Active power decoupling and controlling for single-phase FACTS device

Single-phase FACTS device has a bulky and short-life electrolytic capacitor to absorb the ripple pulsating at twice of the line frequency in DC side, resulting in lower power density. This paper introduced a structure of three-phase bridge which added an additional leg connected to an AC capacitor based on single-phase H-bridge. The 2-ripple energy of the electrolytic capacitor in single-phase H-bridge could be transformed to the film capacitor of the AC side in three-phase H bridge. The size of single-phase FACTS is reduced by ten times compared to the single-phase H-bridge. A simple control strategy had been studied, through two kinds of controllers: the digital quais-PR controller had been used to control gird current and AC capacitor voltage and current; the two cosine controller had been used to eliminate the rest of two-ripple harmonic in the DC side, there was no controller to maintain DC voltage. The experiments verified the feasibility of the control strategy.


Introduction
The single-phase flexible AC transmission systems (FACTS) [1][2][3][4][5] have played an important role for power grids because FACTS device can improve the grid stability, controllability, and reliability, which in turn, enhance power quality and system transmission capability. As we know, all FACTS devices must set an electrolytic capacitor in DC side, resulting in short life-time, bulky volume, and low power density. The DC capacitance is given by [2] C dc = U s I s ωΔU dc U dc (1) where U s is grid-rated voltage, I s is grid-rated current, ω is grid angular frequency, U dc is the average voltage in DC side, ΔU dc is the allowed peak-to-peak voltage ripple. In order to extend the FACTS's lifetime and reduce the DC capacitor bank, a great many researches have been done on topologies and control strategies [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The basic idea of topologies is adding extra-bridge arms and energy storage components such as inductor or capacitor, which permit to transform the two-ripple energy from DC electrolytic capacitor to energy storage component in AC branch. The DC capacitor is only used to filter switching ripples, thus the capacitance is been reduced. The control strategies contain three parts: DC voltage control, grid current control, and AC energy storage component voltage and current controls. The PI controller is used for DC voltage to maintain a constant. The quasi-PR controllers are used to control grid current and insure two-ripple energy transform.
In [13,14], three H-bridge circuit in Fig. 1 is proposed for PWM rectifier application. By adding an auxiliary leg to singlephase H-bridge inverter, an AC film capacitor with minimal energy component is controlled to absorb two-ripple energy. The total capacitor volume is reduced by 13 times. In order to analyse remaining two-ripple in DC side and obtain the voltage and current references for AC capacitor, the control methods in [13,14] are very complicated and time-consuming.
Here, the new topology is proposed as Fig. 1, and a novel control strategy has been studied. The DC voltage has been proved to be self-stabilised without controlling. Through a band-pass FIR filter, the remaining two-ripple energy can be analysed totally. Furthermore, the fast algorithm has been deducted. Then, the references of the AC voltage and current have been received based on total energy transform. This topology and control strategy can transfer the two-ripple energy completely, so that the electrolytic capacitor can be replaced by other kinds of ones.

Theoretical analysis
The novel topology is shown in Fig. 2.
Compared to Fig. 1, a filtering inductor is set in b-phase. Considering the three voltages (u a , u b , u c ) in Fig. 2 as controlled sources, the equivalent circuit is shown in Fig. 3.
Supposed the grid voltage and current is and the voltage and current of the ac capacitor is u ac = U ac sin(ωt + θ) i ac = I ac cos(ωt + θ) The instantaneous power between a and b is where In the same way, the instantaneous power between b and c is where The two-ripper energy from grid should be transformed to the C ac Therefore, the magnitude and phase of AC capacitor are In primary simulink experiments, we found a few of remaining two-ripple energy in DC side. Supposed u dc (t) = U dc + ΔU sin sin(2ωt) + ΔU cos cos(2ωt) As u dc (t) is even function, ΔU sin = 0 is Fourier decomposition. So u dc (t) = U dc + ΔU cos cos(2ωt) The instantaneous power to the DC capacitor is the two-ripple energy should be The voltage and current of AC capacitor are 3 Control strategy Fig. 4 shows the control system for single-phase FACTS device, which consists of grid current control I by controlling the magnitude of grid current and the phase angle φ, ac voltage and current control II by double close-loop, and the remaining tworipple power analysis III. PC1 is a kind of quasi-PR controller in parts I and II, which is used to extract the two-harmonic accurately. PC2 is band-pass FIR controller, which is used to analyse the tworipple ΔU cos .

AC capacitor control
In part II, the quasi-PR controller is used for the capacitor current in inner-loop and voltage in outer-loop. The transfer function of the controller is G PR (s) = K p + 2K r ω c s s 2 + 2ω c s + ω 0 2 (13) where ω 0 is resonance angular frequency, ω c is cut-off angular frequency, K p and K r are the coefficients of the controller. The amplitude frequency characteristic diagram is in Fig. 5.
The Tusin transform is usually used to digitise the analogue quasi-PR controller. Tusin transform keeps a linear relationship in low-frequency stage from s domain to z domain. In order to guarantee the linear relationship in high-frequency, a pre-correction transform has been used where C = ω 0 /(tan(ω 0 T s /2)), T s is sample time.
Bring (14) into (13) where The corresponding difference equation where u(k) and y(k) are the input and output of the controller, respectively. From u cb * to the AC capacitor current i Cac , the transfer function is After digitising The inner-loop transfer function is The inner-close-loop transfer function is The quasi-PR controller parameters are set: K p = 15, K r = 22, ω c = 5 rad/s, ω 0 = 314 rad/s, and Bode plot is shown in Fig. 6. Similarly for voltage outer-loop, from AC capacitor current to AC capacitor voltage, the digital transfer function is The inner-loop transfer function is The outer-close-loop transfer function is The quasi-PR controller parameters are set as K p = 8, K r = 15, ω c = 5 rad/s, ω 0 = 314 rad/s, and Bode plot is shown in Fig. 7. According to Figs. 6 and 7, the dual control loop obtains an acceptable bandwidth to track the reference of AC capacitor voltage and current.

DC voltage analysis
In Fig. 2, there is no load in DC side. When the device is powered on and not controlled, there is a voltage of about 2U s in C dc . During normal operation, C ac can be considered as a source, which will charge for the DC capacitor C dc through the bridge arm 2, 3. At last, the voltage in C dc will be maintained at ∼ 2(U ac + U s ). This voltage magnitude can satisfy the work requirement. Compared to [13], there is no DC voltage control involved here.
Then in part III, the PC2 is a band-pass FIR control, the express of finite impulse response is where N is sample number in a power period. The amplitude-frequency characteristic diagram is shown in Fig. 8. The two-harmonic can be analysed without phase delay.

Simulink results
To verify the effectiveness of the proposed active power decoupling and controlling for single-phase FACTS device, we use the single-phase device which realises a variable active capacitor. A 2-kVA system is designed, the key parameters are listed in Table 1.
If the allowed DC voltage ripple is 5%, the DC capacitance is 17 mF for single-phase H-bridge system [21][22][23]. For the proposed three-phase H-bridge system, because two-ripple energy would be absorbed by the AC capacitor, the DC capacitor only needs to absorb switching ripple, of which the DC capacitance is 50 μF [22]. The AC capacitance calculated based on (3) is 150 μF. However in practice, it is designed to be 200 μF considering a few margin. Compared to the single-phase H-bridge FACTS device, the proposed three-phase structure reduces the total size of all capacitors by ten times.
Three filter inductances L a , L b and L c , if allowed the currents (including i s and i Cac ) ripple is 20%, are designed to be 0.4 mH.
Figs. 9-12 show the simulation results of variable capacitor. u a *, u b * and u c * are the reference sine signals for controlled voltage source u a , u b and u c in Fig. 9. The DC voltage eventually stabilised at about 624 V, and the remaining two-ripple has eliminated by PC2 controller. In Figs. 11 and 12, the total two-ripple energy has been transformed to the AC capacitor.

Conclusion
An active power decoupling and controlling for single-phase FACTS device is proposed. The two-ripple energy can be transformed from the DC capacitor in single-phase structure to the AC capacitor in three-phase structure. The bulky and short-lifetime electronic capacitor can be replaced by film capacitor. Then, FACTS device's volume can be reduced significantly and its lifetime can be extended greatly. Here, a novel strategy that include digital quais-PR controller, band-pass FIR controller and no controller in DC voltage has proposed. The experimental results has verified the feasibility of the topology and control strategy.