Design of a linearized 4-H-bridge STATCOM for load balancing purposes

ABSTRACT


INTRODUCTION
The controlling strategies, harmonic treatment, load compensation, and different configurations of STATCOM's layouts are studied in this work [1]- [3].A new controlling scheme was proposed in [4] to balance the DC buses in cascaded H-bridge converters.The adopted method certifies the convergences of the DC capacitor voltages to a reference value, even though their loads are taking different amounts of power.A new controlling strategy was proposed for a STATCOM built of voltage source inverter based H-bridges in cascaded form [5].The controlling scheme focused on independent balancing of the voltages across the capacitors in the H-bridge converters.To carry out the proposed control strategy, the voltage of the capacitor in each H-bridge is simultaneously compared with a reference voltage.In a four-wire system, a DSTATCOM built of a zigzag transformer equipped with a low power voltage source converter was proposed in [6] for the power quality improvement purposes.
The proposed STATCOM was designed for Var control, harmonics elimination, load balancing, and voltage control at the point of common coupling (PCC).Three control schemes of a 3-phase STATCOM were employed for compensating unbalanced voltages and currents [7].These schemes were voltage control, current control, and integrated control.By selecting suitable controlling schemes, the introduced system can 2081 accomplish voltage regulation, current balancing, and power factor correction.A multilevel converter based STATCOM was discussed in [8].This STATCOM was equipped with a new current controller and it was introduced for fast Var compensation, treatment of harmonics, and load current balancing of a 3-phase AC source using a new algorithm for current control.A harmonic free compensating susceptance built of a TCR and certain filtering circuitries was proposed in [9] for load balancing purposes.It was controlled linearly and continuously in both inductive and capacitive operational modes.A ∆-connected STATCOM built on the basis of cascaded multilevel converters was introduced in [10].The exchange reactors of this STATCOM were serially connected to reactors coupled mutually in order to offer easy paths for the flow of circulating currents.An approach of parameter design of a PI controller for balancing the individual DC voltages of cascaded Hbridge STATCOM was proposed in [11].Using phase shift SPWM, two control loops (phase angle and DC voltage) were exploited to certify the balance of the DC voltages and to calculate parameters of the PI controller.A harmonic free TCR was introduced in [12] as a compensating susceptance controlled linearly and continuously in inductive operational mode, whereas in [13] a TCR equipped with a new current controller and an adaptive filtering scheme was introduced to function as a continuously and linearly controlled capacitive susceptance.Both categories were dedicated for power quality purposes like power factor correction and load balancing.An asymmetric distribution STATCOM provided with DC-link regulation and reactive power control loops for converters built in cascaded multilevel topology was presented in [14] in order to enhance the power quality in distribution systems of medium-voltages.A control scheme was investigated in [15] to enhance the capability of the DC fault ride-through of a multilevel converter station with full-bridge modular, while certifying a stable operation as a safely controlled STATCOM during DC faults without needing to fault isolation.A STATCOM built of cascaded H-bridges was proposed in [16] to operate with low DC capacitances calculated in the case of the maximum acceptable voltage ripple.
The current limit method of the voltage controlling scheme of a STATCOM built using deltaconnected H-bridge and operated under an event of unbalanced voltage fault was discussed in [17].When a certain phase to ground fault occurred, the possibility of heightening the sagging phase voltage was taken into account using symmetric transformation method.An advanced controller was used in [18] to produce the PWM pulses for the switching devices of a STATCOM built of cascaded H-bridges.The feedback control of the proposed STATCOM offered controllable reactive power and reduced THD.The effectiveness of certain controllers can make multilevel inverter based STATCOMs allow effective operation, low harmonic association in the absence of filters, low switching frequency, and high flexibility to achieve any required level of output voltage [19].A certain control scheme for balancing the capacitor voltages of a STATCOM based on cascaded H-bridges and full-bridges was proposed to accomplish the control aims [20].The presented balancing strategy distributed Var among the cells equally and increased the reliability in addition to balancing voltage among capacitors.Disturbances like the fluctuations of voltage resulting from the complexities of grid and conditions of unbalanced loads cause severe power quality issues like voltage unbalance and total harmonic distortion [21].A delta-connected Multilevel STATCOM was proposed to provide both Var and real power support [22].The purpose of this work was to accomplish short-term storage of energy to enable grid support services.The strategies of balancing active power for the satisfactory operation of the most commonly used STATCOMs under unbalanced current and/or voltage conditions were discussed in [23], whereas a new topology for a STATCOM was proposed in [24] for producing multilevel AC voltages.The four-leg distribution STATCOM is suggested to eliminate the current imbalances in low-voltage power system networks [25].In this research, an 11 kV four H-bridge STATCOM is introduced as a linearly and continuously controlled compensating susceptance for load currents balancing issues.

THE PROPOSED FOUR H-BRIDGE STATCOM
The layout of the four H-bridge STATCOM (4-HB STATCOM) is shown in Figure 1.Each H-bridge (HB) in this figure is equipped with a second harmonic filter and a DC chopper.The second harmonic filter is used for smoothing the voltage profile of the HB DC capacitor voltage, while the DC chopper keeps it in balance with the other DC capacitor voltages in the 4-HB STATCOM.The STATCOM reactor is portioned into two equal reactors.LRST1 and RST1 represent the self-inductance and self-resistance of the first reactor, respectively, whereas LRST2 and RST2 represent the self-inductance and self-resistance of the second reactor, respectively.The capacitor CSH is inserted to treat the voltage spikes.The AC supply voltage vac is stepped down to k3vAC, which is an analog voltage having an amplitude of 5 V. Therefore, k3vAC is running at the same phase and frequency f of vAC.In the STATCOM current controller, the analog voltage k3vAC is shifted by a small angle α depending on the demanded STATCOM susceptance k2BS to produce the modulating signal vMOD, which is expressed by: where, AMOD is its amplitude and ω is the angular frequency (2πf) of the AC supply voltage.Generally, sinusoidal pulse width modulation SPWM is usually exploited to trigger STATCOMs.Thus, the instantaneous voltage vVSI across the cascaded 4-H bridges is governed by the modulating signal vMOD.The average values of vVSI constitute a sinusoidal envelope representing its fundamental components v1 and running at the AC supply frequency.Since, v1 follows vMOD, then v1 will be shifted from vAC by an angle α, which represents the STATCOM angle.Therefore, the STATCOM rms current IS can be expressed by: where, VAC and V1 are the rms values of vAC and v1, respectively.The very close approximation in ( 2) is due to the negligible ohmic resistances of the STATCOM reactors compared to their reactance. , then IS will be purely capacitive.The STATCOM current controller is responsible for generating the modulating signal vMOD.The main input signals to this controller are kSiS, k2BS, and k3vAC.The input signal k2BS is an analog signal less than 10 V and proportional to the STATCOM susceptance required to satisfy the reactive current demand.The input signal kSiS is an analog signal proportional to the instantaneous STATCOM current iS and has a maximum amplitude of 10 V.

The STATCOM current controller
Figure 2 illustrates the modeling of the controlling scheme.When iS (the instantaneous current of STATCOM) is detected and converted to the voltage signal kSiS by the current transformer (CT), the latter voltage signal is treated sample and hold circuits to produce kSISm, which is an analogue voltage signal proportional to ISm (amplitude of iS).The constant kS is dependent on the turn ratio of the current transformer and the passive components of its circuitry.The voltage kSISm is then subtracted from another signal called kSIDm, which is directly proportional to IDm (amplitude of reactive demand).The analogue voltage kS∆ISm is the subtraction result, which represents the deviation amount of the actual current drawn by the STATCOM from the required reactive current.ISm is negative when the reactive current demand is inductive and is positive during capacitive current demand.Its value.The phase and magnitude of the current flowing in the STATCOM reactor are identified by detecting ISm.The controlling circuitry of the STATCOM angle is an important part in According to the biasing conditions of Q1 and Q2, the currents of their collector's iC1 and iC2 can be calculated as follows: , Δ() ≥ 0 (3) Where, hFE is the DC current gain of Q1 and Q2 and ∆V(α) is a voltage signal proportionally corresponding to the error associated with the STATCOM angle α.V(α) is proportional to the STATCOM angle and it is definitely the voltage appearing across C capacitor.It represents a voltage signal governing an important circuitry in this controller.This controlling part is designed to generate vMOD, which represents the modulating signal.The C capacitor current iC is given by (5).
The analogue signal V(α) can be expressed as (6).
The STATCOM angle error signal ∆V(α) is determined by (7), where, ∆I and ∆VAV(α) are expressed by: where, VAV(α) is the average value of V(α).∆ISm and ∆ISmAV stand for components of the current errors, which are expressed by: =   −   (11) where, ISmAV is an analogue signal proportional to the instantaneous value of ISm average.When iC rapidly grows positive, V(α) rapidly builds up and it may exhibit noticeable overshoots.The error voltage signals identified by the parameters kS∆ISmAV and ∆VAV(α) reduce the possible chances for V(α) to reveal noticeable overshoots and settle the current of the STATCOM in its desired value.When V(α) approaches its steady state condition, both kS∆ISmAV and ∆VAV(α) vanish.V(α) identifies the phase angle of vMOD with respect to the STATCOM AC voltage.V(α) is varying between -VCC and +VCC.Positive values of ∆V(α) cause the capacitor C charge towards +VCC through the transistor Q1, whereas its negative values make C discharge through Q2 towards -VCC.The generator of the modulating signal is constructed of an analogue multiplier, a 5msec time delayer, a summer, and an amplifier with a forward voltage gain m corresponding to the modulation index of the STATCOM.The signal voltage k3vAC is a low-level sinusoidal voltage signal in phase with the AC voltage source.For a 50 Hz AC source, the time delay of 5msec corresponds to a delay in phase of π/2.If vAC (the AC voltage) is defined by Vmsin(ωt), then vM (the analogue multiplier output) will be determined by: ) ()  = −()   3   os() where, AM is the analogue multiplier gain and Vm is vAC amplitude.The output vS of the summing amplifier is defined by (13).
The modulating signal is obtained after the multiplication of vS by the modulation index m and can be expressed as (14).

The STATCOM triggering scheme
The triggering technique for the proposed 4-HB STATCOM and its corresponding triggering waveforms are shown in Figure 3.For unity modulation index in this technique, the modulating signal amplitude VMOD should be equal to the DC supply voltage VCC.The latter voltage is divided into four equidistant levels (0.25 VCC, 0.5 VCC, 0.75 VCC, and VCC).

The voltage balancing technique of the 4-HB STATCOM DC capacitor voltages
The layout of this technique is shown in Figure 5.The positive and negative potentials of the DC capacitors are stepped down to low levels through potential dividers and then processed by unity gain difference amplifiers to produce the low-level analogue voltages k4VDC1, k4VDC2, k4VDC3, and k4VDC4, which are proportional to the actual DC capacitor voltages VDC1, VDC2, VDC3, and VDC4 respectively.The low-level analogue voltages are summed and divided by four to obtain their average k4VDCAV.Each of k4VDC1, k4VDC2, k4VDC3, and k4VDC4 is compared with k4VDCAV.toproduce the triggering signal of its corresponding DC chopper switching device.The DC chopper triggering signals are VZCH1, VZCH2, VZCH3, and VZCH4.If a certain DC capacitor voltage exceeds the average value of the capacitor voltages, then its corresponding chopper will discharge its excessive charge through a resistor.When the actual DC capacitor voltage becomes equal or less than the average value the chopping process ceases.

The circuit design of the proposed four H-Bridge STATCOM
This STATCOM is designed to be a continuously and linearly controlled compensating susceptance.Three identical STACTOMs connected in delta-form are required to build a compensating system for balancing 3-wire loads.The balancing system is proposed to operate on 11 KV, 50 Hz ungrounded three phase system.Consequently, the proposed STATCOM is designed to operate on an AC voltage vAC (line-to-line voltage) of 11 KV.The proposed STATCOM is designed such that it can satisfy a reactive current demand (capacitive or inductive) of about 733 A (peak value).The main task in this design is how to determine the voltage tolerance of the IGBT that should be used in the construction of each HB voltage source inverter (HB VSI).If the total DC voltages across the four DC capacitors are allowed to acquire a level of 1.3 Vm during the maximum steady state capacitive reactive current demand, then the expected DC voltage across each DC capacitor will be 0.325 Vm.Where, Vm is the amplitude of the AC voltage applied across the STATCOM terminals.Since the amplitude of 11 KV line to line rms voltage is about 15556 V, the expected capacitor voltage is slightly greater than 5 KV.Taking these presumptions into consideration, the IGBT 5SNA 0750G650300, which has maximum continuous voltage and current ratings of 6.5 KV and 750 A respectively is a good choice for meeting the voltage and current requirements.The circuit design of the 4-HB STATCOM is shown in Figure 6.Its design is carried out on PSpice, which is very close in performance to real hardware.

2087
The rough estimation of the reactance of the 4-HB STATCOM reactor can directly be obtained by dividing 0.3 Vm by the STATCOM reactive current rating (733 A (peak value)).Doing this, the inductance of the series reactor is calculated to be 20 mH.This series reactor is divided into two identical reactors and their common point is connected to a shunt capacitor (CSH) in order to decrease the carrier frequency ripples associating the STATCOM current.The resistance to inductance ratio for these reactors is chosen to be 0.025 Ω/mH.This choice serves to obtain pure reactive current and reduce STATCOM losses.The second harmonic filter and the DC capacitors are designed such that maximum swings associating the DC capacitor voltages never exceed 5% of their steady state values at maximum reactive current demand (capacitive or inductive).Consequently, for each H-bridge, the DC capacitor and the second harmonic filter are designed as follows: CDC = 2000 μF, CF = 1000 μF, LF = 1.25 mH, and RF = 0.05 Ω.The controller of the DC choppers installed for balancing the DC capacitor voltages can be adjusted to determine the deviation of each DC capacitor voltage from the average value of the four DC voltages.
The STATCOM current is detected by the current transformer CT and then converted through the resistance RCT to the analogue voltage kSiS.This signal will be processed in the sub-circuit "STATCOM current controller" for generating the 4-HB STATCOM modulating signal vMOD.For CT primary to secondary turn ratio of 0.01 and RCT of 0.683 Ω, the constant kS is calculated to be 0.00683 Ω.The maximum value of kSiS is expected to be +5 V at the STATCOM maximum capacitive current demand.The modulating signal vMOD is processed in the sub-circuit "4-HB STATCOM triggering CCT" for producing the 4-level PWM triggering signals in the mechanism stated above.
The DC capacitor voltages tend to be unbalanced during the STATCOM operation.This behavior leads to the production of distorted current waveform through the STATCOM reactor.For treating such undesirable behaviors of DC capacitors, a voltage balancing technique is devised for this multi-level STATCOM.The technique is involved in equipping each HB VSI with a chopping circuit.Each circuit is constructed of an IGBT connected in series to 50 Ω resistor.When any DC voltage exceeds the average value of the four DC voltages, the corresponding chopper starts to discharge the voltage excess through the chopper resistor.Once the excess has recovered, the chopping process ceases.The sub-circuit denoted by "DC capacitor voltages balancer" is designed on PSpice to achieve the balancing process of the STATCOM DC capacitor voltages.The circuit design of the 4-HB STATCOM includes a sub-circuit responsible for detecting the analogue signal k3vAC called "STATCOM AC voltage detector".Actually, each IGBT needs a proper driving circuit, thus this STATCOM includes the sub-circuit denoted by "4-HB STATCOM driving CCT" which is a bulk driving circuit for all switching devices.The driving circuit of the IGBT used in this STATCOM is designed according to its datasheet specifications.The AC voltage detector, current controller, triggering circuit, DC capacitors voltage balancer, and driving circuit are designed as built in libraries on PSpice using the suitable components available on this application.

RESULTS AND DISCUSSION
The 11 KV, 50 Hz 4-HB STATCOM shown in Figure 6 was tested on PSpice for investigating its control continuity, linearity, and harmonic injection.It is controlled by the analogue voltage k2BS, which is proportional to the reactive current demand and varying in the range of -10 V to +10 V. +10 V corresponds to maximum capacitive reactive demand of 733A (peak value), while -10 V corresponds to maximum inductive reactive current demand 733 A (peak value).It was operated by a zero phase AC voltage of frequency of 50 Hz and amplitude of 15556 V (peak value), which corresponded to a rms value of 11 KV (the line-to-line voltage).The modulation index of the tested STATCOM was 0.98 and the carrier frequency was 5 KHz.The basic instantaneous parameters measured in the PSpice investigations were the AC source voltage vAC; the 4level VSI generated voltage vVSI; the STATCOM current iS; the frequency spectrum F(S) of iS; the DC capacitors voltages VDC1, VDC2, VDC3, and VDC4; the DC choppers currents iCH1, iCH2, iCH3, and iCH4.Firstly, the STATCOM was tested to show its performance during zero reactive current demand.Figure 7 shows the transient and steady states results of this test.The test corresponded to k2BS of zero value.It is obvious that the STATCOM carried zero steady state current at this test.
Disabling the carrier signal for a time of about 200 ms is adopted in this work to speed up the charging process of the DC capacitors in the 4-HB STATCOM.During the disabling of the carrier signal, the discharging process associating the voltage generation of the 4-level VSI inverter is slowed down.STATCOM performance during maximum inductive reactive current is shown in Figure 8.The results of this test corresponded to k2BS of -10 V.The performance of the 4-HB STATCOM during maximum capacitive reactive current is shown in Figure 9.The results of this test corresponded to k2BS of +10 V. To investigate the STATCOM for the current harmonics associating its reactive current fundamental, it was tested during steady state operation at different loading conditions.Figure 10 shows the steady state performance of the STATCOM during zero reactive current demand.Figure 11 shows the steady state performance of the STATCOM during maximum inductive reactive current demand of 733 A (peak value).Figure 12 shows the steady state performance of the STATCOM during maximum capacitive reactive current demand of 733A (peak value).The performance of the proposed STATCOM during an abrupt change in current demand from maximum inductive reactive current to maximum reactive capacitive current is revealed in Figure 13.The abrupt change in current demand occurred at t=300msec.The transition time was about 140 msec.This period of time is required to charge the STATCOM DC capacitors from minimum voltage to maximum voltage.The transition period is governed by the series reactor parameters (resistance and inductance) and the DC capacitor values.High loss reactors significantly reduce the transition time.The frequency spectrums of the STATCOM current in the above steady state tests indicate that it is a harmonic-free reactive device, thus it can be represented by a harmonic-free compensating susceptance.Many tests were carried out on this STATCOM during steady state operation to verify its linearity.The results of those tests are reflected by the graph shown in Figure 14.The devised controller of this STATCOM makes it linearly and continuously controlled within a STATCOM angle range of -5.72° to +5.72°.This is verified by the graph shown in Figure 14.The minus sign in Figure 14 is related to inductive reactive currents.
The STATCOM choppers are responsible for equalizing the voltages of the DC capacitors.Different DC voltages mean generation of current harmonics besides the STATCOM fundamental current.These current harmonics will be injected to the power system network.Figure 15 shows choppers currents at different reactive current demands.

CONCLUSION
The compensating susceptance devised from 4-HB STATCOM is governed by a new adaptive controlling technique and equipped with a voltage equalizer to its DC capacitor voltages.The devised controlling technique makes the STATCOM respond precisely to current demand in a very short time compared with other techniques employing the same passive elements and switching frequency.The controller guarantees continuously and linearly controlled reactive current (inductive and capacitive) without noticeable association harmonics.The DC capacitor voltage of each H-bridge is stabilized by the second harmonic filter installed in parallel with the DC capacitor.This additional modification reduces the need to larger DC capacitor.The 11 KV, 50 Hz 4-HB STATCOM is not in need of charging its DC capacitors initially because it is equipped with a utilized method for charging them rapidly by disabling the STATCOM carrier for a certain period sufficient to build up the required level of DC voltages.This property make this STATCOM adaptive compared to other STATCOMs, since most controlling schemes depending switching frequency control require determined initial values for DC capacitor in order to guarantee balancing them within certain tolerances.This STATCOM is promoted to be deservingly exploited in load balancing systems, which are representing the significant tools for achieving big amount of energy savings in power generation and big reduction in transmission losses.

Figure 1 .
Figure 1.Layout of the proposed STATCOM Int J Pow Elec & Dri Syst ISSN: 2088-8694  Design of a linearized 4-H-bridge STATCOM for load balancing purposes (Abdulkareem Mokif Obais) 2083 this controller.This circuitry comprises Q1 and Q2, which are two identical silicon transistors biased critically in their active regions.The threshold voltage Vγ is the cut in value of the base to emitter voltage of Q1 and Q2.

Figure 2 .
Figure 2. The schematic design of the STATCOM current controller

Figure 3 .Figure 4 .
Figure 3.The triggering mechanism of the proposed STATCOM (a) topology and (b) waveforms

Figure 5 .
Figure 5.The balancing technique of the DC capacitor voltages of the 4-HB STATCOM

Figure 6 .
Figure 6.The PSpice circuit design of the proposed 4-HB STATCOM

Figure 13 .Figure 15 .
Figure 13.The treatment of the 11 KV, 50Hz 4-HB STATCOM to abrupt change in current demand from maximum inductive reactive current to maximum reactive capacitive current