A 4-ary Control Algorithm for Direct Power Control of Three Phase Pulse Width Modulated Rectifier

Objectives: The Direct Power Control (DPC) strategy for front end Pulse Width Modulated (PWM) rectifier employing binary hysteresis controller with two digital outputs and a new 4-ary control algorithm with four digital outputs is investigated. Methods/Analysis: The prototype DPC-PWM rectifier based on conventional binary algorithm and proposed 4-ary control algorithm for hysteresis controllers is designed and modeling and simulation was performed in MATLAB/ SIMILINK® environment. The total harmonic distortion of supply current and average switching frequency under steady state are measured for a load of wide dynamic range for different hysteresis widths. The DC output voltage ripples and power ripples are also observed. Findings: It was found that the total harmonic distortion in supply current was reduced and remained bounded within narrow range in 4-ary control as compared to binary control. The average switching frequency also remained bounded within narrow range in proposed control as compared to conventional hysteresis control. The DC output voltage ripples and power ripples were found to be reduced considerably at heavy loads as compared to binary control. Novelty/Improvement: The tight control of active and reactive powers not only around the hysteresis band but also within the hysteresis band is achieved with simple algorithm.

The control technique using instantaneous active and reactive power rather than current was first proposed by 10 . Subsequently 11 named it as Direct Power Control. In this hysteresis controller based DPC, a proper switching vector is selected from Switching Table (ST), and applied during the next control period on the basis of outputs of hysteresis controllers and position of the supply line voltage space vector which is termed as ST-DPC.
Much research has been carried out to improve the performance of the DPC. The Virtual Flux based DPC (VF-DPC) 12 and DPC using Space Vector Modulation (DPC-SVM) 13 were aimed at improving the performance under unbalance and pre-distorted grid at constant switching frequency. May researchers have proposed different switching tables [15][16][17][18] to reduce the Total Harmonic Distortion (THD) of line currents and the switching losses. The duty cycle based control was also proposed which reduces power ripples and supply current THD 19 . But the performance over the wide range of load current is required to be addressed. In many applications, like industrial motor drives, air conditioning etc, the load current varies significantly over a wide range. Hence, the rectifier designed to power such applications must be able to provide satisfactory control over wide dynamic range of load current. The THD of the supply line current is inversely proportional to the line inductance and switching frequency for PWM rectifier. The maximum permissible value of inductance is inversely proportional to the load current 4 . If high value of inductance is employed then the DC output voltage will have high amount of ripple or even may not built up to the desired value. If significantly low inductance is employed then the current ripples at low load current increases and consequently THD increases. It is not possible to vary the inductance for optimum performance over wide load current range. Hence, there is a need for a control strategy which may allow satisfactory operation of rectifier over a wide dynamic range of load current.
This paper proposes a control algorithm which provides control within the hysteresis band also, for tight control of instantaneous active and reactive power, to improve the performance over wide dynamic range of load current. An overview of the conventional Direct Power Control strategy is presented in Section 2. In Section 3, the instantaneous power within hysteresis band is analyzed and a new control technique is developed for power control within hysteresis band. The simulation and result analysis for DPC-PWM rectifier based on conventional and proposed 4-ary control algorithm for hysteresis control is discussed in Section 4. In DPC strategy, the instantaneous active power and reactive power are computed at every sampling instant and compared with the desired reference values and using hysteresis comparators. If the error is above or below the tolerable limits, appropriate digital control signals are generated as shown below:

Conventional Direct Power Control Strategy
(1) and (2) The stationary coordinates are divided into 12 sectors as shown in Figure 2. The switching table is prepared containing switching vectors as a function of two digital Vol

Power Control within Hysteresis Band (4-ary Algorithm)
The conventional hysteresis controllers described by Equation (1) and (2) But the switching control period employed is practically much smaller than because sufficiently high switching frequencies are employed to control the harmonics within limit. Hence, it may take more than one control periods for instantaneous power to cross the hysteresis band only after which the next switching vector can be applied in conventional hysteresis controller.
The performance during hysteresis band can be improved if can be adjusted such that it approaches the value of . But changing requires change in one or more of the parameters , , , and . The only parameter over which we have control is . Figure 3 depicts the situation of powers outside and within hysteresis band , for active power controller.
For to approach , is adjusted using 4-ary algorithm as shown in Figure 4. It is termed here as 4-ary algorithm, because hysteresis controller generates four levels at its output (four digital outputs). The algorithm shown in grey box is to control power within hysteresis band.   When controller output is either or , the switching vector which decreases power is employed and when it is 1 or 3, the switching vector which increases power is employed. Similar comment is employed for controller output . Hence, 16-state switching table is required as shown in Table 2. In Table 2 Table 1 by using additional logic for ORing controller outputs. The schematics of the controller with additional logic for converting 4-ary output of hysteresis controllers to binary outputs is shown in figure  5 for active power control. The same type of algorithm and control logic as shown in Figure 4 and Figure 5 are employed for reactive power control also.

Simulation and Result Analysis
The conventional binary DPC and DPC with 4-ary control are simulated in MATLAB/SIMULINK environment. The switching table shown in Table 1 is employed in this work as it gives the best results. The performance of conventional DPC using binary control algorithm and DPC with 4-ary algorithm is evaluated. The system specifications and control parameters are shown in Table 3.

Figure 5.
Simulink subsystem for controller output d p shown in Figure 4. The simulation was run for different hysteresis widths of active and reactive powers and for two sampling frequencies ( ) of 50 kHz and 40 kHz. The load resistance was varied during simulation as follows to test the performance over a wide dynamic range of load current.
The Total Harmonic Distortion ( ) and average switching frequency are considered as performance parameters. The THD was measured using 'Powergui' tool of MATLAB/SIMULINK. The gate pulse amplitudes at simulation times are stored in a structure and a script was run to note the gate pulse transitions and corresponding instants, using which average frequency was measured under steady state over 5 cycles of supply voltages for different loads. Figure 6 shows THD vs. hysteresis width as a percentage of with load current as a parameter for a given load and switching frequency. The THD varies considerably as a function of for conventional hysteresis controller where as it remains bounded around the minimum possible value for 4-ary controller. This is because this algorithm tries to maintain the power within a minimum band which is a function of and once power enters into the band as discussed in Section 3. Increasing from 2 to 2.5 , increases THD but it is maintained constant for change in .   Figure 7 shows the average switching frequency vs. load current with sampling frequency (control period) as a parameter. The average switching frequency was found to be inversely proportional to the load current in case of binary controller based DPC, whereas it was maintained within narrow range about a fixed value. As can be seen, the switching frequency can be controlled by varying control period (sampling frequency).   In Figures 8 and 9, instantaneous active and reactive powers are plotted for different loads for = 1%. It is evident that the power ripples are quiet high for high load currents in case of conventional DPC whereas they are sufficiently reduced for DPC with 4-ary control. Figure  10 shows DC output voltage waveforms in which the voltage ripples are quiet reduced at higher load current of 60 A (0.5 to 1.2 sec) and 100 A (1.8 to 2.5 sec) for DPC with proposed algorithm.

Conclusions
In this paper, the new 4-ary algorithm for hysteresis controller is presented for tight control of power within hysteresis band.
The conventional DPC-PWM rectifiers using binary and DPC-PWM with 4-ary control were designed, modeled and simulated using MATLAB/SIMULINK. The THD of supply current increased/decreased as hysteresis width of powers increased/decreased for a given load current in case of conventional DPC, where as it remained almost constant for change in hysteresis width in case of DPC with 4-ary control. The switching frequency varied inversely as load current in conventional DPC whereas it remained within a narrow range in DPC using 4-ary control. The power and DC voltage ripples were quiet high for high load currents in case of conventional DPC whereas they were sufficiently reduced for DPC with 4-ary control. This was because of the fact that the 4-ary algorithm tries to confine the active and reactive power within the hysteresis band and forces them to approach their reference value and also adjusts the hysteresis width to be minimum required for optimum performance.
Hence, PWM rectifier designed using DPC with 4-ary control can give better performance as compared to conventional binary DPC for applications where load current varies dynamically over wide ranges.
The implementation of proposed 4-ary algorithm is very simple hence the system complexity is not much increased. More accurate control can be achieved if the time taken by power to cross the hysteresis band can be calculated and further control is added.