Sensorless Neutral Point Voltage Stabilization in Three-Phase Four-Wire Converters

This paper presents a midpoint voltage balancer (MVB) which provides neutral point voltage stabilization to three-phase four-wire converters. The MVB consists of dual switching legs, two neutral inductors, and two split capacitors. A sensorless approach with open-loop control is adopted. It removes current/voltage sensors and alleviates computational demand. It is a cost effective and robust alternative to the closed-loop MVB. Due to the zero-crossing of the neutral inductor current, all switches of the MVB operates in zero-voltage switching mode when neutral current is smaller than the nominal phase current of the three-phase four-wire converter. Interleaving operation of the MVB minimizes the high-frequency current circulation in the split capacitors. In addition, the two neutral inductors are magnetically coupled to decrease the inductor current ripple. As a result, the size of passive components of the MVB is reduced. The proposed sensorless approach is verified by a 20 kVA prototype.


Introduction
Three-phase four-wire (3P4W) converters, being standalone or grid-connected, provide a path for neutral current. While the standalone can support various single-phase loads in an isolated micro-grid [1], most of the grid-connected inject energy from distributed resources to utility grid. A 3P4W grid-connected converter can offer zero-sequential voltage imbalance compensation to the point of common connection (PCC) in a low-voltage distribution network [2]. Nowadays, the adoption of single-phase rooftop photovoltaic system and electric car are increasing. These may lead to degradation of voltage balance in utility grid. Therefore, research and development of 3P4W grid-connected converters that offers voltage imbalance compensation is necessary.
Popular configurations of 3P4W converters are the split dc bus (2-C) [3], the four-leg converter (4-Leg) [4], the actively control split dc bus (ACSB) [5] , and the midpoint voltage balancer (MVB) [6]. The 2-C configuration is easy to implement. However, it suffers from bulky size of electrolytic capacitors and incapability to process neutral current with dc component. The 4-Leg configuration adopts an extra switching leg to form a neutral point for the 3P4W GCC. Since the control of the fourth switching leg and the control of the three-phase inverter are not decoupled, it requires more development effort. The ACSB configuration combines the idea of 2-C and the 4-Leg, and it is easy to control. In addition, the split dc bus of an ACSB can be implemented using small capacitors.
The MVB configuration proposed in [6] doubles the neutral current handling capability of the 3P4W GCC by adopting dual switching legs, as shown in Fig. 1. Dual-loop control is implemented, and the neutral point voltage ripple is less than 1.5% under severe neutral current transient. It offers zero-voltage switching (ZVS) operation to the dual switching legs under a wide range of neutral current injection.
The ZVS operation is achieved by adopting small neutral inductance so that inductor current cross zero at any switching cycle. Interleaved control is implemented to prevent high-frequency current from circulating into the split capacitor branch. Because of dual-loop control, usage of multiple sensors and high computational demand is inevitable.
In this paper, the control strategy of the MVB is redesigned to allow sensorless neutral point voltage stabilization in the 3P4W converter. This approach is considered as a cost-effective alternative to the MVB proposed in [6]. It provides majority of the advantages existed in its predecessor, while it requires no information on neutral inductor currents, split dc bus voltages, nor neutral current. The MVB operates in open loop with a fixed duty cycle and fixed switching frequency. The neutral inductance is half compared to that in [6]. Nevertheless, same inductor current ripple is maintained due to coupling. In addition, capacitance of the split dc bus is also reduced. Moreover, the neutral point voltage is tolerant to capacitance mismatch, which might happen due to parameter deviation and component degradation.

Description of MVB
The MVB is connected to a 3P4W grid-connected converter, as shown in Fig. 1. It consists of dual IGBT switching legs with S1, S2, S3, S4, two neutral inductors LN1, LN2, and two split capacitors CN1, CN2. Being connected to the common end of the neutral inductors, the midpoint of the split dc bus forms the neutral point N. Table 1 presents the specifications of the 20 kVA 3P4W converter, which adopts the MVB to stabilize the neutral point. This work focus on the MVB, while the design of the three-phase inverter and how it is controlled to offer voltage imbalance compensation is not covered. The MVB operates in open loop mode, requiring no current and voltage measurements. The PWM signals for each switching legs are 180° phase shifted so that the current ripple of the two neutral inductors are interleaved. As a result, the inductor output current iLN is, theoretically, ripple free [7].
A three-phase voltage signal can be decomposed into positive-sequence components, negative-sequence components, and zero-sequence components. An unbalanced three-phase voltage measured at a PCC may contain negative-sequence components. During voltage imbalance compensation, the 3P4W converter injects unbalanced currents to the PCC. The injected currents contain suitable amount of zero sequential currents with reversed polarity to that of the voltage sequential components. The zero sequential currents, i.e. the neutral current directly flows into the midpoint of the dc bus. This current may contain components of fundamental frequency and certain harmonic frequencies based on the power quality compensation mode of the 3P4W converter.
Grid standard, EN 50160-2010, limits voltage total harmonic distortion (THD) at PCC up to 8%. To meet harmonic requirements of grid regulations, the adoption of 3P4W grid-connected converter is a good approach at mitigating harmonics, and compensating voltage imbalance. Since low-order voltage harmonics are dominant in utility grid, the 3P4W converter mentioned in this paper concerns harmonic order up to 13 th . This means that the neutral current could contain harmonic components from 3 rd up to 13 th order with various amplitude.

Three-phase inverter
Unbalanced and non-linear loads With the proposed MVB, this harmonic-abundant neutral current is redirected to the neutral inductor path, keeping the split capacitor free from the neutral current. Therefore, the voltage of the neutral point is stabilized.

Operation principle
The MVB either operates in closed loop [6,8] or open loop. In closed loop, current and voltage signals are fed back to the loop, which modifies duty cycle to alter the neutral point voltage to a desired condition. Fig. 2 (a) shows the control implementation of the MVB, where dual loop is implemented [8]. The voltages of the upper and bottom split capacitor vCN1, vCN2, currents of the neutral inductors iLN1, iLN2, and the neutral current iN are measured. Due to the existence of LC resonance in the MVB circuit, active damping is typically adopted. Two control commands uk_LN1 and uk_LN2 are compared with the 180° phase shifted carrier signals, from which the gate signals G1, G2, G3, and G4 are derived.
The objective here is to keep the neutral point voltage as stable as possible. Since the neutral point voltage should be half of the total dc bus voltage, the duty cycle D of the switches is kept at 50%. Therefore, in open loop, control commands uk_LN1 and uk_LN2 are fixed values, which equal half of the carrier amplitude. As shown in Fig. 2 (b), same to the closed loop, the control commands are compared with the carrier signals, from which gate signals are derived.
According to Fig. 2 Assuming that the dc bus voltage is constant, so dVdc/dt=0, (1) becomes and = Therefore, the MVB can be simplified into a buck converter with dual switching legs, as shown in Fig. 3 (a) [9]. This buck converter is connected to a capacitor CN and a current source IN.
As mentioned before, the duty cycle is 50% with switching pattern interleaved by 180° phase shift. Neglecting dead time effect, there are only two switching states. In state 1, S1 and S4 are switched on, S2 and S3 are switched off; in state 2, the switches work in the opposite. Both states last half switching period Ts. Fig. 3 (b) shows some key waveforms of the MVB under different switching states. Note that the doted lines in Fig. 3 (b) are meant for inductor currents of the MVB with coupled neutral inductor, which is covered in the next section.
In state 1, the inductor voltages are represented as LN1 dc The current through LN1 increases, while the current through LN2 decreases. Assume that the inductance of both inductors is equal, LN1=LN2=LN. Since the duty cycle is 50%, VCN=Vdc/2. The inductor current change during each switching cycle are expressed as Similarly, in state 2, the inductor current change during each switching cycle are denoted as Based on (5) and (6), the increment and decrement of neutral inductor current in each switching cycle are equal. Therefore, the current ripple on the two neutral inductor counteracts each other. Ideally, the total inductor current iLN is a straight line and ripple-free, as shown in Fig. 3

Passive component design
Because of sensorless approach, design of the neutral inductors and dc split capacitors are particularly crucial. According to (2), if iLN counteracts iN, no current flows into CN, which stabilizes the neutral voltage vCN. This requires the impedance of the neutral inductor branch to be much smaller than that of the split capacitor branch at selected frequencies, which range from grid fundamental and its harmonic up to 13 th order as indicated in Table 1. In closed loop, impedance reduction of the neutral inductor branch is achieved by paralleling a virtual impedance to the existing inductor [9,10]. However, this requires multiple sensors and multiloop control implementation. The sensorless approach proposed in this paper removes the need for control loops and keeps the neutral point voltage stable by selecting appropriate neutral inductors and split capacitors.

Split capacitor
As mentioned before, the MVB only has two switching states. At any given time, one of the neutral inductors is connected to the positive potential of the dc bus, while the other is connected to the negative. The circuit diagram of an impedance model of the MVB is shown in Fig. 4, where the neutral inductors LN1, LN2, and the split capacitors CN1, CN2 are represented by ZLN1, ZLN2, ZCN1, ZCN2, respectively. Based on the assumption that LN1 equals LN2, thus ZLN1=ZLN2=ZLN. Therefore, the voltage of the neutral point N is expressed as Given the premise that at frequencies of interest, equation (7) becomes Therefore, as long as (8) is satisfied, the neutral point voltage VN equals half of the dc bus voltage, even if the split capacitors does not match in capacitance.
In [6], the neutral inductance is designed to be LN=220 µH, such that the IGBTs of the MVB operate in ZVS mode under a wide neutral current injection range (IN ≤ 29 Arms). Under this circumstance, the neutral inductor currents iLN1, iLN2 cross zero at any given switching cycle when the neutral current iN is less than the nominal phase current Iabc. Re-arrangement of (8) yields and fN is the frequency of the neutral current, ranging from 50 Hz to 650 Hz. Therefore, two split capacitors of 10 µF are selected to meet the requirement of (10). Note that CN1 and CN2 can be different without deteriorating the neutral point voltage stabilization of the 3P4W converter. In addition, the tolerance of the neutral point voltage stability to split capacitance mismatch is verified through experiments.

Neutral inductor
Interleaved control of two switching legs significantly reduces the output current ripple of iLN. However, the inductor current ripple remains unchanged. On the one hand, inductor current ripple is deliberately increased to facilitate ZVS of the MVB. On the other hand, less inductor current ripple is desired to reduce copper loss. In this paper, neutral inductor coupling is employed to address the trade-off between current ripple and power loss.
By coupling the neutral inductors, as shown in Fig. 5, in a way that the derived ideal transformer is connected out of phase with the polarity dots on opposite ends, one obtains the MVB with coupled neutral inductors. The coupled inductor is represented as an ideal 1:1 transformer, two leakage inductors Llk1, Llk2, and a magnetizing inductor Lm [11]. Same to the MVB with independent inductors, there are only 2 operational states of the MVB with the coupled inductors.
In state 1, the inductor voltages are represented as (3) and (4). As elaborated in [11], the current changes through neutral inductors in this state are ( ) where k is the coupling coefficient of the coupled inductor, Ls is the self-inductance, and Since the duty cycle D is always 50%, the inductor current changes are denoted Similarly, in state 2, the current changes are expressed as For a transformer with perfect coupling, the leakage inductance Llk is zero, and the coupling coefficient k is then equal to 1. Compared to (5) and (6), it is beneficial to build a coupled inductor with k ≈1. Therefore, the current ripple through the coupled neutral inductor ΔiLc is half of that through the independent neutral inductors ΔiLi, as shown in Fig. 3 (b) and expressed as However, as mentioned before, the neutral inductor current ripple is deliberately brought up to maintain ZVS operation under a wide neutral current injection range. To preserve the same amount of inductor current ripple, a 50% neutral inductance reduction becomes a good alternative, hence LN1=LN2=110 µH.

Experimental verification
In order to verify the effective of the proposed MVB, A 20 kVA 3P4W grid-connected converter prototype is built. Main components of the converter are shown in Fig. 6. Key specifications of the converter has already been presented in Table 1.The converter provides harmonic mitigation and voltage unbalance compensation to the PCC. Two three-phase IGBT modules are adopted in the prototype. A dSPACE MicroLabBox is employed to handle current and voltage signal acquisition and PWM signal generation.
Key waveforms of one switching leg during switching operation are shown in Fig. 7. These waveforms include gate signal of S2, neutral inductor current iLN1, current through S2, and voltage across S2. The conventions of these signals are referred in Fig. 5. The inductor current has a high current ripple, and it crosses zero at every switching cycle. During switching period T1, gate signal G2 is positive, however, iS2 ≤ 0, diode D2 conducts until the current reverses its polarity. During switching period T2, G2 is still positive, iS2 > 0, S2 conducts until the G2 goes to negative. After that, in T3, D1 conducts and in T4, S1 conducts. S2 operates in hard turn-off at the transition between T2 and T3, as shown in Fig. 7. However, since the anti-paralleled diode D2 conducts before S2, there is only a diode forward voltage across the emitter and the collector during the turn-on of S2. As a result, the turn-on loss of S2 is almost zero. This operational principle also applies to S1, S3 and S4. Therefore, the ZVS turn-on is great advantage of the MVB, since turn-on loss of IGBT is normally higher than turn-off losses due to diode reverse recovery.
The 3P4W converter injects unbalanced current ia, ib, ic to the PCC, such that a certain amount of iN is injected to the neutral point. Due to component availability, coupled inductor whose self-inductance is 85 µH is chosen instead of 110 µH. To verify the response of the proposed MVB, experimental tests under four different cases were performed, as described in the following.
• Case 2: Closed loop based on independent inductors with CN1=CN2=100 µF, LN1=LN2=220 µH.   It contains iN, vCN, iLN1, iLN2, and iLN. Similarly, a neutral current transient of 60 Apeak is created at 2.44 s to verify the dynamic response of the MVB. It takes the MVB around two grid cycles to fully react to the neutral current transient, and to maintain the Offset -17 A    Even though, the self-inductance of the coupled inductor is 39% of that in case 1, the average current ripple across the coupled inductor is just 47% more than that in case 1. Due to some piratical issues, the coupling coefficient of the inductor is never 1, and the leakage inductance Lk1 and Lk1 are not the same. As it shown in Fig. 10 (f), currents iLN1 and iLN2 does not cancel each other fully, which results a 9.4 Apeak current ripple in iLN. Nevertheless, the coupled implementation of the neutral inductors is a way to reduce core and copper use of the proposed MVB.
In order to show voltage stability tolerance to split capacitance mismatch, CN1 is chosen to be 100% more than that of CN2. The test results of case 4 is shown in Fig. 11, which includes waveforms of iN and vCN. The MVB regulates the neutral point voltage to half of the dc bus voltage with ripple around 15 V rapidly. It can be concluded that the dynamic performance of the MVB is not compromised under split capacitance mismatch.
The comparison between the open loop regulated MVB with sensorless approach and the closed loop controlled MVB is summarized in Table 2. The open loop regulated MVB is inferior in terms of neutral current handling capacity and tolerance to neutral inductance asymmetry. However, considering the fastdynamic performance, absence of control loops and sensor, as well as small passive components, the proposed MVB is a cost-effective and robust alternative to the closed loop controlled MVB.

Conclusion
A voltage stable neutral point is essential to normal operation of 3P4W converters, especially those in voltage imbalance compensation applications. An unstable neutral point could lead to undesired output current distortion, which degrades the compensation performance of the converter at PCC. This paper proposes a cost-effective and robust MVB for neutral point voltage stabilization in 3P4W converters.
The MVB requires no current nor voltage measurements, and it operates in open loop mode. The passive components (110 μH and 10 μF respectively) are carefully selected so that most of the neutral current is re-directed into the inductor branch, keeping the neutral voltage stable. Coupled implementation of neutral inductor is adopted, which cuts the required inductance to half. In order to achieve the best result, high coupling coefficient and symmetrical inductor construction are desired. Due to interleaving operation, high-frequency current circulation inside the split capacitor branch is alleviated. All IGBT switches of the MVB operates under ZVS when the neutral current is less than the nominal phase current of the 3P4W converter.
Compared to the closed loop counterpart, the sensorless approach does reduce the neutral current handling capability of the MVB by about 33%. However, it stabilizes the neutral point voltage much faster by around 300%. In addition, the performance of the proposed MVB is not compromised even under a 100% split capacitance mismatch.