Grid power control of direct matrix converter fed three-phase induction generator

ABSTRACT


INTRODUCTION
In the world of power electronics, matrix converters (MCs) rank among the most desirable converter families.The matrix converter, which is also known as the "all-silicon" solution, is an array of controlled bidirectional semiconductor switches that directly connects the input voltage source to a load/output without using a DC-link stage or any other sort of energy storage device.By conducted research of Venturini and Alesina, this converter's development began in 1980.They presented the circuit configuration together with a comprehensive mathematical model to explain the converter's low-frequency behavior.They were the first who used the term "matrix converter".This converter offers a few appealing qualities, which are: − High power density − Frequency decoupling of the AC input and output voltage − Input and output Sinusoidal currents waveform − Fully operating in regenerative mode − Per required input power factor adjustment Due to their ability to provide a small-footprint solution for a frequency converter, matrix converters are the subject of intense study at the moment.When compared to analogous two-stage power conversion methods, the MC can produce higher power densities.As a result, given the matrix converter's benefits of energy savings and size reduction, it is anticipated that its application areas will grow.Uninterruptible power supply (UPS), power factor correction (PFC) rectifiers for data centers and telecommunications equipment, battery energy storage systems (BESS), and a number of isolated AC-DC matrix converters have recently Grid power control of direct matrix converter fed three-phase induction generator (Ali Salam Al-Khayyat) 2241 been proposed.The matrix converter, that is known as the direct matrix converter (DMC), has been subject to many modulation techniques since the 1980s.As a result, the DMC will be used in this work.Figure 1 depicts the primary force-commutated three-phase AC-AC converters' layout, which is called the DMC [1]- [3].The MC topology considers as one of the most researched converters, but it is not exploit in the industry.The restriction of input/output voltage transfer ration for sinusoidal modulation that is 86% maximum and the limitation of compensate the reactive power, make the MC not to compete with the conventional voltage source converter (VSC).Other issues need to be addressed in order to make the MC as a converter in the power electronic market are the lack of monolithic bidirectional semiconductors and the necessity of complex strategies for the commutation of the bidirectional power switches, which typically necessitates a control system based on FPGA [4], [5].In this paper, the following is achieved: − The direct space vector modulation matrix converter is implemented with double-side modulation due to less harmonics.− The grid power will be controlled by employing simple power control loop that would provide the required frequency of the reference signal for generation the pulses.This is simplest approach of controlling the power without adding complexity to the modulation system, hence it will reduce the burden when the system is implemented experimentally.

DIRECT MATRIX CONVERTER
Direct matrix converter is a designed single-stage that links an m-phase voltage source to an n-phase load using a set of m×n bidirectional power switches.The (3-3) phase matrix converter considered as significant topology, because it connects the grid or any input voltage source to any three-phase output, such as motor.The power circuit of MC consists of nine bidirectional switches, which are arranged in a group of three, each group contains three switches.Additionally, each group may be referred to as a switching cell (SwC).As shown in Figure 1(a), this configuration enables the connection of any of the input phases (a, b, or c) to any of the output phases (A, B, or C).The schematic is arranged like a matrix, with the three output phases (A, B, and C) forming the columns and the three input phases (a, b, and c) forming the rows.Figure 1(b) circles represent the bidirectional switches that connect the rows and columns [1]- [3], [6]- [9].
The concept of the switching function can be used in a mathematical equation to represent the matrix converter operation, where an input phase  is connected to output phase  and is modeled by the switching function,   .The switching function produces a result of 1 when the device is closed and a result of 0 when the device is open.Therefore, the following is the definition of a single device's switching function as (1):

Potential switching states
In MC, there is no freewheeling path that is exist in the conventional VSCs.That would make the safe transition between the permitted state of switching cells, more difficult.In order to satisfy the restriction of Eq.8, the bidirectional switches commutation should be happened instantly and simultaneously.This is not practicable, though, because of propagation delays in command circuits and limited switching times for power semiconductors [3], [7], [10]- [15].There are two key guidelines for safe switching between switches in a switching cell: − To avoid a short circuit of the sources of the input voltage, it is necessary to avoid connecting two devices at once to the same output line.− One device needs to be conducting at all times in order to create a path for the current of the inductive load and avoid over-voltages.Phase-to-Phase short circuits or over-voltages could harm the converter if these rules are not followed.These restrictions can be as (2): The 3 ℎ − 3 ℎ matrix converter looks to have 29 distinct switch combinations, but with these restrictions, there are only 27 permitted switching states.The allowable switch states, which are separated into three groups, are summarized in Figure 2. The three-letter code that identifies which input line the corresponding output phase is attached to for each of these switch combinations gives it a unique look (see Figure 1(b)).As an illustration, the symbol "" indicates that the input lines a, b, and b are each connected to one of the output phases, A, B, or C. One space vector for output voltage and one input current are specified for each switching state of the matrix converter.Voltage (current) switching space vectors (SSV) are another name for these vectors.As a result, the MCs combine the input voltages to create the output voltage (input current) vector (output currents).The 27 permitted switching states are grouped into three categories based on the traits of the SSV connected to each switching state, as illustrated in Figure 2. − Six switching states in Group I create a path between various input and output phases.The amplitudes of these SSV are constant.SSV for current and voltage rotates at the output frequency  0 and   , respectively.− Group II consists of 18 switching states in which two phases of output are connected to one input phase, while the third phase of the output is coupled to a different input phase.The fixed directions of these voltage/current SSVs are uniformly 60 °apart in the αβ frame.These SSVs are referred to as "stationary vectors" for this reason.The magnitude of these voltage/current SSVs is dependent on the phase angles of the input voltage and output current, respectively.The output voltage vectors' magnitude can reach (2 √3) ⁄   , where   represents the current state of the rectified input voltage envelope.− Group III consists of three configurations in which the same input phase is coupled to all three output phases.Since the vectors of output voltage and input current from these SSVs are zero (i.e., at the  frame's origin), they will be referred to as "zero vectors" [2], [3], [7], [9]- [11], [14], [16], [17].

Modulation of direct matrix converter
The SVM representation of the input current and output voltage in the "Park" frame serves as the foundation for the space vector approach.27 variants are viable for the direct matrix converter's three-phase construction.Compared to other techniques, the SVM has advantages which are: − Prompt commutation perception − Highest possible voltage transfer ratio without the use of third harmonics injection is achieved − The power factor of the input and output can be controlled separately − Reduce the switching losses by minimizing the number of times each cycle needs to switch − As little harmonic content as possible and simple digital implementation The representation of instantaneous space vector of the input and output currents and voltages on the  reference frame serves as the basis for space vector modulation.The space vector for the immediate output voltage, the instantaneous input current space vector, and the voltage space vector of the input as (3): Where  =   2 3 ,   , and  0 are the magnitude and angle of  0 ̅̅̅.  and   are the magnitude and angle of   ̅.   and   are the magnitude and angle of   ̅.Group I's output voltage and input current SSVs rotate in the  frame, making it impossible to utilize them to successfully reconstruct the reference vectors.Because of this, in an SVM method, only the stationary and zero vectors are used.The switching configurations of the 3 ℎ − 3 ℎ matrix converter utilized in direct SVM are listed in Table 1.Figures 3(a

Synthesis of vectors
The reference quantities   ̅ and   are completely under the control of the SVM modulation by default.Let's use Figures 4(a) and 4(b) to illustrate how modulation works.The supply voltage controls   ̅, and measurement of its angle   is possible.By lining up vector   ̅ with   ̅, it would acquire unity power factor.By selecting four stationary vectors and applying them at appropriate intervals over the period   , the SVM modulation is accomplished.
It is assumed that  0 ̅̅̅ and   ̅ are both located in sector 1.The components of  0 ̅̅̅ together with the two SSVs are shown in Figure 4(a) as  0 ̅̅̅ 1 and  0 ̅̅̅ 2 .Along with the existing SSVs,   ̅ in Figure 4(b) is similarly divided into   ̅ 1 and   ̅ 2 .The switching configurations that can synthesize the elements of  0 ̅̅̅ and   ̅ are as (4) and ( 5): ̅ 1 : ± 3, ±6, ±9;   ̅ 2 : ± 1, ±4, ±7; Utilizing the common switching states ±7, ±8, ±9, and ±3, we can simultaneously generate  0 ̅̅̅ and   ̅.Only one switching configuration having the same number and the reverse signs is used.They choose the ones with greater voltage values.These guidelines can be used to identify the four switching configurations for each combination of the output voltage sector (  ) and the input current sector (  ).Then, throughout the switching sequence, the four stationary vectors are time-averaged to create  0 ̅̅̅ and   ̅.As was already mentioned, the stationary vectors are applied using the appropriate duty cycles to generate both  0 ̅̅̅ and   ̅.They are calculated as follows using the phase of the input current vector reference (  ̃) and the phase of the output voltage vector reference ( 0 ̃) as ( 6)-( 9): Where the voltage transfer ratio is given by  = | 0 ̅̅̅|/(√3|  ̅|).As seen in Figure 3, the angles utilized in ( 6)-( 9) with regard to the sector's bisecting line were calculated.The output voltage and input current sectors are where they diverge from  0 and   .The following are the limitations for  0 ̃ and   ̃.
The zero-vector duty cycle,  0 ,  0 , and  0 are calculated at fixed sample in order to complete the period of switching, this is shown as (11): As a result, the following restrictions are placed on the switching arrangements duty cycles as (12): By assuming that input and output voltages are balanced and considering in ( 6)-( 12), hence the maximum transfer ratio of the voltage is given by ( 13):

THE APPROACH OF POWER CONTROL
In this paper, the power of the grid would be regulated and simple control is used.Where the threephase reference signal for generation the pulses is achieved.The active power of the Induction Generator IG is calculated then it is compared with the desired active power and the error is processed by PI controller, which would generate the frequency.This frequency is used to generate the three-phase reference signal for pulse generation.The power control structure is shown in Figure 5, and the generation of reference signal for pulses generation.

Controlled three phase generations
The desired operating frequency is imposed into the system after comparing it with the frequency set from the power control loop.Then the angular frequency in / would be used to generate unity three phase balanced signal and they are used for the pulse's generation.The voltage transfer ratio  would  6 shows generation of three phase-controlled reference signals [15], [18]- [23], [14], [24]- [33].

SIMULATION RESULTS AND DISCUSSION
The system is simulated under different conditions.The system parameters are listed in Table 2.The unity reference signals and angular frequency, and input and output voltage sector are shown in Figures 7(a  The first scenario is when the system is tested to operate at different output frequencies with threephase line to line 380   and 100  load.Firstly, the output voltage's amplitude and frequency are set to 0.85 and 50  respectively.The grid voltage and current are shown in Figure 8 and they are in phase, which means unity power factor is achieved.The load current must be bigger than the input current, which would be noticed later.This might be explained by the fact that MC functions resemble to a buck (forward) converter in that it steps down the voltage and assumes that the system is 100% efficient with no energy storage components, thus the AC power that is supplied is equal to the output AC power.The output or load current exceeds the input current because the voltage transfer ratio  is smaller than unity, and this is demonstrated as ( 14) and (15): Where, ∅  and ∅  are the input and output current displacement angles, respectively.The modulation has arranged such that cos(∅  ) ≅ 1.
The voltage transfer ratio  =     ⁄ < 1 and cos(∅  ) is always less than unity therefore the input current is less than the load current   .The second scenario is when the grid power is controlled.Induction generators (IGs) are modeled in the mode where an external signal controls the rotating speed.The controlled three-phase generation block shown in Figure 5 determines the IG operating frequency, and both the frequency and amplitude of the output signal can be adjusted.
In the simulation, the frequency is regulated by the  power controller, while the amplitude is set to 0.85.At  = 1  from the simulation time, its reference, which initially equals zero, changed to −100  while rising to 100  at  = 2 .The rotation frequency of the IG, which is 118 /, rises to 120 / at  = 3 .In Figure 12(a) speed, Figure 12(b) torque and Figure 12(c) (see Appendix) grid power are illustrated, where the IG speed, its torque, and the grid power are displayed.After the initial error, which could be due to the inertia of the IG, is minimized by the  power controller, it can be seen that the reference power value is maintained despite both reference variation and perturbation (rotation speed changing).
One significant feature of MC is the grid current distortion.In Figure 13 (see Appendix), grid current without Figure 13(a) and with a harmonic filter are displayed.5 th harmonic filter is used, where filter ISSN: 2088-8694  Grid power control of direct matrix converter fed three-phase induction generator (Ali Salam Al-Khayyat)

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VA rating would have an impact of the grid current THD as shown in Figures 13(b) and 13(c).The THD is reduced from 6.41 % to 2.31 %.

CONCLUSION
Single stage AC/AC direct matrix converter is operated by space vector modulation directly and it has shown that the input power factor can be changed in addition to the ability to generate input and output sine currents with various frequencies.That would make the matrix converter suitable for variable frequency drive applications.Because double-side modulation improves the harmonic performance of the MC input and output sides at the cost of only slightly increasing the number of branch-switch-overs (BSO) each switching period, it has been employed instead of single-side modulation.The grid power is controlled by implementing a simple power control loop that would generate a three-phase controlled reference signal for Int J Pow Elec & Dri Syst ISSN: 2088-8694 

Figure 1 .
Figure 1.Topology of a direct matrix converter (a) circuit diagram and (b) symbol of switching operation

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ISSN: 2088-8694 Int J Pow Elec & Dri Syst, Vol.14, No. 4, December 2023: 2240-2253 2246 multiply by these unity signals and this would decide the output voltage and input current.The Figure

Figure 5 .Figure 6 .
Figure 5.The power control loop of DMC ) and 7(b) respectively.It is noticed that the angular frequency is locked with the reference signal which means perfect synchronization.

Figure 7 .Figure 8 .
Figure 7. Result for reference signals and sector identification, (a) reference signals and angular frequency and (b) input voltage and load voltage sectors

Figure 9 .
Figure 9.The DMC output phase voltage and current at (a) at 30  and (b) at 100 , output frequency

Figure 10 .Figure 11 .
Figure 10.Responses of load voltage profile at 30  (a) load phase voltage with respect to the load neutral, (b) load phase voltage with respect to the reference point of the source, and (c) output line to line voltage and at 30  output frequency

Table 1 .
Direct space vector modulation uses switching configurations for 3 Phase-3 Phase MC (SVM)

Table 2 .
System parameters