Current Control of Single-Phase Inverter for Wind Turbine Applications L. Barote, C. Marinescu, Members, IEEE Transilvania University of Brasov/Electrical Engineering and Computer Science, Brasov, Romania
[email protected],
[email protected]
Abstract-This paper presents a wind turbine system operating in grid-connected mode. Grid connection of small permanent magnet synchronous generator (PMSG) based wind turbines requires a power conditioning system comprising a bridge rectifier, a dc–dc converter and a grid-tied inverter. The control structure, based on a current controller and a synchronization algorithm are implemented in the grid-tied inverter. The goals of this paper are to implement a control technique for the grid side inverter including a LC filter and a harmonic compensation technique. An evaluation in terms of current harmonic distortion when running in steady state condition is made. Simulation results present the evolution of analyzed current controller, concerning the quality of the delivered energy.
I.
INTRODUCTION
Wind energy conversion is a very promising technology and becomes a more and more interesting player on the Romania market of energy production. Regarding the connection to the consumers of electrical energy, wind turbines (WT) can be used in two operation models: grid connected mode, where WT is connected directly to the grid and stand-alone mode, where WT is not connected to the grid and acts as single voltage source, feeding the local consumers. This paper analyses the grid connected mode of a small power PMSG wind turbine (WT) in variable speed operation mode. Different control structures for grid power converters for distributed generation systems have been analyzed and described in [1]-[4]. Most of the current-controlled WT inverters use Proportional Integral (PI) controllers with grid voltage feedforward in order to get a good dynamic response. The disadvantages of this solution consist in inability to track a sinusoidal reference without steady-state error and poor capability in rejecting the disturbances. By using the PI controller the energy delivered to the grid does not comply the quality standards. Therefore, a better control method is used in order to eliminate the drawbacks of the PI control strategy. This method is based on Proportional-Resonant (PR) controllers. The PR controller can overcome the steady-state error and by adding the Harmonic Compensator (HC) a good harmonics rejection can be obtained [5], [6]. This paper will show that by using the HC the system improves its performances, in terms of Total Harmonic Distortion (THD).
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The paper is organized as follows: in Section II the Romanian technical issues for connection of WT are briefly described. Section III describes the analyzed configuration with the control and synchronization methods, Section IV describe the simulation results, while the conclusions are provided in Section V. II.
WT ROMANIAN GRID CODES
During the last few years, in Romania has been a special interest on the grid integration of wind turbines. The aim of the requirements is to ensure that wind turbines (or wind farms) do not adversely affect the power system operation with respect to security of supply, reliability and power quality. In this context, for WT systems, the Transmission System Operators (TSOs) has proposed a technical standard called Technical conditions for wind turbine systems connected to the public network [7]. Essential grid code requirements are related to frequency, voltage and wind turbine behaviour in case of grid faults. According to [7] the WT must have the capability to (see Fig. 1): − operate continuously at frequencies in the range of: 47.5 to 52 Hz; − remain connected to the grid at frequencies within the range 47 to 47.5 Hz for duration of minimum 20 sec.; − remain connected to the grid during rate of change of frequency of values up to and including 0.5 Hz/sec.; − operate continuously at a connection point voltage in the range 0.90 ÷ 1.10 Vn.
Fig. 1. Voltage-frequency operation limit for Romania
Fig. 2 shows the ride-through capabilities of the WT systems connected at the distribution system. The WT shall remain connected to the grid for voltage dips on any or all phases. During the voltage dip, the WT shall have the technical capability to provide [7]: − active power in proportion to retained voltage without exceeding the WT limits for at least 625 msec. or until the grid voltage recovers to the normal operational range; − maximize reactive current to the grid for minimum time of 3 sec.
90
Shall remain connected Shall disconnect
There are two basic synchronization methods: − Filtered Zero Cross Detection (ZCD); − Phase Locked Loop (PLL). The first method is based on detecting the zero crossing of the grid voltage while the second one, is a feedback control system that automatically adjusts the phase of a logical generated signal to match the phase of an input signal [6]. The PLL technique was adopted in this paper too and Fig. 4 shows the general structure of the single-phase PLL implemented in the WT control system. This algorithm artificially creates the orthogonal component of the grid voltage used to obtain the phase error between the phase of the real grid voltage and the estimated one by the PLL. Usually, the main difference among different single-phase PLL topologies is the orthogonal voltage system generation technique.
15 0 150
625
Vα
3000
Time [msec]
Fig. 2. Voltage ride through requirements in Romania grid code
θ
dq
SYSTEM CONFIGURATION
The analyzed system configuration of the WT is presented in Fig. 3. The configuration consists of a WT system with a PMSG, diode-rectifier bridge, boost converter, a voltage source inverter, a low-pass filter (LC), a transformer and a block that simulates the utility grid. The control part of the simulation schema contains a single-phase PLL circuit, a current controller and a Pulse Width Modulation (PWM) generator. The input side converter ensures the maximum power extraction from the input power source (WT) and transmits the information about available power to the grid side converter.
ω
Vq
αβ
Vg Vβ
III.
ω ff
Vq* = 0
1 2π
Vd
Fig. 4. General structure of a single-phase PLL
Different methods for creating orthogonal components are presented in [8], [9]. In this paper, the proposed orthogonal signal generator method relies on the Second Order Generalized Integrator (SOGI) due to the following advantages: simple implementation independent of the grid frequency and avoidance of filtering delays due to its resonance at the fundamental frequency [10]. The diagram implementation of a SOGI is presented in Fig. 5.
∑
k
1 s
∑
ω0 Ig I
* g
θ
Vβ Vg
Fig. 3. The analyzed WT system
In grid connected WT applications, an accurate and fast detection of the phase angle, amplitude and frequency of the utility voltage is essential to assure the correct generation of the reference signal. It requires the use of a synchronizing algorithm, which is able to synchronize the reference current of the Voltage Source Inverter (VSI) with the grid voltage. A good synchronization of the current with the grid voltage is necessary because the standards require a high power factor (PF>0.92).
fg
VRMS
1 ⋅ Vα2 + Vβ2 2
Vg
ε
θ
Vα
1 s
Fig. 5. Standard SOGI structure
The SOGI, an alternative generalized integrator is adopted to achieve the following transfer function:
SOGI ( s) =
s ⋅ ω0 2 s + ω0
(1)
2
A setting time of 0.15 sec. was considered in order to get a satisfied high bandwidth of the PLL controller. The output of the PI controller in addition with the feed forward frequency ωff is modulated and gives the phase angle (θ). The grid phase angle obtained during simulation is represented in Fig. 6.
The transfer function of a typical HC designed to compensate the 3rd, 5th and 7th harmonics is given as [12]:
7 6
Theta [rad]
5
G HC ( s ) =
4
∑
k ih
h =3,5,7
3 2 1 0 0
0.05
0.1
Time [s]
0.15
Fig. 6. Grid phase angle θ
The PI current control technique with grid voltage feed-forward exhibits stability problems related to the delay introduced in the system by the voltage feedback filter. Moreover, the compensation capability of the low order harmonics is very poor, standing as a major drawback when using it in grid connected systems and consequently noncompliance with international power quality standards [1], [2], [11]. For this reason, PR controller gained a large popularity in the last decade in current regulation of WT grid connected systems. The transfer function of resonant controller is defined as [12]:
G PR ( s ) = k P + k i
s
(2)
2
s + ω 02
According to [13], [14] the injected current in the grid should not have a THD larger than 5 %. Therefore, a harmonics compensation using PR controller is applied in order to obtain an improved power quality in the analyzed system. A general structure of harmonic compensator (HC) is illustrated in Fig. 7.
s
(3)
s + (ω 0 h )2 2
where: ω0 is the resonant frequency and h is the harmonic order of the compensator. Because the HC does not affect the dynamics of the PR controller, this structure is a successful solution in applications with distributed generation systems, where harmonics compensation, especially low order harmonics, is required. IV.
SIMULATION RESULTS
The configuration presented in Fig. 1 is modelled and simulations are carried out using the Matlab/Simulink software. The main purpose of this paper is to control the grid side converter connected to the grid by LC filter and a transformer (1:3). Therefore, the following parameters were considered for simulations: DC voltage of the WT system (Vdc=120 V), the grid RMS voltage (Vg=230 Vrms), frequency of the grid voltage is 50 Hz, the switching frequency of the VSI is 12 kHz and the cut-off frequency of the LC filter is 2.7 kHz. During the simulation, a 1 kW resistive load is connected to the grid. The current and voltage variation are presented in Fig. 8a,b. As it can be seen in Fig. 8c, the PR control technique without compensation provides a THD of 8 %, but is higher than the 5 % limit imposed by the standard IEEE 1547.1 [14]. Therefore, the power quality delivered to the network must be improved by using the HC technique presented in Fig. 7. 400 300
I g* +
Ig
∑
Kp
∑
V g*
-
Ki ⋅s s 2 + ω 02
∑
Grid Voltage [V]
200
Fundamental controller
100 0 -100 -200 -300 -400 0.5
0.52
0.54
0.56
0.58
0.6
Time [s]
0.62
0.64
0.66
0.68
0.7
(a)
K i3 ⋅ s s 2 + 3ω 02
∑
Ki5 ⋅ s s 2 + 5ω02
∑
3
K i7 ⋅ s s 2 + 7ω 02 Harmonic compensator
Fig. 7. HC structure attached to the PR of the fundamental current
Grid Current [A]
2 1 0 -1 -2 -3 0.5
0.52
0.54
0.56
0.58
0.6
Time [s]
(b)
0.62
0.64
0.66
0.68
0.7
V.
CONCLUSIONS
Fundamental (50Hz) = 3.067 , THD= 8.00%
This paper describes the improvements in the quality of the delivered energy in the case of a WT system controlled by the PR with HC control strategy, in terms of THD. In single-phase converters the PI controller capability to track a sinusoidal reference is limited and Proportional Resonant (PR) can offer better performance. Simulations results show that the proposed control method (current controller with PR+HC and a single-phase PLL) is effective for low power WT systems requiring good energy quality.
Mag (% of Fundamental)
5
4
3
2
1
0
0
2
4
6
8
10
12
14
16
18
20
Harmonic order
(c) Fig. 8. The grid voltage (a), current (b) and the current harmonics spectrum (c) for PR without HC controller
After HC implementation, the THD level decreases to 0.01% and a good power quality is obtained. It should be noted that in practical cases, due to sensors errors, the THD value is substantially higher. The results obtained in this case for grid voltage and current with harmonics level are presented in Fig. 9. 400 300
Grid Voltage [V]
200 100 0 -100 -200 -300 -400 0.5
0.52
0.54
0.56
0.58
0.6
Time [s]
0.62
0.64
0.66
0.68
0.7
0.62
0.64
0.66
0.68
0.7
9
10
(a) 3
Grid current [A]
2 1 0 -1 -2 -3 0.5
0.52
0.54
0.56
0.58
0.6
Time [s]
(b) 1.4
x 10
Fundamental (50Hz) = 3.07 , THD= 0.01%
-3
Mag (% of Fundamental)
1.2 1 0.8 0.6 0.4 0.2 0
0
1
2
3
4
5
6
7
8
Harmonic order
(c) Fig. 9. The grid voltage (a), current (b) and the level of harmonics with THD (c) for PR with HC controller
ACKNOWLEDGMENT This paper is supported by the Sectoral Operational Programme Human Resources Development (SOP HRD), financed from the European Social Fund and by the Romanian Government under the project number POSDRU/89/1.5/S/59323. REFERENCES [1] F. Blaabjerg, R. Teodorescu, M. Liserre, and A.V. Timbus, „Overview of Control and Grid Synchronization for Distributed Power Generation Systems”, IEEE Transactions on Industrial Electronics, vol. 53, no. 5, 2006, pp. 1398-1409. [2] M. Liserre, „Current and voltage control of the grid converter”, Power Electronics for Renewable Energy Systems Course (PERES), Aalborg University, 10 Nov. 2010. [3] L. Barote, C. Marinescu, „Storage Analysis for Stand-Alone Wind Energy Applications”, IEEE Proc. of OPTIM’10, 20-22 May, Brasov, Romania, 2010, pp. 1180-1185. [4] L. R. Limongi, R. Bojoi, A. Tenconi, L. Clotea, “Single-phase inverter with power quality features for distributed generation system”, IEEE Proc. of OPTIM’08, 22-24 May, 2008, Romania, pp. 313-318. [5] R. Teodorescu, F. Blaabjerg, U. Borup, M. Liserre, “A New Control Structure for Grid-Connected LCL PV Inverters with Zero Steady-State Error and Selective Harmonic Compensation”, IEEE Applied Power Electronics Conference and Exposition, IEEE Proc. of APEC 2004, Nineteenth, vol. 1, pp. 580-586. [6] A. Timbus, „Grid Monitoring and Advanced Control of Distributed Power Generation Systems”, PhD Thesis, Aalborg University, May 2007. [7] *** Technical Standard: “Condiţii tehnice de racordare la reţelele electrice de interes public pentru centralele electrice eoliene - Technical conditions for wind turbine systems connected to the public network”, ANRE, Nov. 2008. [8] S.M. Silva, B.M. Lopes, B.J.C. Filho, R.P. Campana, W.C. Bosventura, „Performance evaluation of PLL algorithms for single-phase gridconnected systems”, IEEE Proc. of IAS’04, Oct. 2004, pp. 2259 – 2263. [9] P. Rodriguez, R. Teodorescu, I. Candela, A.V. Timbus, M. Liserre, and F. Blaabjerg, „New Positive‐sequence Voltage Detector for Grid Synchronization of Power Converters under Faulty Grid Conditions”, IEEE Power Electron. Spec. Conf. (PESC’06), Jun. 2006, pp. 1‐7. [10] M. Ciobotaru, R. Teodorescu, V. G. Agelidis, „Offset rejection for PLL based synchronization in grid-connected converters”, APEC’08, Feb. 2008, pp.1611 – 1617. [11] R. A. Mastromauro, M. Liserre, A. Dell’Aquila and R. Teodorescu, “Performance Comparison of Current Controllers with Harmonic Compensations for Single-Phase Grid Converter”, IEEE Proc. of OPTIM’06, 18-19 May, 2006, Romania, pp. 1-8. [12] R. Teodorescu and F. Blaabjerg, “Proportional-resonant controllers. A new breed of controllers suitable for grid-connected voltage-source converters,” IEEE Proc. of OPTIM’04, vol. 3, 2004, pp. 9–14. [13] T. Ackermann, „Wind Power in Power Systems”, John Wiley & Sons, Ltd., 2005, ISBN: 0-470-85508-8. [14] *** IEEE 1547.1, “IEEE standard for interconnecting distributed resources with electric power systems”, July 2005.
