140

CHAPTER 4

A SVPWM ALGORITHM FOR NPC-MLI IN OVER

MODULATION REGIONS

4.1 INTRODUCTION

Further avid and investigation on any superior performance PWM

method, is towards widening output controllable range of MLI. Any attempt in

driving the output range to higher range requires thorough investigation and

operation in over modulation regions. The SVPWM is the better choice due to its

merits namely high inverter energy efficiency, waveform quality and voltage

linearity. However, these performance merits may not be guaranteed when it is

extended for OVM regions. The PWM strategy, which performs well at Linear

Modulation (LM) may not perform well in OVM. In this context two issues are to be

taken earnestly. The first one is the SVPWM switching sequences and vector

choices need to be carefully done without affecting the performance. Secondly, the

performance characteristics of the modulator in OVM must be understood well. It

can be interpreted from this discussion that performances of SVPWM in 2-level VSI

is well understood while the same at MLI needs further investigations.

The main issues involved with OVM and its implementation with the

associated literature survey are described in section 2.2.2. This chapter proposes a

simple algorithm for over modulation regions, which is just an intelligence extension

of the linear mode SVPWM (detailed in chapter 3). The proposed algorithm easily

determines the location of reference vector and calculates on-time. It employs a

simple mapping algorithm to generate gating signals for the inverter. The proposed

algorithm can be easily extended to an n-level inverter. It is applicable to 3-level

NPC-MLI topology. Simulation and experimental results are provided for 3-level

141

NPC inverter. The analytical results prove the development of simple yet highly

efficient modulation strategy.

4.2 OVER MODULATION STATUS AND REVIEW

In SVPWM, the normalized output voltage of the inverter is described

with Ma ranging from zero to unity and sub-divided as LM and over OVM [2].

Computation of output voltage more than 0.866, is named as OVM and

corresponding Ma equals 0.907. For a targeted output voltage, a suitable Vref is

fixed. The tip of this Vref traces a circle. Depending upon the Ma values this circle

may be an incumbent or lying out of the hexagon. During the effort of fixing the Vref

in OVM, at any sector (span of 600), the output synthesizes lesser voltage than

desired in mid span of angle and higher voltage on the end spans (LV sides) as

detailed in Figure 4.1.

Figure 4.1. SVD in entire modulation

142

If the SVD hexagon overlapped an OVM boundary circle, then the two

regions (areas) may be noticed in any of the sector. The first area (volt-sec) is

enclosed by the circular boundary and excess to hexagonal boundary (in the middle

of the sector). The second area is the addition of two areas at both ends of the sector

(closer to LVs), which is caused due to the difference between the oversized

hexagonal boundary and the circle. Operations in these two areas/regions are termed

as OVM-I and OVM-II respectively [97].

The OVM scheme is essential, if the drive is required to operate at

extended speed including the field-weakening region and with higher torque and

power characteristics [40], [187]. Hence the researchers tread in this field to give the

significant performance of the MLI in OVM [133], [187], [188].The over

modulation range refers to the operating regions of the SVPWM beyond the linear

range which indicates the inscribed circle of the hexagon. In SVPWM, the

normalized output voltage of the inverter can be described by Ma which ranges from

0 to 1. According to the modulation index, inverter output range is divided into

three regions as shown in Figure 4.1 and described in detail in [2].

The range 0 to 0.907 is LM and 0.907 to 1.0 is called OVM region. The

OVM is classified as OVM-I (Ma: 0.907 to 0.953) and OVM-II (Ma: 0.954 to 1).

Hence the Ma describes the voltage utilization level of the modulator. In this study

Ma is defined as the ratio of the magnitude of the fundamental component of the

inverter output voltage (V1) to (maximum possible) fundamental voltage under six-

step operation (Vsix-step=(2/π)Vdc) for given DC bus voltage [2]. For a given DC-link

voltage Vdc, Ma is given as

(4.1)

If Ma is greater than 1, the desired circular trajectory of Vref crosses the

SVD hexagonal boundary. The available virtual vectors can only synthesize Vref

when the tip of this vector lies inside the hexagonal boundary. Even at this situation

Vref can synthesize using the clever usages of available vector. Even though the Vref

refa

dc

VM = 

(2/π)V

143

over a cycle could be synthesized by exiting vector, instantaneous volt-sec balance

cannot be met out (unlike in LM) when Vref exceeds the hexagonal boundary.

Therefore, there would be portions of the line cycle where the desired Vref could not

be synthesized. The solution to this problem consists of modifying the desired

trajectory of Vref in a way that it lies within the SVD large hexagon and it produces

the same fundamental voltage. This can be done at the expense of introducing low

frequency harmonics in the AC voltages, which are absent in the under modulation

range [125].

OVM-I: A modified voltage vector reference is derived from the

reference voltage vector by changing its magnitude, whereas the phase angle is kept

at its original value. [132].

OVM -II: An actual voltage reference vector is kept at a vertex of the

hexagon for a particular time and a change in the phase angle of the modified

reference vector is required. [132].

4.3 CHALLENGES AND PROBLEM FORMULATION

Many types of SVPWM schemes for a 3-level NPC-MLI with OVM

operation has been developed [105], [127]. The OVM has been first attempted by

Seo et al. for a 3-level MLI [105]. The scheme obtains the Vref magnitude directly

from LM operation which offered difficult trigonometric duty cycle division,

nevertheless it cannot be applied directly to an n-level inverter. And another host of

OVM algorithms are presented in [125]-[130], [187] which allows to extent the

linearity of the inverter output voltage. However, these schemes use complex

trigonometric functions in calculating the modified voltage vector and the duty

cycle.

Mondal et al. [132] have proposed a SVPWM based OVM for a 3-level-

NPC-MLI, where on-time calculation of equations differ for every triangular section

at respective Ma values.

144

a b

Figure 4.2. SVD for sector-1; a. OVM-I, b. OVM-II

Here, the voltage reference V* can be expressed as

(4.2)

Where V1 is the magnitude of original reference voltage and ʽαc’ is the cross over

angle. Since V1 is larger than Vdc/√3, during the rotation of the reference vector, the

vector goes outside the hexagon during the period 1 to 2 as depicted in Figure 4.2.a.

During the period 1 to 2, the reference magnitude need to be limited at hexagonal

boundary (Vdc/√3 cos (π

6− θ)) and the averaged reference magnitude in this period

becomes less than V1 (loss in voltage). They have used V* for Vref, V1 for magnitude

of Vref.

jθ

2 c

* dcc c

jθ

jθ

2 c

V e                                           ;        0 θ  α     

V πV         ;       α   θ   α

π 33 cos θ e

6

π π V e                                         ;        α   θ   

3 3

(4.3)

Where αc is the crossover angle. Concept of Mondal et al. scheme is gaining the loss

voltage in periods P-1 and 2-Q through the circular boundary of higher radius (still

* jθ        

1 c V = Ve   0; θ<α

145

within the hexagonal boundary). As the trajectory in the period 1 to 2 is resituated at

hexagon, it is immaterial whether the circular boundary is increased or not.

Therefore a modified voltage is obtained by Equation (4.3) and Figure 4.2.b where

V2 represents the boosted voltage magnitude to compensate the loss of magnitude in

Vref during period 1-2. Hence during the periods A-B and C-D the reference vector

having a V2 magnitude is located inside the hexagon, and during the period B-C the

reference voltage moves along (C=60-αc). As the modified voltage reference (V*) is

computed by Equation (4.3), it is necessary to calculate trigonometric functions such

as cos (π/6−θ) with the information of magnitude and the angle of Vref [188], [189].

Hence several steps are involved to determine the reference voltage vectors.

Furthermore, this technique utilizes the minimum phase error projection scheme for

generating the duty ratios.

To remove this complexity, Dong-MyungLeehe et al. have proposed

static OVM to generate a new boosted voltage vector with a simple procedure [126].

The scheme obtains the magnitude of a new reference voltage directly from the

modulation index, which is predetermined by the result of the Fourier Series

Expansion (FSE) method and eliminates the decision procedure for the angle and

magnitude of the reference vector. From Figure 4.3 value of V2 is directly obtained

from Ma without finding αc and the angle of the reference vector. During

implementation, these values are obtained from approximate equations of the

magnitude and phase angle which are functions of Ma values.

Figure 4.3. SVD for sector-1

146

In Dong-Myung Leehe et al. method, the required reference value, i.e. V2

which makes the fundamental voltage magnitude after boosting equivalent to V1 is

calculated by employing the FSE Equation (4.4),

(4.4)

Here, the constant coefficients of the FSE on both sides are omitted. This

makes the poor reference voltage estimation. In addition the scheme uses several

steps to determine the reference voltage vectors. Due to the increased computational

complexity, it is cumbersome to extend this scheme to an n-level inverter. To avoid

this computational complexity, some of the researchers have attempted to estimate

the boosted voltage region through magnitude correction factor and angle correction

factor [125]-[130]. The duty ratio calculations are different for each triangles and

hence as the level increases it needs more on-time equations, which increases the

complexity [125]. S B Monge et al. have proposed a SVM for an n-level inverter

including OVM with hexagonal-boundary compression factor calculations and

deliberated the effect of OVM on neutral-point voltage fluctuation in a 3-level

converter [127]. Amit Kumar Gupta et al. proposed an OVM scheme with a neutral

voltage balancing, which does not use the medium voltage vectors that affect the

inverter output voltage [128]. Conversely, the proposed magnitude correction

methods are indirect in nature. Despite the fact, it is obvious that any

simulation/hardware implementation requires correction in terms of duty cycle and

angle results in the poor THD values [131]. .

From the detailed study on OVM the following observations are noted,

i. The magnitude of the Vref samples which are outside the hexagon are

modified by using a Magnitude Correction Factor (MCF) and Angle

Correction Factor (ACF). The duty ratio calculations are different

for different triangles and hence as the level increases the technique

3 3 3

1 2 2

0 0)

3

                       

3 cos(6

cc

cc

j j j j j j j jdc

c

VV e e d V e e d e e d V e e d

147

needs more number of timing equations which results in increased

complexity.

ii. The presented magnitude correction methods are indirect in nature.

It is an obvious expectation that any simulation/hardware

implementation requires correction in terms of duty cycle. The other

options like angle correction results in poor valuation of THD.

iii. In general the OVM range is nonlinear in nature. To handle this

nonlinearity, the magnitude and angle of the Vref are modified. Due

to the composite geometry it needs a pre-processor which makes the

implementation complex and expensive.

4.4 DIRECT MODULATION DEPTH CORRECTION PROCEDURE

FOR OVER MODULATION

The main idea behind the proposed OVM technique is incorporating the

magnitude correction in the timings (on-time of the switches) of constituting vectors

using MCF equations, LUTs and pre-defined calculations. It uses a simple mapping

to generate gating signals for the inverter in LM and OVM regions. This scheme

accurately determines the location of the Vref and calculates on-time. Firstly, the

boundary restriction inherited in the linear modulation hexagon is redefined as

Modulation Depth Loss Factor (MDLF) and quantified for various OVM indices.

Next, the appropriate time correction is carried out in the switching vector timing.

The proposed timing corrected SVPWM strategy hosts a simple assessment and duty

cycle pre-calculation procedure for determining on-times. The Timing Correction

Algorithm (TCA) ingeniously corrects these magnitude losses and gains in terms of

addition and subtraction of a corrective term in the on-time respectively.

The proposed OVM schemes operate the zones of OVM-I and OVM-II

separately. The hexagonal SVD of a three-phase MLI reprises similar tactic of

working in all the six sectors. Hence the operation is explained for the first sector in

the proposed schemes and the same is applicable for other sectors too.

148

4.4.1 Over Modulation-I Zone (0.907 ≤ Ma ≤ 0.953)

When Ma value lies between 0.907 to 0.953, it is called as OVM-I region.

The dotted circle in Figure 4.4 shows the original trajectory of Vref in OVM zone. In

this region, the Vref traverse outside the hexagon (span-2) for some time and for the

remaining time it lies within the hexagon (span-1 and span-3). Multiplication time t

with this span represent area (volt-sec). It is known that OVM comprises of circular

and hexagonal trajectories and the transition from circular trajectory to the

hexagonal trajectory happens at αc which is constant-unique angle for any given Ma

which is given by Equation (4.5). αc is the angle where the Vref first crosses the

hexagon track as shown in the Figure 4.4. In the conventional OVM techniques, the

samples (p, q, r, s) which are outside the hexagon are limited to lie on the hexagonal

boundary (p|, q|, r|, s|). In this proposed work the magnitude of the voltage reference

samples which are outside the hexagon are modified by using a MCF. However

when the original Vref traverses outside the hexagon, the time average equation gives

an unrealistic on-time.

In Figure 4.4, for a particular value of Ma in the OVM, the path K-B-p-q-

r-s-C-L shows the original trajectory of the Vref and the trajectory is modified to

follow the path K|-B|-C|-L| only by modifying the on-time equations. In OVM-I,

only the magnitude of the Vref is changed whereas the angle is chosen without any

changes. If the reference samples lie in area-1 or area-3, then these samples are

synthesized by available space vectors using NTV scheme. For a chosen angle in the

trajectory, pieces lie between (0 to αc) and (π/3-αc to π/3), the vector moves on

circular track and the modulation strategy is same as that of LM and for remaining

part (αc to π/3-αc)of the sector on hexagonal track.

1

c

a

π πα cos

6 (2 3M

(4.5)

The Si identification and ∆i,j determination are same for both the

trajectories and they differ only in on-time calculation. Null vectors will never

participate when the trajectory is along the hexagon.

149

Figure 4.4. First sector 3-level SVD at OVM-I, (0.907≤ Ma ≤0.953)

4.4.1.1 Circular trajectory

If the reference angle 𝛾 does not satisfy the condition αc ≤𝛾< π/3-αc then

the Vref follows the circular trajectory. Identification of Si, determination of ∆i,j and

on-time calculations of the Vref are explained in the following sections.

4.4.1.2 Sector judgment

For applying the SVPWM technique, first it is required to determine the

sector in which the voltage vector lies. For any given Vref, the angle γ and its Si can

be determined by using the same Equation (4.2) and Equation (4.3).

4.4.1.3 Triangle determination

After the sector identification, the sub-triangle determination is the most

significant one which is discussed in section 3.3.2 with the help of X1 and X2

integers.

150

4.4.1.4 On-time calculations for circular trajectory

On-time calculations are based on the location of the Vref. As mentioned

before, there is a loss of fundamental voltage in the region where the Vref exceeds

the hexagon boundary. To compensate this loss, the Vref amplitude is increased to

K|-B| from K-B by using MDLF as shown in Figure 4.4. So the magnitude of the Vref

is changed from the original Vref. A modified Vref trajectory proceeds partly on the

hexagon and partly on the circle.

a

f

M 0.907MDLF D

0.045

(4.6)

When the trajectory remains on the circular part, the switching time of

Ta, Tb, and To in Equation (4.15)-(4.17) are modified to compensate for the loss in

volt-seconds by introducing a MDLF. For a given Ma, the value of the MDLF is

constant and it is given by Equation (4.6). It is also called as Df, where 0.045 is the

value between maximum value of LM zone to minimum value of OVM-II zone.

Figure 4.5 displays the variation between MDLF and Ma. The MDLF increases

when Ma is increased. The modified on-time equations for down triangle are:

s

βos 2

am s αo f o

VT T V    0.5D T

3

(4.7)

s

βo 2

bm s f o

V T T 0.5D T

h

(4.8)

om s am bmT T T T (4.9)

The modified on-time equations for upper triangle are:

s

βos 2

am s αo f o

VT T V   0.5D T

3

(4.10)

151

s

βo 2

bm s f o

V T T 0.5D T

h

(4.11)

om s am bmT T T T (4.12)

Where, Tam, Tbm and Tom are modified value of Ta, Tb and To

Figure 4.5. MDLF versus Ma

4.4.1.5 Hexagonal trajectory

If the angle 𝛾 satisfies the condition αc ≤𝛾<π/3-αc then the Vref follows the

hexagonal trajectory. The Si judgment and ∆i,j determination can be done in the

similar manner as in the circular trajectory. During hexagonal trajectory, the

coordinates of the Vref are given in terms of angle 𝛾 and level of inverter output n

which are expressed as follows:

α

3 n 1 V

( 3 tan γ)

(4.13)

β

3 n 1 tan γ  V

3 tan γ

(4.14)

152

4.4.1.6 On-time calculations for Hexagonal trajectory

The on-time durations for the region where the modified reference

trajectory is moved along hexagonal track can be derived as

s

βos

a s αo

V T T V

3

(4.15)

b s a                       T T T (4.16)

oT 0  (4.17)

When Vref lies outside the hexagon, the summation of Ta+Tb exceeds Ts and this

begins to appear when the length of the Vref becomes greater than the radius of the

hexagon-inscribed circle (i.e., OVM)

4.4.2 Over Modulation-II Zone (0.953˂Ma≤ 0.999)

In some applications such as field weakening vector control, the drive is

required to operate at extended speeds, and hence the OVM with Ma extending near

to unity is essential [3]. In the OVM-II, the controller affects both the magnitude and

the angle of the Vref [2]. After OVM-I has reached the maximum limit as Ma=0.953,

OVM-II becomes active. Under OVM-II, if the Vref lies in the area-4, then the

essential feature is that the particular active large vector (LV1) closer to the Vref is

used with increasing duty cycle and angle. In OVM-II, the circular part of the

trajectory vanishes and the switching in this region is characterized by a holding

angle (αh).The αh is expressed as a function of Ma, i.e., αh=f (Ma). Its value is limited

between [0 to π/6] as shown in Figure 4.6. Figure 4.7 shows the first sector of 3-

level SVD at OVM II.

153

4.4.2.1 Holding angle calculation

Normally αh is a nonlinear function of modulation index and obtained by

a lookup table. In this chapter, the holding angle αh is obtained using a strategy

similar to one discussed in [133]. αh is the angular velocity of the Vref . The angular

velocity is proportional to modulation index Ma [130].

Figure 4.6. αh versus Ma

(4.18)

hh h

a

h h

a

h h

a

h

a

h

a

h

π π - 2α

α α3 3 =   +  +M 1 1 0.9535

2 α 2 α π π-  =  - 

1 0.9535 3 M 3 (0.9535)

1.907 α - 2 α π 1 1 =   - 

0.9535 3  M (0.9535)

π π-  0.2920 α  =  

0.9535 M

1 2.99α =    0.314-   

0.2789 M

10.72α = 11.26- 

M

a

h

a

h a

10.72α = 11.26- 

M

α = 10.72(1.05-1 /M

)

154

Hence, in Equation (4.18), for a given Ma only two arithmetic operations

i.e. one division and one subtraction are required to obtain the holding angle αh. It

shows the simplicity of implementing SVPWM in overmodulation mode II.

Figure 4.7. First sector of 3-level SVD at OVM-II, (0.953˂ Ma ≤1)

When the Vref is in the span (area-6), it contains an angle from (π/3-αh) to

π/3 such that the vector is made to hold at its respective nearest large vector (LV2).

If the chosen angle is between αh and π/3-αh (area-5) then the Vref follows the

hexagonal path and the Ta and Tb are calculated by using the same on-time

calculation as that during the hexagonal trajectory in OVM-I Equation (4.15)-(4.18).

For a given switching frequency, the current distortion increases with the Ma value.

The distortion strongly increases when the reference waveform become

discontinuous in the OVM-II. During 0≤ 𝛾<αh and (π/3-αh)≤ 𝛾<π/3, the reference

vector is held at one of the six vertices of the hexagon. At Ma=1.0, hexagonal track

vanishes and vector Vref is only held at the six large vectors sequentially. This is six-

step operation similar to 2-level inverter. Therefore, a multilevel inverter when

operated at Ma=1.0, mislays its MLI characteristics [131].

155

4.4.2.2 On-time calculations for hexagonal trajectory

During the on-time for the region where the modified reference trajectory

obeys conditions: 0≤ 𝛾<αh and (π/3-αh)≤ 𝛾<π/3, the reference vector is held at one of

the six vertices of the hexagon and the on-time values are given by,

h a s b o 0 γ  α  ;  T T ,  T T 0 (4.19)

h b s a o

π π α    γ  ;   T T ,T T 0

3 3 (4.20)

Figure 4.8. Flowchart of calculating on-time in the entire Ma

Go to Δi,j calculation

for linear modulation

Go to Cross over

angle (αc) calculation

Go to Holding

angle(αh)

calculation

NO

LM OVM-I OVM-II

Va,Vb,Vc,

Ma

abc to dq

Transformation

Complex to

polar

Sector identification

Gamma calculation

Uref = 3Ma (n-1)/ π

Ma>0.90 Ma>0.95

Ta = Ts(Vαos − Vβo

s √3 )

Tb = Ts(Vβos h )

To = Ts − Ta − Tb

0 ≤ 𝛾 < 𝛼ℎ; 𝑇𝑎 = 𝑇𝑠, 𝑇𝑏 = 𝑇𝑜 = 0

𝛱 3 − 𝛼ℎ ≤ 𝛾 < 𝛱 3 ; 𝑇𝑏 = 𝑇𝑠, 𝑇𝑎 = 𝑇𝑜 = 0

Ta = Ts(Vαos − Vβo

s √3 )

Tb = Ts − Ta To = 0

Vector mapping

YES NO YES

156

This is summarized as a flowchart and shown in Figure 4.8 and 4.9. It

determines parameters such as sectors and triangles, and calculates on-time. These

details are subsequently used by mapping unit to generate gating signals. Table 4.1

shows the switching sequences of all the sectors for a 3-level SVM in the entire

modulation region.

Figure 4.9. Flowchart of calculating ∆i,j and on-times in OVM-I and OVM-II

αc ≤ γ< π 3 − αc

Compensation

factor

(Cf) calculation

Cross over

angle

Calculation

Holding angle

Calculation

αh ≤ γ< π 3 − αh

Calculation of

modified

on-times

MDLF

𝑉𝛼 = √3 (𝑛 − 1) (√3 + tan 𝛾)

𝑉𝛽 = √3(𝑛 − 1) tan 𝛾 (√3 + tan 𝛾)

𝛼𝑐 = (𝛱 6) − 𝑐𝑜𝑠−1(𝛱 2√3𝑀𝑎 ) 𝛼ℎ = 10.5(1.05 − 1 Ma )

X1 = (n − 2) X2 = int(Vβ h )

Vαos = Vα − X1 + 0.5X2 Vβ0s = Vβ − X2h

Δj = X12 + 2X2

Return

Vector mapping

YES YES NO NO

157

Table 4.1. ∆i,j and on-time calculation for OVM-I and OVM-II

Modulation Timing calculations Si,j

Vector mapping

Linear

modulation(LM)

Ta = Ts(Vαos − Vβo

s √3 )

Tb = Ts(Vβos h )

To = Ts − Ta − Tb

[0-1-1] [0-10] [1-10] [100] [101]

[111] [101] [100] [000] [0-10] [0-1-1] [111]

[101] [1-11] [1-10] [0-10]

[100] [1-10] [1-1-1] [0-1-1]

OVM

-I

Circular

trajectory

Tam = Ta + 0.5Cf2To

Tbm = Tb + 0.5Cf2To

Tom = Ts − Tam − Tbm

[-101] [1-11] [1-10] [0-10]

[0-1-1] [1-10] [1-1-1] [100]

Hexagon

al

trajectory

Ta = Ts(Vαos − Vβo

s √3 )

Tb = Ts − Ta

To = 0

[1-11] [1-10] [1-10] [1-11]

[1-10] [1-1-1] [1-1-1] [1-10]

OVM

-II

Hexagon

al

trajectory

Ta = Ts(Vαos − Vβo

s 3)

Tb = Ts − Ta

To = 0

[1-10] [1-1-1] [1-1-1] [1-10]

[1-11] [1-10] [1-10] [1-11]

Holding

trajectory

Ta = Ts , Tb = To = 0

Tb = Ts , Ta = To = 0

[1-11]

[1-1-1]

S1,1

VZ

VS1 VM6 VS1 VS6 VS6

VS6 VL6 VM6 VS6

VS1 VM6 VL1 VS1

VL6 VL6 VM6 VM6

VM6

VM6 VL1 VL1

VL6 VL6 VM6 VM6

VM6

VM6 VL1 VL1

VL1

VL6

VZ

S1,2

S1,3

S1,4

S1,3

S1,4

S1,3

S1,4

S1,3

S1,4

S1,3

S1,4

To/3 To/3 To/3 Ta/2 Ta/2 Tb/2 Tb/2

Tom/2 Tom/2 Tam Tbm

Tom/2 Tom/2 Tam Tbm

Tb2

Ta/2 Tb/2 Tb/2 Ta/2

Ta/2 Tb/2 Tb/2 Ta/2

Ta

VS6 VS1 VS1 VZ VS6

VL1

VS6 VM6

VM6 VS1 VS6

VS6 VL6

To/2 To/2 Ta/2 Ta/2 Tb

To/2 To/2 Tb Ta

To/2 Ta Tb To/2

Ta/2 Tb/2 Ta/2 Tb/2

Tb/2 Ta/2 Ta/2

Tb

158

4.5 SIMULATION STUDY

The performance of the proposed MLI SVPWM algorithm is investigated

and simulated by MATLAB 11.b/Simulink for 3-level 12 switch NPC-MLI drive

with 300V DC-link, two 100µF capacitors, and 3kHz switching frequency.

4.5.1 Simulink Schematization of Proposed OVM

Figure 4.10. Flow chart for OVM- MATLAB implementation

3-2 Coordinate

Transformation

𝑉∗, 𝛼 Calculator

V∗=

√Vα2 + Vβ

2

γ=

tan−1 V ∝Vβ

Sector

Detector

Module

𝛾 Identifier

K1,K2

Calculator

𝑉𝛼𝑖,𝑉𝛽𝑖

Calculator

Sub

triangle

Identifier

𝑉𝛼𝑜𝑠 ,𝑉𝛽𝑜

𝑠

Calculator

Switching Pattern

for S1

Switching Pattern

for S2

Switching Pattern

for S3

Switching Pattern

for S4

Switching Pattern

for S5

Switching Pattern

for S6

Sub triangle Switching State

Timing Calculations

𝑉𝛼 𝑉𝛽

𝑉∗

𝑉𝛼𝑜𝑠

𝑉𝛽𝑜𝑠

Ts

Ta Tb To

Sector & 𝜸 Identifier Module

Local Vector Generator Module Sector Selector Module

Switching Pulse Generator

Si

Si

𝛾𝑖

SA1

SA2

SA3

SA4

SB1

SB2

SB3

SB4

SC1

SC2

SC3

SC4

Switching

Sequence Park’s Transformation

OVM-I

OVM-II

Trajectory Identifier

Ma

𝛾𝑖

𝛾𝑖

159

Figure 4.10 shows the MATLAB/Simulink simulation model of OVM.

This implementation is similar to LM except the 4th block (sector selector module).

The difference lies in the inclusion of OVM region trajectory identification and its

on-time calculations. The block includes modified trajectory identifier, its angles (αc

and αh ), MCF and the modified switching time calculator which are used to

calculate the timing of the OVM-I and OVM-II regions. The inputs of this block are

types of the sub-triangles, Vαos , Vβo

s and the sampling time period (Ts= 1/fs). In the

same block, the sample and hold blocks are used after Ta and Tb calculator block.

The purpose of these blocks is to hold the values of Ta and Tb fixed during each

PWM period.

The times To, Ta, and Tb are obtained from the calculations and Ts is the

sampling time of inverter. By using these timing values the switching sequence is

determined. Then this timing values are given to the different sub-triangles based on

the sub-triangle block.

4.5.2 Simulation Results

The performance of the proposed scheme is studied and understood by an

extensive simulation study by using MATLAB/Simulink 11.b in entire modulation

ranges, including OVM region with 3kHz switching frequency. Initially, the

simulation study conceded for maximum LM range (0.907), Vline is resulted as

268.4V with THD value of 15.66%. When the inverter is operated in proposed OVM

scheme at Ma values 0.95, 0.98 and 0.99, the Vline(peak voltage) values are observed

as 285V, 294V and 297V respectively. The aforementioned simulation results

confirm the theoretical values.

Figure 4.11 shows the Vline and Iline waveforms for OVM-I at Ma=0.953.

As a result the Vline is observed as 284.7V with VTHD as 19.70% as shown in Figure

4.12. It is demonstrated that the proposed OVM-I scheme utilizes the maximum

modulation boundary till 0.953.

160

Figure 4.11. Simulation results for OVM-I with Ma=0.953; Three-phase Vline

[200V/div] [1ms/div], Iline [2A/div] [1ms/div]

161

Figure 4.12. Simulation results for OVM-I; Harmonic spectrum of Vline at

Ma=0.953

Figure 4.13. Simulation results for OVM-I with Ma=0.99; Three-phase Vline

[200V/div] [1ms/div], Iline [2A/div] [1ms/div]

162

Figure 4.14. Simulation results for OVM-II; Harmonic spectrum of Vline at

Ma=0.99

When Ma value is increased above 0.953, then the proposed scheme

works under OVM-II zone with usages of LVs and this mode extends up to 1.

Superfluously, the proposed SVM-OVM-II scheme works in extreme modulation

range with peak amplitude of 0.99. Figure 4.13 shows the Vline and Iline waveforms

for OVM-I at Ma=0.99. Here, Vline is measured as 297.1V. The harmonic spectrum

of OVM-II is revealed as 27.70% in Figure 4.14 which is less than previously

reported OVM schemes [125], [188], [189]. The line voltage and THD performance

analysis of suggested OVM schemes are carried out and plotted for different Ma.

Figure 4.15 shows the chart of fundamental voltages versus Ma. Based on the study,

it could be understood that the fundamental voltage increases on increasing the Ma.

Figure 4.16 shows the chart of voltage THD for the different Ma values. It is

understood that, as the THD values are increasing, the inverter operates in higher

modulation indices. Particularly in OVM-II zone, the THD is higher because of

pulse dropping.

163

Figure 4.15. Fundamental Vline versus Ma

Figure 4.16. Line voltage THD versus Ma

4.6 IMPLEMENTATION OF PROPOSED OVER MODULATION

FOR NPC-MLI

This section discusses about the experimental setup of SVPWM fed

NPC-MLI drive and FPGA implementation of the suggested OVM scheme is

provided. The test is performed on the same laboratory prototype 2kW NPC-MLI

drive system. Corroboration is done using a SPARTAN III-3A XC3SD1800A-

FG676 DSP-FPGA processor. FPGA implementation of this OVM scheme is done

using Xilinx ISE 10.1 system generator navigator tool.

164

4.6.1 FPGA Implementation Results

4.6.1.1 RTL view

Figure 4.17 shows the overall RTL view of proposed OVM architecture.

This implementation is similar to LM with a small alteration. The difference lies in

the inclusion of OVM region’s trajectory identification and its calculations. The

block includes modified trajectory identifier (circular and hexagonal), its angles (αc

and αh), MCF and the modified switching time calculator, which is used to calculate

the timing of the OVM-I and OVM-II regions arguments. Figure 4.18 shows

ModelSim 5.8e hardware pulse pattern (S1A - S4C) for OVM-II scheme at 0.99 Ma.

Figure 4.17. Overall RTL view of proposed OVM implementation

Figure 4.18. Hardware pulse pattern (S1A-S4C) for OVM-II scheme at 0.99 Ma

using ModelSim 5.8e

165

4.6.1.2 Device utilization report

The recommended work has also considered some key design measures

for improving computation accuracy and simplifying hardware design. Fixed-point

arithmetic unit is adopted for implementing the calculations on FPGA. The observed

(V*) and αc calculations are influenced only by the Ma value. As an outcome, the

modified Vref and associated duty cycle calculation of vectors require very simple

equations as compared to the existing schemes. Hence the proposed OVM scheme

uses less hardware resources, which is 8% of the total resources avilable on the

SPARTAN–III-3A XC3SD1800A-FG676 DSP-FPGA processor board. This is 2%

higher than LM scheme resource utilization on this same FPGA processor. Figure

4.19 depicts the resource utilisation of the proposed algorithm. In addition, due to

simple calculations, the proposed OVM-I and OVM-II algorithms exhibit the

processing speed of 15.4µsec and 16.03µsec respectively which is less compared to

reported scheme [126]. Hence it is very suitable for motor control applications.

Figure 4.19. Resource utilization of the proposed OVM algorithm

166

4.7 EXPERIMENTAL RESULTS AND THEIR ANALYSIS

The corroborating experimental results are captured using six channel

YOKOGAWA make power analyzer. Initially the investigation is carried out for

maximum LM range Ma of 0.907. The output voltage is obtained with help of

maximum SV and MV duty cycle and minimum LV duty cycle as 265.48V peak

Vline with 16.57% THD spectrum. The next experiment is carried out for the

proposed schemes with OVM-I and OVM-II zones. When the drive is accelerated to

OVM-I by increasing Ma to 0.953, the proposed simplified OVM scheme helps to

increase the voltage profile by utilizing maximum LV duty cycle from 265.48V with

minimum computational process. As a result the Vline is observed as 284.24V and

fortified VTHD is 19.94%. Figure 4.20 shows the Vline and Iline waveforms for OVM-I

at Ma=0.953. It is demonstrated that the proposed OVM-I scheme utilizes the

maximum modulation boundary till Ma=0.953. When Ma value is increased above

0.953, then the proposed scheme works under OVM-II zone with the help of 100%

LV duty cycle and this mode extends up to 1. Superfluously, the proposed SVM-

OVM-II schemes works in extreme modulation range with Ma of 0.999.

a

Figure 4.20. (Continued)

167

b

c

Figure 4.20. Experimental results of OVM-I with Ma = 0.953; a. Vline

[300V/div] [1ms/div], Iline [3A/div] [1ms/div], b. Vline [300V/div]

[1ms/div] and its harmonic spectrum, c. Three-phase Vline

[300V/div] [1ms/div], Iline [3A/div] [1ms/div]

168

a

b

Figure 4.21. (Continued)

169

c

Figure 4.21. Experimental results of OVM-II with Ma = 0.998; a. Vline

[300V/div] [1ms/div], Iline [3A/div] [1ms/div], b. Vline [250V/div]

[1ms/div] and its harmonic spectrum, c. Three-phase Vline

[300V/div] [1ms/div], Iline [3A/div] [1 ms/div]

Figure 4.21 shows the Vline, Iline and harmonic spectrum of OVM-II at Ma

=0.99. Here Vline and its harmonic spectrum is measured as 296.35V and 28.64%.

These both OVM-I and OVM-II experimental results are in good agreement with the

simulation results.

Table 4.2 lists the values of peak Vline magnitudes and THD at different

Ma for the proposed SVPWM technique. From the table, it is observed that the

output voltage is equal to 272.87V at Ma=0.917 and with Ma=0.937, it is found that

the Vline=280.42V. This voltage is further increased to a value of 284.25V and

293.23V when the inverter is operated at OVM-I(0.953) and OVM-II(0.985)

respectively. Hence it is evident that the output voltage of the inverter increases as

the operating value of Ma moves towards the OVM region up to 0.99. Based on

these analysis, the Ma value moves towards the OVM region and output voltage

magnitudes obtained are high when compared to LM by properly utilizing the DC-

170

link voltage.The Table 4.2 shows the Vline and its VTHD for the inverter, for different

Ma values. It can be seen that VTHD increases when Ma is increased. At higher Ma

(OVM region), due to result in pulse dropping the THD value is high in OVM.

Table 4.2. Experimental results for the proposed OVM

Zone Ma Vline(V) VTHD (%)

OVM-I

0.917 272.87 17.94

0.927 276.82 18.51

0.937 280.42 18.99

0.947 282.40 19.45

0.953 284.25 19.94

OVM-II

0.968 287.27 22.46

0.975 290.09 24.34

0.985 293.23 26.97

0.995 296.35 28.64

4.8 SUMMARY

In this chapter, the theoretical analysis, design habitat, FPGA

implementation and experimental verification of the proposed OVM, based on

standard 2-level SVPWM, has been successfully exhibited. This scheme uses a

timing correction algorithm (TCA). The on-time calculation equations do not change

with triangle. A simple method of calculating on-times in the over modulation range

is used. Hence a solution to complex equations and LUTs are not required. This

leads to ease of implementation in FPGA. The proposed implementation is general

in nature and can be applied to a variety of modulation schemes. The simulation and

experimental results are presented in order to confirm the performance merits of the

offered OVM at different modulation ranges of the inverter.

171

The salient features of the proposed OVM strategies are as follows:

Duty ratio calculations are similar to 2-level inverter and can be

easily validated for any number of levels n ≥3. There are no

significant changes in computation with the increase in number of

levels.

The considered OVM scheme delivered maximum Vline compared to

the existing schemes [125],[126],[189]

The proposed OVM scheme has low THD compared to the present

SVPWM schemes [125],[189], the existing zero-sequence voltage

injection technique [190] and the optimal carrier based PWM strategy

[191].

Computational Complexity: The proposed algorithm reduces the

memory space in the real time implementation as 8%. In addition, the

algorithm minimizes the processing time of OVM-I and OVM-II as

15.4μsec and 16.03μsec respectively which is less than reported

seheme [126]

The proposed algorithm is tested with open loop three-phase squirrel

cage induction motor speed control drive, accelerated from the LM to

OVM and then to SM, unlike in general OVM reported schemes.

This elucidates that the suggested SVPWM can be directly

functioning to open-loop drives.

The proposed OVM approach maintains the volt-sec balance equation

throughout the modulation range.

The main benefits of the proposed strategy is its simplicity and that it

can be implemented for field weakening operations.