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2014 17th International Conference on Electrical Machines and Systems (ICEMS),Oct. 22-25, 2014, Hangzhou, China
Abstract — Neutral-point-clamped (NPC) multilevel-converter
(MLC) is very popular in high voltage converters with multilevel
topology. However, the dc-link capacitor voltage unbalance of
this topology is a key issue in the NPC applications, and which
will cause distortion and asymmetry of the output voltages, and
also increase the voltage stress of power switches. In this paper,
the three-level (3L) NPC with unbalance capacitor voltages is
analyzed. A capacitor voltage balancing control strategy based on
fuzzy logic controller (FLC) for the 3L-NPC-MLC is studied andpresented. A fuzzy membership function is ratiocinated and
determined, and based of which a capacitor voltage control
strategy to suppress the capacitor voltage imbalance is proposed.
Finally, simulation results show that both the balancing strategy
and the FLC are effective.
I.
I NTRODUCTION
Multilevel power converters are a fast developing
technology and potentially useful for wide range of
applications, such as active power filtering, static VAR
compensators, wind power, photovoltaic power, marine drivers,
steel rolling mills, and other adjustable speed motor drivers, to
name a few. Many of these processed have been continuouslyincreasing their demand for power which can be dealt through
the following two different ways:
1) Maintaining traditional converter topologies and through
developing semiconductor technology to reach higher nominal
voltages and currents [1]-[2].
2) Developing new converter topologies with traditional
semiconductor technology such as multilevel converters [3]-
[4].
The first approach inherits the benefit of well-known
circuit structures and control methods. However, the newer
semiconductors are more expensive and need power filters to
fulfill power quality requirements. While the second approach
uses the well-known and cheaper semiconductors, but needsmore complex circuit structures.
Three-level neutral-point-clamped multilevel-converter
(3L-NPC-MLC) was initiated by invention of NPC inverter by
the authors in [5], and it is now proven technology for
medium-/high-voltage high-power applications [6]-[7].
However, the 3L-NPC-MLC has an inherent problem of
unbalanced voltages across dc-link capacitors due to various
internal and external factors such as load unbalance,
nonuniform distribution of charges, nonidentical properties of
dc-link capacitors and so on [3][8].
Neutral-point (NP) voltage balancing issue in 3L-NPC-
MLC has been widely discussed in the past [9]-[11]. Many
balancing control strategies have been proposed to solve this
problem in the last decades. Reference [12] discusses a
transformerless hybrid active filter which consists of an active
filter using a three-level diode-clamped converter and a passive filter tuned to seventh harmonic frequency, and
voltage balancing control characterized by superimposing a
sixth harmonic zero-sequence voltage on the three-level
converter with triangle carrier modulation to keep the two dc
capacitors voltages well-balanced. A novel NP controller with
full power-factor range and low distortion has been proposed
in [13], which has the minimum common voltage injection at
no unbalance or slight unbalance conditions. In [14], the
proposed modulation has a strong balancing ability at all
regions, yet it will increase the switching events and output
total harmonic distortion.
A capacitor voltage balance control strategy based on FLC
with little effect on switch events and output voltage is presented in this paper.
II. A NALYZE U NBALANCED CAUSES OF NPC-MLC
The topology of three-phase 3L-NPC-MLC is shown in Fig.
1, and the relationship between the phase-voltage of 3L-NPC-
MLC and the state of switches is listed in Table I which takes
phase A for an example.
Fig. 1. Topology of three-phase 3L-NPC-MLC
A Voltage Balancing Controller with Fuzzy Logic
Strategy for Neutral Point Clamped Multilevel
Converter
Bingyong Tai,
Congzhe Gao*
, Xiangdong Liu, Jingliang LvScholl of Automation, Beijing Institute of Technology, China
E-mail: [email protected]
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Table I
Relationship between phase-voltage and switch state of phase A
1 xS
SwitchState
out V
11S 12S 13S 14S
( )2dc
V p+ on on off off
0(o) off on on off
( )2dcV n− off off on on
Under the condition of adopting fundamental frequency as
the control signals of switches, the phase-voltage changes
between2
dcV − , 0 and2
dcV + , at the same time, the line-
voltage can be synthesized as five-level staircase waveform
without unbalance of NP voltage. The output voltage
waveform of three-phase 3L-NPC-MLC where 800VdcV = is
shown as Fig. 2, which has less harmonic component and
much more close to sine waveform.
Fig. 2. Waveform of phase-voltage and line-voltage of 3L-NPC-MLC with
balanced NP voltage
Fig. 3. Waveform of phase-voltage and line-voltage of 3L-NPC-MLC with
unbalanced NP voltage
However, the synthesized five-level staircase waveforms
have produced distortion when the NP voltage is unbalanced,as shown in Fig. 3. And the voltage distortion will be moreserious with the increase of load current.
As can be seen from Fig.1, the relationship between upper
capacitor current1C
i and lower capacitor current2C
i under the
condition of 1 2C C C = = can be expressed as:
1 22
m
C C
ii i= = (1)
where mi is the NP current.
In dynamic state, mi can be expressed as:
2 22 22 2 2
C C m C
du dui i C C
dt dt = = − = − (2)
The relationship between NP voltage NP V and NP current
mi is determined as in (3) when the NP voltage is referenced to
the negative terminal of DC bus.2 2
2 2
NP C C mdu du i i
dt dt C C = = − = − (3)
According to expression (3), it can be seen that the
unbalanced voltage in NP is caused by the NP current mi , and
which is also related with the capacitance of DC bus. However,
as shown in Table I, each phase has three switch states “p”,“o”, and “n”, and the neutral point connects with load via
clamped-diode in state “o”. NP balanced voltage also depends
on whether the load is balance and the power factor of the load.
The following design of NP balance controller and the fuzzy
logic strategy is based on balance load and adjusts the switches
of state “o” to keep the NP current mi a constant which is
closed to zero.
III. CONTROLLER DESIGNED WITH FUZZY LOGIC STRATEGY
Fuzzy logic has rapidly become one of the most successful
of today’s technologies for developing sophisticated control
systems. With the aid of fuzzy control, complex requirementsmaybe implemented in amazingly simple, easily maintained,
and inexpensive controllers. The same fuzzy technology, in the
form of approximate reasoning, is also resurfacing ininformation technology, where it provides decision-support
and expert systems with powerful reasoning capabilities bound
by a minimum of rules [15]. The structure of FLC which
consists of fuzzification, fuzzy reasoning, fuzzy knowledge base and defuzzification is shown in Fig. 4.
Fig. 4. Structure of FLC
The designed NP voltage balancing controller with fuzzylogic strategy is based on Mamdani Fuzzy System which
requires two input variables (e, ec) to control the outputvariable (u), and where “e” is the voltage deviation of down
capacitor, “ec” is the variation of “e” and “u” is the controlled
parameter that adjusts switch state of state “o”.
The domain of discourse of “e”, “ec” and “u” is defined as
follows:
e = {-6, -5, -4, -3, -2, -1, -0, +0, +1, +2, +3, +4, +5, +6};ec = {-6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6};
u = {-6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6};
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Table II
Valuation of the fuzzy variable “e”
e
( ) A x µ
E
-6 -5 -4 -3 -2 -1 -0 +0 +1 +2 +3 +4 +5 +6
NB 1.0 0.8 0.4 0.1 0 0 0 0 0 0 0 0 0 0
NM 0.2 0.7 1.0 0.7 0.2 0 0 0 0 0 0 0 0 0
NS 0 0 0.1 0.5 1.0 0.8 0.3 0 0 0 0 0 0 0
NO 0 0 0 0 0.1 0.6 1.0 0 0 0 0 0 0 0
PO 0 0 0 0 0 0 0 1.0 0.6 0.1 0 0 0 0
PS 0 0 0 0 0 0 0 0.3 0.8 1.0 0.5 0.1 0 0PM 0 0 0 0 0 0 0 0 0 0.2 0.7 1.0 0.7 0.2
PB 0 0 0 0 0 0 0 0 0 0 0.1 0.4 0.8 1.0
Correspondingly, the fuzzy set of “e”, “ec” and “u” isdefined as follows:
E = {NB, NM, NS, NO, PO, PS, PM, PB};
EC = {NB, NM, NS, O, PS, PM, PB};
U = {NB, NM, NS, O, PS, PM, PB};2( )
( ) x a
b A
x e µ −
−
= (4)
Normal function such as (4) is adopted to determine the
membership functions, where
( , 4, 2, 0, 0, 2, 4, ), 0a b b b∈ − − − − + + + + >
and “b” is also a positive number.
The values of all the three fuzzy variables “e”, “ec” and “u”
have been ratiocinated and calculated in this paper, but onlythe value of “e” is listed in Table II. However, membership
functions of all three variables which are determined finally
and used in simulations are illustrated in Fig. 5, Fig. 6 and
Fig.7 separately.
Fig. 5. Membership function of input variable “e”
Fig. 6. Membership function of input variable “ec”
Fig. 7. Membership function of output variable “u”
And the behavior of the control surfaces is defined asfollows, which is listed in Table III. Using MATLAB/Fuzzy
Logic Toolbox, the 3D visualization of the inference rules is
shown in Fig. 8.
Table III
Fuzzy rulesE
UEC
NB NM NS NO PO PS PM PB
NB PB PB PB PM PM PM NM NB
NM PB PB PS PS PM PM NM NB
NS PB PM PS PS PS PS NM NB
O PB PM PS O O NS NM NB
PS PB PM NS NS NS NS NM NBPM PB PM NM NM NM NS NS NB
PB PB PM NM NM NM NB NB NB
Fig. 8. 3D visualization of the inference rules
IV. SIMULATION R ESULTS
Structure of NP voltage balancing controller with fuzzy
logic strategy is studied and designed, and based of which the
simulation model using MATLAB/Simulink Toolbox is
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detailed in Fig. 9. The NP voltage balancing control unit is
formed by fuzzy calibration unit and FLC which consists offuzziness of inputs, setting-up of fuzzy control rules and
certainty of output.The effectiveness of the voltage balancing strategy and the
FLC was verified by simulations, and the simulation results
were shown in Fig. 13, Fig. 14, Fig. 15 and Fig. 16. In order to
contrast, the simulation results of 3L-NPC-MLC without NP
voltage balancing strategy as shown in Fig. 10, Fig. 11 and Fig.12.
In the simulation, the dc-link voltage was set to 800V , and
1 2800V =400V
2 2dc
dc dc
V V V = = = . The Three-Phase Series
RL Branch was taken as three-phase load where R 5= Ω and
L 5mH= .
Fig. 9. Simulink model of 3L-NPC-MLC with NP voltage balancing FLC
The NP voltage unbalance of 3L-NPC-MLC is caused byvarious internal and external factors. The unbalance voltage
state which has been simulated in this paper was illustrated in
Fig. 10, where the unbalance voltage offset compared with thereference voltage
2dc
V has been up to 100V± .
Fig.10. Unbalancing voltages of equalizing capacitors
Under the unbalancing condition as shown in Fig. 10, output
voltages of the 3L-NPC-MLC without NP voltage balancing
strategy and FLC have produced serious distortion. Line-
voltage abU , phase-voltage aU and U was shown in Fig. 11
and Fig. 12.
Fig. 11. Line-voltageabU without NP voltage balancing FLC
Fig. 12. Output voltages without NP voltage balancing FLC
Under the same unbalancing condition which is shown in
Fig. 10, but the NP voltage balancing strategy and FLC has
been adopted, the NP voltage has been controlled balance as
shown in Fig. 13. At the same time, output voltages have got
good waveform and the load current has low total harmonicdistortion. Fig. 14, Fig. 15 and Fig. 16 show the simulation
waveforms separately.
Fig. 13. Balancing voltages of equalizing capacitors
Fig. 14. Line-voltageabU with NP voltage balancing FLC
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Fig. 15. Output voltages with NP voltage balancing FLC
Fig. 16. Three-phase load current
V. CONCLUSION
The NP voltage balancing FLC for 3L-NPC-MLC presented
in this paper has good capacitor voltage imbalance suppressionability. The fluctuation of output voltages can be controlled
nearly at zero and the NP voltage has low ripple as well. At thesame time, with three-phase load, the waveforms of three-
phase load current are more close to the sinusoidal waveform
and also have much lower total harmonic distortion.
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