Enhancing Power Grid System Analysis with Medium Voltage
Cascaded H-Bridge Motor Driver Dynamic Model
ADIL ALAHMAD1, FIRAT KACAR1, CENGIZ POLAT UZUNOGLU1, NIKOS MASTORAKIS2
1Electrical and Electronics Engineering Department,
Istanbul University-Cerrahpasa,
34320 Avcılar, Istanbul,
TURKEY
Abstract: - Medium voltage cascaded H-Bridge motor drives (MV-CHBMD) are popular with renewable
applications because of their scalability, reliability, and modularity. The MV-CBHMDs are used in different
medium voltage applications and significantly affect grid flexibility, performance, and efficiency. Even with
the famous use of MV-CHBMD, the provided simulation models need to be more detailed to cover grid
connection dynamic investigations. This study provides a dynamic design of MV-CHBMD, connected with the
power grid source and induction motor (IM) with load, which provides a compliance large-scale analysis for
the dynamic act of the power grid system. The proposed model of dynamic MV-CHBMD is suitable for power
system studies. The model provides an analytical analysis of the grid connection with the cascaded H-bridge
motor driver (CHBMD) and IM on the load side of the driver. It accurately represents the dynamic of the total
system under different disturbances. The main factors affected during any perturbation are variable frequency
and voltage, which are deeply considered in the proposed model. A simulation analysis verifies the model's
accuracy, reliability, and effectivity. The mode sensitivity analysis depends on the impact of the variable
parameters on the system acting and responding. The proposed model is easily insertable in the extensive grid-
simulating system, which provides more accurate results in power grid dynamic studies.
Key-Words: - Medium Voltage Systems, Cascaded H-Bridge, Motor Driver, Dynamic Studies, Simulation
Analysis, Optimized Design.
Received: April 8, 2023. Revised: October 24, 2023. Accepted: November 21, 2023. Published: December 31, 2023.
1 Introduction
For more than three decades, representing power
grid systems has been recognized, which helps to
study the performance of different factors that
impact power system stability. CHBMD system
provides complete control of torque and speed of the
IM by converting voltage and frequency to
controllable values. In high-power applications
requiring medium voltage levels, CHBMD delivers
the same output power but with a lower current. As
the grid is operated and designed to be stable on a
specific margin, all connected device simulation
models are essential to overall system expectations
under critical situations, [1]. Despite the big efforts
of scientists and researchers’ system simulation
modelling is not enough to cover all new types of
loads and the effect of each load on the grid
efficiency, [2]. The CHBMD with IM combination
is a widely used application in the industrial sector
as sequence modelling driver and motor
combination become more essential because of the
enormous increase in usage level in the systems
over time. The averaged-value dynamic model of a
three-phase voltage system connected with an
inverter is presented using differential equations in
[3]. The model, [4], is only for the inverter, but the
other components, like the multi-pulse transformer,
rectifier system, DC link and IM load, are not
included in the model, [5]. Although
MATLAB/Simulink has a standard library with
some detailed models of different components, but it
is not usable in significant simulation software of
grids, [6]. To fill the MV-CHBMD modelling gap
authors in [7], present propose a "linearization
approach" method. The [8], model was improved by
transferring the mathematical reaction of a low-
voltage system, [9]. In real life, VM-CHBMDs will
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.45
Adil Alahmad, Firat Kacar,
Cengiz Polat Uzunoglu, Nikos Mastorakis
E-ISSN: 2224-350X
460
Volume 18, 2023
2English Language Faculty of Engineering,
Technical University of Sofia,
Clement Ohridski 8, 1000
Sofia,
BULGARIA
disconnect from the grid automatically when big
disturbances at the same time they are capable of
handling small disturbances. The proposed model
perfectly fits minor disturbances in the power
system, so it can test minor disturbances and
analyze them to get stability of the system.
Therefore, the MV-CHBMD model can improve the
system functions, [10], [11]. Using the proposed
model in big system analyses helps to understand
the transfer function, the behaviors of each
component and its reaction to various disturbances
in the grid. it is also easy to implement on big
simulations of the power grid, [12].
2 Study and Analysis of MV-CHBMD
Model
The MV-CHBMD is the famous topology for
medium voltage applications especially with high-
speed and big scales motors, [13]. The CHBMD
structure consists of many power cells operating in
low voltage and high current power electronics. By
connecting the power cells in series higher voltage
could be obtained example two power cells per
phase in the five-level driver, three cells per phase
in the seven-level driver and four cells per phase in
the nine-level driver, [14]. The seven-level VM-
CHBMD has three power cells per phase, so in total,
it has nine power cells and can produce more than
1,4 kV at the output side. Figure 1 shows the
proposed eighteen-pulse transformer, seven-level
MV-CHBMD structure with its nine power cells,
and IM.
Fig. 1: The seven-level VM-CHBMD System
Each power cell has a unique PWM control
signal, to control its H bridge power electronic
switches. The power flows through a multi-pulse
transformer to the rectifier system in each power
cell, which delivers current to the DC link, then to
the H bridge at the endpoint power cells connected
in series to the IM. Each pulse of the eighteen-pulse
transformer provides a 480V AC, [15]. The pulses
of the transformer are connected to the power cells
which have the rectifier system, DC link and full
bridge of power electronic switches. The rectifier
system supplies 640Vdc to the DC link, which is
connected to the motor through the switches. The
power electronic switches operate according to the
control signals.
2.1 Analytic Model of Power Cell
The DC link has no shifts, so there is no effect on
the phase shifting of the multi-pulse transformer, as
the rectifier system converts the alternative current
to direct current, [15]. The output voltage (V0) of a
single power cell can be calculated using (1)
equation. The Edc refers to voltage of DC link. The
C is referring to duty cycle, [16].
V0 = C * Edc (1)
The IM phases voltage calculated by (2) equations.
(2)
The np refers to the number power cells used in
MV-CHBMD. The ωs is referring to the electrical
field speed in the stator of IM. The abc sequence is
not usable in control algorithms because that is
covered to dq0 as shown in equation (3). The vqs
refers to the terminal voltage at the IM in the
quadrature -axis, and the same vds refers to the
direct-axis.
(3)
The actual power from the driver to IM (Pac-IM)
is calculated using equation (4).
(4)
The iqs and ids refer to the current of the stator
of IM. The DC link power (Pdc-link) for all power
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.45
Adil Alahmad, Firat Kacar,
Cengiz Polat Uzunoglu, Nikos Mastorakis
E-ISSN: 2224-350X
461
Volume 18, 2023
cells in the driver is related to the actual power of
the driver, as shown in equation (5).
(5)
The iI refers to the per power cell input dc
current. The id refers to the current at the driver
output and it calculated using iI, Edc and Cdc-link
capacitor as shown in equation (6).
(6)
Assuming there are no power losses in
connection points and power electronic switches,
the actual power of the driver is equal to the DC link
power. As a result, the relation between the per
power cell input dc link current and the current of
the stator of IM is calculated after applying Laplace
Transform as shown in equation (7), [17].
(7)
2.2 Analytic Model of Power Cell
The MV-CHBMD control algorithm utilizes the
close loop method, and for another control methods,
the user needs to improve or develop the
mathematical model for it. The duty cycle is
important to obtain the driver position to get the
motor synchronous and the voltage at the
quadrature-axis. The duty cycle and voltage of the
IM in the quadrature and direct axis’s relation are
explained by equation (8), [18].
(8)
The ce refers to the angel between the reference
displacement of CHBMD and the synchronous
reference. The closed-loop control algorithm
calculated by equations (9), (10), (11), (12) and
(13).
(9)
(10)
(11)
(12)
(13)
The Kpm and Kim refer to the proportional and
integral of speed controller PI, respectively. The Vb
refers to the phase voltage of IM. The ωr refers to
IM rotor electrical angle. The ωSL refers to a slip of
electrical angle. The star next to the variable refers
to the reference value, and the parameters have a 0
referring to initial values. The value of ωr calculated
by solving equation (10), as shown in equations
(14), [19].
(14)
The value of irqs calculated by solving equation
(7), as shown in equations (15) and (16), [20].
(15)
(16)
The value of Vqs calculated by solving equations
(3) and (17), as shown in equation (18), [21].
(17)
(18)
2.3 Dynamic Model Deriving of CHBMD
The total actual power of the MV-CHBMD system
(Pac) is the sum of the actual power of each power
cell divided by two. It is the same for total reactive
power (Qac). Accordingly, the (Pac) and (Qac) of
seven levels MV-CHBMD calculated as per
equations (19) and (20), respectively.
(19)
(20)
The overall equation of MV-CBHMD is
calculated by combining all the differential
equations of the system compensation, as shown in
equations (21) and (22), [20].
(21)
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DOI: 10.37394/232016.2023.18.45
Adil Alahmad, Firat Kacar,
Cengiz Polat Uzunoglu, Nikos Mastorakis
E-ISSN: 2224-350X
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(22)
The parameters GPi and GQi refer to are the 7th-
order functions. All equations obtained were
converted to a code in the MATLAB environment.
The user can change the parameter to obtain
different result, according to, their own system
requests, [22]. The IM parameters are 1500HP,
2300V, 50Hz, 0.035Ω, 0.002H, 1800 RPM,
and1500Nm. The CHBMD parameters are 10e-3F,
1.3V for diode, 50 Hz, Kpm=9 and Kim =10. Power
source parameters are 480V, 1.2mH and 50Hz.
3 The CHBMD Model Verification
The verification of the proposed model was
conducted by MATLAB simulation of medium
voltage CHBMD seven-level, connecting with the
grid through eighteen pulse transformer, and
induction motor. The control method is PWM-
enhanced algorithm. The output of the simulation
model will compare with the standard MATLAB
models, to show the reaction of the developed
model. The mode takes dependence voltage and
frequency under consideration. The dynamic acting
of the models under different situations of
disturbances will be analyzed.
To confirm the voltage reliance of the provided
model, three controlled faults are applied to the
input side of the CHBMD model, which reduces the
voltage by 90%. The fault begins at 3.3 s and ends
at 3.9 s. The total simulation duration is 4 seconds.
Figure 2 shows the dynamic reaction of the actual
power in the simulation model under voltage
changes. It clearly verified the accuracy of the
proposed model according to the actual power under
voltage disturbances. The actual system varies under
voltage changes. Thus, it is not easy to presume
CHBMD as constant load.
To study the frequency performance of the
proposed model, a frequency value change between
52.5 Hz to 47.5 Hz is applied at the grid source.
This frequency validation starts at 3.3 s and ends at
3.9 s. Figure 3 shows the dynamic reaction of the
actual power in the simulation model under
frequency changes. It clearly verified the accuracy
of the proposed model according to the actual power
under frequency disturbances.
After studying and confirming the sensitivity of
the proposed model in disturbances situations of
voltage and frequency, the accurate study of the
proposed model is done by analyzing the system
response in different situations like changes in
motor torque, the value of DC link capacitance, and
the PI controller parameters.
Fig. 2: Reaction of Proposed Model under Voltage
disturbances
Fig. 3: Reaction of Proposed Model under
Frequency disturbances
Three study cases were considered to study the
MV-CHBMD system sensitive to torque changing.
The three statuses are 75%, 100%, and 125%
loading to the motor. Figure 4 shows the proposed
model responses under torque changing.
Fig. 4: Reaction of Proposed Model under torque
changing
It clearly verified the accuracy of the proposed
model according to the actual power under torque
changing. The simulated results show the load
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.45
Adil Alahmad, Firat Kacar,
Cengiz Polat Uzunoglu, Nikos Mastorakis
E-ISSN: 2224-350X
463
Volume 18, 2023
significantly affects steady and responses for the
actual power. Three cases were considered to study
the MV-CHBMD system sensitive to changing DC
link capacitance values. The three values of DC link
capacitance are 9.2mF, 10mF, and 18mF. Figure 5
shows the proposed model responses under DC link
capacitance different values.
Fig. 5: Reaction of Proposed Model under DC link
capacitance different values
It clearly verified the accuracy of the proposed
model according to the actual power under DC link
capacitance different values. Three cases were
considered to study the MV-CHBMD system
sensitive to changing PI controller parameters. The
three values of PI controller parameters are
(Kp=1.25 & Km=1.26), (Kp=8 & Km=9), and
(Kp=0.25 & Km=0.02). Figure 6 shows the proposed
model responses under PI controller parameters with
different values.
Fig. 6: Reaction of Proposed Model under PI
controller parameters different values
It clearly verified the accuracy of the proposed
model according to the actual power under PI
controller parameters with different values. The
proposed model can recover after a short time of
disturbances and back to steady-state values. it is
essential to use specific PI controller parameters for
the model, otherwise, the model will not back to the
steady status after big disturbances, therefore, the
results of the simulation will not match the actual
results.
4 Conclusion
The accurate analysis of the proposed model shows
that critical parameters of the system have a
significant effect on the overall response and
reaction of the model. The user should take into
consideration the system parameters' impact,
operating situation, and disturbances limits when
creating its own model. If it is not provided, it could
be assumed the closest value possible to actual
value. The MV-CHBMD model system is proposed
in this work using the mathematical equation. The
Model sensitivity is confirmed by applying different
situations, like voltage and frequency disturbances.
The most important parameters that affect the
stability of the system are evaluated and analyzed
with various values, which confirm the model's
accurately and sensitivity. The proposed model has
the perfect ability to implement in the big system
simulation results without any effect on the
accuracy or the memory of used software due to its
low space program.
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Adil Alahmad, Firat Kacar,
Cengiz Polat Uzunoglu, Nikos Mastorakis
E-ISSN: 2224-350X
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Volume 18, 2023
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Cengiz Polat Uzunoglu, Nikos Mastorakis
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WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.45
Adil Alahmad, Firat Kacar,
Cengiz Polat Uzunoglu, Nikos Mastorakis
E-ISSN: 2224-350X
466
Volume 18, 2023
