Power Distribution Control between Cells with
Imbalanced Load for Modular Multilevel Multiport
Converter
Takumi Yasuda
Dept. of Science of Technology
Innovation
Nagaoka University of Technology
Nagaoka, Japant_yasuda@stn.nagaokaut.ac.jp

Jun-ichi Itoh
Dept. of Science of Technology
Innovation
Nagaoka University of Technology
Nagaoka, Japan
itoh@vos.nagaokaut.ac.jp

Abstract— This paper proposes a balancing control method
for load imbalance in one arm of a multiport converter based ona modular multilevel converter (MMC) topology. In themultiport converter with load imbalance, a balanced threephase current is achieved thanks to power distribution control.
However, the multiport converter has a limitation on theamount of load imbalance that can be compensated. This paper
derives the theoretical limitation of the compensation
capabilities using the proposed balance control for the load
imbalance. The proposed control method is demonstrated bysimulation, showing that balanced three-phase grid current isobtained in spite of the load imbalance and that the DC link
voltage error is limited to 1.4%. In addition, simulation andexperimental results clarify that the proposed controller haslarger compensation capability for the load imbalancecompared to the conventional control strategy.
Keywords—multiport converter, modular multilevel converter,
intra-arm balance controller

I. INTRODUCTION
In recent years, multiport converters have been actively
researched along with the development of a smart-grid andrenewable energy sources [1]-[2]. In particular, the multiportconverter with an MMC topology has been proposed as alarge-capacity battery energy storage system (BESS), a PV
power conditioner, and so on [3]-[5].
Fig. 1 depicts a multiport converter based on MMC for
BESS. The loads modeling the battery modules are connectedto each cell. The cascaded structure with low-voltage devices
eliminates the necessity of the line frequency transformer toconnect to the medium voltage grid and reduces the system
volume and the cost. In addition, the MMC topology has abetter fault-tolerance than other converter topologies thanks to
its high flexibility and scalability.
In the multiport converter, the power is interchanged
among cells in order to achieve both the balanced grid current
and the desired power distribution. Intra-arm balance
controller injects a different compensation voltage to the input
voltage of the cell in order to compensates the load imbalanceamong the cell belonging to the same arm. However, the intraarm balance controller has a limitation of the compensation
capability due to the over-modulation. Many studies have
utilized the conventional intra-arm balancing controller,
which distributes the arm voltage reference to the cell in
proportion to the load of the cell [5]-[7]. In contrast, the intraarm balance controller in [8] has improved the compensation

XXX-X-XXXX-XXXX-X/XX/$XX.00 ©20XX IEEE

Giuseppe Guidi
Energy Systems
SINTEF Energy Research
Trondheim, Norway
Giuseppe.Guidi@sintef.no

capability by an optimized combination of DC and the gridfrequency component of the input voltage of the cell. However,
the method in [8] does not consider the optimized phase angleof the grid frequency component. In contrast, Ref. [9] adjusts
the phase angle of the input voltage of the cell to extend thecompensation capability for the multi-port converter based on
MMC with single-star bridge cells (MMC-SSBC). However,the DC component is not considered in [9] because MMCSSBC has no capability of flowing the DC current due to its
topology. Therefore, the intra-arm balancing controller in [9]is not suitable for the multiport converter shown in Fig. 1.
This paper proposes an intra-arm balance controller withan extended compensation capability. The proposed controllerchanges the frequency of compensation voltage depending on
the state of the arm current. In addition, the theoretical limit of
the load imbalance that can be compensated with the proposed
controller is clarified. The proposed method is evaluated bysimulations and experiments. The simulation and theexperimental result under the load imbalance of 8.0%
demonstrates that the total harmonic distortion (THD) of thethree-phase grid current becomes 0.9% and DC link voltage
error is limited to 1.4% thanks to the proposed method.
Furthermore, these results show that the selection of thecompensation voltage has little effect on the other controllers.

iarm

cell
1

varm

cell
N
MV
AC

L

load

load

cell
1
cell
N

load

load

cell
1
cell
N

load

load

6.6 kV

cell
1
cell
N

load

load

cell
1
cell
N

load

load

load
cell
vcell,k
1

cell
N

cell
k

load

Pcell,k
C
Vc,k

load

Fig. 1. Concept of multiport converter based on MMC.

II. CONTROL STRATEGY FOR MULTIPORT CONVERTERThis paper discusses the operation of the system whendifferent loads are connected to each cell. The cells
interchange the power with each other in order to balance thegrid current.
A. Overview of controllers for multiport converter
Fig. 2 illustrates an outline of the control block diagram
for the multiport converter. The grid side control part and thebalance control part in Fig. 2 are the same to the control
method of the conventional MMC [4]. The traditional PI
control is applied for each controller in this paper. The gridside control part is implemented for the balanced three-phasegrid current. The total power controller controls input power
to the converter. The balance controller compensates the load
imbalance between the arms by the circulating current. The
circulating current consists of the DC and the grid frequency
component. The sum of the outputs from the grid side control
part and the balance control part is the command of the arm
voltage varm*, which consists of the DC and the grid frequency
component as in,NVcvarm =+ 2Vg cos  g t ,2(1)

where N is the number of cells in one arm, Vc is the DC link
voltage of the cell, Vg is the RMS value of the grid phasevoltage, and g is the angular frequency of the grid. The DC
link voltage Vc is assumed to contain no ripple voltage in thefollowing theoretical analysis. The arm current is the sum of
the grid current ig/2, which is distributed to the upper andlower arms evenly, the DC current I0 used for powerinterchange between the phases, and the grid frequency
component iω used for power interchange between the upper
and the lower arms, as shown in,

1
iarm = ig + I 0 + i  I 0 + 2 I1 cos (g t + i ) , (2)2where i is the phase difference of the arm current from thegrid frequency component of the arm voltage varm.
Voltage redundancy  is defined for the following
analysis as,
=

NVc
2 2Vg

.

(3)

The voltage redundancy  indicates the ratio of the peak-peakvalue of the arm voltage in (1) and the maximum output
voltage of one arm. The voltage redundancy of more than 1 isnecessary to shape the arm voltage without zero sequence
voltage, which is the condition for this paper.
B. Proposed intra-arm balance control
Fig. 3 depicts the proposed intra-arm balance controller.
The intra-arm balance controller regulates the DC link
voltage of the cells in one arm with the DC or the gridfrequency compensation voltage. Larger amplitude of thecompensation voltage is required as the load imbalance
increases. Meanwhile, the injection of the large compensation
voltage may cause the over-modulation. The proposed intraarm balance controller has two operation modes and selects
the mode which compensates the load imbalance with asmaller amplitude of the input voltage of the cell. The
proposed controller contains the following two compensation

Grid side control
Grid current
reference

Total
power
controllerLegbalancecontroller

+

+

Arm
balancecontroller(k: 1, 2, ..., N)

Gridcurrent
controller

Circulating
current
reference

Circulating
current
controller+Armvoltagereference
varm*

1
N

+

Cell
voltagereference*+ vce ll ,k+Intra-armbalancecontroller Compensation voltage
reference v,k *Balancing control
Fig. 2. Control block diagram.
mode 1

Eq. (4)
Selector(DC compensation voltage)

1 N
Vc,k
N k =1

+
Vc,k

Gdc
PI

V,k*

Gac
mode 2v,k* + N
+
×
*
varm*
v,1,kN
2 cos  t + V,0,k*(grid frequency
compensation voltage)

(

g



vcell,k*)Fig. 3. Proposed intra-arm balance controller.

methods.
<mode 1> DC voltage compensation mode: DC voltage isutilized for the compensation voltage v,k.
<mode 2> Grid frequency voltage compensation mode:
Grid frequency component is utilized for the compensation
voltage v,k. In the grid frequency voltage compensationmode, the phase angle of the compensation voltage  is set
according to the phase angle of the arm current i toachieve a maximized compensation capability.
The compensation capabilities of mode 1 and mode 2 dependon the arm current. For instance, under the arm current
condition of I0 = 0, the load imbalance cannot becompensated with mode 1 because the DC voltage generates
no active power. Similarly, mode 2 has no compensation
capability under the condition of I1 = 0. Thus, the mode
selection is performed according to the arm current. Mode 1
is selected under the arm current condition expressed in (4).


12 (  − 1) I 0    − max cos i   I1 .


(4)

The proposed controller selects mode 2 when (4) is false. The
proposed control extends the compensation capability by
selection of the modes with (4) compared to the conventional
controllers. The sum of the compensation voltage injected toeach cell in one arm is always zero and the arm voltage varm
always follows (1) in any loaded condition. Hence, the intraarm balance controller does not affect the other controllers
even when the mode change.
The compensation power becomes maximum when the
input voltage of the cell becomes in-phase with the arm
current as a result of injection of the compensation voltage.
On the other hand, the compensation power becomesminimum when the phase angle of the input voltage of thecell becomes opposite to the phase angle of the arm current.
However, the maximum and the minimum compensation
power cannot be achieved with same phase angle of thereference waveform . In order to improve thecompensation capability, the phase angle of thecompensation voltage is set as,Vc / 2Averagedarm
voltageImArmcurrent

2V g
NAveragedarm
voltagecompensation
voltage forheavier load

i



i

Arm
current

compensation
voltage forlighter load

Vc / 2

Vc / 2(a) For compensation voltage inphase with arm current.

Vc / 2Averagedarm
voltageIm

2V gN
Vc / 2compensation
voltage forlighter load
Vc / 2Re

compensation
voltage forheavier load(b) For compensation voltage
inversed in-phase with arm
current.
Arm
currentiVc / 2N

Vc / 2Re
Vc / 2

Vc / 2

2V g Im
Vc / 2N
2V g

Arm current

Vc

Cell voltage

iarm
angle

varm
N

Arm current

Voltage forcells with Vc
lighter load

iarm

i

Cell voltage

varmN

Voltage foricells with O
angle(a) With DC compensation heavier load (b) With grid frequency
O

angle

voltage.
compensation voltage.
(mode 1)(mode 2)
Fig. 5. Example of cell voltages with proposed intra-arm balance
control under imbalanced load in one arm.

imbalance.
compensation
voltage forheavier loadRe
Vc / 2compensation
voltage forlighter load(c) Reference waveform of 90
degree lead from arm voltage.
Fig. 4. Phasor diagram of grid frequency component of reference
waveform sin(gt+).

 sin i1−1...  cos i   Tan cos i − 1 sin i1 =  − Tan −1...  cos i  −  .
 cos i + 1






1

sign i  ...  cos i  
2






(5)

Fig. 4 shows phasor diagrams of the compensation
voltage of the grid voltage compensation mode (mode 2). In
mode 2, the phase angle of the reference waveform  is set
according to the arm current. The maximum available
amplitude of the grid frequency component of the input
voltage for the cell is Vc/2. The compensation voltage is
injected to the averaged arm voltage varm*/N as in Fig. 4. Fig.
4(a) shows the first row of (5). This condition is enabled when
the phase angle of the arm current i is close to that of the arm
voltage. As a result of the injection of the compensation
voltage, the input voltage of the cell can be in-phase with thearm current i. Hence, the compensation capability for theheavier load is maximized. In this condition, thecompensation capability for the lighter load imbalance islarger than that for the heavier load imbalance. That is
because the large amplitude of the compensation voltage isavailable for the compensation of the lighter load imbalance
as shown in Fig. 4(a). Fig. 4(b) shows the second row of (5).
This condition is enabled when the phase difference of thearm current and the arm voltage is relatively large. The phaseangle of the input voltage for the cell can be inversed withrespect to the arm current by the compensation voltage.
Hence, the compensation capability for the lighter load
imbalance is maximized. In this condition, the compensation
capability for the heavier load imbalance is larger than thatfor the lighter load imbalance. That is because the larger
amplitude of the compensation voltage is available for thecompensation of the heavier load imbalance. Fig. 4(c) shows
the third row of (5). This condition is enabled when theimaginary part of the arm current is relatively large as in Fig.
4(c). In this condition, the proposed controller has same
compensation capabilities for the heavier and the lighter load

Fig. 5 illustrates an example of the input voltages for thecell with the proposed method. In mode 1 shown in Fig. 5(a),the proposed controller injects the DC voltage to the input
voltage for the cell in order to compensate the load imbalance.
On the other hand, the proposed controller in mode 2 injects
the grid frequency voltage as shown in Fig. 5(b). In mode 2,
the phase difference between the arm current and the input
voltage for the cells is decreased as the cell has the heavier
load imbalance. Meanwhile, the phase difference is increased
as the cell has the lighter load imbalance. The input power toeach cell tracks to the command thanks to the proposed
controller.
III. THEORETICAL COMPENSATION CAPABILITY OF PROPOSEDINTRA-ARM BALANCE CONTROLLER
The command of the input voltage for the cell is decided
by the loads of the cells in the converter. In order to preventthe over-modulation, there is a limitation of the compensation
capability for the load imbalance with the proposed controller.
The minimum value of the input voltage for cell has to belarger than zero and the maximum value of the of the input
voltage for cell has to be smaller than the DC link voltage ofcell Vc as in,
0  vcell , k (t )  Vc .

(6)

Equation (6) causes the limitation of the compensation
capabilities due to the limitation of the available amplitude of
the compensation voltage.
Fig. 6 presents the limitation of the compensation
capability of the proposed intra-arm balance controller derived
from (6). Voltage redundancy  is shown on the horizontal
axis, and the load of each cell Pcell,k normalized by theaveraged load of the cells in the arm Parm/N is shown on thevertical axis. The proposed controller is able to compensate
the load imbalance when all loads in the arm are within theshaded region in Fig. 6. Otherwise, the arm current distortion
occurs due to the over-modulation. The simulation and theexperimental condition is indicated in Fig. 6(c). The larger
voltage redundancy extends the operation region in both mode
1 and mode 2 because the larger voltage redundancy, whichmeans larger DC link voltage Vc, increases the maximum
available amplitude of the compensation voltage. In mode 1,
the operation region extends as the DC current I0 increases
compared to the grid frequency component I1 as shown in Fig.
6(a). In the grid frequency voltage compensation mode, theoperation region extends as the grid frequency component ofarm current I1 increases compared to the DC current I0 as
shown in Fig. 6(b). In addition, the operation region with theheavier load imbalance extends when the phase difference of
the arm current i* increases as in Fig. 6(b) and (c). On theother hand, the operation region with the lighter load

Loa d of cell normaliz ed P
cellby ave raged load of
Parm / Ncells in arm [%]I0:I1=1: 1

200

I0:I1=1:0

I0:I1=1:1

100

Operation region0100Prohibited
200
1.0

2.0
NVc
Voltage redundancy 2 2V

3.0

g

(a)

With DC compensation voltage. (mode 1)

Loa d of cell normaliz ed P
cellby ave raged load of
Parm / Ncells in arm [%]I0:I1= 0.2:1(c)

I0:I1=1:1

6.0
0.0
6.0

Operation region50

I0:I1=0:1

0

200 Prohibited
100
0
100

2.0
NVc
Voltage redundancy 2 2V

3.0g

I0 : I1 = −0.2 :1

200

Grid current [A] (THD: 0.47%)

0.0

I0:I1=1:10

1.0

10 [ms](a) Grid phase voltage and grid current.
Modulation waveform [-]Modulation waveform [-]1.0 For lighter
For heavier
For heavier

0.5

100

10
0
10

Operation region100

I0:I1=0:1
Prohibited

200
1.0

Grid phase voltage [kV]

50

200
1.0

With grid frequency compensation voltage (mode 2) and i*=0.

Loa d of cell normaliz ed P
cellby ave raged load of
Parm / Ncells in arm [%](b)

TABLE I. SIMULATION CONDITIONS.
Parameter
SymbolValue
Rated power of cellPcell
2.2 kW
Grid line-line voltage
3Vg
6.6 kV (RMS)
Grid frequency
fg
50 Hz
Number of cells per arm
N50
DC link voltage of cellVc
269 V
Arm inductanceL
70 mH (0.20p.u.)
Cell capacitanceC
2.1 mF (UCC=35 mJ/VA)

2.0
NVc
Voltage redundancy 2 2V

3.0g

With grid frequency compensation voltage (mode 2) and i*=/6.
The maximum and the minimum load imbalance for thefollowing simulation and experimental conditions (Fig. 8 andFig. 12) are indicated.
Fig. 6. Theoretical maximum/minimum input power to cell.

imbalance becomes narrows when the phase angle of the arm
current i* increases.
IV. SIMULATION RESULT
Table I describes the simulation conditions. The maximum
load imbalance between the cells in each arm is 8.0% and theysatisfy the limitation as shown in (6). The unit capacitanceconstant (UCC) [10] of the cell capacitor is set to 35 mJ/VA.
Fig. 7 shows the steady state operation of the multiportconverter with the proposed controller. Fig. 7(a) shows thegrid phase voltage and current. The grid current with theproposed method is balanced with a THD of 0.40% and unity
power factor. Fig. 7(b) shows the modulation waveforms forthe cell with mode 1. The modulation waveforms for the cellwith the heavier load has the larger DC component than thatfor the cells with the lighter load in order to compensates theload imbalance. Fig. 7(c) shows the modulation waveforms
with mode 2. The modulation waveforms for the cell with theheavier load has larger amplitude of the grid frequency
component for the compensation of the load imbalance. In
addition, the phase angle of the modulation waveform for thecell with the heavier load becomes close to the phase angle of
the arm current. The proposed controller selects thecompensation voltage according to the state of the arm current.
Fig. 7(d) shows the DC link voltage of all 300 cells. The
voltage error between the averaged DC link voltage of eachcell and the command value of 246 V is approximately 1.6 V,

load

For
lighter load

Arm current [A]

20 [ms](b) Modulation waveforms forcells with DC compensation
voltage (mode 1).

300
250

0.5

load

load

0.0
50
0
50

Arm current [A]

20 [ms](c) Modulation waveforms forcells with grid frequency
compensation voltage (mode 2).

DC link voltage of cells [V] (error: 0.02%)

Command200
10 [ms](d) DC link voltage of all 300 cells.
Fig. 7. Simulation result of steady state operation with the proposed
method.

which is approximately 0.5%. These simulation results verify
the validity of the proposed controller.
Fig. 8 shows the operation when the intra-arm balancing
controller is switched from the proposed controller to theconventional controller [5]-[7]. The loaded condition isindicated in Fig. 6(c). The loaded condition satisfies (6) when
the proposed controller is applied, whereas it does not satisfy(6) when the conventional controller is applied. The converter
gains of these controllers are adjusted so as to prevent a shockat the controller change. Before the change, the cells operate
without over-modulation and the DC link voltage of the cells
are balanced. After the controller changes, the modulation
waveforms for some cells begin to saturate because theconventional controller cannot compensate the load
imbalance without the over-modulation. The DC link
voltages of cells are converged even if the conventional
controller is applied. However, the over-modulation causedby the conventional controller results in the distortion of thegrid current as shown in comparison with Fig. 8(b)-(c). This
simulation result reveals that the proposed controller
compensates larger load imbalance than the conventional
controller.

1.0

Modulation waveform [-]

Load

0.5
0.0
400
300
200
100
(a)

DC link voltage of cell [V]commandController change

0.2 [s]Transient behavior of modulation waveform and DC link voltage
of cells under controller change from proposed controller toconventional controller.
Grid current [A]Grid current [A](THD: 0.1%)(THD: 15.6%)
60
60

0

0

60

60

20 [ms]20 [ms](b) Grid current when the(c) Grid current 0.66 s after
proposed controller is applied.
controller change.
Fig. 8. Simulation result of operation with proposed controller andconventional controller.

V. EXPERIMENTAL RESULT
Fig. 9 shows the experimental setups. Table II describes
the experimental condition. The parameters for the simulation
are scaled down. The load imbalance in one arm of 8.0% isadded as in the simulated condition.
Fig. 10 depicts experimental waveforms of the steady state
operation of the multiport converter. Fig. 10(a) shows theexperimental result of the grid current with the proposed
controller. The grid current is balanced and in-phase with thegrid phase voltage. THD of the grid current is 0.9%. Fig. 10(b)and (c) show the modulation waveforms for the cells withmode 1 and mode 2, respectively. The proposed controller
selects the compensation voltage according to the state of thearm current as the simulation results. Fig. 10(d) shows the DC
link voltage of the cells in the phase. The voltage error
between the averaged DC link voltage of each cell and thecommand value of 21 V is 0.29 V, which is approximately
0.14%. These experimental results also verify the validity ofthe proposed controller.
Fig. 11 shows the transient behavior under a load changethat causes a change in the compensation mode. The load isbalanced before the load change and the load imbalance after
the load change are in the theoretical compensation capabilityof the proposed controller as indicated in Fig. 6(c). After theload change, a DC link voltage error appears and the DC
compensation voltage is injected to the modulation waveform
because the arm current has relatively large DC component
before the load change. The grid frequency component of thearm current is increased in order to compensate the load
imbalance between arms caused by the load change. As aresult, the proposed controller switches the mode and changes
the compensation voltage from the DC component to the gridfrequency component 0.14 s after the load change. The modeswitching of the proposed controller does not affect neither
the grid current nor the DC link voltage. The DC link voltage
converges to the command value of 21 V within 0.2 s after
the load change. This experimental result clarifies that the
proposed controller compensates the load imbalance without

Multi-port converter prototype
Fig. 9. The experimental setup of multiport converter prototype.

TABLE II. SIMULATION CONDITIONS.
Parameter
Rated power of cell
Grid line-line voltage
Grid frequency
Number of cells per arm
DC link voltage of cell
Arm inductance
Cell capacitance

Symbol
Pcell
3Vg
fg
N
Vc
L
C

Value
90 W
122 V (RMS)
50 Hz
12
21 V
1.5 mH (0.20p.u.)
15 mF (UCC=35 mJ/VA)

any effect on the other control loops, even in the event of amode change.
Fig. 12 shows waveforms when the intra-arm balancing
controller is changed from the proposed controller to theconventional controller [5]-[7]. The loaded conditions and theconverter gain are set same as in the simulation of Fig. 8.
Before the controller change, the cells operate without overmodulation and both the grid current and the DC link voltageof the cells are balanced. After the controller changes, themodulation waveforms for some cells are saturated. The
conventional intra-arm balancing controller cannot
compensate the load imbalance without entering overmodulation. The DC link voltages of the cells are balanced by
the conventional controller. However, the over-modulation
caused by the conventional controller increases the DC current
to the grid as shown in comparison with Fig. 12(b)-(c). This
experimental result verifies the theoretical analysis and theextended compensation capability of the proposed controller
compared with the conventional method.

VI. CONCLUSIONSThis paper proposed an intra-arm balance controller withan extended compensation capability. The proposed controllerchanges the frequency of compensation voltage with larger
compensation capability depending on the state of the arm
current. In addition, the limitation of the proposed controller
was clarified for the load imbalance conditions. The proposed
method was evaluated by simulations and experiments. The
simulation and the experimental result with the load
imbalance of 8.0% demonstrated that THD of three-phasecurrent became 0.9% and DC link voltage error became lessthan 1.4% thanks to the proposed method. Furthermore, these

150
0
150

Grid phase voltage [V]0
Grid current [A] (THD: 0.9%)

20

20

0.5

20

20 [ms]0.0

1.0(a) Grid phase voltage and grid current.
Modulation waveform [-]Modulation waveform [-]
1.0

0.5

0.5

20

0.0

0.0

15

Arm current [A]

20 [ms](b) Modulation waveforms forcells with DC compensation
voltage (mode 1).

25

20
0
20

25

Arm current [A]

15
0
15

20 [ms](c) Modulation waveforms forcells with grid frequency
compensation voltage (mode 2).

DC link voltage of cells [V] (error: 0.14%)

1.0

Command25(d) DC link voltage of cells in one phase.
Fig. 10. Experimental result of steady state operation with the proposed
method.

results showed that the selection of the compensation voltage
had little effect on the other controllers in the system.
ACKNOWLEDGMENT
This work was supported by the project Modular
Megawatt range Wireless EV Charging Infrastructure
Providing Smart Grid Services (MoMeWeC), funded under
the EIG CONCERT Japan program, Joint Call on Efficient
Energy Storage and Distribution, with project number 284231.
REFERENCES

[4]

[5]

[6]

Arm current [A]Load change

Mode change

Modulation waveform [-]0.0

20 [ms][3]

Command

0.5

15

[2]

Capacitor voltage of cell [V]

0.1 [s]Fig. 11. Experimental result of transient behavior with proposed
method under load change.

20

[1]

Modulation waveform [-]

1.0

0

10
0
10

Grid current [A]20

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20
15
(a)

CommandController change

0.2 [s]Transient behavior of modulation waveform and DC link voltage
of cells under converter change from proposed controller toconventional controller.
Grid current [A]Grid current [A](THD: 1.5%)(THD: 3.4%)
30
30

0

0

30

30
20 [ms]20 [ms](b) Grid current when the(c) Grid current 0.36 s after the
proposed controller is applied.
controller change.
Fig. 12. Experimental result of transient behavior under controllerchange from proposed controller to conventional controller.
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