turbine located on a single-phase feeder line by providing extra control and ... permanent magnet generator into a uniform D ... For a single-phase inverter using.
Design and Control of a Single-Phase D-STATCOM Inverter for Wind Applications Colin Tareila, Pedram Sotoodeh, and Ruth Douglas Miller Electrical and Computer Engineering Department, Kansas State University, Manhattan, KS 66506
Abstract-- Application of renewable energy systems has become very popular. Since most utilities do not track the end points of their distribution lines carefully, where most of the wind turbines are connected to the grid, increasing the application of renewable energies in utilities can result in problems for the whole system dynamics. This paper presents the design and control of a D-STATCOM inverter for small to mid-sized wind turbines (10kW-20kW) to solve the problem of power factor correction of the grid. The proposed D-STATCOM Inverter can control the VARs on each single feeder line while the output of the renewable energy source, especially wind, is varying. Active power is controlled by shifting the phase angle while reactive power control is achieved by modulation index control. Also, the inverter is able to eliminate a large amount of harmonics using the optimized harmonic stepped waveform (OHSW) technique. The proposed inverter utilizes the hybrid-clamped topology. All simulations were done in MATLAB/Simulink environment.
Index Terms— D-STATCOM, Hybrid-Clamped Topology, MMC Topology, Multi-Level Inverter, OHSW Harmonic Elimination Technique.
I. INTRODUCTION
At the end of 2011 the United States had a total installed capacity of 41,181 MW of wind power, providing the equivalent generation of 10 nuclear facilities [1-2]. From the curtailment issues in wind in places like Texas over the last few years, it is clear that in order to achieve the penetrations of wind and other renewables our administration is asking for, the electric grid will have to be greatly expanded and new concepts for control will have to be exploited [3]. One of the areas for increasing the penetration of wind lies within power electronics which can add a great deal of flexibility and control to existing systems both at the transmission and distribution levels. To this date, much of the focus of powerelectronic devices including the vast array of FACTS devices lies within the transmission sector, for the sole reason that these technologies are expensive and need to be placed in locations where they can realize the greatest return on investment. This approach would leave out the vast majority
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of the electric grid which is the distribution system on the lowvoltage side of distribution transformers. At this voltage and power level it is almost impossible to justify the immense cost of implementing any kind of power electronics that can regulate line voltages, power flows, and VAR support. To overcome the large cost associated with FACTS type devices it is advantageous to turn towards a smaller and more distributed scale. Rather than having one large FACTS device on a distribution line, such as a unified power flow controller, these types of control can be incorporated into the power electronics of small distributed wind turbines that already exist or can be economically added in the rural windy Midwest at the residential and small commercial scale. This paper explains a new kind of inverter that can replace the existing inverter of a small to medium sized permanent-magnet wind machine (10kW to 20kW) that can offer VAR control and power factor correction in a dynamic manner. This inverter is called a D-STATCOM Inverter.
II. DESIGN AND STRUCTURE OF THE D-STATCOM The proposed inverter is able to correct the power factor of the line, especially at the end points of the distribution lines where there is not enough attention to the line behavior. Multiple D-STATCOM inverters on the feeder lines would help utilities increase their knowledge of the distribution system leading to greater efficiency, reliability, and control. The unique work in this paper is the bringing together and combination of several relatively new concepts. The design objectives of the project include: minimize the overall switching frequency of the inverter; minimize the total harmonic distortion in order to maintain compliance with IEEE standards and maximize energy conversion efficiency; and finally, keep the cost of the inverter as low as possible. The D-STATCOM Inverter falls under the category of devices known as custom power electronics. Most of the research on custom power electronics has stemmed from the research done on STATCOM devices that integrate battery energy storage. Generally, the purpose of the D-STATCOM Inverter is to increase the value to the utility of a small wind turbine located on a single-phase feeder line by providing extra control and information. The D-STATCOM Inverter represents one stage of a three-stage power electronics block
that makes up the entire converter structure. The first of these wer point tracker stages is the wind turbineಬs maximum pow (MPPT). This stage transfers the maximum m power from the wind turbine while transforming the quasi D DC output of the permanent magnet generator into a uniform D DC voltage.
STATCOM DC link ܧ௦ , the voltagee of the secondary side of the transformer ܧ , the range of thee voltage angle , and the range of the modulation index m. m In defining these four variables a few assumptions are mad de. One is that the range of the modulation index is from 0.6 to 1. The second is the t design, the inductance inductance of the transformer. For this of the transformer is 0.05 H an nd the X/R ratio of the transformer is assumed to be large so o that Equations (1) and (2) will hold. The final variable is the an ngle which is assumed to have an operating range from –90 degrees d to +90 degrees in order to maintain quarter-wave symm metry. Figure 2 provides a graphic view of the designed op perating range of the DSTATCOM Inverter in accordance with w the chosen values and Equations (1) and (2).
Figure 1: System structure
The second stage, the DC-DC boost, boosts the DC voltage provided by the MPPT to the desired D DC Link voltage required by the D-STATCOM Inverter. The ffinal stage, the DSTATCOM Inverter and focus of this reseaarch, is a voltagesource converter that can provide the grid w with VAR control and power factor correction independent of tthe wind turbineಬs production. This provides the utilities with booth control of and information about the feeder line which they never had before, thus increasing the value and potential pennetration of small wind. Figure 1 shows the structure of the systtem. The design of the D-STATCOM Invertter incorporates a 5-level topology called the hybrid-clamped [[4-6] and uses the OHSW technique [7-10]. In designing the innverter there were three basic criteria: 1) the inverter should bbe able to support turbines rated from 10 to 20 kW; 2) the inverrter should be able to provide up to 20 kVARs of capacitivve compensation regardless of the active power conversion; annd 3) The inverter must be connected to a single-phase feeder linne. The active and reactive power flow of thee D-STATCOM is governed by Equations (1) and (2) which are listed below.
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ாೄ ாಽ
ߜ
ாೞ ாಽ ୡ୭ୱ ఋିாಽమ
(1)
Figure 2: Overview of the D-STA ATCOM Inverter design
III. DEFINING THE OPTIMIZ ZATION PROBLEM The optimization problem as deffined by Barkati [11] is to solve, for a given modulation ind dex, a series of equations defined by (3). Equation (3) reprresents the amplitudes of every harmonic. ܪ ሺȽሻ ൌ
ସ
σିଵ ୀଵ
ሺ݊ߙ ሻ
(3) For a single-phase inverter using g quarter wave symmetry, containing m-levels, k switching angles, and j DC link capacitors, the system of equationss to be solved contains k non-linear equations and is representted by the following: గ
݆ߨܯ Ͷ
ሺ͵ߙଵ ሻ
ሺ͵ߙଶ ሻ ڮ
ሺ͵ߙ ሻ ൌ ݄ଷ ൌ Ͳ
ሺߙଵ ሻ
ሺߙଶ ሻ ڮ
ሺߙ ሻ ൌ (2)
The two equations have four variables w which govern the active and reactive power range. These vvariables are the inductance of the transformer X, the voltage of the
ሺͷߙଵ ሻ
ሺͷߙଶ ሻ ڮ
ሺͷߙ ሻ ൌ ݄ହ ൌ Ͳ ڭ
ሺ݊ߙଵ ሻ
ሺ݊ߙଶ ሻ ڮ
ሺ݊ߙ ሻ ൌ ݄ ൌ Ͳ
(4)
Where M represents the modulation index that fundamental component should be solved for. The Fourier series of this waveform is written as: ܸሺݐݓሻ ൌ ܸ σ ܪ ሺߙሻሺ݊ݐݓሻ
(5)
Where ܸ represents the DC voltage across one DC link capacitor. A. 5-Level Two Angle OHSW The two equations to be solved for a 5-level inverter are: ଶగ
ሺߙଵ ሻ
ሺߙଶ ሻ ൌ ܯ ସ
ሺ͵ߙଵ ሻ
ሺ͵ߙଶ ሻ ൌ Ͳ
(6) (7)
Where M is the modulation index and ranges from 0.6 to 1. The objective function or cost function is given by, ݊݅ݐܿ݊ݑܨݐݏܥሺߙଵ ǡ ߙଶ ሻ ൌ ݓଵ ȁʹ ܯെ ܪଵ ȁ ݓଶ ȁܪଷ ȁ(8)
(a)
IV. SIMULATION The D-STATCOM Inverter was designed and simulated using MATLAB/Simulink. At the highest level, the model consists of five distinct parts. These are a Thevinin equivalent of the grid, a data acquisition block, the D-STATCOM controller, the power electronics circuit, and the wind turbine model. To confirm the operation of the D-STATCOM Inverter, different cases and simulations were carried out in SimPowerSystems toolbox. Figures 3(a) and 3(b) show the results of a 20-second simulation in which the load on the grid was initialized to 50 kW and 34.835 kVARs, giving a power factor of 0.82 (lagging). The voltages for both the DC link and auxiliary capacitors in the hybrid clamped topology are initialized to 1000 V. For the first 6 seconds of the simulation the output of the wind turbine is set to 0 W in order to give the D-STATCOM Inverter enough time to adjust to the required compensation demanded by a target power factor of 0.9 (lagging). The top graph of Figure 3(a) shows the power factor of the feeder line during the course of the 20-second simulation. Starting at the 0th second, the power factor of the line is 0.82 (lagging) as it is defined entirely by the load. As soon as the simulation starts, the D-STATCOM Inverter begins to provide compensation and the power factor is adjusted. The second graph shows the P and Q provided by the feeder line to the load. Initially, the feeder line is supplying the entire load of 50 kW and 34.8 kVARs. When the DSTATCOM Inverter provides capacitive VAR compensation, the amount of VARS provided by the feeder line to the load is decreased to about 20 kVARs. Additionally, as the output of the wind turbine, shown in Figure 3(b), is increased, the amount of active power provided by the feeder line to the load is decreased by the same amount.
(b) Figure 3: (a) Feeder line power factor, feeder line P and Q, D- STATCOM power factor, and delivered P and Q of the D-STATCOM. (b) Modulation index, angle delta, and wind turbine output power
In the above figures the maximum output power of the turbine is 11 KW, but the control system works properly for up to 20 KW wind turbines. Overall, the D-STATCOM Inverter is able to provide the feeder line with VAR compensation which is independent of the active power provided by the wind turbine. Figure 4 depicts the voltage of the DC link along with the individual voltages across each of the link and auxiliary capacitors. Figures 5 depicts the power factor of the feeder line, the P and Q on the feeder line, the output power factor of the inverter, the output P and Q of the inverter, the modulation index, the angle delta, and the power produced by the wind turbine/solar array.
level. Table 1 summarizes the differences between the simulated and predicted values. The presence of even harmonics is the result of non-optimal switching times in the simulation, inductances and capacitances in the inverter, and variations in the current and voltage waveforms. The contribution to the THD by the even harmonics is of little concern as all of the even harmonics are relatively the same size and the higher order ones can be further suppressed with the use of a small filter. The simulated THD is actually lower than the predicted THD. This is due to some of the harmonics being suppressed by the inductances and capacitances in the circuit.
Table 1: Simulated vs. Predicted Results for THD for the OHSW Method up to the 100th harmonic
Figure 4: Variation of capacitor voltages using OHSW
Time 1 = 4s THD 3rd Harmonic Percentage of Fundamental Modulation Index Time 2 = 9.37s THD 3rd Harmonic Percentage of Fundamental Modulation Index
Simulated Predicted 29.10% 29.39% 0.30%
0.00%
0.878 0.878 Simulated Predicted 29.13% 29.39% 0.86%
0.00%
0.867
0.867
V. CONCLUSION In this paper, a new D-STATCOM Inverter is presented for small to mid-sized wind turbine applications. The proposed 5-level inverter is capable of regulating the power factor of the line using hybrid-clamped multi-level topology. It is also able to eliminate a great number of harmonics using OHSW technique. Simulations are carried out in MATLAB/Simulink. The results show that the OHSW technique is a feasible modulation scheme for the D-STATCOM Inverter and that the hybrid-clamped topology is capable of operating under the dynamic conditions presented by a wind turbine. Also, simulation results show that the THD is actually lower than the predicted THD because some of the harmonics are suppressed by the inductances and capacitances in the circuit.
VI. REFERENCES [1] AWEA, “AWEA U.S. wind industry annual market report year ending 2010,” American Wind Energy Association, Washington DC, 2011. Figure 5: Feeder line power factor, feeder line P and Q, D-STATCOM power factor, and delivered P and Q of the D-STATCOM
The output waveform of the 5-level OHSW should contain no even harmonics, because of quarter-wave symmetry, and the 3rd order harmonic should be eliminated due to the OHSW technique. Results show that while the 3rd and even harmonics have not been eliminated they have been suppressed to a low
[2] AWEA, “AWEA U.S. wind industry annual market report year ending 2009,” American Wind Energy Association, Washington DC, 2010. [3] S. Fink, C. Mudd, K. Porter, and B. Morgenstern. “Wind energy curtailment case studies May 2008-2009”. National Renewable Energy Laboratory: Golden, CO. NREL/SR-550-4671, 2009. [4] A. Chen and X. He, “Research on hybrid-clamped multilevel-inverter topologies,” IEEE Trans. Industrial Electronics, vol. 53, no. 6, pp. 1898– 1907, 2006.
[5] A. Chen and X. He, “A hybrid multilevel inverter topology with neutral point voltage balancing ability,” IEEE Annual Power Electronics Specialist Conference, Aachen, Germany, pp. 3952-3956, 2004. [6] J. Zhao, X. He, R, Zhao, “A novel PWM control method for hybridclamped multilevel inverters,” IEEE Trans. Industrial Electronics, vol. 37, pp. 2365-2373, 2010. [7] S. Barkati et al, "Harmonic elimination in diode-clamped multilevel inverter using evolutionary algorithms," Electric Power Systems Research, pp. 1736-1746, Elsevier, 2008. [8] S. Barkati, E.M. Berkouk, M.S. Boucherit, “Partical swarm optimization for harmonic elimination in multi-level inverters,” Electrical Engineering 91, Springer, pp. 221-228, 2009. [9] R. N. Ray, D. Chatterjee, S. K. Goswami, “An application of PSO technique for harmonic elimination in a PWM inverter,” Applied Soft Computing 9, Elsevier, pp. 1315-1320, 2009. [10] S. Sirisukprasert, “Optimized harmonic stepped-waveform for multilevel inverter,” M.S. thesis, Department of Electrical Engineering, Virginia Polytechnic Institute State University, Blacksburg, VA, 1999. [11] S. Barkati, E.M. Berkouk, M.S. Boucherit, “Partical swarm optimization for harmonic elimination in multi-level inverters,” Electrical Engineering 91, Springer, pp. 221-228, 2009.
VII. BIOGRAPHIES
Colin Tareila (Student Member, IEEE) received the BS degree in Electrical and Computer Engineering at Lafayette College and an MS in Electrical Engineering at Kansas State University. He is currently employed at AWS Truepower, where he works on wind farm site assessment and design.
Pedram Sotoodeh (Student Member, IEEE) was born in Isfahan, Iran. He received the B.S. degree in electrical engineering in 2008 and the M.Sc. degree from Sharif University of Technology, Tehran, Iran in 2010. He is currently pursuing PhD degree at Kansas State University, Manhattan, KS, USA in the field of power electronics and renewable energy systems. His areas of interest include utility application of power electronics, electrical drives, renewable energy systems, and machine design. Pedram Sotoodeh is a member of IEEE and Iranian Association of Electrical and Electronics Engineers (IAEEE).
Ruth Douglas Miller (Senior Member, IEEE) received her BS Degree from Lafayette College and her MS and PhD degrees from the University of Rochester, all in electrical engineering. She has taught in the Electrical and Computer Engineering department at Kansas State University since 1990, specializing in bioelectromagnetics in the 1990s and in renewable energy since 2007. She is the Director of the Kansas Wind Applications Center, which coordinates the Wind for Schools program in Kansas and also runs the High Plains Small Wind Test Center in Colby, Kansas. The Wind Applications Center also coordinates research in power electronics for wind and photovoltaics, wind resource estimation and prediction, and renewable energy grid integration.
