2018 IEEE International Conference on Renewable Energy and Power Engineering
Distributed Generator in Grid-Connected Mode Using Improved Exponential
Sliding Mode Control
S. Sinan1, A. Elnady2 and M. Al-Shabi3
Electrical and Computer Engineering Department
University of Sharjah
27272 Sharjah, United Arab Emirates
E-mail: ssinan03@gmail.com1, anady@sharjah.ac.ae2, malshabi@sharjah.ac.ae3
considered to operate the DGS in both modes:
Grid-connected mode and stand-alone mode. In this section
the literature review is focused on the schemes used for the
grid-connected mode because the distributed generation
system in this paper is operated in a grid-connected mode.
Voltage oriented control (VOC), also called voltage
vector control, has been adopted to control the distributed
generation systems in a grid-connected mode such that it can
be used to inject active and reactive power based on the
system conditions [4-6]. Voltage oriented control is an
indirect scheme to control the output power since it controls
active and reactive power through the direct and quadrature
currents, respectively. The main controller in the control
loops is the PI controller or PR controller. The good
performance of the VOC is not guaranteed at different
operating conditions.
Another scheme used with the DGS is the sliding mode
control (SMC) [7-10]. The main structure of this scheme is
similar to the VOC because the power references is converted
into current references. The current error, generated between
the current reference and its corresponding feedback, is
controlled by the SMC to operate the DG. Several versions of
the 1st order SMC have been utilized to control the DGS.
These versions are classified based on the adopted reaching
law and the definition of the sliding surface, (sliding
manifold). The SMC with a differential form of the sliding
surface is employed in [7] to the control the DGS in a
grid-connected mode. The integral form of the sliding surface
is presented in [7-10]. A constant-rate reaching law, which is
expressed by the signum function, is utilized for the DGS
in [10]. A power-rate reaching law accompanied by a
boundary layer is used in [7-9] to improve the reaching mode
and to reduce its chattering at the sliding mode. All versions
of the 1st order SMC suffer from chattering in its output
power/current. This drawback triggers the utilization of some
advanced sliding mode controllers to control the DGS [11],
[12]. A 2nd order SMC, super-twisting technique, has been
formulated and employed to control the distributed generator
in a grid-connected mode and in stand-alone mode as
presented in [11]. The super-twisting technique presents a
better performance at the sliding mode in terms of the
chattering. Its performance is compared to the 1st order SMC
in [7]. The exponential SMC has been published before in
[13-14], and it is proved that this version offers a better
performance than the conventional SMC. This classical
Abstract—This paper shows the operation of the
distributed generation system using an innovative control
scheme. The core of this distributed generation system is the
distributed generator, which is based on the 5-level diode
clamped inverter. This distributed generator is operated by an
improved version of the exponential sliding mode control.
This developed sliding mode control perfectly fits the power
electronics based distributed generator to control the output
injected power, and it gives the shortest reaching time with
much less chattering at its output power. The performance of
the whole suggested control scheme along with the improved
sliding mode controller is verified using simulation results.
Keywords—Exponential sliding mode control, distributed
generation system, PD-PWM, and power control.
I. INTRODUCTION
The distributed generation system (DGS) has been
proliferating in distribution systems because it supplies the
distribution system with extra power needed for the operation
of the distribution system when the distribution system is
heavily loaded. The DGS is characterized by the generation
capacity of its distributed generator (DG) that is mainly
determined by the rating of the inverter circuit. The
generation capacity of the DG ranges from few KVA to few
MVA [1-3].
The penetration of the DGS in the distribution system is
continuously increasing nowadays because it brings a lot of
benefits to the distribution system when it’s tied to the
distribution system. The DGS achieves the following
benefits:
x It regulates the voltage at the point of common coupling
where it is installed.
x It injects more active power to the distribution system
under heavy loading conditions.
x It increases the overall stability of the system.
x It reduces the voltage drop and the power losses over the
distribution feeders since the power direction is reversed
in some feeders.
The DGS entails a control algorithm that precisely
controls the operation of the distributed generator in a fast
and accurate manner. Many control schemes have been
developed and employed for the DGS. These schemes are
978-1-5386-9365-0/18/$31.00 ©2018 IEEE
7
exponential SMC is modified in [15] to fit the operation of
the power electronics circuits. Its control law is modified by
adding one constant-proportional term to the discrete term of
its control law.
The most recent scheme to control the DGS is the direct
power control (DPC) [16-18]. This scheme is originated from
the direct torque control used to control the drive systems.
The DPC adjusts the power directly not through the currents
as mentioned before. The conventional DPC depends a
hysteresis controller and the space vector modulation (SVM),
which cause oscillation shown in the output power and
variable switching frequency. Several modifications have
been introduced to the DPC in order to improve its
performance and minimize its drawback. A look-up-table is
used to minimize the switching frequency [16]. Predictive
control is merged with the DPC to improve the performance
of the SVM and hysteresis controllers [17], [18].
The contribution of this paper is exemplified in using an
improved exponential sliding mode control to accurately
control the currents and consequently the injected power.
This improvement gives a better performance than what is
published in [13-14]. This paper has five sections, where the
second section shows the formulation of the exponential
sliding mode control. The third sections depicts the suggested
control scheme along with the proposed controller. The
fourth section displays the simulation results. The last two
sections demonstrate the findings and appendix of this paper.
where G 0 is a strictly positive offset less than 1, U is a
strictly positive integer, and D is strictly positive. The
formulas in (1-3) prove to be better than the conventional
SMC in terms of the reachability time defined and proved in
[13], [14]. The chattering is reduced at the sliding mode
because at the beginning of this reaching mode the value of
k
s is large; so the magnitude of the udis tends to be
.
G0
While at the end of the reaching mode, the value of
just
derived using the Lyapunov stability criterion. The final
expression of the ueq is given as,
1
1- The sliding surface in this research is defined by its
integral form as given in (7), while the sliding surface in
[13-15] is defined by its differential form, which does not
guarantee the minimum steady-state error (For instance some
results in [14] shows a clear steady-state error). This integral
SMC is defined as,
s
udis
(2)
The contribution in [13-14] is the definition of the
discrete input udis given as,
(3)
(4)
signum function and N ( s) is defined by,
( )=
+ (1 −
)
| |
k
N( s )
tanh( s )
(8)
modified from what given in (6) to fit the state-space model
of the system understudy since the state-space model is given
as,
x Ax Bu Fd
(9)
The continuous input u eq is modified to be
where k1 , k2 and k are the positive constant, the sign is the
traditional
(7)
The tanh function is selected because the signum
function does not perfectly match the operation of the power
electronics based systems like the system under study in this
paper since it causes sudden sharp changes in its output and
spontaneous deviation of the states from the sliding surface
leading to possible unstable operation. While the tanh
function is different since it does not produce these sharp
changes.
3- The definition of the continuous input u eq is slightly
(O1 O2 dt ) e
sign ( s )
N (s)
While in [15], the contribution is exemplified as,
k
u dis k1s 2 sign ( s )
N (s)
(O1 O2 ³ dt ) e
It is proved that the integral SMC gives less error than any
other form for the sliding surface [7].
2- The discrete term udis of the control law in this
research is innovatively defined as,
continuous input used to keep the states of the system on the
sliding surface (sliding mode). In [13-15], the sliding surface
is defined by its differential form as,
k
(6)
The improvement in the exponential SMC in this paper is
different from what has been published in [13-15] in the
following aspects:
where the udis is the discrete input, which is responsible
for reaching mode used for transferring the states of the
system from one sliding surface to another. The ueq is the
ª ws B º ws Ax
«¬ wx »¼ wx > @
ueq
The exponential SMC has been introduced in [13-15].
The contribution of this exponential SMC is in the definition
of its control law, which is expressed as,
u udis ueq
(1)
u dis
udis tends to be
k . The other term of the control law is the ueq , which is
becomes small; then the magnitude of the
II. FORMULATION OF EXPONENTIAL SLIDING MODE
CONTROL
s
s
=−
(5)
8
[
+
−
]
(10)
The proof of the formula in (10) along with its stability
analysis is given in the Appendix. After incorporating all
aforementioned changes, the improved exponential SMC is
ready to be merged with the proposed control scheme that
will be explained in the next section.
injected voltage of the distributed generator in the d-q frame
Ed DG required , Eq DG required . These two voltages are used
to generate a control signal whose magnitude and phase are
defined as,
M control signal
III. PROPOSED CONTROL SCHEME
( Ed2 DG required Eq2 DG required ) / Vdc
(12)
The proposed control scheme is illustrated in Fig. 1 along
with the model of the distribution system. In the
grid-connected mode, the DGS is tied to the distribution
system. Therefore, the DGS should be operated at a
constant-power mode. The power is controlled through the
injected currents. The power references are converted into
current references as,
Vq DG º ª P ref º
ª I d ref º
ª Vd DG
3
«
»
»
«
»«
2
2
Vd DG »¼ «¬Q ref »¼
«¬ I q ref »¼ 2(Vd DG Vq DG ) «¬Vq DG
(11)
where Vd DG ,Vq DG are the DGS voltages in the d-q frame.
T control signal
E
tan 1( q DG required )
Ed DG required
(13)
This generated control signal is utilized to operate the
in-phase disposition pulse width modulation (PD-PWM) [19]
to operate the inverter based distributed generation.
IV. SIMULATION RESULTS
This section shows the results of the proposed control
scheme of Fig. 1 for the DGS when it is connected to the
distribution system.
A. Power System Under Study and Distributed Generator
I d ref , I q ref are the required injected currents (current
The distributed system under is already depicted in Fig. 1,
and its parameters are listed in Table 1. The parameters of the
exponential sliding mode controller are given in Table 2.
references) in the d-q frame. These current references are
compared to the feedback currents I d DG , I q DG as shown
in the Fig. 1.
TABLE I: DISTRIBUTION SYSTEM PARAMETERS
Description of Parameters
Values
Rating of the DGS
2.5 MVA
Type of the transformer
Step-up
Rating of the transformer
2.5 MVA
Turn’s ration of the transformer
5
Resistance of the tie feeder
0.9 Ω
Inductance of the tie feeder
3 mH
Rated voltage of Distribution system
6.6 kV
Loads at distribution system
Parameter
k
G0
D
U
Figure 1. Proposed control scheme with distribution system understudy.
50+31.4j
TABLE II: CONTROLLER PARAMETErs
Its value for active
Its value for reactive
power loop
power loop
25
25
0.003
0.003
0.06
0.06
0.5
0.5
O1
1
1
O2
225
405
The topology of the distributed generator (DG) with its
typical output voltage is illustrated in Fig. 2-a and Fig. 2-b,
respectively. The typical voltage of the 5-level inverter and
The current error is processed by the proposed
exponential SMC formulated in the previous section to
generate the input control law, which represents the required
9
the voltage after the transformer are illustrated in Fig. 2-b.
The adopted topology of the distributed generator is the
5-level diode clamped inverter of Fig. 2-a, which is
intentionally selected to reduce the injected harmonics
compared to the 2-level or 3-level converter circuits.
Figure 3a. Active power control using proposed exponential SMC scheme.
Figure 3b. Reactive power control using proposed exponential SMC
scheme.
Figure 3. Power control using improved exponential SMC scheme in
grid-connected mode.
Figure 2a. Topology of 5-level diode clamped inverter per phase.
The output of the control law for the suggested controller
is the required injected voltages
Ed DG required and
Eq DG required by the distributed generator in the d q
frame. These voltages are used to generate a control signal
using inverse Park transformation. These voltages are
portrayed in Fig. 4 to show the outputs of the suggested
controller.
Figure 2b. Voltages of distributed generator and inverter per phase.
Figure 2. Topology of the distributed generation with its output voltage
waveforms.
B. Performance of Control Scheme
The performance of the presented control scheme along
with the developed controller is depicted in Fig. 3-a for active
power and in Fig. 3-b for reactive power for some arbitrary
power references shown in red.
Figure 4. Output of control law for the proposed controller.
To prove the advantageous performance of the suggested
control scheme, its output is compared to the exponential
10
SMC (classical exponential SMC) given in [13-14] and
formulated in (1-5) for the same parameters defined in Tables
1 and 2. The active and reactive power tracking performance
is given in Fig. 5-a for active power and Fig. 5-b for reactive
power. Also, the output of the classical exponential sliding
mode controller is given in Fig. 6.
C. Impact of Distributed Generation System on Distribution
System
The impact of the DGS on the distribution system is
exemplified in this section since the DGS injects active and
reactive power based on the requirements of the distribution
system. Fig. 7 clarifies this beneficial impact such that the
DGS supplies the loads with its power and the surplus is
injected to the upstream system; in this figure the negative
power means injected power and vice versa. In Fig. 7 for t < 5
s, the injected power of the distributed generation system
PDGS is not enough to supply the whole power required by the
load Pload , then the distribution system supplies power PDS to
the loads as well; meaning that both the distributed
generation system and distribution system supply the loads.
For 5 s < t < 10 s, the PDGS is increased such that the whole
loads are supplied from the distributed generation system and
the surplus is absorbed by the distribution system. In this
duration, the PDS becomes positive, which means the
Figure 5a. Active power control using classical exponential SMC.
upstream system absorbs active power. For t > 10 s, the PDGS
is decreased such that both the distributed generation system
and distribution system are supplying loads. In this duration,
the PDS is reversed to be negative, which means that the
distribution system is supplying active power. A similar
performance can be obtained for the reactive power.
Eventually, the DGS helps the distribution system supply
power, which fetches a better performance for the
distribution system as described in the introduction section of
this paper.
Figure 5b. Reactive power control using classical exponential SMC.
Figure 5. Power control using classical exponential SMC scheme in
grid-connected mode.
Comparing Fig. 3 to Fig. 5 and Fig. 4 to Fig. 6 reveals that
the improved version, presented in this paper, has a better
transient performance with much less overshoot. On the other
hand, the classical exponential SMC shows a slightly less
chattering at some duration especially for the reactive power
performance for time from 20 s to 30 s.
Figure 7. Performance of active power for distribution system, distributed
generation system and loads.
V. CONCLUSION
This paper introduces a tangible improvement of the
exponential SMC to enhance its reaching mode compared to
the classical exponential SMC. Several modifications have
been introduced to the classical exponential SMC in this
research. These modifications have improved the overall
performance of the control scheme and alleviate the
drawbacks of classical exponential SMC such as steady-state
Figure 6. Output of control law for the classical exponential controller in
[13-14].
11
error and compatibility of the discrete input of the control law
with power electronics-based systems. The suggested control
scheme is applied on the distributed generation system to
operate it in a grid-connected mode. The simulation results
prove that the improved version outperforms the classical
exponential SMC in terms of reaching mode and overall
tracking performance.
[7]
[8]
APPENDIX
[9]
This section shows the proof of the formula given in (10)
of Section II. The distribution system of Fig. 1 can be
modeled by a state-space equation as,
x
Ax Bu Fd
s
1 O2 ³
[10]
I ref dq I DG dq
e, edq
To guarantee the stability of the system in the sliding mode, the
Lyapunov criterion should be fulfilled. Therefore, the Lyapunov
function is selected to express the Euclidian distance between the
state variables and the sliding surface defined as,
1
V
2
[11]
sT s
[12]
For stability of the system in the sliding mode, the derivative of
the above Lyapunov function should be less than zero, which leads
to s 0 that can be rewritten as,
̇= ̇+ 2
̇= ̇ − ̇+
̇=−
−
=−
−1
[
−
+
[13]
2
+ 2 =0
− 2 ]
[14]
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