The Single-Phase Voltage and Power Control Algorithm of a 4-Leg Type CVCF Inverter for an Off-Grid Micro-Grid System

Abstract

In general, severe load imbalances in small AC micro-grid systems can degrade their operational performance and their maintenance. This is because the unbalanced load in the micro-grid affects the energy flow and the voltage regulation functions of each phase. In order to solve the voltage imbalance problem, several algorithms for the 3-phase 4-leg CVCF inverter have been proposed, but the control algorithms are not enough to operate the 4-leg CVCF inverter in a stable manner. Therefore, this paper proposes a single-phase voltage and power control algorithm for the 3-phase 4-leg CVCF inverter based on a dq control in order to improve the voltage imbalance problem caused by a severely unbalanced load, where the single phase voltage control algorithm is composed of an αβ-dq and a dq-αβ transformer, a voltage and a current controller, and an off-set controller and a PWM, and the single-phase power control algorithm is also composed of an αβ-dq and a dq-αβ transformer, an active/reactive power and a current controller, and an off-set controller and a PWM. Additionally, this paper performs modeling of the single-phase voltage and the power controller for a 4-leg CVCF inverter using the Matlab/Simulink S/W. From the simulation results, it is confirmed that the transient stability of the proposed single voltage control algorithm can be improved compared to the conventional control algorithm, and voltage control can also be maintained in a stable manner under extremely unbalanced conditions. Further, it is confirmed that 3-phase currents of the proposed single-phase power control algorithm are controlled in a stable manner under extremely unbalanced conditions.

1. Introduction

An off micro-grid system has been considered as one of the solutions for effective power supply systems for islands away from the power grid. The micro-grid system is basically composed of diesel generators, customer loads, and renewable energy such as ESS, PV, and wind turbine. However, severe load imbalances in small AC micro-grid systems can degrade their operational performance and their maintenance. This is because the unbalanced load in the micro-grid affects the energy flow and the voltage regulation functions of each phase [1,2,3,4,5]. Most customer loads are consumed in a single-phase connection, and they are also being operated under unbalanced conditions, but the inverters of PV, wind turbines, and CVCF are generally designed and operated as a balanced 3-phase system [6,7]. If the degree of imbalance for a single-phase load is worsening, the power flow of one phase could be in a state of discharging and the other phases could be charging, which may cause an unstable voltage control of the off-grid CVCF inverter. In order to solve the voltage imbalance problem, several algorithms for the 3-phase 4-leg CVCF inverter have been proposed, but the control algorithms are not enough to operate the 4-leg CVCF inverter in a stable manner [8,9,10,11,12,13,14]. Therefore, this paper proposes a single-phase voltage and power control algorithm for the 3-phase 4-leg CVCF inverter based on a dq control in order to improve the unbalanced voltage problems caused by a severely unbalanced load, where the single-phase voltage control algorithm is composed of a αβ-dq and a dq-αβ transformer, a voltage and a current controller, and an off-set controller and a PWM, and the single-phase power control algorithm is also composed of an αβ-dq and a dq-αβ transformer, an active/reactive power and a cur-rent controller, and an off-set controller and a PWM. Additionally, this paper performs modeling of the single-phase voltage and power controller for a 4-leg CVCF inverter using the Matlab/Simulink S/W. From the simulation results, it is confirmed that the transient stability of the proposed single-voltage control algorithm can be improved compared to the conventional control algorithm, and voltage control can also be maintained in a stable manner under extremely unbalanced conditions. Further, it is confirmed that 3-phase currents of the proposed single-phase power control algorithm are controlled in a stable manner under extremely unbalanced conditions.

2. Characteristics of Unbalanced Control for CVCF Inverter in Off-Grid MG System

2.1. Operation Mode of CVCF Inverter

A micro-grid system is composed of a diesel generator, a CVCF inverter, renewable energy, an ESS, and a customer load, where a CVCF inverter can be operated with the following two operation modes based on the customer load and the output of renewable energy. When the customer load is bigger than the output of renewable energy, a diesel generator performs constant voltage and constant frequency control; a CVCF inverter can be operated in a grid-connected mode as shown in Figure 1a. On the other hand, when the customer load is smaller than the output of renewable energy, the CVCF inverter performs constant voltage and constant frequency control, and the diesel generator is separated from the grid, as shown in Figure 1b.

2.2. Characteristics of Existing CVCF Inverter Control Algorithm

Generally, 3-phase CVCF inverters in an MG system have adapted a dq0 control algorithm with a PI controller based on synchronous coordination, as shown in Figure 2. This control algorithm, which adds 0-axis control from the d-q control algorithm of an existing 3-phase 3-wire CVCF inverter, generates a 0-axis signal through the abc-αβ and the αβ-dq0 transformers. Additionally, the output signals of d, q, 0-axis calculating voltages, and the current controller are converted with the dq0-αβ inverse transformers; and, they are delivered to the 3D SVPWM to control the 3-phase CVCF inverter. However, the conventional control algorithms are usually adjusted by a 3-phase controller, which cannot maintain the balanced 3-phase voltages in a stable manner because it can partially compensate for the deviation of the 3-phase voltage through a 0-axis control algorithm. In order to overcome the unbalanced load problem, the configuration and the control block diagram of a 4-leg CVCF inverter to adapt a linear/nonlinear or a balanced/unbalanced load is illustrated, as shown in Figure 2. The idea of a 4-leg CVCF inverter is to add one leg to the bridge of a conventional 3-phase 3-wire CVCF inverter to compensate for the deviation of the line-to-line voltage depending on the unbalanced load. The 4-leg CVCF inverter adopts an offset SVPWM algorithm to directly control the reference voltage of the N-phase as offset voltage, as shown in Figure 3 [15,16,17,18,19,20].

3. Single-Phase Control Algorithm for 4-Leg CVCF Inverter

The concept of a single-phase control algorithm for a 4-leg CVCF inverter is to control the 3-phase voltage and current with the control algorithm of a single-phase CVCF inverter, which maximizes the performance of the unbalanced voltage and current by controlling the phase-basis power flow and the unbalanced load. Additionally, the proposed algorithm can be classified into single-phase voltage control and into power control.

3.1. Single-Phase Voltage Control Algorithm

The proposed single-phase voltage control algorithm is composed of an αβ-dq and a dq-αβ transformer, a voltage and a current controller, and an off-set controller and a PWM, as shown in Figure 4, where in order to transform each phase voltage with an αβ-dq transformer, each phase voltage V_x^α (x is to be substituted with a, b, or c) is as shown in Equation (1), each phase voltage with a 90° lagging V_x^β is as shown in Equation (2), and the transformation matrix to convert the abc coordinate with a stationary coordinate is expressed as shown in Equation (3). Therefore, based on Equations (1)–(3), the dq components of each phase voltage are obtained in Equation (4).

$$V_x{}^{\alpha }=\sqrt{2}{v}_x\cos {\theta }_x$$

(1)

where V_x^α is each phase voltage [V].

$$V_x{}^{\beta }=\sqrt{2}{v}_x\sin {\theta }_x$$

(2)

where V_x^β is each phase voltage with a 90° lagging [V].

$$R({\theta }_x)=\left(\begin{array}{cc}\cos {\theta }_x& \sin {\theta }_x\\ -\sin {\theta }_x& \cos {\theta }_x\end{array}\right)$$

(3)

where $R\left(\theta \right)$ is the transformation matrix to convert the abc coordinate with a stationary coordinate.

$$\left(\begin{array}{c}{v}_{Cf,x}{}^d\\ v_{Cf,x}{}^q\end{array}\right)=R\left({\theta }_x\right)\left(\begin{array}{c}{V}_x{}^{\alpha }\\ V_x{}^{\beta }\end{array}\right)$$

(4)

where v_Cf,x^d is the d component of each phase voltage, and v_Cf,x^q is the q component of each phase voltage.

On the other hand, voltage errors are calculated from the dq components of each phase voltage considering reference voltages; they create reference currents with the PI voltage controller. Additionally, current errors are calculated from each measured phase current considering reference currents, and then they create each phase current with the PI current controller. Phase currents are compared with reference currents, and then are delivered to the SPWM through the dq-αβ transformer. Therefore, the gate signals of the upper and the lower switches for each phase are integrated with the SPWM output signal and the off-set control signal.

3.2. Single-Phase Power Control Algorithm

The proposed single-phase power control algorithm is composed of an αβ-dq and a dq-αβ transformer, an active/reactive power and a current controller, and an off-set controller and a PWM, as shown in Figure 5, where in order to transform each phase current with an αβ-dq transformer, each phase current I_x^α (x is to be substituted with a, b or c) is as shown in Equation (5), each phase current with a 90° lagging I_x^β is as shown in Equation (6), and the transformation matrix to convert the abc coordinate with a stationary coordinate is expressed as Equation (3). Therefore, based on Equations (3), (5), and (6), the dq components of each phase current are obtained in Equation (7). Additionally, based on Equations (4) and (7), the dq components of the active power P_x^d and the reactive power Q_x^q are obtained as in Equations (8) and (9), respectively.

$$I_x{}^{\alpha }=\sqrt{2}{i}_x\cos {\theta }_x$$

(5)

where I_x^α is each phase current [A].

$$I_x{}^{\beta }=\sqrt{2}{i}_x\sin {\theta }_x$$

(6)

where I_x^β is each phase current with a 90° lagging [A].

$$\left(\begin{array}{c}{i}_{Lf,x}{}^d\\ i_{Lf,x}{}^q\end{array}\right)=R\left({\theta }_x\right)\left(\begin{array}{c}{I}_x{}^{\alpha }\\ I_x{}^{\beta }\end{array}\right)$$

(7)

where i_Lf,x^d is the d component of each phase current, and i_Lf,x^q is the q component of each phase current.

$$P_x^d=\frac{2}{3}\left(v_{Cf,x}{}^d\times i_{Lf,x}{}^d+v_{Cf,x}{}^q\times i_{Lf,x}{}^q\right)$$

(8)

where P_x^d is the d component of the active power of each phase.

$$Q_x{}^q=\frac{2}{3}(v_{Cf,x}{}^d\times i_{Lf,x}{}^d-v_{Cf,x}{}^q\times i_{Lf,x}{}^q)$$

(9)

where Q_x^q is the q component of each phase reactive power.

On the other hand, power errors are calculated from the dq components of the power in each phase, considering reference powers; and, then they create reference currents with the PI power controller. Additionally, current errors are calculated from each measured phase current, considering reference currents; and then they create each phase current with the PI current controller. Phase currents are compared with reference currents, and then they are delivered to the SPWM through the dq-αβ transformer. Therefore, the gate signals of the upper and the lower switches for each phase are integrated with an SPWM output signal and an off-set control signal.

4. Modeling of Voltage and Power Controller Using Matlab/Simulink S/W

4.1. Modeling of Single-Phase Voltage Controller

Based on the Matlab/Simulink S/W, the proposed 3-phase voltage controller using three single-phase control algorithms is represented as shown in Figure 6, where the values of v_Cf,a, v_Cf,b, and v_Cf,c are obtained by an inverse transform to the abc frame for the outputs of each voltage controller—v_Cf,x^d and v_Cf,x^q (where x is a, b, and c)—which are used as switching patterns for the 4-leg in the off-set PWM block. The analog signals of measured voltages are transformed into discrete signals using ZOH (zero order hold), as expressed in Equation (10). Therefore, by combining Equations (1), (2) and (10), the dq components of each phase voltage is transformed into discrete signals, which can be obtained as shown in Equation (11).

$$G(s)=\frac{1-e^{-Ts}}{s}$$

(10)

where G(s) is the ZOH, and T is the sampling frequency.

$$\left(\begin{array}{c}{v}_{Cf,x}{}^d(s)\\ v_{Cf,x}{}^q(s)\end{array}\right)=R\left({\theta }_x\right)\left(\begin{array}{c}{V}_x{}^{\alpha }\\ V_x{}^{\beta }\end{array}\right)G(s)$$

(11)

where v_Cf,x^d(s) is the d component of each phase voltage transformed into discrete signals [V], and v_Cf,x^q(s) is the q component of each phase voltage transformed into discrete signals [V].

4.2. Modeling of Single-phase Power Controller

Using the Matlab/Simulink S/W, the proposed 3-phase power controller with three single-phase control algorithms is represented as shown in Figure 7, where the values of i_Lf,a, i_Lf,b, and i_Lf,c are obtained by an inverse transform to the abc frame for the outputs of each current controller—i_Lf,x^d and i_Lf,x^q (where x is a, b, and c)—which are used as switching patterns for the 4-leg in the off-set PWM block. The analog signals of measured voltages are transformed into discrete signals using ZOH (zero order hold), as expressed in Equation (10). Additionally, by combining Equations (5) and (6) with Equation (10), the dq components of each phase current is transformed into discrete signals, which can be obtained as shown in Equation (12). Therefore, based on Equations (11) and (12), the dq components of the active and reactive power in each phase is transformed into discrete signals, which can be obtained as shown in Equations (13) and (14).

$$\left(\begin{array}{c}{i}_{Lf,x}{}^d(s)\\ i_{Lf,x}{}^q(s)\end{array}\right)=R\left({\theta }_x\right)\left(\begin{array}{c}{I}_x{}^{\alpha }\\ I_x{}^{\beta }\end{array}\right)G(S)$$

(12)

where i_Lf,x^d(s) is the d component of each phase current transformed into discrete signals [V], and i_Lf,x^q(s) is the q component of each phase current transformed into discrete signals [V].

$$P_x{}^d(s)=\frac{2}{3}(v_{Cf,x}{}^d(s)\times i_{Lf,x}{}^d(s)+v_{Cf,x}{}^q(s)\times i_{Lf,x}{}^q(s))$$

(13)

where P_x^d(s) is the d component of each phase active power transformed into discrete signals [W].

$$Q_x{}^q(s)=\frac{2}{3}(v_{Cf,x}{}^d(s)\times i_{Lf,x}{}^d(s)-v_{Cf,x}{}^q(s)\times i_{Lf,x}{}^q(s))$$

(14)

where Q_x^q(s) is the q component of the reactive power of each phase transformed into discrete signals [var].

5. Case Studies

5.1. Simulation Conditions

In order to evaluate the operation characteristics of the presented single-phase voltage and power controller, the simulation conditions are assumed as in Figure 8 and Figure 9, where the simulation conditions adapt the system parameter of the demonstration projects for the micro-grid system. Figure 8 shows the stand-alone mode of an off-grid MG, which is composed of a CVCF inverter, a PV inverter, and customer loads, where if the 3-phase PV inverter supplies 3-phase balanced power by an MPPT operation and the customer load is in an unbalanced condition, the CVCF inverter may be in an extremely unbalanced condition—suppling power at two phases and consuming power at one phase, as shown in Figure 8.

Figure 9 shows the grid-connected mode of an off-grid MG, which is composed of a diesel generator, a CVCF inverter, and customer loads, where the CVCF inverter is operated in a grid-connected mode. If the 3-phase diesel generator supplies 3-phase balanced power and the customer load is in an unbalanced condition, the CVCF inverter may be in an extremely unbalanced condition—suppling power at two phases and consuming power at one phase, as shown in Figure 9.

Furthermore, the customer loads in Figure 8 and Figure 9 are assumed as single-phase or 3-phase 4-wire R loads, the DC input voltage of the 4-leg CVCF inverter is 700 V, and the switching and sampling frequencies are 10 kHz, respectively. Additionally, the reference voltage of the CVCF inverter in standard mode (v_a, v_b, v_c) is assumed as 311 V, and the reference power of the CVCF inverter in grid-connected mode (P_a, P_b, P_c) is 6.2 kW. Further, the unbalanced factors of the CVCF inverter in standard mode are assumed at 42.9% and 28.6%, respectively, the unbalanced factors of the CVCF inverter in grid-connected mode is 60%, and the detailed system parameters are expressed as shown in

Table 1. System parameter.

Items		Contents
DC voltage		700 [V]
switching frequency		10 [kHz]
inverter serial filter		2 [mH]
filter capacitor		20 [uF]
grid-connected transformer		380/380 V, Y-Y connection
sampling frequency		10 [kHz]
standard mode	reference voltage of CVCF inverter (va, vb, vc)	311 V
	unbalanced load rate	42.9% (time interval t2 to t3) 28.6% (time interval t4)
grid-connected mode	reference power of CVCF inverter (Pa, Pb, Pc)	6.2 kW
	unbalanced load rate	60% (time interval t2)

[21].

5.2. Characteristic of Single-Phase Voltage Control

Based on the simulation conditions in Figure 8, the performances of the proposed single-phase voltage control algorithm and the conventional 3-phase dq0 control algorithm are demonstrated as shown in Figure 10 and Figure 11, where Figure 10a and Figure 11a are phases of the output voltage and Figure 10b and Figure 11b are the current of the customer load, Figure 10c and Figure 11c are the dq0 component of the grid voltage, and Figure 10d and Figure 11d are the dq0 components of the current of customer load. Additionally, as shown in Figure 11c, the d and the q components of the proposed control algorithm are properly maintained as 311 V and 0 for the 75/50/50A_peak and the 80/70/60A_peak unbalanced conditions, respectively. Therefore, this paper assumes four different operation conditions, which are 60A_peak balanced load, 75/50/50A_peak unbalanced load, 100A_peak balanced load, and 80/70/60A_peak unbalanced condition, as shown in Figure 10 and Figure 11. As shown in Figure 10, the 3-phase grid voltages of the conventional 3-phase dq0 control algorithm are maintained in a stable manner for the 75/50/50A_peak and the 80/70/60A_peak unbalanced condition, but the values of the d component at each phase voltage drop significantly to 106 V at t₃ time interval.

Furthermore, as shown in Figure 11c, the d and the q components of the proposed control algorithm are properly maintained as 311 V and 0 for the 75/50/50A_peak and the 80/70/60A_peak unbalanced conditions, respectively. Additionally, it is clear that the 3-phase grid voltages of the proposed single-phase voltage algorithm are maintained in a stable manner for the unbalanced conditions, and the values of the d component at each phase voltage drops to 71 V, as shown in Figure 11. Therefore, by comparing the proposed algorithm in Figure 11 with the conventional algorithm in Figure 10, it is confirmed that the transient stability of the proposed algorithm can be improved, and voltage control can also be maintained in a stable manner under extremely unbalanced conditions.

5.3. Characteristics of Single-Phase Power Control

Based on the simulation conditions in Figure 9, the performances of the proposed single-phase power control algorithm are demonstrated as shown in Figure 12, where Figure 12a is each phase current of the CVCF inverter, Figure 12b is the d-component of each phase current, and Figure 12c is the q-component of each phase current. Additionally, this paper adapts two different operation scenarios, which are the −40A_peak balanced load and the −40/−40/20A_peak unbalanced load, as shown in Figure 12. From the simulation results, it is clear that the d-components of each phase current are controlled from −40/−40/−40A_peak to −40/−40/20A_peak, as shown in Figure 12b; and, the q-components of each phase current are maintained at 0, as shown in Figure 12c. Therefore, it is confirmed that 3-phase currents of the proposed single-phase power control algorithm are controlled in a stable manner under extremely unbalanced conditions.

6. Conclusions

In order to overcome the voltage unbalance problem of the off-grid micro-grid system, this paper has proposed a single-phase voltage and power control algorithm for the 4-leg CVCF inverter. The main results of this paper are summarized as follows.

(1)

The conventional control algorithms are usually adjusted by a 3-phase controller, which cannot maintain the balanced 3-phase voltages in a stable manner because it can partially compensate for the deviation of the 3-phase voltage through a 0-axis control algorithm.

(2)

From the simulation results, it is confirmed that the values of the d component at each phase voltage drop significantly to 106 V in a conventional 3-phase dq0 control algorithm, but the 3-phase grid voltages of the proposed single-phase voltage algorithm are maintained in a stable manner for the unbalanced conditions, and the values of the d component at each phase voltage drop to 71 V. From the simulation results, it is confirmed that the transient stability of the proposed single voltage control algorithm can be improved compared to the conventional control algorithm, and voltage control can also be maintained in a stable manner under extremely unbalanced conditions.

(3)

Additionally, it is clear that the d-components of each phase current are controlled from −40/−40/−40A_peak to −40/−40/20A_peak, and the q-components of each phase current are maintained at 0. Therefore, it is confirmed that 3-phase currents of the proposed single-phase power control algorithm are controlled in a stable manner under extremely unbalanced conditions.

(4)

Furthermore, the single voltage and power control algorithm can control voltage and power under different conditions if the CVCF inverter is designed according to capacity, and it will be studied in a large-scale micro-grid system in the future.