Software Phase Locked Loop Technique for Grid- Connected Wind ...

Software Phase Locked Loop Technique for GridConnected Wind Energy Conversion Systems Mahmoud M. Amin Student Member, IEEE

O. A. Mohammed Fellow, IEEE

Electrical and Computer Engineering Department Florida International University Miami, FL 33174, USA [email protected]

Electrical and Computer Engineering Department Florida International University Miami, FL 33174, USA [email protected]

Abstract—Accurate and fast detection for phase angle of the generated voltage is important in parallel grid- connected wind energy conversion systems (WECSs) utilizing converter-inverter unites. Software Phase Locked Loop (SPLL) technique is presented here for precisely detecting the phase angle during presence of the 5th and 7th harmonics. A second-order loop filter design is proposed here as a good trade-off of the filter performance and system stability. Also, this proposed technique is studied under frequency change and generated voltage unbalance conditions. The developed technique is also implemented in a laboratory setup which includes two synchronous generators (SGs: 250 W, 2.2 kW) each driven by a variable speed prime mover (VSPM) to emulate a wind turbine behavior, two 3-phase PWM based converter-inverter systems, 3phase line inductors connected between wind generators and converters, and a digital signal processor (DSP TMS320F240). The experimental results confirm the validity of the proposed technique for parallel integrated WECSs. Keywords-Software phase locked loop (SPLL); wind energy conversion systems (WECSs); pulse width modulation (PWM); grid connected systems.

I. INTRODUCTION A good detection of the phase angle of the generated power is highly recommended in wind energy conversion systems utilizing converter-inverter unites. This is also required for a grid-connected operation to increase the usability of the local power generation systems. In both cases (autonomous power generation or grid-connected) power factor control is essential to insure unity power factor (UPF) for perfect transmission of the generated power without any circulating energy [1, 2]. It is necessary for the power factor control to detect accurate phase for both the generation voltage and the utility voltage. A zero voltage crossing detection method, where the zero voltage must be accurately detected each half period, can be used [3]. However, the synchronization must be updated not just at the zero voltage but continuously during the whole period, because multi zero crossing can occur with the existence of noise. The Phase Locked Loop (PLL) technique can be applied here for precise detecting the phase angle. PLL is widely used in communication engineering because of its excellent noise rejection capability [4]. It can detect phase and frequency with high resolution for signals deeply embedded in noise. It has

been adopted to be used widely in the area of power electronics such as the speed control of electric motors [5, 6]. With today’s high technology, the control system of the converter-inverter can be implemented by a single chip microcontroller or DSP. The analog PLL functions can be realized by a more precise program even if three phase detectors are introduced. A hybrid (hardware & software) PLL was introduced by Jovan [7] for synchronizing a single phase PWM inverter (UPS) with the grid. However, it was not fully software. In this paper, a fully software PLL for the phase angle detection of the three phase generator voltage is introduced using the dq synchronous reference frame. The advantages of the proposed technique over other techniques are that it has more flexibility and less complexity since it is fully software. Also, it has a very fast and accurate detection capability during wind speed variation which leads to a good control performance of the overall system. Moreover, it has strong filter properties due to the two integrators in the series forward path. The basic idea of the analog PLL and its analysis are introduced first in brief, and then the characteristics of the software PLL using the dq transform of the three phase variables are given. II. SYSTEM DESCRIPTION Variable speed wind turbine (VSWT) systems are preferred for the higher output power generation. In general, the electrical components of grid-connected WECSs are generator, rectifier and inverter, and LC-filter for grid connection. Fig. 1 shows a typical electrical system utilized for the proposed parallel-integrated VSWT connected to the utility grid. Rectifier DC Bus Wind Turbine

Inverter

SG

LC Filter

Rectifier Wind Turbine

SG

Figure 2. Proposed parallel SG-based WECS.

GRID

III. SYSTEM MODELING A. Model of wind turbine According to Betz theory, the mechanical power generated by wind turbine is shown as: Pwt =0.5πρv3 R2 Cp λ, β

(1)

where is the air density, is the rotor radius of wind turbine, and the wind speed. The power coefficient depends on the blade pitch angle and the tip speed ratio which is defined as the ratio between the linear blade tip speed and the wind speed as . / , where is the rotor speed of wind turbine. The output torque of wind turbine is: Pwt =0.5πρv2 R3 CT (λ, β) (2) Ω , , / . where the torque coefficient Considering the wind speed, the WECS can be divided into on load, partial load and full load state. When the wind speed is below the cut-in wind speed or above the cut-out wind speed, wind turbine operates in the no load region. When the WECS is in the full load region, the output power must be regulated at rated power , which can be achieved by changing the pitch angle. In order to maximize the captured power, the tip speed ratio needs to be controlled. Fig. 2 represents the relation between generator speed and output power according to wind speed change. It is observed that the maximum power output occurs at different generator speeds for different wind velocities.

and the converter line voltage . When voltage the angle between the two voltage sources, , and amplitude of converter voltage are controlled, we control indirectly phase and amplitude of line current. In this way the magnitude and sign of the DC current, , is subject to controlled and determine the active power conducted through converter. The reactive power could be controlled independently according to the relative phase of fundamental harmonic current with respect to voltage .

+

Twt =

C

Figure 3. Three-phase power circuit for the PWM converter.

Assuming that the generator line voltage is a three phase balanced voltage source, so it can be represented by the state equation as, . cos . cos . cos

2 /3 2 /3

(3)

is the maximum amplitude of the generator line where voltage. Assuming a virtual line-line currents as: , and . , In other words, let us define this transformation: 1 0 1

1 1 0

0 1 1

(4)

Referring to Fig. 3, the dynamic equation for the input side of the three phase converter system can be summarized as, _

Figure 2. Mechanical power versus rotor speed with the wind speed as a parameter.

B. Voltage source PWM converter Three-phase representation for the input and output sides of the converter circuit is shown in Fig. 3 where and represent a line inductor mounted between the generator and the converter terminal, the generator phase voltage and the bridge converter voltage controllable according to the demanded DC voltage level. The inductors, which are connected between the converter input terminals and the generator lines, are integral part of this circuit. It brings current source character of input circuit and provides the boost feature of the converter. The line current is controlled by the voltage drop across the inductance interconnecting two voltage sources (generator and converter). The inductance voltage equals the difference between the line

_

_

_

(5)

where and are the generator and converter terminal line voltages, respectively, and is the inductor internal resistance. Referring to Fig. 3, the dynamic equation for the output side of the three phase converter system can be written as, (6) . The line voltage, the virtual line current and where the terminal voltage of the PWM converter can be transformed to a dq synchronous reference frame using Park transformation such that [8]; 0 0

(7)

where is the derivative operator, i.e. / . The converter system in S-domain can be obtained by applying Laplace transformation to the dynamic equations in the synchronous frame directly such as, 1 . (8) 1 . For the converter output side, (9)

1 The converter plant model in S-domain representation is shown in Fig. 4. 1

+ −

SVPWM

Converter Controllers

+

3 2

(12)

+

AC Utility Grid

_ Figure 5. The main electric circuit of the VSI connected to the utility grid.

1

ωL ωL −

−

1

+

Figure 6. Simplified circuit of a grid connected VSI.

Figure 4. Converter model block diagram.

C. Voltage Source PWM Inverter The main circuit of the VSI connected to a three phase public grid is shown in Fig. 5. An inductance works as line filter is mounted between the utility grid and the VSI having an internal resistance . The line potentials of the VSI denoted as , , and . The line potentials of the utility , , and . The imaginary line grid denoted currents flowing from the DC-link to the VSI denoted as , , and , while the DC-link current and , and respectively. voltage are denoted as In order to design a VSI control systems, mathematical models are important tools for predicting dynamic performance and stability limits of different control laws and system parameters. The system to be modeled is shown in Fig. 6. The is assumed to be zero. The assumption of grid inductance the balanced state of the grid is presented, therefore, it can be represented by the state equation as, . . .

2 /3 2 /3

(10)

where and is the angular frequency and maximum amplitude of the grid line voltage vector, respectively. The AC side of the inverter system is modeled by the differential equations for 3-phases such that, (11) By using vector notation, the last equation can be written in the αβ stationary frame such as,

Equation (12) can be written in the rotating reference frame synchronized with grid voltage using Park transformation such as [8], (13) The decoupled equation can be written in the state space form as, .

(14)

.

where the state vector and the input vector are defined by (15)

,

(16) Respectively, the system matrix and the input matrix are given by ⁄

(17)

⁄ 1⁄ 0

0 1⁄

1⁄ 0

0 1⁄

(18)

The DC side of the system is modeled by the equation, (19) IV. THE PROPOSED CONTROL SYSTEM The voltage oriented control (VOC), which guarantees high dynamics and static performance via internal current control loops, has become very popular and has constantly been developed and improved [9].

Inverter

Rectifier

R

L

R

Grid

SG1 Line voltages & currents measurements

SVPWM SPLL

SG2

+

+

PI

Reference currents calculation

Line voltage & Current measurement

SPLL

+ PI +

SVPWM

+

Active & Reactive power demanded calculation

VOC

Figure 7. Schematic diagram of the overall proposed WECS control system connected to grid.

It is giving the ability to control each current component (in the synchronous dq frame) separately without any effect from the other component which improves the dynamic performance of the system. Therefore, VOC algorithm is proposed to be utilized here for both rectifier and inverter control where it gives the reference values for the space vector (SVPWM) switching technique which calculates the proper conduction time for the converter switches. The schematic diagram of the WECS connected to the grid and its vector current controller is shown in Fig. 7. The VOC PWM converter is based on coordinate transformations between the stationary abc and αβ frames to the synchronous rotating dq reference frame and vice versa. By controlling the converter in a synchronous dq frame the currents being regulated will be DC quantities which eliminate the steady state error [10]. According to the converter dynamic equations in synchronous frame, (7), there are coupling terms between these equations which degrade the dynamic performance (slow the controller transient and cause high overshoots) of the system. These terms are the coupling q current ) and generator voltage on the d-axis component ( , while coupling d current component ( ) equation, and on the q-axis equation. VOC will decouple these terms, giving the ability to control each current component separately without any effect from the other component. Fig. 8 shows two SVPWM converters sharing one DCbus. It is assumed that the converters are rectifying the output voltage of two wind generator systems. It is not convenient to let each unit controlling the DC link voltage separately without any information from the other units. A discrepancy could happen between the controllers. The Master-Slave

scheme can solve this problem. One converter unit is selected to be a Master whereas the others are treated as slaves. Each of the slave unit has a self governing system, i.e., it has its inner current control feedback loop. Only the master unit has the outer DC voltage control feedback loop giving the reference current to the entire slave units. By 0, the unity power factor operation is achieved. setting The other is the d-current controller with reference set by the outer DC voltage controller and decides the active power flow between the wind generator and the DC link. _ +

PI

PI

PI

Controllers PI

PI

+ + + _

S V P W M Plants S V P W M

Figure 8. Controllers and plants diagram for parallel converters sharing one DC link.

VOC is also proposed here to use the voltage sources inverter (VSI) as a dynamic VAR compensator system. The basic principle of the VOC method is to control the instantaneous active and reactive grid currents and, consequently, the active and reactive power, by separate controllers independently of each other. The grid voltages and currents are first sensed. By means of SPLL, the grid phase angle and frequency can be detected in order to synchronize the VSI output with grid. The demanded amount of power is first estimated from the utility grid at the desired power factor, in consequence, the reference currents in a synchronous frame synchronized with grid voltage are calculated. Consequently, the current controllers are trying to bring the actual currents to its references. A. General operation of the SPLL The applied PLL is a feedback control system that maintains a constant phase difference between a reference signal and an oscillator output signal. Fig. 9 shows a basic block diagram of the applied PLL. The phase frequency detector compares the phase of the reference signal , with the phase of the voltage controlled frequency, oscillator (VCO) output frequency, . A phase detector output pulse is generated in proportion to that phase difference. This pulse is smoothed by a loop filter. The resulting DC is used as the input voltage for controlling the , is fed-back to the phase VCO. The output of the VCO, frequency detector input, and comparison continue until both frequency and phase are made the same and the phase and frequency of the VCO are in locked state with reference , . signal i.e. + -

Phase detector gain

Loop filter

VCO

, Figure 9. Basic PLL block diagram.

B. Analysis of a PLL as a feedback control system The closed loop transfer function of the PLL system of Fig. 9 can be expressed as; 1

(20)

The VCO transfer gain is a function of time, since phase is the time integral of frequency, it may be written as: (21)

proportional-integral (PI) loop filter of the second order can be expressed in the form: where K and K denote the gain parameters of the PI loop filter, therefore; (24) The general form of the closed loop transfer function of the second order system is given by;

Comparing (24) with (25); 2

and

(26)

C. Phase detection in dq synchronous frame The configuration of the PLL system using the dq components in the synchronous reference frame of the three phase input voltage is shown in Fig. 10. The phase voltages , , and are measured and converted to and , then transformed to stationary reference voltages the synchronous voltages and in a frame synchronized to the generator angular frequency using a phase angle · obtained by integrating the PLL frequency · . Therefore; ·

· ·

·

(27)

·

The PI loop filter of the PLL can be used as a regulator to obtain the value of · or · which in turn drive the feedback to the commanded value, i.e. it works towards voltage and to zero. At the bringing the difference between time when the frequency command is identical to the generator frequency, the voltages and appear as DC values. and can be selected using (26) The regulator gains =314 rad/sec, the such that the natural frequency damping ratio =0.707 and the voltage 120√2 , which is the phase detector gain. We obtain =2.6163, and =580.9825. The configuration of the PLL system using the dq components in the synchronous reference frame of the three phase input voltage is shown in Fig. 10. · 1 · PI ·

/

There are several methods to design the loop filter. The second order loop filter is commonly used as a good tradeoff of the filter performance and system stability [11]. The

(25)

2

The phase frequency detector gain, , is assumed to be independent of frequency. With unity VCO gain, 1, Equation (20) can be written as: (22)

(23)

/

Current & Voltage Controllers for converter

Figure 10. SPLL applied for wind generation converters

, ·

∆

In order to investigate the performance of the proposed technique, an experimental setup for rectifier-inverter system has been constructed and connected to the local grid. A digital board containing a digital signal processor (DSP TMS320F240) has been tested and used as the control heart of the system. Each unit of the system is built and tested alone, and then the whole system is connected and tested. A simulation program using Simulink™ was carried out using simulation parameters shown in Table I. The space vector pulse width modulation (SVPWM) presented in this paper has been used with a 5 kHz switching frequency. VOC strategy discussed in section IV is utilized in the simulation. A low pass filter with LC elements and 205 Hz cut-off frequency is connected before the isolation transformer in order to improve the quality for the injected power. The experimental setup includes fabricated built circuit boards, 2wind generators modeled by 2-variable speed prime-movers (VSPMs) coupled with 2-SGs, and grid connected VSI. The machine ratings are listed in Table II in the appendix. Photograph for the experimental proposed WECS connected to the utility grid is shown in Fig. 11. The PLL has been software-wise implemented using the DSP TMS320F240. The three phase inputs are generated internally to simulate the generator output voltages. Fig. 12 shows the transient response of the SPLL for a 120V, 60Hz three phase voltages. The synchronous reference frame dq voltage appears as dc values. The SPLL is locked on very fast producing a clear phase angle signal. An evaluation of the SPLL system is carried out as follows:

,

V. EXPERIMENTAL RESULTS

A. Frequency step response A step change in the supply frequency appears as a ramp · change in the phase angle . This causes the error ∆ to increase. The ability of the SPLL to respond to the generator frequency variations depends on its ability to bring the error ∆ to zero as quickly as possible. The influence of the frequency step change on the SPLL system is shown in Fig. 13. A step change from 30 Hz to 60 Hz is presented. time 5 msec / div Figure 12. The SPLL transient response.

B. Harmonics influence Small ripple of the 5th and 7th harmonics, 5% and 3%, respectively, are injected to the phase voltages. While the harmonic components will not affect the SPLL locking capability, they will propagate to the associated phase angle θ· , in the form of 4th and 6th harmonics. To eliminate the harmonics a filter is used either for the sampled voltage or the error ∆ of the control loop. However, it should be noted that the SPLL has a strong filter properties due to the two integrators in the series forward path. Fig. 14, 15 shows the harmonics influence on the SPLL system at frequency 60 Hz. Figure 11. Laboratory prototype of the 3-kW parallel WECS connected to the utility grid.

C. SPLL under unbalanced input voltage conditions Fig. 16 shows an extreme case for unbalanced condition such that;

100cos 75cos 180cos

95° 214°

·

This unbalance doesn’t affect the locking capability but propagates to the detected phase angle as huge harmonic but the harmonics are components. The filter smoothes still present in .

,

, and

.

,

,

·

Figure 15. SPLL harmonics contents for

time 20 msec / div

·

·

,

Figure 13. Frequency step response (from 30 to 60 Hz frequency jump).

time 10 msec / div time 10 msec / div Figure 14. SPLL harmonics influence under 5th and 7th harmonic insertion.

Figure 16. SPLL response under extreme unbalances condition (three phase input voltage, , and .

[5]

VI. CONCLUSION In this paper, the synchronous frame SPLL technique has been proposed to give a fast detection for the phase and frequency variation resulting by the variable speed operation in the grid-connected WECSs. A second-order loop filter design was proposed here as a good trade-off of the filter performance and system stability. The VOC grid connected rectifier-inverter system has been investigated for high performance control operation. This technique achieved high accuracy (error ∆ 0.04) which leads to better performance for the control system, very fast transient response within a fraction of millisecond (0.1 msec) during frequency step change due to wind speed and high resolution to detect the phase angle for signals deeply embedded in noise (5th and 7th harmonic injection) has been achieved. Also, SPLL confirms its robustness under unbalance condition. This technique has been implemented using a digital signal processor (DSP TMS320F240) as the control heart of the proposed system and all the interfacing circuits to the analog power circuits. All results obtained confirm the effectiveness of the proposed system for WECSs. APPENDIX TABLE I. Symbol fg Vdc L

SIMULATION PARAMETERS FOR CONVERTERS Quantity

Value

Generator frequency

60 Hz

DC link voltage

400 V

Line inductor

2.7 mH

R Cdc fsw

Internal resistance DC link capacitor Switching frequency

0.7 Ω 1200 µf 5 kHz

Vg

Generator output voltage

TABLE II. Symbol Po(Small) Po(Large) Vn

120 V r.m.s

SMALL AND LARGE SYNCHRONOUS GENERATOR RATINGS Quantity Output power Output power Nominal voltage,

Value 1/3 hp 3 hp 120/208 V r.m.s

n

Nominal speed

1800 rpm

In(Small)

Nominal current

1.7 A

In(Large)

Nominal current

8.7 A

Field voltage

125 V

Vf

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[2]

[3]

[4]

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