An Innovative Linear Susceptance Model Deploying a Thyristor Controlled Reactor with Harmonic Suppression Circuitry and Advanced Current Controller

Page:

1391-1400

DOI:

https://doi.org/10.18280/mmep.100434

Received:

11 February 2023

Revised:

5 April 2023

Accepted:

2 May 2023

Available online:

30 August 2023

© 2023 IIETA. This article is published by IIETA and is licensed under the CC BY 4.0 license (http://creativecommons.org/licenses/by/4.0/).

OPEN ACCESS

Abstract:

The Thyristor Controlled Reactor (TCR), an operative reactive power device, is controlled non-linearly in its inductive operational mode, resulting in injection of odd current harmonics. This introduces challenges regarding power quality, which necessitates conditioning of the device. In this study, the development of a continuously and linearly controlled compensating susceptance, constructed from a TCR equipped with harmonic suppression and absorption features, is presented. The series suppression circuitry incorporated within the design consists of a series RLC circuit, resonating at the frequency of the AC source. Simultaneously, the shunt absorption circuitry is specifically designed to eliminate the third and fifth harmonic current components produced by the TCR. This innovative arrangement substantially minimizes the odd harmonics generated by the TCR. In addition, an advanced current controller has been introduced, allowing the reactive current of the proposed susceptance to be linearly controlled in both inductive and capacitive modes. The proposed susceptance was designed and simulated on PSpice, utilizing a 50Hz, 220V AC source. Simulation results demonstrate that the susceptance current reaches its steady-state value within approximately 100ms. Furthermore, the susceptance current in the steady-state region is almost completely devoid of harmonics. Notably, the proposed susceptance displays remarkable linearity during its response to reactive current demands across both inductive and capacitive operational modes. This research provides a significant step forward in addressing the challenges associated with TCR power quality.

Keywords:

*harmonic reduction, linear susceptance, power quality, Thyristor Controlled Reactor *(*TCR*)*, static var compensator*

1. Introduction

Static Var compensators (SVCs) are commonly utilized to address power quality issues such as poor power factor, harmonic associations, voltage instability, and unbalanced loads. This work provides a comprehensive review of various SVC technologies. Traditional SVCs encompass Thyristor Controlled Reactors (TCRs), thyristor-switched capacitors (TSCs), and Thyristor-Switched Reactors (TSRs). In contrast, power converter-based SVCs include voltage source converter (VSC) based SVCs and Current Source Converter (CSC) based SVCs. Synchronous static compensators, denoted as STATCOMs, are either VSC or CSC based power converters.

A typical shunt SVC was modeled [1] to evaluate its steady-state and step response errors. The results indicated a significant effect of the currents' phase on the steady-state error. A comprehensive overview of various technologies related to the development of devices used in reactive power compensation was introduced [2]. This review discussed different device arrangements spanning from the inception of static Var compensation to 2009.

Prototypes of two FACTS devices composed of a TSR and a TCR were developed and studied within single machine infinite bus and 3-bus systems [3]. The simulation results from [4] demonstrated that the use of a thyristor-controlled series reactor in the transmission network could significantly reduce the flicker levels caused by an arc furnace.

The harmonics associated with TCR operation were mitigated using specific filtering circuits and an efficient current controller [5]. The developed SVC was proposed for load current balancing purposes. Specialized circuits were developed [6] for testing thyristors in FACTS devices. The results revealed that the developed circuits, with suitable protection and control strategies, are capable of successfully testing thyristors used in FACTS.

A harmonic-free TCR configuration was proposed [7] for energy conservation. In this SVC, the TCR was designed to provide continuous and linearly controlled behavior as a purely inductive device. A hybrid passive filter, combining a shunt passive filter with a series passive one, was suggested to overcome the limitations of traditional shunt passive filters [8].

A TCR equipped with a new adaptive current controller and specific filtering circuits was proposed to automatically correct the power factor of an inductive load, eliminating harmonic injection on the AC source side [9]. The optimal design of new topologies of TSRs was suggested [10] to achieve uniformly distributed Var control in power system networks. Protection methods for common static Var compensators were reviewed [11], with event analysis conducted for TCR, TSC, and Harmonic filters, to validate the strengths and weaknesses of typical protection methods.

A novel topology of a TCR power circuit, featuring a delta-connected set of TCRs and a delta-connected set of back-to-back thyristors with a balanced set of reactors, was proposed [12]. An Artificial Neural Network (ANN) was introduced [13] to decrease the total harmonic values resulting from dynamic voltage supply, with the reduction controlled by adjusting the TCR/TSC firing angles. A new TCR topology was proposed, where the harmonics produced by the TCR were minimized through the use of an active power filter [14].

Two TCR topologies were proposed [15] for smooth Var compensation in a low-voltage grid. The first topology was based on a single-core, 3-phase TCR, and the second topology incorporated a separate reactor for each phase. The characteristics of TCR, TSR, and TCS were obtained through the construction of Simulink models for both single and hybrid systems [16]. It was demonstrated that Var compensators constructed from these devices can enhance power quality and power stability in power system networks.

The thyristor-controlled series capacitor (TCSC) was considered in the frequency domain as a harmonic admittance matrix using the Fourier transform of the switching function and terminal voltage [17]. A fast decoupled method was employed [18] to ascertain the voltage on each bus in a power system, with the observed parameters being the power factor (PF), Var, voltage, and the active power. Efficient algorithms based on the Newton-Raphson method were proposed [19] for estimating the firing angle of the FC-TCR Var compensators. A TSC and a TCR were utilized [20] to address power quality issues in Rwanda, with synchronous and PV generators. The study focused on the delays of communication signals and methods to address and identify the failure of the communication system in the grid context.

Sinusoidal pulse width modulation was proposed for controlling a voltage source converter, aiming to avoid the use of additional filters and achieve better harmonic reduction for different types of loads [21]. A voltage-controlled adaptive DC-link was suggested for a thyristor-controlled LC-coupling hybrid active power filter (TCLC-HAPF) to decrease switching noise and loss while improving compensating performance [22]. It was confirmed that the proposed DC-link for TCLC-HAPF resulted in satisfactory compensation performance. It was verified that the STATCOM provides better support than a static Var compensator under faulted conditions due to its ability to provide dynamic compensation to the transmission system [23]. A complete system for Var compensation in high DC power industries or railways was proposed to offer a reliable and technically adaptive solution at a significantly reduced cost [24]. Intelligent methods were proposed to control traditional compensation equipment in distribution grids, ensuring local harmonic and Var compensations in case of low voltage problems in the utility grid [25].

A crucial power quality issue, unbalanced loads, necessitates the use of static compensators comprising linear compensating susceptances controllable in both capacitive and inductive operational modes. This paper proposes a compensating susceptance that is linearly and continuously controlled for load balancing purposes. It is designed to operate in both inductive and capacitive modes without harmonic association, and consists of a TCR equipped with a novel current controller and two harmonic reduction circuits.

2. Proposed Susceptance

The proposed system scheme is shown in Figure 1. In this figure, the TCR is shunted by a harmonic absorbing circuitry and the resulted parallel configuration is connected in series to a harmonic suppressing circuitry. The harmonic suppressing circuitry is a simple series RLC circuit designed to offer an easy path with negligible impedance to the current fundamental of AC supply. The harmonic absorbing circuit is designed such that it offers easy paths to the most significant odd harmonics released by the TCR. In this design, the third and the fifth harmonics are considered as the most significant odd harmonics. Therefore, the harmonic absorbing circuitry will be built of two series passive harmonic filters connected in parallel. If the supply angular frequency is denoted by ω, then the series third and fifth harmonic filters will resonate at 3ω and 5ω, respectively.

**Figure 1.** The proposed susceptance scheme

Figure 2 shows the power circuit of the proposed susceptance. The harmonic suppressing circuit is designed such that it resonates at the AC supply frequency angular frequency ω, thus it can be written:

$\omega {{L}_{1}}=\frac{1}{\omega {{C}_{1}}}=\sqrt{\frac{{{L}_{1}}}{{{C}_{1}}}}$ (1)

where, *L _{1}* and

**Figure 2.** The power circuit of the proposed susceptance

Since the series third and fifth harmonic filters are designed to resonate at *3ω* and *5ω*, respectively, then it can be written:

$3\omega {{L}_{3}}=\frac{1}{3\omega {{C}_{3}}}=\sqrt{\frac{{{L}_{3}}}{9{{C}_{3}}}}$ (2)

$5\omega {{L}_{5}}=\frac{1}{5\omega {{C}_{5}}}=\sqrt{\frac{{{L}_{5}}}{25{{C}_{5}}}}$ (3)

where, *L _{3}* and

Figure 3a shows a TCR supplied directly from an AC voltage *v _{AC}* and fired at an angle

${{I}_{1}}=\frac{{{V}_{m}}}{\pi \omega {{L}_{TCR}}}\left( \pi -2\alpha -\sin \left( 2\alpha \right) \right)$ (4)

where, *V _{m}* is the amplitude of

$0\le {{I}_{1}}\le \frac{{{V}_{m}}}{\omega {{L}_{TCR}}} \;\;\;, \text{ for }\frac{\pi }{2}\ge \alpha \ge 0$ (5)

The maximum value of *I _{1}* is

${{I}_{1\max }}=\frac{{{V}_{m}}}{\omega {{L}_{TCR}}}, \;\;\; \text{ }\alpha =0$ (6)

(a) TCR circuit

(b) voltage and current waveforms

**Figure 3.** The TCR and its associated waveforms

At the fundamental frequency, the circuit of Figure 2 can be closely modeled in frequency domain as shown in Figure 4. In this model, the TCR is replaced by *α* dependent reactance and the harmonic suppressing circuit is replaced by a short circuit. Note that the all-reactor’s self-resistances are not included in the model due to their negligible effects on the circuit analysis. The peak current *I _{F}* of the harmonic absorbing circuit at the fundamental frequency and zero firing angle can be computed as follows:

${{I}_{F}}=j{{V}_{m}}\left( \frac{\omega {{C}_{3}}}{1-{{\omega }^{2}}{{L}_{3}}{{C}_{3}}}+\frac{\omega {{C}_{5}}}{1-{{\omega }^{2}}{{L}_{5}}{{C}_{5}}} \right),\text{ }\alpha =0$ (7)

**Figure 4.** Modeling the proposed susceptance at the fundamental frequency

If *L _{3}* and

$\omega {{L}_{3}}=\omega {{L}_{5}}=X$ (8)

Solving for *ωL _{3}* and

$\omega {{C}_{3}}=\frac{1}{9X}$ (9)

$\omega {{C}_{5}}=\frac{1}{25X}$ (10)

Substituting for Eqs. (8), (9), and (10) into Eq. (7) yields.

${{I}_{F}}=j{{V}_{m}}\left( \frac{1}{8X}+\frac{1}{24X} \right)=j\frac{{{V}_{m}}}{6X},\text{ }\alpha =0$ (11)

Since the proposed susceptance is required to be controlled in capacitive and inductive modes of operation, then the TCR peak current rating should be twice that of the harmonic absorbing circuit at zero firing angle or in other words it can be written:

${{I}_{1\max }}=\frac{{{V}_{m}}}{\omega {{L}_{TCR}}}=2{{I}_{F}}=2\frac{{{V}_{m}}}{6X},\text{ }\alpha =0$ (12)

Or

${{L}_{TCR}}=3{{L}_{3}}=3{{L}_{5}}$ (13)

The harmonic suppressing reactor can be chosen such that:

${{L}_{1}}=0.5{{L}_{TCR}}$ (14)

The *kth* harmonic current *I _{k}* of the actual TCR current is given by [6-9]:

${{I}_{k}}=\frac{{{V}_{m}}}{\omega L}\frac{4}{\pi }\left( \frac{\sin \left( \alpha \right)\cos \left( 2\alpha \right)-k\cos \left( \alpha \right)\sin \left( k\alpha \right)}{k\left( {{k}^{2}}-1 \right)} \;\;\;\; \right)$ (15)

where, *k* is a positive odd integer greater than unity.

Considering the *kth* harmonic current defined in Eq. (15), the equivalent circuit of proposed susceptance can be reduced to the circuit shown in Figure 5. In this figure, the TCR is modeled by a current source *I _{k}* and the AC voltage supply is replaced by a short circuit. The current

**Figure 5.** The *kth* harmonic equivalent circuit

The impedances of the harmonic absorbing circuitry *Z _{Fk}* and harmonic suppressing circuitry

${{Z}_{Fk}}=\frac{1}{\frac{1}{jk\omega {{L}_{3}}+\frac{1}{jk\omega C{}_{3}}}+\frac{1}{jk\omega {{L}_{5}}+\frac{1}{jk\omega {{C}_{5}}}}}$ (16)

${{Z}_{1k}}=jk\omega {{L}_{1}}+\frac{1}{jk\omega {{C}_{1}}}$ (17)

Substituting for Eqs. (1), (8), (9), (10), (13), and (14) into Eqs. (17) and (18) gives:

${{Z}_{Fk}}=j\frac{X({{k}^{2}}-9)({{k}^{2}}-25)}{2k({{k}^{2}}-17)}$ (18)

${{Z}_{1k}}=j\frac{3X}{2k}\left( {{k}^{2}}-1 \right)$ (19)

It is obvious that the harmonic absorbing circuitry offers zero impedance to both third and fifth current harmonics and inductive impedances to those odd current harmonics beyond the fifth harmonic. Also, the harmonic suppressing circuitry offers very high inductive impedances to all odd current harmonics and almost zero impedance at the fundamental frequency. The *kth* harmonic current components *I _{Sk}* flowing in the AC source side and

${{I}_{Sk}}={{I}_{k}}\frac{{{Z}_{Fk}}}{{{Z}_{1k}}+{{Z}_{Fk}}}\text{ }$ (20)

${{I}_{Fk}}={{I}_{k}}\frac{{{Z}_{1k}}}{{{Z}_{1k}}+{{Z}_{Fk}}}\text{ }$ (21)

Substituting for Eqs. (18) and (19) into Eqs. (20) and (21) gives:

${{I}_{Sk}}={{I}_{k}}\frac{({{k}^{2}}-9)({{k}^{2}}-25)}{3({{k}^{2}}-1)({{k}^{2}}-17)+({{k}^{2}}-9)({{k}^{2}}-25)}\text{ }$ (22)

${{I}_{Fk}}={{I}_{k}}\frac{3({{k}^{2}}-1)({{k}^{2}}-17)}{3({{k}^{2}}-1)({{k}^{2}}-17)+({{k}^{2}}-9)({{k}^{2}}-25)}\text{ }$ (23)

**2.1 The TCR current controller**

Figure 6 shows the schematic design of the proposed controlling scheme. The susceptance instantaneous current *i _{S}* is detected by the current transformer (C.T) as

**Figure 6.** The susceptance controlling scheme

*k _{S}I_{S }*is compared with

${{V}_{e}}={{k}_{S}}\left( {{I}_{D}}-{{I}_{S}} \right)$ (24)

The error voltage *V _{e}* is limited by a voltage limiter VLIM to Δ

${{\Delta }_{e}}=0.25{{V}_{e}}$ (25)

This current controller is designed on the basis of delta-modulator principles, where the controlling voltage *V _{C}* will be built up as long as Δ

$0\le {{V}_{C}}\le +5V$ (26)

The controlling voltage *V _{C}* governs the TCR firing angle as shown in Figure 7. In this figure,

**Figure 7.** The TCR triggering mechanism

**2.2 Circuit design of the proposed susceptance**

The filters of the harmonic absorbing circuitry are designed with high quality factors at their operating frequencies in order that they offer easy paths for their corresponding harmonic current components. A quality factor *Q* of 30 is a satisfactory choice for both filters. Applying this choice results in:

${{Q}_{3}}=\frac{3\omega {{L}_{3}}}{{{R}_{3}}}=30$ (27)

${{Q}_{5}}=\frac{5\omega {{L}_{3}}}{{{R}_{5}}}=30$ (28)

In this work, a compensating susceptance having a reactive current rating of ±100A (peak value) will be designed to operate on *V _{AC}* of 50Hz, 220V (rms value). The amplitude

**Figure 8.** The circuit diagram of the proposed compensating susceptance

3. Results and Discussion

First of all, Eqs. (4) and (15) are simulated to show the variations of the normalized TCR fundamental current *I _{1}*/

The impacts of harmonic suppressing and absorbing circuitries are reflected by the simulations of Eqs. (22) and (23). Figure 11 shows the normalized AC source harmonic current *I _{Sk}*/

**Figure 9. **TCR normalized current fundamental against the firing angle α

**Figure 10.** TCR normalized current harmonics against its firing angle α

**Figure 11. **The normalized current harmonics flowing in the AC source side and the harmonic absorbing circuitry

Both currents in Figure 11 are normalized to the TCR harmonic current component *I _{k}*. In this figure the third and fifth harmonic current components are completely absorbed by the harmonic absorbing circuitry and thus, they disappeared in the AC source side. The harmonic current components beyond the fifth harmonic are significantly reduced in the AC source side.

The circuit of Figure 8 was tested on PSpice to show its performance during responding to reactive current demand. The parameters measured in transient and steady states are the AC source instantaneous voltage *v _{AC}*, the susceptance instantaneous current or the AC source current

(a) AC source voltage *v _{ac}* and susceptance current

(b) TCR current *i _{TCR}* and harmonic absorbing current

(c) Controlling voltage *V _{C}* and error voltage

**Figure 12.** The susceptance response to an inductive current demand of -100A (peak value)

Figures 13-16 show the susceptance responses to peak values of reactive current demands of -50A (inductive), zero, +50A (capacitive), and +100 (capacitive), respectively.

(a) AC source voltage *v _{ac}* and susceptance current

(b) TCR current *i _{TCR}* and harmonic absorbing current

(c) controlling voltage *V _{C}* and error voltage

**Figure 13.** The susceptance response to an inductive current demand of -50A (peak value)

(a) AC source voltage *v _{ac}* and susceptance current

(b) TCR current *i _{TCR}* and harmonic absorbing current

(c) controlling voltage *V _{C}* and error voltage

**Figure 14.** The susceptance response to zero current demand

(a) AC source voltage *v _{ac}* and susceptance current

(b) TCR current *i _{TCR}* and harmonic absorbing current

(c) controlling voltage *V _{C}* and error voltage

**Figure 15.** The susceptance response to a capacitive current demand of +50A (peak value)

(a) AC source voltage *v _{ac}* and susceptance current

(b) TCR current *i _{TCR}* and harmonic absorbing current

(c) Controlling voltage *V _{C}* and error voltage

**Figure 16.** The susceptance response to a capacitive current demand of +100A (peak value)

In the above figures, the susceptance current starts approaching its steady-state value within a time of about 100ms. Figures 17-21 show the instantaneous steady-state currents *i _{S}*,

(a) The steady-state currents* i _{S}*,

(b) The frequency spectrums of the currents* i _{S}*,

**Figure 17.** Steady-state response to an inductive current demand of -100A (peak value)

(a) The steady-state currents* i _{S}*,

(b) The frequency spectrums of the currents* i _{S}*,

**Figure 18.** The susceptance steady-state response to an inductive current demand of -50A (peak value)

(a) The steady-state currents* i _{S}*,

(b) The frequency spectrums of the currents* i _{S}*,

**Figure 19.** Steady-state response to zero current demand

(a) The steady-state currents* i _{S}*,

(b) The frequency spectrums of the currents* i _{S}*,

**Figure 20.** The susceptance steady-state response to a capacitive current demand of +50A (peak value)

(a) The steady-state currents* i _{S}*,

(b) The frequency spectrums of the currents* i _{S}*,

**Figure 21.** The susceptance steady-state response to a capacitive current demand of +100A (peak value)

The linearity of this susceptance is shown in Figure 22, which is plotted using the steady-state responses to reactive current demand in the range of -100A (peak value) to+100A (peak value).

**Figure 22.** Susceptance steady-state current versus reactive current demand

4. Conclusions

In this paper, a continuously and linearly controlled susceptance is proposed. This susceptance is designed and tested on PSpice. The simulation results have revealed continuous and linear control in both capacitive and inductive operational modes. The frequency spectrum of the susceptance or AC source current certifies the absence of harmonic current contents in the AC source side. The susceptance current approaches its steady-state value within a time of about 100ms. This promotes the proposed susceptance to be suitable for treating abrupt changes in reactive current demand. Such a proposed susceptance can be exploited in power quality application like load current balancing. The simulation results ensure almost zero no-load operating losses.

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