P.Kaseem1, M.Ramasekhara Reddy2
PG Scholar, Power and Industrial Drives,
Dept. of EEE, JNTUA college of Engg., Ananthapuramu, AndhraPradesh, India1
Assistant Professor, Dept. of EEE, JNTUA College of Engg.,
Ananthapuramu, Andhra Pradesh, India2
Abstract
This
paper proposes a detailed control strategy for multiple parallel connected
converter units integrated with wind turbine driving PMSG. A model of multiple
rectifiers in parallel with common dc link and zero sequence current dynamics
are derived and analyzed. The structure of parallel back to back pulse width
modulation converters are adopted for multi megawatt high power generation
system. The fuzzy based controller is developed to restrain circulating currents
flows between the power modules caused by power device discrepancy and asynchronous
operation of the parallel units. The control driving signals are generated by individual
current control and produced by carrier phase shifting synchronously. The effectiveness of the proposed control
strategy is verified through MATLAB simulations.
KEYWORDS: PMSG, Zero sequence
current, parallel operating controllers, Fuzzy logic controller
Introduction
Wind
is one of the most abundant renewable sources of energy in nature. Wind energy
can be harnessed by a wind energy conversion system (WECS) 4-5 composed of
a wind turbine, an electric generator, a power electronic converter and the
corresponding control system. Based on the types of components used, different
WECS structures can be realized to convert the wind energy at varying wind
speeds to electric power at the grid frequency. The most advanced generator
type is perhaps the permanent magnet synchronous generator (PMSG). This machine
offers, compared at the same power level and machine size, the best efficiency
among all types of machines with high robustness and easy maintenance due to
slip ring?less
and exciter?less
features. The inherent benefit of permanent magnet which supplies rotor flux in
synchronous machines without excitation loss supports the wind power generation
development. This thus results in the increasing use of PMSG 3.
The
rectifiers in parallel connected to the PMSG have the advantage of higher
reliability, high efficiency, and lower grid side harmonics The parallel
configurations 2–9 can be classified as parallel voltage source converters(VSC)
with separate direct voltage links and parallel VS converters(VSC) with a common direct voltage link. For
multiple converters in parallel with a common dc bus, when discontinuous Space-Vector
Modulation (SVM)7 is used, due to different switching characteristics and
impedance discrepancy of individual converter, even if synchronized control of
each converter is applied, the switching status of the converters in parallel
will differ from each other. This creates currents that flow among power
switching devices and will flow in a circular loop between the power converters
and not affect the net current in either the generator or the power grid. The
circulating currents load switching devices and other components heavily,
distort waveforms, and might damage converters. Further, these currents may
cause a direct error in the measurement of ground fault currents of that loop,
thereby making fault detection more difficult. Large common mode inductors are
required to limit the amount of circulating currents between the converters.
The particular discontinuous SVM modulation scheme was proposed without using
zero vectors. However, since it was not attempted to reject zero sequence
disturbance, any mismatches between the parallel converters can still cause
zero sequence current even without using zero vectors. New modulation schemes
8 introduce a new control variable to adjust the duration of zero vectors
instead of eliminating the zero vectors. This method can effectively inhibit
the zero sequence circulation.
As
shown in Fig.1, The structure of parallel back to back PWM converters is adopted
for multi megawatt high-power
generation system
Fig.1.
High-power direct-drive variable-speed PMSG wind generator system connected to
the power grid.
Fig.2.
Multiple three-phase PWM rectifiers with parallel connection.
This
model provides separate control of the generator side converter and grid-side
converter. The interconnection of the power converters in this manner can
accommodate not only multiphase but also three phase generators for WTs. In
this paper, zero-sequence circulation mathematical model is derived and
analyzed. An improved space vector SVPWM parallel control strategy is presented
to repress the zero-sequence circulating current. Independent current
regulation is implemented for each branch power module.
II. CIRCULATING CURRENT CONTROLLER
The
term circulating current has been generally used to depict streams that stream
among the converter units in parallel 1. In rehearse; a circling current is
thought to be a present that goes amiss from the sought burden current level
just as shared by the paralleled units.
A.
Expression of the Circulating Current at Generator Side
Fig.
2 shows n rectifiers in parallel; all the active switches are assumed to be ideal
switches, and the equivalent series resistances of inductors are also
considered.
Fig.
3. Circulating current among multi converters.
Applying
Kirchhoff’s voltage law, the following equations can be obtained corresponding to
a-phase, respectively:
(1)
is the voltage between the negative end of
and neutral point. Where Zj =
d/dt + Rj,j?{1, 2, . . . , n}, the
general phase current expression for any individual branch unit in parallel
connection.
(2)
Where
k ?{a, b, c};
is the k-phase line current of the jth
converter,
is the source voltage. The circulating
currents for n paralleled three-phase converters in Fig. 3 can be
defined as follows. Considering the circulating current for the first
branch unit B1 as displayed in the Fig.3,
denotes the circulating current between
B1 and B2.
denotes the circulating current between B1
and B3. Similarly, the circulating current between B1 and Bn
is denoted as CCk1n. Therefore, the k-phase
circulating current of the first converter CCk1 consists of n circulating-current
components as follows:
(3)
The
expression for the k-phase circulating current of the jth
converter can be derived 9 as follows
(4)
Where
i ? j and
and
are the k-phase line current of the jth and
ith converter respectively. The general expression of the circling current of
the jth converter is determined as
(5) It is shows that both the output dc voltage
and the three ac phase voltages contribute to the generation of the circulating
currents. The impedance of the kth converter in a particular circulating
path also influences the magnitude of its circulating current.
B. Circulating-Current Model of Three-Phase
Parallel Converters in abc Coordinate
A
phase-leg-averaged model for a single two-level three phase rectifier is shown
in Fig. 4 8.
Fig.
4. Phase-leg-averaged model of a single two-level three-phase rectifier.
Applying
Kirchhoff’s voltage law and the current law to node n ( at
) results in a set of differential
and algebraic equations
(6)
The
system equation can be written as
(7)
Applying
Kirchhoff’s voltage law to loops that are formed among the converters results
in 3n ? 1 algebraic equations
(8)
Where
k ? (a, b, c) and Rs and Ls are the equivalent
resistance and inductance of the PMSG, respectively
Applying
Kirchhoff’s current law to node n (at
) results in one algebraic equation
(9)
Differentiating
(9), we get,
(10)
Assuming
=
= · · · = Ln and
=
= · · · =
Further
arranges the set of equations as the state-space form
(11)
Where
T
Is the State vector
U=
,
,
,
,
,
, . . . . ,
,
,
T
I
is the input vector. Y is the output vector. The state matrix is
A=
And
the input matrix is
B=
The
output matrix C is the identity matrix with the dimensions of 3n × 3n
T
=
I is the identity matrix
with the dimensions of 3× 3. The transfer function matrix is calculated
in the Laplace domain based on the state-space model.
G(s)
= C(sI-A)-1B
=
(12)
Where
the first terms represent the circulating-current part and the second terms
represent the currents that flow from the PMSG to the converters
C.
Model of Three-Phase Parallel Converters in d?q?0 Rotating Coordinate
Assuming
that the voltage udc and current are continuous and with small ripples,
the phase voltage expression is ukj = dkjudc. Compared with the
inductance, the resistance of each power module is small. Neglecting
resistance, the state-space equations for the two converters in parallel
connection are
(13)
(14)
By
transforming (13) and (14) from the stationary reference frame into the
synchronous d?q?0 rotating reference frame 6
(15)
(16)
(17)
Where
? is the ac line frequency. Ud?uq?u0 is the d?q?0 axis
components of the ac voltage in the d?q?0 reference frame, respectively.
id1?iq1?i01 and id2?iq2?i02 are the d?q?0
components for the first converter and second converter, respectively. dd1?dq1?d01
and dd2?dq2?d02 are the d?q?0 components of the
duty cycles for the first converter and second converter, respectively.
u0 = usa + usb + usc and
d0 = da +db + dc. The equivalent circuit of
three-phase parallel rectifiers in the d?q?0 rotating reference frame is
shown in Fig. 5. It is noted that a zero-sequence current occurs in the 0-axis
and plays a significant role in the paralleled multiple rectifiers.
D. Zero-Sequence Current
Control Scheme
Fig. 6. Shows the designed control scheme for zero
sequence dynamics developed according to the equivalent circuits of three phase
parallel Converters in d-q-o rotating reference
frame.
.
Fig.
5. Equivalent circuit of three-phase parallel rectifiers in d?q?0
rotating Reference frame.
Fig.6.
Zero-sequence current control scheme.
A modified SVPWM control strategy is proposed
for parallel converters. Individual branch unit uses a separate current
regulator. The controlling algorithm can be summarized as follows: First, the
zero sequence current is suppressed by using a fuzzy controller on the 0-axis
which produces the output zero-sequence voltage
. The reference voltage vectors
and
are transformed
into the stator coordinate by coordinate transformation, according to the
sector in which the reference vector stays by using SVPWM modulation, and duty
cycles are calculated. Second, the zero sequence output voltage is normalized
and superposed with modulation duty cycles. Finally, the resulting duty cycle
will be compared with the modulating carrier wave, and the switching function
is obtained.
From
the Fig. 5, the two parallel rectifiers contain a zero sequence current path in
d?q?0 reference frame due to the discrepancy of 0-axis duty cycle components. From
(15) and (16), The dynamics of zero-sequence current
are expressed The second term on the right can
be expected as a disturbance.
The
fuzzy controller can be cascaded with the plant to achieve closed-loop current
regulation. The bandwidth of the
control can be designed to be high, and a
strong current regulation that suppresses the zero sequence current can be
achieved. For n number of rectifiers in parallel, the sum of zero
sequence currents is equal to zero, i.e.,
+
+ · · · +
= 0. Due to the
interaction among the n currents, the number of independent
zero-sequence currents is n ? 1. The number of zero sequence current
controllers should be n ? 1 for n parallel rectifiers.
III. FUZZY LOGIC CONTROLLER
Fuzzy
logic controller, approaching the human reasoning that makes use of the
tolerance, uncertainty, imprecision and fuzziness in the decision making
process and manage to propose a very satisfactory operation, without the need
of a detailed mathematical model of the system, just by integrating the expert’s
knowledge into fuzzy rules. In addition, it has essential abilities to deal
with noisy date or inaccurate, thus it has able to develop control capability
even to those operating conditions where linear control techniques fails i.e.,
large parameters variations.
Rule
Base: It consists of a number of If-Then rules. Then side of rules is called
the consequence and If side is called antecedent. These rules are very similar
to the human thoughts and then the computer uses the linguistic variables. Rule
base of FLC is listed in table 1
TABLE 1.MEMBRSHIP FUNCTI0N TABLE
FUZZY RULES
E(n)
NB
NS
ZE
PS
PB
NB
NS
ZE
PS
PB
ZE
PB
PB
PS
PS
PS
PS
PS
ZE
ZE
PS
ZE
ZE
ZE
NS
ZE
ZE
NS
NS
NS
NS
NS
NB
NB
ZE
IV.
CONTROL OF PMSG WITH MULTIPLE RECTIFIERS
In
wind turbine PMSG systems, three system variables need to be strictly
controlled 6: (1) the optimal power generated by the PMSG at different wind
speed levels; (2) the active and reactive power injected into the grid; (3) the
DC bus voltage of the back to back converter. The proposed system contains a
direct-drive wind turbine PMSG fed by a back-to-back converter. The use of
parallel converters compared with a solution with only one converter is higher
reliability, higher efficiency, and the possibility of extremely low grid
harmonics.
In
parallel connection, one converter unit functions as a master and the others
function as slaves. A serial communication bus is arranged between the
converter units in which each unit has its own modulation cycle counter and it
is synchronized with each other on the basis of serial communication messages.
In this manner, the modulation counters operate as simultaneously as possible.
Fig.
7. Overall structure for the control of parallel multi converters on the
machine side
Carrier
phase-shifting modulation technique 10 has a great advantage for power
converters in parallel. When a module fails to operate, the master controller
just changes the corresponding carrier phase angle and limits the capacity of
the system, other modules can continue to work, standby unit can also be
activated, and full-power operation can still be achieved. The PMSG is
controlled by two 750-kW generator-side converters connected in parallel in a
rotor rotating d?q axis frame, with the d-axis oriented along the
rotor-flux vector position. In this way, the d-axis current is held to
zero to obtain maximum electromagnetic torque with minimum current. The optimum
active power setting or torque reference can be calculated according to maximum
power point tracking strategies. The two sets of PWM driving signals are
generated by using separate current regulators and produced by
carrier
phase-shifting synchronously. The rotor position is fed by the rotor position
observer without any position sensor. Each converter module is independent of
each other identifying the rotor flux position. The currents of each module are
balanced and synchronized with respect to each other producing the optimal
total generator torque. This arrangement will reduce the requirements for large
impedance needed to equalize the current sharing and allow increasing the power
handling capability for a converter with parallel connection. The zero-sequence
current fuzzy controllers have been integrated with the control of parallel
converters.
V. Simulation Results
Fig8.Ten
kilowatt generator side circulating current with PI controller
Fig.9.
Ten kilowatt grid side circulating current with PI controller
Fig.10.Generator
currents of individual
converter when generator operated at 1.5KW with PI controller.
Fig.11.
Three phase Generator currents of individual converter when generator operated
at 1.5KW with PI controller.
Fig.12.Ten
kilowatt generator side circulating current with Fuzzy controller
Fig.13.
Ten kilowatt grid side circulating current with Fuzzy controller
Fig.14.
Three phase Generator currents of individual converter when generator operated
at 1.5KW with Fuzzy controller.
Fig.15.Generator
currents of individual
converter when generator operated at 1.5KW with Fuzzy controller
OBSERVATION TABLE
Circulating
currents
Total
harmonic distortion (THD)
With
PI controller
Fuzzy
Logic Controller
Generator(10KW)side
circulating current
29.20%
17.52%
Grid
side circulating current
33.14%
28.16%
Generator(1.5MW)
currents of individual converter
35.86%
25.26%
Three
Phase Generator(1.5MW) currents of individual converter
34.13%
20.20%
V. CONCLUSION
This
paper has described the control schemes of a permanent magnet wind power
generator connected to parallel converters with common dc link. A dynamic model
of zero-sequence currents has been derived and analyzed for a number of n three-phase
PWM rectifiers in parallel connection.
The
zero sequence currents are effectively controlled and suppressed by using the
model technique SVPWM with fuzzy logic controller.
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