Abstract
This paper presents a new gridconnected control strategy based on a new type of Zsource inverter. For this Zsource inverter, a coupled inductor is used to displace the inductor connected to the positive of the power supply in traditional Zsource topology and its position relative to the threephase inverter bridge has changed. In contrast with traditional Zsource inverter, it can achieve higher voltage gain, lower capacitor voltage stress during steady state and suppress inrush current at startup. Last, it is modeled in twophase static frame and then a gridconnected power loop and a capacitor voltage loop are used to realize it to connect grid. Simulation results show that by this new gridconnected strategy, this Zsource inverter can reach its grid connection with high power factor and the system can work in good stability, strong robustness and dynamic performance.
1. Introduction
Zsource inverter makes the shootthrough phenomenon of the upper and lower devices of each phase leg become a normal state by using its unique impedance network while conducting its work [1, 2] and also avoids the distortion of output voltage waveform with the insertion of dead time. So it can overcome the shortcomings of traditional voltage and current source inverters [3, 4]. However, traditional $Z$source inverter also remains many deficiencies [58]: Inrush current which is easy to damage the devices of threephase inverter bridge at startup. High capacitor voltage stress on impedance network during steady state, therefore large volume of capacitors is required and then the cost increases for this inverter. In addition, due to the shootthrough zero vectors were replaced part of traditional zero vectors, so the circle synthetic generated by SVPWM is not so smooth and then quality of AC output voltage is affected. In order to further improve this topology, the scholars have proposed a variety of different Zsource inverter Topologies: a modified Zsource inverter was proposed [9, 10]. It has many advantages with no inrush current at startup and lower capacitor voltage stress during steady state compared to the traditional Zsource inverter, but its boosting capacity has not been improved. It was presented a type of Zsource inverter named switching inductive Zsource inverter in [11], this topology reduces the capacitor voltage stress and upgrades boot capacity, but on account of increasing the number of inductor elements, and thus increase the cost a lot. Last, two types of Zsource inverters called switching inductive quasi Zsource inverter and high gain Zsource inverter were proposed in ref [12, 13]. Although they can improve boost capacity, the capacitor voltage stress is still high during steady state. What’s more, the high gain Zsource inverter forms great inrush current when it starts working and is easy to damage components in the circuit. [14] lists many Zsource topologies, all have different properties, but they master boost capacity through adding shootthrough zero vectors to replace traditional zero vectors, in turn the waveform of output voltage are affected to a certain extent.
Zsource inverter is used to connect to the grid finally. As to the control strategy of grid connection for Zsource inverter, [15] proposed a control strategy named Hysteresis Current Control, it has advantage of simple control to any topologies to realize tracking control, but whether its function can achieve is based on hysteresis width. Due to the parameters complicated setting for hysteresis width, the stability of whole control system cannot be guaranteed. [16] established mathematical mode of threephase voltage source inverter in $\alpha \beta $ frame, PR controllers were adopted to control state variables and LCL filter was included to implement better filtering effect in ac side, but it generates resonance meanwhile. In addition, parameters of PR controllers are hardly to set accurately and then the stability cannot be also guaranteed.
As can be seen from the above analyses, although the Zsource inverters mentioned above overcome some deficiencies of traditional Zsource inverter to some extent, there are still substantial shortcomings. So a new type of Zsource inverter named isolated shootthrough Zsource inverter with Coupled inductor (ISTZSIWCI) is proposed in this paper, whose inrush current does not exist, capacitor voltage stress is much lower during steady state, boost capacity is improved a lot. And the separation between shootthrough vector and traditional zero vector can be realized owing to adding the electric electronic component IGBT. It overcomes all deficiencies of Zsources inverter mentioned above. Last, it is modeled in $\alpha \beta $ frame and then a gridconnected power loop and a DC bus voltage loop are used to realize it to connect grid with high power factor, strong robustness, and then the system can work in good stability and dynamic performance. Simulation results show that the above theoretical analyses are correct and verifying the superiority of this novel topology.
2. Isolated shootthrough Zsource inverter with coupled inductor (ISTZSIWCI)
The topology of ISTZSIWCI is shown in Fig. 1. It consists of threephase inverter and Zsource network including capacitors ${C}_{1}$, ${C}_{2}$ and inductors ${L}_{1}$, ${L}_{2}$. Especially, a coupled inductor is used to replace one of inductors of traditional Zsource network, and the relative position between Zsource network and threephase inverter bridge is different from tradition Zsource inverter to suppress inrush current. Its boost capacity is based on the polarity change of primary and secondary winding of coupled inductor and turning on or off diode to implement boost. Whereby, controlled device IGBT is used to individually control the insertion of shootthrough zero vector and achieve separation between shootthrough zero vectors and traditional zero vectors, Capacitor ${C}_{u}$ is used to suppress fluctuation of bus voltage due to the insertion of shootthrough zero vector. In order to avoid capacitor ${C}_{u}$ discharging through IGBT. So the diode VDS is added to make isolation.
Fig. 1Topology of this novel inverter
2.1. Modulation strategy
Space vector pulse width modulation (space vector pulse width modulation, SVPWM) [15, 16] is selected in this paper. Compared to the modulation strategy of SPWM, it has advantages including higher utilization of DC voltage, lower harmonic content, fast dynamic response and less volatile, etc.
Fig. 2Control theory of SVPWM
a) The synthesis of space vector
b) Control signal in one switching cycle for Zsource inverter
2.2. Working principle of ISTZSIWCI
Assuming that ${T}_{1}$ is a shootthrough interval in a switching cycle, ${T}_{2}$ is a traditional zero vector state interval in a switching cycle, ${T}_{3}$ is an effective vector state interval in a switching cycle. so $T={T}_{1}+{T}_{2}+{T}_{3}$. Ratio of ${T}_{1}/T$ can be denoted by ${D}_{1}$ i.e. shootthrough duty ratio. Similarly, ${D}_{2}$ and ${D}_{3}$ are nonshootthrough duty ratio, ${U}_{dc}$ is input DC voltage, ${U}_{L}$ is inductor voltage in the Zsource passive network, ${u}_{C1}$ and ${u}_{C2}$ are the capacitor voltages in the Zsource network during steady state.
As to the coupled inductor of the novel Zsource network, it is equivalent to a magnetizing inductor ${L}_{m}$ and a leakage inductor ${L}_{S}$ as well as an ideal transformer whereby, the coupled coefficient of coupled inductor and turns ratio of ideal transformer are respectively as follows:
where, ${N}_{1}$ and ${N}_{2}$ are respectively the turns of primary winding and secondary winding.
The novel Zsource inverter works in the same state with traditional Source inverter: shootthrough zero vector state, traditional zero vector state, effective vector state. Modulation control of simple boost (SVPWM) is used for this novel Zsource inverter.
Interval 1 (${t}_{0}<t<{t}_{1}$): (Fig. 3(a)). The novel Zsource inverter works in shootthrough zero vector state, the inverter bridge leg is shortcircuited, because ${u}_{2}=n{u}_{1}$ ($n>$1), diode VD1 is in offstate and then the power ${U}_{dc}$ forms a loop with primary winding of transformer through capacitor ${C}_{2}$, and ${i}_{m}$ increases from the minimum value at the same time. So the increase of ${i}_{m}$ can be written as:
And the power ${U}_{dc}$ forms a loop with inductor $L$ through capacitor ${C}_{1}$ and ${u}_{L}={u}_{C1}+{U}_{dc}$, thus the increase of inductive current is:
Interval 2 (${t}_{1}<t<{t}_{2}$): (Fig. 3(b)). The novel Zsource inverter works in the traditional zero vector state, threephase inverter bridge leg is open, primary and secondary e mf polarity of ideal transformer changes, the leakage inductor energy is transferred from VD0 branch (shortcircuited this moment) to the capacitor ${C}_{1}$ and charges it, the interval of leakage inductor energy releasing to zero can be taken as the interval of working in traditional zero vector state for this novel Zsource inverter. During this period, the changes of current across magnetizing inductor can be stated as:
Fig. 3Equivalent circuit of this novel Zsource inverter indifferent states
a)${t}_{0}<t<{t}_{1,T}$
b)${t}_{1}<t<{t}_{2}$
c)${t}_{2}<t<{t}_{3}$
The energy of inductor $L$ is transferred from diode VD0 branch (shortcircuited this moment) to the capacitor ${C}_{1}$ and charges it, reduction of inductive current is:
Due to the expression ${u}_{2}>{u}_{1}$, Diode VD2 is turnoff and diode VD1 is turnon at the same time after the release of the energy of leakage inductor ${L}_{S}$. The current of secondary winding is transferred from diode VD0 branch (shortcircuited this moment) to capacitor ${C}_{2}$ and charges it, accordingly, secondary current decreases. The voltage of magnetizing inductor is ${u}_{c1}/N$ and DC voltage across the voltage is ${u}_{i}={U}_{dc}+{u}_{L}+{u}_{c1}$. It has been improved.
Interval 3 (${t}_{2}<t<{t}_{3}$): (Fig. 3(c)). The novel Zsource inverter works in an effective vector state; threephase inverter bridge can be taken as a current source. ${u}_{c1}$ forms a loop with secondary winding of transformer through original VD0 branch (shortcircuited this moment) and voltage of magnetizing inductor is ${u}_{c1}/N$ at this point. Current across magnetizing inductor is expressed as:
The current across inductor $L$ flows to capacitor ${C}_{2}$ and charges it, Reduction of inductive current is:
2.3. Boost property of the novel Zsource inverter
According to the voltsecond balance theorem of inductor voltage, average voltage across inductor is zero over a time period $T$, so we have:
They can be also drawn from the above two formulas:
where, ${D}_{2}$ is the duty ratio. It also can be regarded as the duty ratio for energyreleasing of the leakage inductor.
The analysis shows that the peak DC voltage across the inverter ${\widehat{U}}_{i}$ is:
Boost factor of the novel Zsource inverter is $B={\widehat{U}}_{i}/{U}_{dc}$, for the same shootthrough duty ratio, when coupled inductor is fully coupled, boost factor is the highest. So when $k=$1, ${D}_{2}=$0, the highest boost factor can be obtained, the simplified expression is derived for the boost factor:
2.4. Design of coupled inductor for the novel Z source inverter
The expression of coupled inductor for this novel Zsource inverter is [17]:
where $,{L}_{S}+{L}_{m}={L}_{1}$, ${L}_{2}=M/n={L}_{m}/{n}_{2}$, $M$ is the mutual coupled inductor.
The inductor and capacitor in passive Zsource network are designed by their suppression of higher ripple current of inductor and higher ripple voltage of capacitor during steady state:
where, $a$% and $b$% are respectively the percentage of the ripple current of inductor and ripple voltage of capacitor, ${I}_{av}$ is the average value of current flowing through the network, $f$ is the frequency of switch, ${u}_{C}$ is the average value of two pieces of capacitor in the network in steady state.
Traditional Zsource inverter [18, 19] is used as a object to compare with this Zsource inverter in properties.
Capacitor voltage and the peak DC voltage across the inverter during steady state of traditional Zsource inverter can be obtained by voltsecond theorem of the voltage of inductance. Expressions are shown as follows:
Assuming coupled coefficient of coupling inductor $k=$1, turns ratio of ideal transformer $n=$2 and then comparison between traditional Zsource inverter and novel Zsource inverter in their capacitor voltage and boost factor $B$ in steady state are relatively as follows.
Fig. 4Characteristic contrast of two kinds of ZSource inverter
It can be seen from the simulation that in the same shootthrough duty cycle, compared with traditional Zsource inverter for their capacitor voltage and boot factor, the capacitance voltage of novel Zsource inverter is much lower in steady state and its boost factor is much higher.
3. Control of Gridconnected ISTZSIWCI
ISTZSIWCI can be seen as a threephase voltage source inverter combined with Zsource network. The output AC voltage is determined by DClink voltage which is related with the shootthrough dutyratio, and therefore, it is needed to model based on switching function for this Zsource inverter.
3.1. Mathematical model for ISTZSIWCI
First, three phase voltage source inverter mathematical model at the switching function.
Assuming the switching function as ${S}_{X}\left(a,b,c\right)$, when $Sx=$0, the lower device of threephase inverter leg is in onstate, the upper one turns off simultaneously and vice versa. In order to simplify the analysis, neglecting high frequency components in switching function. So we have:
For ISTZSIWCI topology shown in Figure1 and ignoring the switching losses of devices in inverter bridge as well as using $L$ filter, based on KVL, mathematical model of threephase voltage source inverter is available as follows:
where, ${U}_{A0}$, ${U}_{B0}$, ${U}_{C0}$ are output AC voltages of threephase inverter; ${i}_{a}$, ${i}_{b}$, ${i}_{C}$ are AC output currents of threephase inverter; ${U}_{ga}$, ${U}_{gb}$, ${U}_{gC}$ are threephase voltages across the grid; ${U}_{AN}$, ${U}_{BN}$, ${U}_{CN}$ and ${U}_{N0}$ are AC output voltages relative to neutral point and neutral voltage relative to the ground, respectively.
Owing to the symmetric threephase circuit, so ${U}_{A0}+{U}_{B0}+{U}_{C0}=0$. Due to the relationship between switching functions and input voltage of inverter, according to Eqs. (15) and (16), mathematical model described by switching functions can be expressed as follows:
Conducting Clark coordinate transformation, we have:
where, ${i}_{\alpha}$, ${i}_{\beta}$, ${d}_{\alpha}$, ${d}_{\beta}$ and ${U}_{g\alpha}$, ${U}_{g\beta}$ are currents, duty ratios and voltages, respectively in $\alpha \beta $ frame system.
The voltage across the inverter is equal to DClink voltage of this novel Zsource inverter, formula ${U}_{i}=B{U}_{dc}$ is plugged into Eq. (18), so we can get:
3.2. Dualloop control for ISTZSIWCI
As shown in Eq. (19), For ISTZSIWC, DC link voltage determines the property of gridconnected system and stable and continuous DClink voltage makes sure higher quality of output AC electrical energy for the system.
The primary task of the inverter connected to the grid is to achieve unity power factor running. Due to the coupling between active power across the grid, in order to achieve unity power factor running of ISTZSIWCI, so it is necessary to make the decoupling between them. Therefore, double control loops, including power loop and voltage loop are used in this paper.
For power loop, the decoupling process between reactive power and active power is as follows.
Fig. 5 shows the phase relationship between the grid voltage space vector ${\overrightarrow{u}}_{g}$ and output voltage space vector of inverter in the twophase static coordinate system.
Fig. 5Phase diagram between gridconnected voltage vector and AC output voltage vector
Fig. 6Phase diagram between gridconnected voltages and threephase AC output voltages
From Fig. 5, we have:
where:
$\mathrm{s}\mathrm{i}\mathrm{n}\delta =\frac{\mathrm{\Delta}{u}_{p}}{\left{\overrightarrow{u}}_{}\right},\mathrm{}\mathrm{}\mathrm{}\mathrm{c}\mathrm{o}\mathrm{s}\delta =\frac{\left{\overrightarrow{u}}_{g}\right+\mathrm{\Delta}{u}_{Q}}{\left{\overrightarrow{u}}_{}\right},$
According to Eq. (20) and Clark inverse transformation, the phase relationship between grid voltage space vector and AC output voltage space vector is shown in Fig. 6.
For A phase, $\mathrm{\Delta}{\overrightarrow{u}}_{aQ}>0$ in reference direction, then reactive current whose phase is lagging 90 degrees compared to grid voltage can be generated across inductor $L$, active current whose phase is the same as grid is produced simultaneously by $\mathrm{\Delta}{\overrightarrow{u}}_{ap}$ across inductor $L$ .Similarly for B and C phases.
Output power of each phase for inverter is:
where, $\omega $ is the fundamental angular frequency of the grid.
According to Eqs. (20) and (21), the target voltage space vector is calculated and input signal of SVPWM can be get naturally. Finally, the connection and break of devices in threephase inverter arm are controlled by SVPWM to realize the decoupling between active power and reactive power.
From above theoretical analysis, schematic diagram of ISTZSTWCI gridconnected control can be shown as Fig. 7.
As can be seen, for the voltage loop, it is used to regulate dclink voltage indirectly. The capacitor voltage is sampled, compared with its reference value and difference between them is sent to PID controller. Then ISTIGBT is driven by output signal of PID controller.
For the power loop, the actual output of the active power and reactive power are sampled and compared with their references and difference between them are sent to two PI controllers. Then, according to Eq. (21), output voltage references ${u}_{\alpha}^{*}$ and ${u}_{\beta}^{*}$ can be calculated and regarded as the input signals for SVPWM to control the connection and break of devices in threephase inverter bridge.
Fig. 7Control principle diagram of ISTZSIWCI
3.3. Double closedloop controllers design
Double closedloop controllers design is shown in Fig. 8. For Fig. 8(a), the actual capacitor voltage signal ${u}_{c}$ is collected and compared with its reference value, then difference between them are sent to regulator ${G}_{c}\left(s\right)$ and regulated by it to ensure ${u}_{c}$ can track its reference value accurately and reach optimum effect. The same control process for power with power loop is get in block diagram Fig. 8(b).
Fig. 8System control block diagram
a) Capacitor voltage loop block diagram
b) Power loop control block diagram
3.4. Stability analysis with double closedloop controller
According to linear control theory [20], the characteristic of $G\left(s\right)$ can be defined as:
The poles of $G\left(s\right)$ are the roots of the characteristic equation ${\alpha}_{G}\left(s\right)=0$. In complex plane, if all poles are located on the left of the imaginary axis, the system characterized by $G\left(s\right)$ can be seen stable, and instable if there is one pole located on the right side of the imaginary axis or imaginary axis in the complex plane, inversely.
The use of state feedback $H\left(s\right)$ can change the transfer function of the system, $G\left(s\right)$ is converted to GC(s), i.e. and then characteristic equation changes from ${\alpha}_{G}\left(s\right)$ to ${\alpha}_{GC}\left(s\right)\text{,}$ correspondingly, the roots of the characteristic equation are changed meanwhile. In other words, to get desired properties, we can apply various feedback matrix $H\left(s\right)$ to change the location of zeros and poles. for they have significant influence on the characters of the system. In this paper, from Fig. 7 and Fig. 8, we can select suitable $H\left(s\right)$ to change the location of the zeros and poles, so that the expected dynamical properties can be obtained.
4. Matlabbased simulation
Verification of the parameters chosen: the inductances of coupled inductor: ${L}_{1}=$190 μH, ${L}_{2}=$ 5 mH, turns ratio of ideal transformer: $n=$4, Coupled coefficient $k=$0.98, DCside input voltage ${U}_{dc}=$ 120 V, the modulation ratio $m=$0.8, shootthrough duty ratio ${D}_{1}=$0.3, and the impedance network ${C}_{1}={C}_{2}=$ 100 μF, $L=$ 6 mH. Modulation strategy of SVPWM in which the trigger pulse is applied alone to make ISTIGBT conduct is used in this paper. Verification results are as follows:
Input DC voltage is shown in Fig. 9(a), the DC voltage across the inverter ${U}_{i}$ is shown in Fig. 9(b).
Fig. 9Features of novel ZSource inverter
a) Input DC voltage
b) Dclink voltage across the inverter
As can be seen from Fig. 9, when DC input voltage is 120 V, dclink voltage is 430 V accordingly. Showing that this inverter achieves a greater degree of boost.
The output waveforms of dclink voltage and primary and secondary winding of coupled inductor current as well as the inductor current in passive network are shown in Fig. 10.
It can be seen from Fig. 10 that waveforms are in line with above theoretical analyses and verifying the correctness of theoretical analysis.
As shown in Fig. 11, by controlling of capacitor loop, capacitor voltage of the Zsource inverter always follows its reference value.
Fig. 12 shows that when $t=$0.05 s, the DC power voltage descends from 120 V to 90 V, dclink voltage of the Zsource inverter is hardly affected by the fluctuation of DC power voltage, quickly restored to its original value after a minor fluctuation. Proving that under the control of the voltage loop, this system has good robustness and is suitable for power fluctuation occasions.
When the active and reactive power reference value are stated respectively as $P=$8.5 kW, $Q=$ 0 VAR, the tracking waveforms of the actual output active power and reactive power are given in Fig. 13. As can be seen from figures, under the control of power loops, the actual output power values track their reference values. Indicating that the active and reactive powers can be controlled independently, i.e. decoupled excellently by this control strategy.
Fig. 10The waveform of structure and principle for the novel ZSource inverter
a)${u}_{i}$ is DC voltage across the inverter, ${u}_{1}$ and ${i}_{1}$ are respectively the voltage of and current for the primary winding of coupled inductor
b)${i}_{2}$ and ${u}_{2}$ are the voltage and current for secondary winding of the coupled inductor
c)${U}_{i}$ is dclink voltage, ${i}_{L}$ is the inductor current in passive network
Fig. 11Waveform of DClink voltage tracking reference voltage
Fig. 12DClink waveform of input voltage changing
a) Input DC voltage
b) Dclink voltage across the inverter
Fig. 13Waveform of power tracking
Fig. 14 shows the waveforms of threephase grid voltages and currents. It can be visible that they are in phase and the novel Zsource system runs under the condition of higher power factor.
Fig. 14Current and voltage waveforms of gridconnected ISTZSIWCI
5. Conclusion
This paper proposes a novel Zsource inverter called improved Zsource inverter with coupled inductor which is introduced coupled inductor and its position relative to threephase inverter is different from traditional Zsource inverter. Simulation validates that the novel Zsource inverter has much higher boost capacity and lower capacitor voltage stress during steady state, and then smaller size and weight of the devices can be used for this economical topology. Because of its position relative to the threephase inverter being changed, inrush current will not exist at startup so that components in the circuit can avoid damage done by inrush current. Finally, shootthrough zero vectors are inserted solely through fullcontrolled device ISTIGBT in SVPWM modulation strategy to make the separation between boost factor and modulation factor and thus improve the boost capacity as well as quality of AC voltage .Aiming at the novel Zsource inverter, it was modeled in $\alpha \beta $ frame ,avoid crosscoupling of current state variables and then, dual loops control strategy with PI controller including a voltage loop and a power loop are introduced to control the inverter connecting to the grid. Simulation results showed that under the condition of the control strategy, the novel system achieve unity power factor running and has good dynamic property and robustness. Verifying that the novel Zsource inverter has many superior performances and broad application prospects.
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About this article
This work is supported by the National Natural Science Foundation of China (Grant No. 61263004) and Gansu Province Natural Science Foundation (Grant No. 1212RJZA071).