and Inductor Selection:
Choose appropriate filter components and inductors to reduce harmonic distortion and losses. Properly
designed filters can minimize the impact of harmonics and improve power quality while reducing losses.
• Efficient Heat Dissipation:
Implement effective thermal management techniques to remove heat generated by the inverter. This can
include using efficient heat sinks, fans, or liquid cooling methods to maintain the temperature within
acceptable limits and reduce losses due to heat.
• Implement Maximum Power Point Tracking (MPPT):
If the inverter is used in renewable energy systems, such as solar or wind power, incorporate MPPT
algorithms to track and extract the maximum available power from the source. This ensures that the
inverter operates at its highest efficiency point.
Application of three-phase inverter;
Three-phase inverters have various applications across different industries and sectors. Some common applications of
three-phase inverters include:
• Renewable Energy Systems:
Three-phase inverters are widely used in renewable energy systems such as solar photovoltaic (PV) and wind power
systems. They convert the DC power generated by solar panels or wind turbines into AC power suitable for grid
connection or local consumption.
• Motor Drives:
Three-phase inverters are extensively used in motor control applications. They convert DC power from a power supply
into three-phase AC power to drive three-phase AC motors. These inverters are employed in industries such as
manufacturing, robotics, HVAC systems, electric vehicles, and more.
• Uninterruptible Power Supplies (UPS):
Three-phase inverters are utilized in large-scale UPS systems to provide backup power during utility grid outages. These
inverters convert DC power from battery banks into three-phase AC power to support critical loads in commercial
buildings, data centers, hospitals, and other facilities.
• Industrial Applications:
Three-phase inverters find applications in various industrial processes such as welding, metalworking, material
handling, and industrial automation. They provide AC power for equipment and machinery that require precise control
and high power levels.
• Electric Vehicle (EV) Charging:
Three-phase inverters play a vital role in EV charging infrastructure. They convert AC power from the grid into DC
power for charging the batteries of electric vehicles. High-power three-phase inverters are employed in fast charging
stations to provide rapid charging capabilities.
• Railway Traction Systems:
Three-phase inverters are utilized in railway traction systems to convert DC power from overhead lines or onboard
energy storage into three-phase AC power for driving electric trains and locomotives.