Maximum Loading Point in Distribution System with Renewable Resources Penetration Khaled Ras Guerriche
Tarek Bouktir
Department of Electrical Engineering Setif1 University Setif, Algeria
[email protected]
Department of Electrical Engineering Setif1 University Setif, Algeria
[email protected]
Abstract— In the recent years a large power oscillation have being seen in the distribution power system as a result of the integration of distributed generation resources (DGs). So a static and dynamic modeling of this system must be understood in order to ensure the reliable operation of the distribution system. The purpose of this paper is to study the effect of various small scale DG types on the voltage stability and the overall system loadability. The study has been carried out using the IEEE 33Bus radial distribution system. Continuous power flow method is used to test the increasing loadability margin and it is found that the type of DG units significantly decreases or increases the loadability margin of the power distribution system. Keywords-Distributed Generation; Voltage Stability Analaysis; Maximum Loading Margin; CPF; Renawable Resources
I.
INTRODUCTION
In the traditional power system, most of power is produced by a small number of large power plants placed at adequate locations and that makes a big separation between the production centers and consumers. However, the increasing concerns of environmental and economical issues have change the power system configuration and opened the door for more sustainable electrical sources; so-called distributed generation resources, which can be renewable or nonrenewable. Wind and photovoltaic are the most used and encouraging distributed generation technologies. Fuel cell (FC) also gained a big interest due to their fast technology development and many advantages that it has [1]. Many studies and investigations have been carried out in order to achieve the desired performance in DG resources, minimize power loss, improve the voltage profile, increase reliability and improve the power quality parameters of the electric grid. The effect of DG units on the distribution network is investigated in [2-4]. A methodology to evaluate the impact of wind generation on the voltage stability of a power system is presented in [5]. In [6], the impact of small photovoltaic generator (SPVG) on the operation of distribution systems is examined. In [7], the impact of fuel cells (FCs) and micro turbines (MTs), on power system stability for various penetration levels are studied. The electrical impact of solar PV penetration at the distribution level, and their effects on the voltage profile when installed in rural radial lines is examined in [8]. In [9], stability comparisons between
Prof. Tarek Bouktir acknowledges support from MESRS (Algeria), grant number J0201220130046.
conventional synchronous generators and wind farms are done. The authors use Power Voltage (P-V) curves for the analysis of the static load margins. In [10], the stability analysis of selected DG units (wind generators, and micro turbines) in a radial distribution system is presented. In this paper a comparison between three different DGs technologies based on the maximum loading margin, is presented, to show the impact of different DG types on the static voltage stability in radial distribution system. Section II explains the proposed distributed generation models. A brief review about voltage stability analysis is presented in Section III. Results are discussed in Section IV. And finally the conclusion is given in Section V. II.
DISTRIBUTED GENERATION MODELS
Three distributed generation units types are studied here. A. Wind Turbine Generator Nearly all the wind turbines installed use one of the three following generators:
Squirrel cage induction generator.
Doubly fed induction generator.
Direct drive synchronous generator.
The data of wind turbine used in this work which is based on squirrel cage induction generator are taken from [12]. It’s a fixed speed wind turbine with a direct-grid connected induction generator. This type of wind turbine is usually used in distribution systems [13]. Fig.1 shows the simplified equivalent circuit of the fixed-speed wind turbine. Where xm is the excitation reactance, x1 and x2 are the stator reactances respectively, r2 is the rotor resistance and stator resistance is ignored, s is the slip.
P+jQ X2
Rs
X1
I
r2 /s
Id
Ipv Xm
Rp
V
V
Figure 2. Equivalent Circuit of the PV-Cell
Figure 1. Equivalent Circuit of the Fixed-Speed Wind Turbine
The following equations can be obtained from Figure.1:
V
P(s x r2 s
Q (
2 2
V Rs I V R I s I I pv I 0 e ( kT / q ) a 1 Rp
r22 )
v2 P x ) xm r2
(1)
x x1 x2
Where V,I : the terminal voltage and current for the PV-cell.
Which can be converted to:
S
v 2 r2 v 4 r22 4 P 2 x 2 r22
Q
2p x
Ipv : the current generated by the incident light.
2
(2)
v v v 4 P x f (v ) xm 2x 2
(3)
2
4
I0 : the leakage current of the diode.
2 2
Rs, Rp : the equivalent series and parallel resistance.
Where
q : the electron charge.
S : is the total power. Q : is the reactive power. P : is the active power.
k : Boltzmann constant (1.3806503 x 10-23).
From (2) Q is a function of voltage and P is a constant. So, we will adopt the PV bus power flow model of fixed speed wind generation bus, because from (2) the fixed speed wind generation bus can’t deal with as PQ Bus in power flow calculation [14].
a : the diode ideality factor.
B. Photovoltaic Generator The photovoltaic generator (PV-cell) used here is based on current-source converter (CSC). Two models are proposed in [15], P-Q model (constant P and constant Q) for the representation of the constant power factor control and P-V model (constant P and constant V) for the representation of the voltage control. The P-V model is used here. Fig.2 describes simple equivalent circuit of a PV-cell is given in fig.2 [16].
T : the temperature of the p-n junction (in kelvin).
C. Fuel Cell The fuel-cell is an electrochemical static energy conversion device that converts the chemical energy to electrical energy [17]. There are different types of fuel cell used in the distribution generation, SOFC (Solid Oxide Fuel Cell) and PEMFC (Proton Exchange Membrane Fuel Cell) [18-20]. In this paper we use the FC based on [21]. Fig.3 shows the equivalent circuit of the fuel cell. PWM VS
VR RR
V0
L
RS
CR
DC/AC
Rloss
Cs
VDC
Figure 3. Equivalent Circuit of the Fuel-Cell
The Second one, in which there are two DG types connected to the same optimal bus of the first scenario. The PV curves here are presented for two combined DG, so-called hybrid system (Wind-turbine/PV-cell, Wind-turbine/FC).
Where V0 : the open circuit reversible cell potential . VR : a signal representing the output from the reformer. Rloss : nonlinear-loss resistance. III.
This study is carried out using PSAT [22]. It is a MATLAB toolbox for power system analysis. It includes power flow, optimal power flow, continuation power flow (CPF), small signal stability analysis and time domain simulation.
STABILITY ANALYSIS
a. Voltage Stability Analysis The voltage stability is the ability of power system to maintain steady voltages at all buses within acceptable limits after a disturbance from a given initial operating conduction [11]. The continuation power flow CPF is one of the most common methods used in voltage stability analysis. It is used to see the system responses to load variation in order to avoid system collapse, ensure the security and to control the power distribution. A P-V characteristic curve resulted from the CPF analysis provides useful information about voltage stability and study state stability limits (maximum loading points) at the study state conditions. b. Transient Stability Analysis
IV.
RESULTS AND DISCUSSION
The IEEE 33-Bus radial distribution system which is used here to test and compare the various types of DG units is illustrated in Fig.4 this system consists of 33 buses and 32 lines and has a voltage of 12.66kV, load size of 3.715MW and 2.3MVar. The size of the distributed generation unit used is 30% of the total load. The DG unit voltage is 12.66kV, the lower and upper voltage in the system is set between 0.95p.u and 1.05p.u. This will be able to show the impact of the various DG units on the loadability margin of the power system. In order to give a clear evaluation of the different DGs units impacts on the distribution system the study will be done with a fixed optimal placement and fixed DG penetration level. The DG unit placement chosen under an optimization technique with a fixed penetration level (30% from the total load). The behavior of the under study system with various DG types is studied for two different scenarios: The first one, where there is only one type of DG units is connected to the optimal bus. The P-V curves here are presented for three DGs types; Wind turbine, photovoltaic cell (PV-cell) and fuel cell (FC).
Figure 4. IEEE 33-Bus Radial Distribution System
The voltage profile before (reference case) and after DG unit installation is shown in Fig.5. The lowest voltage occurred in the Bus 18 with the amount of 0.91 p.u. Notice an important improvement of voltage profile after the installation of DG unit compared to the reference case.
1.02 Refrence Case (system without DG) system with DG unit
1
0.98
Voltages [p.u.]
Transient stability is the ability of the power system to return to stable operating point (synchronism) when subjected to a severe disturbance (e.g fault, short circuit, tripping generator or line) [11]. One of the most common methods for transient stability analysis is based on the time domain simulation. Time domain simulation technique is employed here to evaluate the impact of DG type on the transient stability of the distribution system.
0.96
0.94
0.92
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Bus numbers
Figure 5. Voltage Magnitude Profile for 33-Bus System with and without DG Units
1.04 1.02 1 0.98 Voltages [p.u.]
Fig.6 shows the P-V curve of the buses 1,18,33, and 6 simultaneously. A collapse or maximum loading point appear where the system Jacobian matrix become singular at λmax=3.610 p.u (refrence case).
1.4
0.96 0.94 0.92
V
VBus33
1.2 0.88
Voltages [p.u.]
V
Bus6
0.86
1
0.84
0.8 0.6
V
Bus1
V
0
0.5
1
1.5 2 2.5 Loading Parameter [p.u.]
3
3.5
4
Figure 8. P-V Curves for 33-Bus System with PV-Cell
VBus18
0.4
Bus33
VBus6
0.2 0
Bus1
VBus18
0.9
0
0.5
1
1.5 2 2.5 Loading Parameter [p.u.]
3
1.02
3.5
1 0.98
Figure 6. P-V Curves for 33-Bus System without DG Units
Voltages [p.u.]
0.96
1.35 V 1.3
Voltages [p.u.]
0.92 0.9
V
VBus33
0.86
VBus33 VBus6
Bus1
VBus18
0.88
Bus1
VBus18
1.25
0.94
V
Bus6
0.84
1.2
0.82
1.15
0
0.5
1
1.5 2 2.5 Loading Parameter [p.u.]
3
3.5
4
1.1
Figure 9. P-V Curves for 33-Bus System with Fuel Cell 1.05
1
0.95
0
0.5
1 1.5 Loading Parameter [p.u.]
2
2.5
Figure 7. P-V Curves for 33-Bus System with Wind Turbine
As can be seen from Fig.7 a considerable variation in the maximum loading margin after the integration of wind turbine compared to the case when the system is without DG unit. From the P-V curves, the maximum loading parameter decreases compared to the reference case.
From Fig.8 and 9 we can observe that the integration of PVCell and FC improves the static voltage stability margin of the system. Moreover the maximum loading parameter is considerably increased with a maximum value of 0.469p.u for PV-cell and 0.494p.u for FC, mean λmax=4,079 and λmax=4.104p.u which represent better performance than in the previous cases.
According to the results shown in Table.I the maximum loading parameter is affected with the type of DG unit where the DG unit can increase or decrease the maximum loading margin. It is obvious that the PV cell and fuel cell give the maximum loading margin with a maximum value of 0.469p.u for PV-cell and 0.494p.u for FC, mean λmax=4,079 and λmax=4.104p.u which represent better performance than in the previous cases.
1.04 1.02 1
Voltages [p.u.]
0.98 0.96 0.94 V 0.92
Bus1
VBus18 VBus33
0.9
V
System System System System System
1.1
Bus6
0.88 1.05
0
0.5
1 1.5 2 Loading Parameter [p.u.]
2.5
3
Figure 10. P-V Curves for 33-Bus System with Wind Turbine/PV-Cell
Bus 18 Voltage [p.u.]
0.86
with Wind Turbine with PV-Cell With FC with Wind turbine/PV-Cell With Wind turbine/FC
1
0.95
0.9
1.02 0.85
1
0.8
Voltages [p.u.]
0.98
0
0.5
1
1.5
2
2.5 time (s)
3
3.5
4
4.5
5
0.96
Figure 1. Time Domain Simulation at Bus 18 for the Test System with Different DG
0.94 V
Bus1
VBus18
0.92
VBus33 V
0.9
0.88
0
0.5
Bus6
1 1.5 2 Loading Parameter [p.u.]
2.5
3
Figure 11. P-V Curves for 33-Bus System with Wind Turbine/Fuel Cell
The hybridization between two different DG units has its effect in the distribution system as can be seen in the Fig.10 and 11. The static stability margin of the system is improved compared to the first and second cases; and the new maximum load parameter for this two last cases is λmax=3.216p.u and λmax=3.179p.u mean that the maximum loading parameter is reached with 0.394p.u and 0.431p.u. compared to reference case. TABLE I.
MAXIMUM LOADING PARAMETER AT EACH CASE λmax [p.u.]
Without DG Wind turbine PV-Cell Fuel Cell Wind turbine /PV-Cell Wind turbine/Fuel Cell
3.610 2.813 4.079 4.104 3.216 3.179
Fig.12 shows a comparison of the voltage magnitude at bus 18 for a fault clearing time after 1s for all cases. Noticed a quick response in the case of FC and PV-Cell and the fault was cleared after 0.692 s when the system with FC and after 1.629 s when the system with PV-Cell. V.
CONCLUSION
This paper present a simple comparison between three different DG technologies based on the maximum loading margin, in order to show the impact of different DGs types on the static voltage stability of the system. Found that the type of DG unit has a significant impact in the static voltage stability. It can increase or decrease the maximum loading margin. As can be seen from the results, the PV-Cell and fuel cell have the maximum loading margin compared to the wind turbine and hybrid system. In the transient stability analysis the quick response is noticed from the fuel cell and photovoltaic cell mean that this two DGs technologies can improve the ability of the power system to return to stable operating point (synchronism).
[3]
APPENDIX The DG Data used in this paper are as follow: TABLE II.
INDUCTION GENERATOR PARAMETERS
Xs (p.u.)
0.0313
Xr (p.u.)
0.0306
Xm (p.u.)
1.0938
Rr (p.u.)
0.0044
Rs (p.u.)
0.0031
Ht (sec)
2.5
Hm (sec)
0.5
Ks (p.u.)
0.3
[4]
[5]
[6]
[7]
[8]
[9]
[10] TABLE III.
PHOTOVOLTAIC CELL PARAMETERS
τP (sec)
0.015
τq (sec)
0.015
Kp
0.04
Ki
20
[11]
[12]
TABLE IV.
FUEL CELL PARAMETERS
τref (sec)
2
τst (sec)
3.37
τd (sec)
0.8
Rin (ohm)
0.2778
Km
100
τm (sec)
10
mmax
1.2
mmin
0.8
Xt (p.u.)
0.05
[13]
[14]
[15]
[16]
[17]
[18]
ACKNOWLEDGMENT The author thanks Prof. Tarek Bouktir and all members of his SMART GRID team. REFERENCES [1]
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