Quasi-Z-Source Inverter based PMSG Wind Power Generation System Liu Yushan1,3, Ge Baoming1,2, Member, IEEE, Fang Zheng Peng2, Fellow, IEEE Abu Rub Haitham3, Senior Member, IEEE, Aníbal T. de Almeida4, Senior Member, IEEE and Fernando J. T. E. Ferreira4,5, Student Member, IEEE 1 School of Electrical Engineering, Beijing Jiaotong University, Beijing, China 2 Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824 USA 3 Department of Electrical and Computer Engineering, Texas A&M University at Qatar, Doha 23874, Qatar 4 Department of Electrical and Computer Engineering, University of Coimbra, 3030-290 Coimbra, Portugal 5 Department of Electrical Engineering, Engineering Institute of Coimbra (ISEC), 3030-199 Coimbra, Portugal E-mail:
[email protected],
[email protected]
voltage stress and capacity of devices. To solve this issue, the boost circuit is usually added in DC link to keep the DC bus voltage constant and reduce the inverter stress, especially in the situations that the ranges of dc source voltage are relatively wide. Whereas, it will increase the cost as well as reduce the efficiency of wind power generation system.
Abstract—In view of the buck and boost capabilities of quasiZ-Source inverter (qZSI), an application of qZSI to a permanent magnet synchronous generator (PMSG) with wind power generation system (WPGS) is presented. The traditional space vector PWM (SVPWM) technique is modified to satisfy the shoot-through characteristic of qZSI. The closed-loop control of shoot-through duty cycle is designed to obtain the desired DC bus voltage. The DC-link boost control and ACside output control are presented to reduce the impacts of disturbances on grids. Further, some significant simulations are done in MATLAB / SIMULINK. The simulated results verify the validity and superiority of the proposed control strategies, indicating a significant method to enhance the antiinterference performances of wind power generation systems.
The voltage-fed quasi-Z-Source inverter (qZSI), exhibiting both voltage buck and boost capabilities, has been presented advantageous for overcoming the barriers and limitations of traditional VSI [1]. As the additional LC impedance network, qZSI beneficially utilizes the shootthrough states to boost the dc bus voltage by gating on both the upper and lower switches of a phase leg. In this way, it can buck and boost voltage to a desired output voltage greater than the available DC bus voltage. The introduction of quasi-Z-Source network provides a reliable, highly efficient, and low-cost structure for buck and boost power conversion. For these reasons, the qZSI is well suitable for wind power systems due to the fact that the wind turbine output power varies widely along with wind speed changes.
Keywords- Modified SVPWM control, PMSG, quasi-Z-source inverter, wind power generation
I.
INTRODUCTION
PMSG wind power generation system (PMSG-WPGS) is considered to be one of the mainstream systems in today’s variable speed constant frequency (VSCF) wind generation technology area due to its lower weight and volume, high efficiency and stability, etc. In the traditional PMSG-WPGS, the AC outputs from generator are transformed to grids via AC / DC / AC converters. Thus high-capacity C-filter is needed in the DC link and voltage source inverter (VSI) is applied to convert DC to AC. However, the traditional VSI is a buck converter, whose input dc voltage must be greater than the peak ac output voltage. Therefore, the voltage of VSI needs to be designed high enough, leading to high
Developed from Z-Source inverter (ZSI), the qZSI can be controlled using any methods which can be used to control the traditional ZSI [1]. These methods have been explored in detail, eg. in [2]-[4]. The simple boost control method introduced in [5] uses two straight lines to control the shootthrough states. Maximum boost control was presented in [3], [4] to maximize output voltage for a given modulation index and minimize the voltage stress across the switches. However, they have the drawbacks of higher switching frequency than traditional VSI, which increases switching losses and design requirements of filters [6]. Toward this end, more and more researchers began to study the space vector PWM (SVPWM) control of ZSI [7]-[9]. The SVPWM control strategy has been widely used at industrial applications of traditional PWM inverters because of lower
This work was supported in part by the NPRP-Qatar National Research Fund under grant No. 09-233-2-096, partly by the Power Electronics Science and Education Development Program of Delta Environmental & Educational Foundation under grant No. DREG2010001, and partly by the Beijing Jiaotong University Foundation under grant No. 2009JBM093, Beijing, China. The statements made herein are solely the responsibility of the authors.
978-1-4577-0541-0/11/$26.00 ©2011 IEEE
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current harmonics, high voltage utilization efficiency and a higher modulation index [10]. Applying the SVPWM strategy to qZSI not only preserves the advantages of traditional SVPWM, but also plays the role of buck-boost conversion. In [7], the SVPWM method of a single-phase ZSI was introduced briefly. Reference [8] analyzed the principle of SVPWM in three-phase ZSI, but it didn’t clarify the specific implementations. Reference [9] gave the switching control sequence in each sector. While it needs to be set in every sector separately, which is complex for DSP programming. By periodically inserting shoot-through states, this paper presents a modified SVPWM technique, the switching frequency of which is in accordance with traditional SVPWM. Especially, equations for controlling switching signals are derived, which is prone to realize the modified SVPWM on DSP.
C2
L1
+ V − in
L2 C1
Figure 1. Quasi-Z-Source inverter. VC 2
− + vL1 − Vin
In order to reduce DC link voltage fluctuations, it is necessary to bring in the closed-loop control of peak DC-link voltage in qZSI. Reference [11] describes a method to control peak DC-link voltage through capacitor voltage of Znetwork. However, the capacitor voltage is not exactly the same as peak DC-link voltage of Z-network, so is it in quasiZ-Source network. To achieve the more ideal performances of both DC-boost and AC-output voltage of qZSI, the peak DC-link voltage control is introduced in this paper. Meanwhile, the voltage-current closed-loop control of shootthrough duty cycle is also designed to acquire desired buck or boost capacities.
−vdiode +
r I L1
+
R
r
+ vL 2 −
iC 2
IL2
+
R
+
Vdc I 0
+
VC1
−
− iC1
−
(a)
−
+ vL1 − Vin
− vdiode +
r I L1
VC 2
+
R
+ vL 2 −
r
R
+
I L2
+ Vdc
+
VC1
−
iC 2
− iC1
I0
−
(b) Figure 2. Equivalent circuit of qZSI. (a) Shoot-through state. (b) Nonshoot-through state.
To date, most of the research works published on controlling and applications of qZSI are of photovoltaic (PV) systems [12]. Contributions of this paper are presenting the application of the qZSI to PMSG wind power generation system. The organization of the paper is as follows. Basic operation principles of qZSI are demonstrated in section II. In Section III, the control strategy of the proposed system is explained in detail. Section IV presents the simulated results. At last, some conclusions are summarized and future work is presented in section V. II.
D1
As verified in the basic principles, the average values of capacitor voltages VC1and VC2 in quasi-Z-Source network are
1− D ⎧ V = V ⎪⎪ C1 1 − 2 D in , ⎨ ⎪V = D V C2 in 1 − 2D ⎩⎪
BASIC PRINCIPLES OF Q-ZSI
The topology of voltage fed qZSI with continuous input current [1] is shown in Fig. 1. The quasi-Z-Source network is made of an LC impedance network, which can boost the DClink voltage of inverter in respect to the interval of shootthrough zero state during a switching cycle. In the qZSI, there is an addition shoot-through state than traditional VSI, which is advantageously utilized to boost the DC bus voltage. The equivalent circuits of qZSI in two basic operation modes are illustrated in Fig. 2. In Fig. 2 (a), the inverter bridge is equivalent to short circuit when shoot-through zero vectors are working; in Fig. 2 (b), the inverter bridge is replaced by a constant current source in non-shoot-through states. In the figure, R is the series resistance of capacitors and r is the parasitic resistance of inductors.
where Vin is the dc source voltage of qZSI, D is shootthrough duty cycle, defined as D= Tsh / T, T is switching cycle, and Tsh is the shoot-through time interval over a switching cycle [1]. Relationship between the average value of DC-link voltage Vdc and dc source voltage Vin can be written as
Vdc =
T 1 Vin = Vin = BVin . T − 2Tsh 1 − 2D
(2)
Thus, the boost factor B resulting from the shoot-through state can be given as B=
1 1 − 2D .
(3)
The peak value of the AC-side voltage is Vac = MB
where M is the modulation index. 292
(1)
Vin 2 ,
(4)
III.
And the open-loop transfer function of the inner current loop is
SYSTEM CONFIGURATION AND CONTROL STRATEGIES
The traditional PMSG-WPGS with DC boost chopper is shown in Fig. 3. While in the qZSI based PMSG-WPGS, the DC boost chopper is replaced by the quasi-Z-Source network, as illustrated in Fig. 4. Through MPPT control of wind turbine, the maximum power PWmax generated by wind turbine is delivered to the direct-drive PMSG. The threephase AC is converted to DC as the dc source voltage Vin of qZSI by diode rectifier with input capacitors Cr. Then the DC-side voltage of qZSI is regulated to the commend signal Vdc* by the modified SVPWM control and shoot-through duty cycle control. The reference voltages u α *, u β * of SVPWM are obtained by AC-output voltage control. The whole control system mainly contains shoot-through duty cycle control, the modified SVPWM control for qZSI, as well as DC-link and AC-output voltage control.
GiLd ( s ) =
Therefore, we adopt the voltage-current double closedloop control, namely the inner loop is quasi-Z network inductor current and the outer loop is peak DC-link voltage. In order to reduce the non-minimum phase effect, stabilize output voltage and increase system stability, a PI controller is cascaded to control the peak DC-link voltage. Its output is the command signal for inner current loop. There is no RHP zero in inner current loop, making design simpler. The main
C2
C rec
L1
i L2
Lg
L2
D1
C1
vC1
vdc u a ub uc
Cr
ωm vdc
∗
i a ib
PI
iL 2
vdc
∗
vin
abc
D
P i L2
uβ∗
uα∗
vC1 /(1 − D)
αβ dq vC1
∗ ∗ C1
v
(6)
Here, K1 = LCs 2 + ( R + r )Cs , K 2 = Ls + R + r , L1 = L2 = L , 1− D I0 , C1 = C2 = C , I 11 = I 0 − 2 I L , I L = I L1 = I L 2 = 1 − 2D V11 = VC1 + VC 2 − I 0 R . However, it can be seen that the capacitor voltage transfer function in (5) has a RHP (right half plane) zero. This is a clear indication of the presence of non-minimum phase. The non-minimum phase problem is handled with having two loops, inner current and outer voltage loops [13]. A similar technique is proposed here to obtain a stable feedback controller.
Figure 3. Traditional PMSG-WPGS with DC boost chopper.
vin
K 2 (1 − 2 D ) I11 + K1V11 . K 2 [ K1 + (1 − 2 D) 2 ]
PI
id
∗
ud∗
PI id
u d + ωLi q
id iq
θ
uq∗
dq
iq
θ
ud uq
iq
PI − ωLi d
ic
∗
Q∗ ud
Figure 4. Structure of the proposed system with qZSI.
purpose of inner loop control is to improve the dynamic response speed, so a proportional controller is employed. After a low-pass filter (LPF), the inner loop outputs the signal of shoot-through duty cycle D. On the one hand, the shoot-through duty cycle is inputted to quasi-Z-Source SVPWM module to generate PWM pulses. On the other hand, it feeds back to calculate the DC bus voltage in real time. The peak DC-link voltage is derived from online calculation of shoot-through duty cycle and capacitor voltage of quasi-Z-Source network. In this way, the voltage fluctuations from the front rectifier, loads and other disturbances can be overcome by the voltage-current double closed-loop control.
A. Closed-Loop Control of Shoot-Through Duty Cycle From equations (2) and (3) we can see that the boost factor B can be regulated by controlling shoot-through duty cycle D, and then to keep the DC-link voltage invariable. Here, we adopt the state space average method. Laplacetransform functions of the quasi-Z-Source network were derived. The transfer function from shoot-through duty cycle to the capacitor voltage of quasi-Z-Source network is GVcd ( s ) =
LI11s + ( R + r ) I11 + (1 − 2 D)V11 . LCs 2 + ( R + r )Cs + (1 − 2 D) 2
(5)
293
boost factor B can be adjusted too, resulting in the demanded DC-link voltage.
B. Modified SVPWM Control The traditional SVPWM control must be modified to adapt the shoot-through characteristic of qZSI. We modify the SVPWM algorithm by taking part of the zero vector action time as shoot-through state time without having effects on the resultant voltage vector and switching frequency compared with traditional SVPWM.
The switching control timing sequence of SVPWM is shown in Fig. 5. It can be seen that in one control cycle, the action time of shoot-through zero vector is equally divided into six parts. They are inserted into the switching states transition moment averagely. In this way, only one phase-leg is short-circuited in one switching cycle, and every bridge leg has two shoot-through states in each switch cycle. Thereby, no other switching operations are added compared with traditional SVPWM. And no dead time is needed in phase legs, achieving high reliability. Meanwhile, the action time of effective vectors is invariant, making the switching loss is identical to that of the traditional VSI.
The well-known algorithm for SVPWM, comprising [9]
⎧T1 = TS M sin(60D − θ + 60 D (i − 1)) ⎪⎪ D , ⎨T2 = TS M sin(θ − 60 (i − 1)) ⎪T = T − T − T S 1 2 ⎪⎩ 0
(7)
T1 T + V2 2 , TS TS
(8)
Vref = V1
Comparing the switching sequences, it can be found that the insertion of shoot-through vectors could be realized by modifying (advance or delay) the switching vector transition time of traditional SVPWM. The modified vector transition time is derived as follows, which is apt to the DSP programming.
where i=1, 2, ..., 6 is the number of the segment to calculate the duration of the two involved active states. The time interval TS is switching cycle, T1 and T2 are the action time of active state vectors V1 and V2 in a cycle, T0 is the action time of traditional zero vector V0, θ is the included angle of reference voltage Vref and V1. The modulation factor M is defined as M = 3Vref / Vdc , in which Vdc is the DC-link voltage.
T ⎧ T ⎧ ⎧ T = Tmax + sh ⎪Tmid + = Tmid − sh ⎪Tmin + = Tmin − sh T ⎪⎪ max + ⎪ 12 12 ⎪ 4 . (11) ⎨ ⎨ ⎨ Tsh ⎪ Tsh ⎪ Tsh ⎪T Tmid − = Tmid + = Tmax + = Tmin − T ⎪⎩ max − 12 ⎪⎩ min − 4 ⎪⎩ 12
Besides six active states and two non-shoot-through zero states, shoot-through zero states are additionally inserted. Then the reference voltage becomes
Vref = V1
T T T1 T + V2 2 + V0 0 + Vsh sh , TS TS TS TS
where, Tmax, Tmid, Tmin are the maximum value, middle value, and minimum value of switching vector transition time in traditional SVPWM, separately; Tmax+, Tmid+, Tmin+ is the corrected values to control on and off states of upper bridge arms; Tmax-, Tmid-, Tmin- is the corrected values to control on and off states of lower bridge arms.
(9)
where Vsh is the equivalent shoot-through voltage, Tsh is its action time. Ts / 2
Because the shoot-through states only take up zero vectors, it does not affect active vectors, that is T T V0 0 + Vsh sh = 0 , then the reference voltage can be TS TS reduced to
Vref
T T = V1 1 + V2 2 , TS TS
Ts
CMPR3CMPR3+ CMPR1CMPR1+ CMPR2CMPR2+
(10)
0 Tsh / 6
which is the same as traditional SVPWM in (8). Thereby, the resultant voltage vector would not be changed.
Tsh / 12
Tsh / 6 Tsh / 12
t
Tsh / 6 Tsh / 12
PWM1
In the following, the control of switch signals is demonstrated. In the traditional SVPWM method, the switch signals of the same bridge leg are complementary. In order to apply SVPWM strategy to the qZSI, the switch signals of the same bridge leg should be no longer complementary [14]. To avoid additional switching operations and related losses, this paper inserts the shoot-through intervals before the beginning or after the end of every active interval. This will ensure the switching frequency remain unchanged. By adjusting the time length of inserted shoot-through state, the
PWM2 PWM3 Modified 000 SVPWM Traditional 000 SVPWM
010
110
111
110
010
110
111
110
010 010
Figure 5. Switching timing sequence of SVPWM.
294
000 000
detect its peak value. From (1) and (2), the relationship between capacitor voltage VC1 and the peak voltage can be obtained as
C. DC-Link and AC-Output Voltage Control 1) MPPT control of wind energy The power captured from wind energy through wind turbine can be expressed as
PW = 0.5Cp (λ )πρR v , 2 3
∧
v dc =
(12)
⎛
1 0.035 ⎞ - 3 ⎟. ⎝ λ + 0.08β β + 1 ⎠
γ = 1/ ⎜
(15)
with the relationship between VC1 and Vin in (1), we can eliminate the middle variable D, then the commend signal of VC1 is
where ρ is air density in kg/m3; R is blade radius in m; v is wind speed in m/s; λ is tip speed ratio, defined as λ=ωR/v, ω is angular speed of wind turbine in rad/s; Cp is power coefficient of wind turbine, which is related to pitch angle β and tip speed ratio λ, with an expression of Cp = 0.22 (116 / γ − 0.4 β − 5 ) e −12.5/ γ ,
1 VC 1 , 1− D
∗
VC 1 =
(13)
∧ ∗ 1 ∗ (Vin + v dc ) , 2
(16)
∗
where v dc is set by grid requirements, while Vin* depends on the MPPT control as what mentioned before. Consequently, ∧ VC1 is used to control v dc indirectly, as shown in Fig. 4. ∧
(14)
where γ is intermediate variable.
3) AC output control If the reference frame is oriented along the grid voltage, the power equations in the synchronous reference frame are expressed as [16]
When β remains unchanged, Cp only depends on λ. Therefore, the maximum utilization factor Cpmax can be reached if the wind turbine is operating at optimal tip speed ratio λopt, which will produce the highest conversion efficiency of wind turbine. Thus, the curves of power versus rotor speed with the wind speed as a parameter can be obtained, shown in Fig. 6.
3 ⎧ ⎪⎪ P = 2 u d id , ⎨ 3 ⎪Q = − u i d q ⎪⎩ 2
To capture the maximum wind energy so as to obtain optimum dc input voltage of qZSI, the widely used hillclimbing algorithm [15] is adopted to realize maximum power point tracking (MPPT) control. The speed ω is adjusted in time to maintain maximum power of wind turbine when wind speed changes. Then the optimum power is delivered to the PMSG. Therefore, the obtained rectifier voltage Vin, that is the dc source voltage of qZSI, is highest by this way.
(17)
where P and Q are active and reactive power, respectively, u is the grid voltage, and i is the grid current. The subscripts “d” and “q” stand for direct and quadrature components, respectively. From this, we know that the independent control of P and Q can be achieved by controlling the direct and quadrature components of the grid currents id and iq. The decoupling algorithm is [17] KI ⎧ * * ⎪⎪ u d = − ( id − id )( K P + s ) + u d + ω Li q . ⎨ ⎪ u * = − ( i * − i )( K + K I ) + u − ω Li q q P q d ⎪⎩ q s
(18)
Through the decoupling control, the direct and quadrature components of the voltage ud* and uq* can be obtained. Then they are converted to the stationary reference frame by Clarck inverse transform. From this way, the ACside grid-connected control is achieved, as demonstrated in Fig. 4. IV.
SIMULATED RESULTS
Based on the aforementioned PMSG-WPGS, some relevant simulations are performed in MATLAB / SIMULINK. The parameters of wind turbine are as follows: air density is 1.225 kg/m3, wind wheel radius is 38.8 m. The command signal of peak DC-link voltage is set to 1500 V. Other parameters are listed in Table I. The operation conditions are: 0
