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Abstract--This paper focus on the study of a two-stage, multi-string photovoltaic (PV) system connected by a common DC bus to a centralized inverter, interfaced with a utility grid. The distribution network model, load model and DC bus model are ud for simulation. PV system exhibits non-linear v-i characteristics and an intermediate boost converter is employed to operate the PV array at its maximum power point. An incremental conductance algorithm is employed to control the boost converter. A centralized inverter is controlled via a decoupled current control method and interfaced to the utility grid through a distribution transformer. The control of inverter is completely independent of maximum power point control of boost converter. Finally system stability is assd with respect to variation in solar radiation of the PV and distribution network parameters.
Index Terms--Photovoltaic, multi-string, two-stage, voltage-source converter, MPPT.
I. N OMENCLATURE
V s Inverter-filtered voltage; PCC voltage
V l Load voltage
V g Substation (grid) bus voltage
V dc DC-link voltage
i Inverter current
i g1Distribution line current between PCC and load
i g2Distribution line current between load and grid
i l Load current
i pv PV module current
V pv PV module voltage
P Real power output of PV system at PCC
Q Reactive power output of PV system at PCC
N Interface transformer turns ratio
L Inductance of interface reactor
R Resistance of interface reactor
C f Shunt capacitance at PCC
R1Line resistance between PCC and load
L1Line inductance between PCC and load
R2Line resistance between load and grid
L2Line inductance between load and grid
This work was supported in part by the Florida Energy System Consortium under Grant HB7135.
The authors are with Centre for Advanced Power Systems, Florida State University, Tallaha, FL 32310 USA (e-mail: edrington; sarithab; {@caps.fsu.edu}, jc09u@fsu.edu).
C l Power factor correction capacitor at load在我的世界里
C dc DC link capacitance
R dc DC bus resistance
L dc DC bus inductance
ω dq-frame angular speed
ρ dq-frame reference angle
II. I NTRODUCTION
ENEWABLE energy sources like solar, wind, biomass
and fuel cells are good alternatives for conventional
power generation. In recent years, due to the reduction in
cost of photovoltaic (PV) arrays, penetration of medium
power PV systems into utility grid is becoming more
common. The voltage rating up to 30 kV and power in the
range of 10-100 MVA are classified as medium power with
reference to AC side. The commercial scale PV panels of
25MW capacity are planned for installation in Florida.Sun
Power Corporation has installed more than 400 MW of large-
scale solar power systems around the world [1]. The perfor mance analysis of PV system is esntial in order to ensure the reliability of grid. PV systems can be connected to
the grid using single-stage or two-stage topologies. A two-
stage multi-string converter configuration, where one or more
strings of PV cells are connected to a single inverter, as in Fig.
1, is more suitable for medium power applications [2].
Fig. 1. Multi-string converter configuration
The maximum power point tracking (MPPT) technique can be implemented in DC/DC converters to achieve maximum efficiency of PV systems. Among the available DC/DC
Analysis and Control of a Multi-string
Photovoltaic (PV) System Interfaced with a
Utility Grid
Chris S. Edrington, Senior Member, IEEE, Saritha Balathandayuthapani, Member, IEEE, and Jianwu Cao
R
978-1-4244-6551-4/10/$26.00 ©2010 IEEE
converters, buck and boost converters have a higher efficiency for a given cost [2]. Boost converters show significant advantages over buck converters, due to the prence of blocking diodes that prevent rever flow of current into the
PV cell [3]. The Incremental conductance (IncCond) method
is ud for controlling the boost converter. The IncCond
technique [4] can be implemented utilizing a DSP, which can easily keep track of previous values of current and voltages and make all the switching decisions. The current control of the inverter is imple
mented in the synchronous reference frame which yields a fast dynamic respon and eliminates steady state error in three-pha inverter current. The decoupled current control and MPPT control were implemented in [5]; however, the distribution network model and DC bus model were not taken into account. Moreover, a detailed analysis of multi-string PV systems has yet to be accomplished.
Many previous works deal with the penetration of PV systems into grid. In [6] the authors have conducted studies on single-pha two-stage PV systems with DC bus models. Isolated DC/DC converters in a single-pha two-stage PV system with emphasis on Eigen value analysis is given in [7]. The u of multiple PV systems with a boost converter and
inverter connected to each module is illustrated in [8]. The common AC bus interconnecting the PV inverters is connected to the grid through an interfacing reactor. However, the distribution network and load model were not ud in the analysis in [7-8]. Reference [9] has a detailed analysis of a single-stage PV system connected to the utility grid, using a distribution network and load model for stability analysis of the system. It is noted that, multi-string PV system with a centralized inverter and DC bus model were not ud for any of the referenced studies.
In this paper, the simulation of two-stage multi-string PV system connected by a common dc bus to a centralized inverter, interfaced with the utility grid are prented. The
形容感情的成语distribution network model, load model, DC bus model are
ud for simulation. Maximum power point control is
歌曲《父亲》原唱
implemented in boost converter and decoupled current control is implemented in voltage source inverter (VSI). The rest of the paper is organized as follows- The system description is given in ction III, the control of DC/DC converter and VSI are discusd in ction IV and V, the small signal analysis is discusd in ction VI, the simulation results are discusd in ction VII, followed by conclusion in ction VIII. III. D ESCRIPTION OF THE SYSTEM
Fig. 2 demonstrates the one-line diagram of a multi-string PV system connected to the grid. Each PV module consists of 176 parallel and 150 ries arrays. The output of the PV is highly non-linear and thus can not be reprented by a simple current or voltage source in parallel with the diode. The model of a PV module is built using PLECS library components [10] as shown in Fig. 3. The output voltage of the PV module, V PV , is a function of solar radiation and environmental temperature. The voltage V PV is fed to the inverter through a dc transmission line. The dc line is considered to be a short transmission line and reprented by RL equivalent circuit. The boost converters are assumed to be at an equal distance from the centralized inverter. The capacitor C dc is a dc link capacitor at t
he input of the inverter. The output of inverter is connected to the distribution network through an interfacing reactor at the point
of common coupling (PCC). The filter capacitor C f provides the low-impedance path for the current harmonics generated by inverter.
The distribution network consists of a transformer T r1, load
and capacitor C l . The capacitor C l is ud for load power
factor correction. The low voltage side of T r1 is delta
connected to the PV inverter and its high voltage side has a
grounded wye connection. The transmission line between load and PCC is reprented by R 1 and L 1. The distribution network is connected to the grid V g
through a transmission
line reprented by R 2 and L 2, assuming a short line approximation.
Fig. 2. Single-line schematic diagram of multi-string PV system interfaced to a utility grid
Fig. 3. Circuit reprentation of a PV module
IV. C ONTROL OF BOOST CONVERTER
High initial cost and limited life span of PV arrays make it more important to extract as much power from them as
possible. Several MPPT algorithms have been propod in literature with the IncCond method [11] being one of the more
popular among them. PV arrays must be operated at a V ref PV , where maximum power can be extracted from the PV. The
IncCond control strategy is bad on the fact that the slope of the PV array power curve is zero at the maximum power point
(MPP), positive on the left and negative on the right of MPP. By comparing the instantaneous conductance (i/v) to the incremental conductance (Δi/Δv), the reference voltage V ref PV is adjusted.
At the MPP, V ref PV is equal to V MPP PV . Once the MPP is reached, the operation of the PV array is maintained at V MPP
PV unless there is a change in ΔI, in which the algorithm decrements or increments V ref PV to track the new MPP. The
increment size determines how fast the MPP is tracked. Fig. 4. Control circuit of boost converter
In a boost converter, the input capacitor voltage is compared with the V ref PV , which is obtained from the IncCond algorithm. When the capacitor voltage exceeds V ref PV , the switch is turned ON and capacitor is discharged. When the capacitor voltage reduces below a lower limit, the switch is turned off. The desired switching frequency of the boost converter f d is lected as 20KHz. The lower limit is a function of switching frequency and current i pv . There is a trade-off between switching frequency and capacitor value C 1 to get the desired voltage variation. This control structure is implemented in [12] to control the buck converter of a current source inverter. In this paper, the same control strategy as shown in Fig. 4 is ud to control the boost converter feeding the voltage source inverter.
V. C ONTROL OF VOLTAGE SOURCE INVERTER
The real power output of inverter is regulated by controlling i d and the reactive power is regulated by controlling i q . The voltage V PV and I PV of PV module is ud
for calculating the real power output of the inverter, pumped
into distribution network. ...2211++=PV PV PV PV ref I V I V P
(1) The reactive power Q ref injected into the network from the
inverter is t to zero. When the output voltage and power references are known, the current reference can be calculated via a power calculator. The references are calculated according to
⎥⎦⎤⎢
⎣⎡⎥⎦⎤⎢⎣⎡−+∗=⎥⎦
⎤⎢⎣⎡ref ref sd sq sq sd q d qref dref Q P V V V V V V I I 221
32 (2) The error signal e d = i dref - i d and e q =i qref -i q
are pasd through
a PI controller. The PI controller constants are chon such that
i i i p R
K L K ττ=
=
(3) W here τi is time constant of current control loop. The switching frequency of inverter is 3 kHz and the time constant
τi is taken as ten times smaller than the switching time [9]. It should be made small for a fast current-control respon, but adequately large so that the bandwidth of the clod-current loop is smaller than the switching frequency.
Fig. 5. a) Switch model in PSCAD b) Linear model in MATLAB
VI. S MALL SIGNAL ANALYSIS
The linear model of the system is built in Matlab for stability analysis. The overall system is given by
U B X A X sys sys +=* (4) The linear model is the function of steady state operating point
of PV system. Eigen values lie in left hand side of the S-plane and the system is stable. The model is validated by comparing
the results with switching model in PSCAD. The solar radiation in PV2 is varied from S=1 to 0.5 at t=0.7s. The change in interface current is compared in Fig. 5. The steady state values of current are equal but the transients differ as
dynamics of boost converter is not considered in linear model.
In future studies, we plan to include the dynamics of Boost
converter in our study. VII. S IMULATION RESULTS
Simulation of the model given in Fig. 2 has been accomplished using Simulink and PLECS. The parameters of the system are given in Table I.
A. Solar irradiation S=1 in PV1 and PV2
The diode rectifier, induction motor and RL load are connected to the distribution network. The size of the loads is available in Table I. Both the PV modules have solar radiation S= 1000 w/m 2 and plot of dq axes inverter currents are shown in Fig. 6. The dc voltage of the inverter V dc is shown in Fig. 7. The PCC current and voltage are shown in Fig. 8.
Time (Sec)
C u r r e n t (A )
Fig. 6. I d and I q of PV inverter with S=1 in both PV modules
Time (c)
V o l t a g e (V )
Fig. 7. V dc of PV inverter with S=1 in both PV modules
B. Change in Solar irradiation of PV2
A disturbance in the system is caud by changing the solar irradiation of the 2nd PV module from S = 1 to S = 0.2 at t = 0.4s. As can be en, there is a change in the operating point of PV2 and the inverter current is varied accordingly as shown
in Fig. 9. The voltage V dc of the inverter changes, as in Fig. 10.
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TABLE I S YSTEM PARAMETERS
T r1 nominal Power 3.5 MVA
T r1 Voltage Ratio 6.6/0.48 KV T r1 leakage inductance 0.1 pu T r1 Resistance 0.02 pu Interface resistance 3e-3 Ω Interface inductance 250e-3 H Filter capacitance
600e-6 F Switching frequency of inverter 3e3 Hz
DC bus resistance 3e-3 Ω per unit length DC bus inductance
50e-6 H per unit length Length of Common DC bus to inverter 10 units Length of DC bus from Boost converter to Common DC point 2 units Grid voltage 6.6 KV rms
Line inductance 0.105e-3 H per unit length Line resistance
5e-3 Ω per unit length Length of Transmission line 20 units R-L Load Parameter Resistance Inductance
50 Ω 10e-3 H Diode Rectifier Load Resistance Load inductance
100 Ω 10e-3 H Induction Motor Stator resistance Stator inductance Rotor resistance Rotor inductance
Magnetizing inductance Inertia
0.8 4e-3 0.8 2e-3 70e-3 0.1
Time (Sec)
V o l t a g e (V ),C u r r e n t (A )
Fig. 8. PCC current and voltage with S=1 in both PV modules
C. Fault at PV2
When a PV module develops a fault, it is isolated by virtue of, from the boost converter. This is simulated in the 2nd PV module at t = 0.4s and it is shown that the system will remain stable with only PV1 energizing the inverter. The change in inverter current is shown in Fig. 11.
Time (c)
爸爸妈妈我想对您说C u r r e n t (A )
宦官当道Fig. 9. I d of PV inverter under change in solar radiation
Time (c)
V o l t a g e (V )
Fig. 10. V dc of PV inverter under change in solar radiation
Time (c)
C u r r e n t (A )
Fig. 11. I d current of PV inverter with PV2 open
D. Change in load connected to the grid
The RL load is connected to the grid and a diode rectifier is introduced into the distribution network at t = 0.35 s. The PV
modules are operating at their MPP and the introduction of non-linear load affects the harmonic content of the inverter current. Fig. 12 shows the increa in RMS value of grid current, to supply the power required by the non-linear load and inverter output current. When an induction motor is line started at t = 0.3s, there is a high inrush current in the network. It is reflected as transients in the inverter current, as en in Fig. 13.
E. Drop in grid voltage绿色壁垒
With the diode rectifier and RL load connected into the network, there is a drop in grid voltage by 20% at t = 0.35s and the voltage restores its level after 200ms. In [7], when the voltage drops for a longer duration (200ms), the PV system collaps. In our model, the PV system is stable and it is abl
e to restore its original value as en in Fig. 14. The PV system is stable due to decoupled current control algorithm.
F. Fault at DC Bus
When the RL load is connected into the network, there is a fault at DC bus clo to the voltage source inverter at t=0.5s. The dc voltage drops to zero and the transients in interface current is shown in Fig. 15. The circuit breaker opens at t=0.6s. The fault is cleared at t=0.75s and the breaker reclos at t=0.8s. The system attains its pre-fault condition without error.
Time (c)
C u r r e n t (A )
Time (c)
C u r r e n t (A )
Fig. 12. I d of PV inverter and grid current with non-linear load in the network
Time (c)
C u r r e n t (A )
Fig. 13. I d of PV inverter with line-start induction motor in the network
Time (c)
C u r r e n t (A )
Time (c)
V o l a t g e (V )
Fig. 14. I d and V d of PV inverter with drop in grid voltage and fault cleared after 200 ms
Time (Sec)C u r r e n t (A )
Fig. 15. I d at PCC with fault at DC bus at t=0.5s and fault cleared after
250 ms
VIII. C ONCLUSION A Multi-string PV system is interfaced into a distribution network and has been investigated. The MPPT control of DC/DC converter and decoupled current control of inverter are employed in the system. The transient respon of the system has been studied under disturbance conditions and a
basic analysis has been conducted. It can be concluded from
the simulated results that the combined PV–utility system is stable under different disturbance conditions and that performance is acceptable.
IX. R EFERENCES
[1] Mike R. Lopez, “Florida power & light breaks ground for biggest solar photovoltaic installation in the US”, ecoed , para. 1, March 03,
2009. [Online]. Available: d/en/general-green-news/green-business-news/corporate-communications/846. [Accesd:
Feb. 05, 2010].
[2]
G. Walker and P. Sernia, “Cascaded DC/DC converter connection of
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[3] Weidong Xiao, Nathan Ozog, and William G. Dunford, “Topology study
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[4] W. Wu, N. Pongratanankul, W. Qiu, K. Rustom, T. Kasparis, and I.
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[5] M. Milovic, G.Anderson, and S. Garbic, “Decoupling current control
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[6] Li Wang, and Ying-Hao Lin, “Dynamic stability of a photovoltaic array
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X. B IOGRAPHIES
Chris S. Edrington (S’94, M’04, SM’09) received his Ph.D. in electrical engineering from the
University of Missouri-Rolla in 2004 where he was
both a GAANN and IGERT fellow. From 2004 ~ 2007, he was an Assistant Professor of Electrical Engineering in the College of Engineering at Arkansas State University. He currently is an Assistant Professor of Electrical and Computer Engineering with the FAMU-FSU College of
Engineering and is a rearch associate for the
Florida State University-Center for Advanced Power Systems. His rearch interests include modeling, simulation, and control of electromechanical drive
systems; applied power electronics; and integration of distributed energy
resources.
Saritha Balathandayuthapani (S’01, M’03, SM’07) received the Ph.D. degree in electrical
engineering from Indian Institute of Technology,
Madras, India in 2007. She was with GE Global rearch, India. She joined CAPS, Florida State
University, FL, USA in 2009, where she is currently pursuing Post-doc. Her rearch interests include control of power electronic converters, renewable
energy, machines and drives.
Jianwu Cao (S’09) received the B.Eng degree in Electrical Engineering from Huazhong University of Science and Technology, Wuhan, China, in 2009. He joined the Center for Advanced Power Systems, Florida State University, Tallaha, FL, in 2009, where he is currently pursing his Ph.D. degree. His rearch interests include distributed generation, renewable energy, and power system.
