Hybrid STATCOM with wide compensation range and low DC-link voltage

Abstract

A hybrid-STATCOM for providing compensating reactive power required by a load, the hybrid-STATCOM comprising: a TCLC part for each electric power phase, each TCLC part comprising: a coupling inductor; a power filter capacitor; and a thyristor-controlled reactor connected in series with a power filter inductor; and an active inverter part comprising: a voltage source inverter for each electric power phase; and a DC-link capacitor connected in parallel with the voltage source inverters. The control strategy of the hybrid-STATCOM is separated into two parts: TCLC part control and Active inverter part control. The TCLC part control is based on the instantaneous pq theory and aims to compensate the loading reactive power with the controllable TCLC part impedance. The active inverter part control is based on the instantaneous active and reactive current i.sub.d-i.sub.q method and aims to improve the overall performance of the hybrid-STATCOM under different voltage and current conditions.

Claims

1. A hybrid static synchronous compensator (hybrid-STATCOM) system for providing compensating reactive power required by a load in an electricity distribution network, the hybrid-STATCOM system comprising: a thyristor-controlled LC (TCLC) part for each electric power phase in the electricity distribution network, each TCLC part comprising: a coupling inductor; a power filter capacitor; and a thyristor-controlled reactor connected in series with a power filter inductor; wherein the power filter capacitor is connected in parallel with the thyristor-controlled reactor connected in series with the power filter inductor; and wherein the coupling inductor is connected in series with the parallel-connected power filter capacitor and thyristor-controlled reactor connected in series with the power filter inductor; and an active inverter part comprising: a voltage source inverter for each electric power phase in the electricity distribution network; and a DC-link capacitor connected in parallel with the voltage source inverters.

2. The hybrid-STATCOM system of claim 1, wherein the thyristor-controlled reactor is a pair of bidirectional switches; wherein when the thyristor-controlled reactor is switched off, the TCLC part for each electric power phase in the electricity distribution network comprises a coupling inductor connected in series with a power filter capacitor; and wherein when the thyristor-controlled reactor is switched on, the TCLC part for each electric power phase in the electricity distribution network comprises a coupling inductor connected in series with a combination of a power filter capacitor and a power filter inductor.

3. The hybrid-STATCOM system of claim 1, wherein the compensating reactive power required by the load for the electric power phase x, Q.sub.cx,TCLC(a.sub.x), is provided by the TCLC part and is governed by: $Q_{\mathrm{cx},\mathrm{TCLC}}\left({}_x\right)=\frac{V_x^2}{X_{\mathrm{TCLCx}}\left({}_x\right)};$ wherein V.sub.x is a RMS value of the load voltage and X.sub.TCLCx(a.sub.x) is the TCLC part impedance as controllable by firing angle, a.sub.x.

4. The hybrid-STATCOM system of claim 3, wherein the TCLC part impedance, X.sub.TCLCx(a.sub.x), is governed by: $X_{\mathrm{TCLCx}}\left({}_x\right)=\frac{X_{L_{\mathrm{PF}}}{X}_{C_{\mathrm{PF}}}}{X_{C_{\mathrm{PF}}}\left(2-2{}_x+\sin 2{}_x\right)-X_{L_{\mathrm{PF}}}}+X_{L_c};$ wherein X.sub.L.sub.c, X.sub.L.sub.PF, and X.sub.C.sub.PF are fundamental impedances of the coupling inductor, the power filter inductor, and the power filter capacitor, respectively.

5. The hybrid-STATCOM system of claim 3, wherein a minimum TCLC part inductive impedance and in turn a maximum inductive compensating reactive power are provided by setting a.sub.x to 90; and wherein a minimum TCLC part capacitive impedance and in turn a maximum capacitive compensating reactive power are provided by setting a.sub.x to 180.

6. The hybrid-STATCOM system of claim 1, wherein the active inverter part is configured to limit a compensating current to a reference compensating current value via pulse width modulation (PWM) triggering signals driving one or more switching devices in the active inverter part.

7. The hybrid-STATCOM system of claim 1, wherein the power filter capacitor is determined by: $C_{\mathrm{PF}}=\frac{Q_{\mathrm{Lx}\left(\mathrm{MaxInd}\right)}}{{}^2{Q}_{\mathrm{Lx}\left(\mathrm{MaxInd}\right)}{L}_c+V_x^2};$ wherein C.sub.PF is the power filter capacitor capacitance, is a fundamental angular frequency, V.sub.x is a RMS voltage value of the load, L.sub.c is the coupling inductor inductance, Q.sub.Lx(MaxInd) and Q.sub.Lx(MaxCap) are loading maximum inductive and capacitive reactive power respectively.

8. The hybrid-STATCOM system of claim 1, wherein the power filter inductor is determined by: $L_{\mathrm{PF}}=\frac{V_x^2+L_c{Q}_{\mathrm{Lx}\left(\mathrm{MaxCap}\right)}}{-Q_{\mathrm{Lx}\left(\mathrm{MaxCap}\right)}+{}^3{L}_c{C}_{\mathrm{PF}}{Q}_{\mathrm{Lx}\left(\mathrm{MaxCap}\right)}+{}^2{V}_x^2{C}_{\mathrm{PF}}};$ wherein L.sub.PF is the power filter inductor inductance, is a fundamental angular frequency, V.sub.x is a RMS voltage value of the load, L.sub.c is the coupling inductor inductance, Q.sub.Lx(MaxInd) and Q.sub.Lx(MaxCap) are loading maximum inductive and capacitive reactive power respectively.

9. The hybrid-STATCOM system of claim 1, wherein the coupling inductor is determined by: $L_c\frac{V_{DC}}{8.Math.f_s.Math.i_{L_{c}max}};$ wherein L.sub.C is the coupling inductor inductance, f.sub.s is a switching frequency of the active inverter part, i.sub.LCmax is a maximum allowed output current ripple value, and V.sub.DC is a DC-link voltage across the DC-link capacitor.

10. The Hybrid-STATCOM system of claim 1, wherein V.sub.DC of the active inverter part is determined by $V_{\mathrm{DCx}}=\sqrt{6}{V}_x.Math.1+\frac{Q_{\mathrm{Lx}}}{Q_{\mathrm{cx},\mathrm{TCLC}}\left({}_x\right)}.Math.$ $V_{DC}=\max \left(V_{\mathrm{DCa}},V_{\mathrm{DCb}},V_{\mathrm{DCc}}\right)$ wherein x is a, b or c, V.sub.DCx is the required DC-link voltage of each phase, Q.sub.Lx is the reactive power of the loading, Q.sub.cx,TCLC(a.sub.x) is the reactive power provided by the TCLC part, V.sub.x is the RMS phase load voltage and the final V.sub.DC is determined by choosing the largest DC voltage among phase a, b and c.

11. The hybrid-STATCOM system of claim 1, wherein the TCLC part is configured to compensate the load reactive power with the TCLC part impedance; wherein the TCLC part impedance required is determined by: $X_{\mathrm{TCLCx}}=\frac{V_x}{I_{\mathrm{Lqx}}}=\frac{{.Math.v.Math.}^2}{\sqrt{3}{\stackrel{\_}{q}}_{\mathrm{Lx}}};$ wherein X.sub.TCLCx is an instantaneous value of the TCLC part impedance in each phase, v is a norm of three phase instantaneous voltage of the load, and q.sub.Lx is a DC component of the phase reactive power of the load, and x is a, b or c; wherein v is obtained by: $.Math.v.Math.=\sqrt{v_a^2+v_b^2+v_c^2};$ wherein v.sub.a, v.sub.b, and v.sub.c are the three phases instantaneous voltage of the load; wherein q.sub.Lx is obtained by: $\left[\begin{array}{c}{q}_{\mathrm{La}}\\ q_{\mathrm{Lb}}\\ q_{\mathrm{Lc}}\end{array}\right]=\left[\begin{array}{c}{v}_b.Math.i_{\mathrm{Lc}}-v_c.Math.i_{\mathrm{Lb}}\\ v_c.Math.i_{\mathrm{La}}-v_a.Math.i_{\mathrm{Lc}}\\ v_a.Math.i_{\mathrm{Lb}}-v_b.Math.i_{\mathrm{La}}\end{array}\right];$ and wherein q.sub.La, q.sub.Lb, and q.sub.Lc are the three phase reactive power of the load.

12. The hybrid-STATCOM system of claim 11, wherein the impedance of the TCLC part is controllable by selecting a firing angle; wherein the firing angle is determined by solving: $X_{\mathrm{TCLCx}}\left({}_x\right)=\frac{X_{\mathrm{TCR}}\left({}_x\right)X_{C_{\mathrm{PF}}}}{X_{C_{\mathrm{PF}}}-X_{\mathrm{TCR}}\left({}_x\right)}+X_{L_c}=\frac{X_{L_{\mathrm{PF}}}{X}_{C_{\mathrm{PF}}}}{X_{C_{\mathrm{PF}}}\left(2-2{}_x+\sin 2{}_x\right)-X_{L_{\mathrm{PF}}}}+X_{L_c};$ and wherein a.sub.x is the firing angle, X.sub.L.sub.c, X.sub.L.sub.PF, and X.sub.C.sub.PF are fundamental impedances of the coupling inductor, the power filter inductor, and the power filter capacitor respectively.

13. The hybrid-STATCOM system of claim 12, further comprising a look-up table (LUT) between X.sub.TCLCx and a.sub.x for determining the firing angle for the TCLC part impedance required; wherein the control of the TCLC part impedance is triggered by comparing the firing angle with the load voltage phase angle.

14. The hybrid-STATCOM system of claim 1, wherein the active inverter part is configured to limit a compensating current to a reference compensating current value to avoid mistuning problem, resonance problem, and harmonic injection problem in the TCLC part under different voltage and current conditions; wherein the reference compensating current value is determined by: $\left[\begin{array}{c}{i}_{\mathrm{ca}}^{*}\\ i_{\mathrm{cb}}^{*}\\ i_{\mathrm{cc}}^{*}\end{array}\right]=\sqrt{\frac{2}{3}}.Math.\left[\begin{array}{cc}1& 0\\ -1/2& \sqrt{3}/2\\ -1/2& -\sqrt{3}/2\end{array}\right].Math.\left[\begin{array}{cc}\cos {}_a& -\sin {}_a\\ \sin {}_a& \cos {}_a\end{array}\right].Math.\left[\begin{array}{c}{\tilde{i}}_d\\ i_q\end{array}\right];$ wherein i.sub.ca*, i.sub.cb*, and i.sub.cc*are the three phases reference compensating current values, i.sub.d and i.sub.q are instantaneous active and reactive current respectively, which include DC components .sub.d and .sub.q, and AC components .sub.d and .sub.q; wherein .sub.d is obtained by passing i.sub.d through a high-pass filter; wherein i.sub.d and i.sub.q are obtained by: $\left[\begin{array}{c}{i}_d\\ i_q\end{array}\right]=\left[\begin{array}{cc}\cos {}_a& \sin {}_a\\ -\sin {}_a& \cos {}_a\end{array}\right].Math.\left[\begin{array}{c}{i}_{}\\ i_{}\end{array}\right]$ and $\left[\begin{array}{c}{i}_{}\\ i_{}\end{array}\right]=\left[\begin{array}{ccc}1& -1/2& -1/2\\ 0& \sqrt{3}/2& -\sqrt{3}/2\end{array}\right].Math.\left[\begin{array}{c}{i}_{\mathrm{La}}\\ i_{\mathrm{Lb}}\\ i_{\mathrm{Lc}}\end{array}\right];$ wherein i.sub.La, i.sub.Lb, and i.sub.Lc are the three phases load current; and wherein the active inverter part is further configured to limit the compensating current to the reference compensating current value via pulse width modulation (PWM) triggering signals driving one or more switching devices in the active inverter part.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Embodiments of the invention are described in more details hereinafter with reference to the drawings, in which:

(2) FIG. 1 shows a circuit configuration of a hybrid-STATCOM in accordance to an embodiment of the present invention;

(3) FIG. 2a depicts the V-I characteristics of a traditional STATCOM;

(4) FIG. 2b depicts the V-I characteristics of a C-STATCOM;

(5) FIG. 2c depicts the V-I characteristics of the hybrid-STATCOM;

(6) FIG. 3 shows the control block diagram of the hybrid-STATCOM;

(7) FIG. 4 depicts the dynamic performance of the hybrid-STATCOM for different loadings compensation;

(8) FIG. 5a, FIG. 5b, and FIG. 5c depict the dynamic compensation waveforms of v.sub.x and i.sub.sx by applying the hybrid-STATCOM under (a) inductive load, (b) capacitive load and (c) changing from capacitive load to inductive load respectively;

(9) FIG. 6 depicts the dynamic reactive power compensation of phase a by applying the hybrid-STATCOM;

(10) FIG. 7a, FIG. 7b, FIG. 7c, and FIG. 7d depict the source current harmonic spectrums of phase a: (a) before compensation of inductive load, (b) after compensation of inductive load, (c) before compensation of capacitive load, and (d) after compensation of capacitive load respectively;

(11) FIG. 8 depicts the dynamic compensation waveforms of v.sub.x and i.sub.sx by applying hybrid-STATCOM under unbalanced loads;

(12) FIG. 9a, FIG. 9b, FIG. 9c, FIG. 9d, FIG. 9e, and FIG. 9f depict the source current harmonic spectrums under unbalanced loads before compensation: (a) phase a, (b) phase b, (c) phase c, and after hybrid-STATCOM compensation: (d) phase a, (e) phase b, (f) phase c respectively;

(13) FIG. 10 depicts the dynamic compensation waveforms of v.sub.x and i.sub.sx by applying hybrid-STATCOM under voltage fault condition;

(14) FIG. 11a, FIG. 11b, FIG. 11c, FIG. 11d, FIG. 11e, and FIG. 11f depicts the source current harmonic spectrum under voltage fault before compensation: (a) phase a, (b) phase b, (c) phase c, and after hybrid-STATCOM compensation: (d) phase a, (e) phase b, (f) phase c respectively; and

(15) FIG. 12 depicts the dynamic compensation waveforms of v.sub.x and i.sub.sx by applying hybrid-STATCOM during voltage dip.

DETAILED DESCRIPTION

(16) In the following description, STATCOMs and methods of controlling thereof and the likes are set forth as preferred examples. It will be apparent to those skilled in the art that modifications, including additions and/or substitutions may be made without departing from the scope and spirit of the invention. Specific details may be omitted so as not to obscure the invention; however, the disclosure is written to enable one skilled in the art to practice the teachings herein without undue experimentation.

(17) Circuit Configuration of Hybrid-STATCOM

(18) FIG. 1 shows a circuit configuration of a hybrid-STATCOM in accordance to an embodiment of the present invention, in which the subscript x stands for phase a, b, and c in the following analysis. v.sub.sx and v.sub.x are the source and load voltage; i.sub.sx, i.sub.Lx, and i.sub.cx are the source, load, and compensating current, respectively. L.sub.s is the transmission line impedance. The hybrid-STATCOM consists of a TCLC and an active inverter part.

(19) The TCLC part is composed of a coupling inductor L.sub.c, a parallel capacitor C.sub.PF, and a thyristor-controlled reactor with L.sub.PF. The TCLC part provides a wide and continuous inductive and capacitive reactive power compensation range that is controlled by controlling the firing angles a.sub.x of the thyristors. The active inverter part is composed of a voltage source inverter with a DC-link capacitor C.sub.DC, and the small rating active inverter part is used to improve the performance of the TCLC part. In addition, the coupling components of the traditional STATCOM and C-STATCOM are also presented in FIG. 1.

(20) V-I Characteristics of Traditional STATCOM, C-STATCOM and Hybrid-STATCOM

(21) The purpose of the hybrid-STATCOM is to provide the same amount of reactive power as the loadings (Q.sub.Lx) consumed, but with the opposite polarity (Q.sub.cx=Q.sub.Lx). The hybrid-STATCOM compensating reactive power Q.sub.cx is the sum of the reactive power Q.sub.cx,TCLC that is provided by the TCLC part and the reactive power Q.sub.invx that is provided by the active inverter part. Therefore, the relationship among Q.sub.Lx, Q.sub.cx,TCLC, and Q.sub.invx can be expressed as:
Q.sub.Lx=Q.sub.cx=(Q.sub.cx,TCLC+Q.sub.invx)(1)

(22) The reactive power can also be expressed in terms of voltage and current as:
Q.sub.Lx=V.sub.xI.sub.Lqx=(X.sub.TCLCx(a.sub.x)I.sub.cqx.sup.2+V.sub.invxI.sub.cqx)(2)
where X.sub.TCLCx(a.sub.x) is the coupling impedance of the TCLC part; a.sub.x is the corresponding firing angle; V.sub.x and V.sub.invx are the root mean square (RMS) values of the coupling point and the inverter voltage; and I.sub.Lqx and I.sub.cqx are the RMS value of the load and compensating reactive current, where I.sub.Lqx=I.sub.cqx. Therefore, (2) can be further simplified as:
V.sub.invx=V.sub.x+X.sub.TCLCx(a.sub.x)I.sub.Lqx(3)
where the TCLC part impedance X.sub.TCLCx(a.sub.x) can be expressed as:

(23) $\begin{array}{cc}{X}_{\mathrm{TCLCx}}\left({}_x\right)=\frac{X_{\mathrm{TCR}}\left({}_x\right)X_{C_{\mathrm{PF}}}}{X_{C_{\mathrm{PF}}}-X_{\mathrm{TCR}}\left({}_x\right)}+X_{L_c}=\frac{X_{L_{\mathrm{PF}}}{X}_{C_{\mathrm{PF}}}}{X_{C_{\mathrm{PF}}}\left(2-2{}_x+\sin 2{}_x\right)-X_{L_{\mathrm{PF}}}}+X_{L_c}& \left(4\right)\end{array}$
where X.sub.L.sub.c, X.sub.L.sub.PF, and x.sub.C.sub.PF are the fundamental impedances of L.sub.c, L.sub.PF, and C.sub.PF, respectively. In (4), it is shown that the TCLC part impedance is controlled by firing angle a.sub.x. And the minimum inductive and capacitive impedances (absolute value) of the TCLC part can be obtained by substituting the firing angles a.sub.x=90 and a.sub.x=180, respectively. In the following discussion, the minimum value for impedances stands for its absolute value. The minimum inductive (X.sub.ind(min)>0) and capacitive (X.sub.Cap(min)<0) TCLC part impedances can be expressed as:

(24) $\begin{array}{cc}{X}_{\mathrm{Ind}\left(min\right)}\left({}_x=90\right)=\frac{X_{L_{\mathrm{PF}}}{X}_{C_{\mathrm{PF}}}}{X_{C_{\mathrm{PF}}}-X_{L_{\mathrm{PF}}}}+X_{L_c}& \left(5\right)\\ X_{\mathrm{Cap}\left(min\right)}\left({}_x=180\right)=-X_{C_{\mathrm{PF}}}+X_{L_c}& \left(6\right)\end{array}$

(25) Ideally, X.sub.TCLCx(a.sub.x) is controlled to be V.sub.xX.sub.TCLCx(a.sub.x)I.sub.Lqx, so that the minimum inverter voltage (V.sub.invx0) can be obtained as shown in (3). In this case, the switching loss and switching noise can be significantly reduced. A small inverter voltage V.sub.invx(min) is necessary to absorb the harmonic current generated by the TCLC part, to prevent a resonance problem, and to avoid mistuning the firing angles. If the loading capacitive current or inductive current is outside the TCLC part compensating range, the inverter voltage V.sub.invx will be slightly increased to further enlarge the compensation range.

(26) The coupling impedances for traditional STATCOM and C-STATCOM, as shown in FIG. 1, are fixed as X.sub.L and X.sub.L-X.sub.C. The relationships among the load voltage V.sub.x, the inverter voltage V.sub.invx, the load reactive current I.sub.Lqx, and the coupling impedance of traditional STATCOM and C-STATCOM can be expressed as:
V.sub.invx=V.sub.x+X.sub.LI.sub.Lqx(7)
V.sub.invx=V.sub.x(X.sub.C-X.sub.L).Math.I.sub.Lqx(8)
where X.sub.c>>X.sub.L. Based on (3)-(8), the V-I characteristics of the traditional STATCOM, C-STATCOM, and hybrid-STATCOM can be plotted as shown in FIG. 2a, FIG. 2b, and FIG. 2c respectively.

(27) For the V-I characteristics of traditional STATCOM as shown in FIG. 2a, the required V.sub.invx is larger than V.sub.x when the loading is inductive. In contrast, the required V.sub.invx is smaller than V.sub.x when the loading is capacitive. Actually, the required inverter voltage V.sub.invx is close to the coupling voltage V.sub.x, due to the small value of coupling inductor L [5]-[8].

(28) For the V-I characteristics of C-STATCOM as shown in FIG. 2b, it is shown that the required V.sub.invx is lower than V.sub.x under a small inductive loading range. The required V.sub.invx can be as low as zero when the coupling capacitor can fully compensate for the loading reactive current. In contrast, V.sub.invx is larger than V.sub.x when the loading is capacitive or outside its small inductive loading range. Therefore, when the loading reactive current is outside its designed inductive range, the required V.sub.invx can be very large.

(29) For the V-I characteristics of the hybrid-STATCOM as shown in FIG. 2c, the required V.sub.invx can be maintained at a low (minimum) level (V.sub.invx(min)) for a large inductive and capacitive reactive current range. Moreover, when the loading reactive current is outside the compensation range of the TCLC part, the V.sub.invx will be slightly increased to further enlarge the compensating range. Compared with traditional STATCOM and C-STATCOM, the hybrid-STATCOM has a superior V-I characteristic of a large compensation range with a low inverter voltage.

(30) In addition, three cases represented by points A, B, and C in FIG. 2 are simulated below. Based on FIG. 1, the parameter design of hybrid-STATCOM is discussed in the following part.

(31) Parameter Design of Hybrid-STATCOM

(32) The TCLC in accordance to an embodiment of the present invention is a SVC structure, which is designed based on the basis of the consideration of the reactive power compensation range (for L.sub.PF and C.sub.PF) and the filtering out of the current ripple caused by the power switches (for L.sub.c). The active inverter part (DC-link voltage V.sub.DC) is designed to avoid mistuning of the firing angle of TCLC part.

(33) Design of C.sub.PF and L.sub.PF

(34) The purpose of the TCLC part is to provide the same amount of compensating reactive power Q.sub.cx,TCLC(a.sub.x) as the reactive power required by the loads Q.sub.Lx but with the opposite direction. Therefore, C.sub.PF and L.sub.PF are designed on the basis of the maximum capacitive and inductive reactive power. The compensating reactive power Q.sub.cx range in term of TCLC impedance X.sub.TCLCx(a.sub.x) can be expressed as:

(35) $\begin{array}{cc}{Q}_{\mathrm{cx},\mathrm{TCLC}}\left({}_x\right)=\frac{V_x^2}{X_{\mathrm{TCLCx}}\left({}_x\right)}& \left(9\right)\end{array}$
where V.sub.x is the RMS value of the load voltage and X.sub.TCLCx(a.sub.x) is the impedance of the TCLC part, which can be obtained from (4). In (9), when the X.sub.TCLCx(a.sub.x)=X.sub.Cap(min)(a.sub.x=180) and X.sub.TCLCx(a.sub.x)=X.sub.Ind(min)(a.sub.x=90), the TCLC part provides the maximum capacitive and inductive compensating reactive power Q.sub.cx(MaxCap) and Q.sub.cx(MaxInd), respectively.

(36) $\begin{array}{cc}{Q}_{\mathrm{cx}\left(\mathrm{MaxCap}\right)}=\frac{V_x^2}{X_{\mathrm{Cap}\left(min\right)}\left({}_x=180\right)}=-\frac{V_x^2}{X_{C_{\mathrm{PF}}}-X_{L_c}}& \left(10\right)\\ Q_{\mathrm{cx}\left(\mathrm{MaxInd}\right)}=\frac{V_x^2}{X_{\mathrm{Ind}\left(min\right)}\left({}_x=90\right)}=-\frac{V_x^2}{\frac{X_{L_{\mathrm{PF}}}{X}_{C_{\mathrm{PF}}}}{X_{C_{\mathrm{PF}}}-X_{L_{\mathrm{PF}}}}+X_{L_c}}& \left(11\right)\end{array}$
where the minimum inductive impedance X.sub.Ind(min) and the capacitive impedance X.sub.Cap(min) are obtained from (5) and (6), respectively.

(37) To compensate for the load reactive power (Q.sub.cx=Q.sub.Lx), C.sub.PF and L.sub.PF can be deduced on the basis of the loading maximum inductive reactive power Q.sub.Lx(MaxInd) (=Q.sub.cx(MaxCap)) and capacitive reactive power Q.sub.Lx(MaxCap) (=Q.sub.cx(MaxInd)). Therefore, based on (10) and (11), the parallel capacitor C.sub.PF and inductor L.sub.PF can be designed as:

(38) $\begin{array}{cc}{C}_{\mathrm{PF}}=\frac{Q_{\mathrm{Lx}\left(\mathrm{MaxInd}\right)}}{{}^2{Q}_{\mathrm{Lx}\left(\mathrm{MaxInd}\right)}{L}_c+V_x^2}& \left(12\right)\\ L_{\mathrm{PF}}=\frac{V_x^2+L_c{Q}_{\mathrm{Lx}\left(\mathrm{MaxCap}\right)}}{-Q_{\mathrm{Lx}\left(\mathrm{MaxCap}\right)}+{}^3{L}_c{C}_{\mathrm{PF}}{Q}_{\mathrm{Lx}\left(\mathrm{MaxCap}\right)}+{}^2{V}_x^2{C}_{\mathrm{PF}}}& \left(13\right)\end{array}$
where is the fundamental angular frequency and V.sub.x is the RMS load voltage.

(39) Design of L.sub.c

(40) The purposes of L.sub.c in TCLC is to filter out the current ripple caused by the power switches of active inverter part, and the value of the L.sub.c can be designed as:

(41) $\begin{array}{cc}{L}_c\frac{V_{DC}}{8.Math.f_s.Math.i_{L_c}\max }& \left(14\right)\end{array}$
where f.sub.s is the switching frequency of active inverter, i.sub.Lcmax is the maximum allowed output current ripple value, and V.sub.DC is the DC-link voltage.

(42) Design of V.sub.DC

(43) Different with the traditional V.sub.DC design method of the STATCOM to compensate maximum load reactive power, the V.sub.DC of Hybrid-STATCOM is designed to solve the firing angle mistuning problem of TCLC (i.e., affect the reactive power compensation) so that the source reactive power can be fully compensated. Reforming (3), the inverter voltage V.sub.invx can also be expressed as:

(44) $\begin{array}{cc}{V}_{\mathrm{invx}}=V_x\left[1+\frac{V_x{I}_{\mathrm{Lqx}}}{\frac{V_x^2}{X_{\mathrm{TCLC}}\left({}_x\right)}}\right]=V_x\left[1+\frac{Q_{\mathrm{Lx}}}{Q_{\mathrm{cx},\mathrm{TCLC}}\left({}_x\right)}\right]& \left(15\right)\end{array}$
where Q.sub.Lx is the load reactive power, Q.sub.cx,TCLC(a.sub.x) is the TCLC part compensating reactive power, and V.sub.x is the RMS value of the phase load voltage. Then the required DC-link voltage V.sub.DCx of each phase and V.sub.DC for hybrid-STATCOM can be expressed as:

(45) $\begin{array}{cc}{V}_{\mathrm{DCx}}=\sqrt{6}{V}_x.Math.1+\frac{Q_{\mathrm{Lx}}}{Q_{\mathrm{cx},\mathrm{TCLC}}\left({}_x\right)}.Math.& \left(16\right)\end{array}$
and
V.sub.DC=max(V.sub.DCa, V.sub.DCb, V.sub.DCc).

(46) Ideally, Q.sub.cx,TCLC(a.sub.x) is controlled to be equal to Q.sub.Lx so that the required V.sub.DC can be zero. However, in the practical case, the Q.sub.cx,TCLC(a.sub.x) may not be exactly equal to Q.sub.Lx due to the firing angle mistuning problem. The worst case of mistuning Q.sub.Lx/Q.sub.cx,TCLC(a.sub.x) ratio can be pre-measured to estimate the required minimum V.sub.DC value. Finally, a slightly greater V.sub.DC value can be chosen. Based on (12), (13), (14), and (16), the system parameters C.sub.PF, L.sub.PF, L.sub.c, and V.sub.DC of hybrid-STATCOM can be designed accordingly.

(47) Method of Controlling the Hybrid-STATCOM

(48) A method of controlling the hybrid-STATCOM is provided by coordinating the control of the TCLC part and the active inverter part so that the two parts can complement each other's disadvantages and the overall performance of hybrid-STATCOM can be improved. Specifically, with the controller in accordance to various embodiments of the present invention, the response time of the hybrid-STATCOM can be faster than SVCs, and the active inverter part can operate at lower DC-link operating voltage than the traditional STATCOMs. The control block diagram of hybrid-STATCOM is shown in FIG. 3.

(49) TCLC Part Control

(50) Different from the traditional SVC control based on the traditional definition of reactive power [2]-[3], to improve its response time, the TCLC part control is based on the instantaneous pq theory [4]. The TCLC part is mainly used to compensate the reactive current with the controllable TCLC part impedance X.sub.TCLCx. Referring to (3), to obtain the minimum inverter voltage V.sub.invx0, X.sub.TCLCx can be calculated with Ohm's law in terms of the RMS values of the load voltage (V.sub.x) and the load reactive current (I.sub.Lqx). However, to calculate the X.sub.TCLCx in real time, the expression of X.sub.TCLCx can be rewritten in terms of instantaneous values as:

(51) $\begin{array}{cc}{X}_{\mathrm{TCLCx}}=\frac{V_x}{I_{\mathrm{Lqx}}}=\frac{{.Math.v.Math.}^2}{\sqrt{3}{\stackrel{\_}{q}}_{\mathrm{Lx}}}& \left(17\right)\end{array}$
where v is the norm of the three-phase instantaneous load voltage and q.sub.Lx is the DC component of the phase reactive power of the load, and x can be a, b or c. The real-time expression of v and q.sub.Lx can be obtained by (18) and (19) with low-pass filters.

(52) 0$\begin{array}{cc}.Math.v.Math.=\sqrt{v_a^2+v_b^2+v_c^2}& \left(18\right)\\ \left[\begin{array}{c}{q}_{\mathrm{La}}\\ q_{\mathrm{Lb}}\\ q_{\mathrm{Lc}}\end{array}\right]=\left[\begin{array}{c}{v}_b.Math.i_{\mathrm{Lc}}-v_c.Math.i_{\mathrm{Lb}}\\ v_c.Math.i_{\mathrm{La}}-v_a.Math.i_{\mathrm{Lc}}\\ v_a.Math.i_{\mathrm{Lb}}-v_b.Math.i_{\mathrm{La}}\end{array}\right]& \left(19\right)\end{array}$

(53) In (18) and (19), v.sub.x and q.sub.Lx are the instantaneous load voltage and the load reactive power, respectively. As shown in FIG. 3, a limiter is applied to limit the calculated X.sub.TCLCx in (9) within the range of X.sub.TCLCx>X.sub.ind(min) and X.sub.TCLCx<X.sub.Cap(min) (X.sub.Cap(min)<0). With the calculated X.sub.TCLCx, the firing angle a.sub.x can be determined by solving (4). Because (4) is complicated, a look-up table (LUT) is installed inside the controller. The trigger signals to control the TCLC part can then be generated by comparing the firing angle a.sub.x with .sub.x, which is the phase angle of the load voltage v.sub.x. .sub.x can be obtained by using a phase lock loop (PLL). Note that the firing angle of each phase can differ if the unbalanced loads are connected (see (4) and (17)). With the control algorithm, the reactive power of each phase can be compensated and the active power can be basically balanced, so that DC-link voltage can be maintained at a low level even under unbalanced load compensation.

(54) Active Inverter Part Control

(55) In the control method, the instantaneous active and reactive current i.sub.d-i.sub.q method [7] is implemented for the active inverter part to improve the overall performance of hybrid-STATCOM under different voltage and current conditions, such as balanced/unbalanced, voltage dip, and voltage fault. Specifically, the active inverter part is used to improve the TCLC part characteristic by limiting the compensating current i.sub.cx to its reference value i.sub.cx*so that the mistuning problem, the resonance problem, and the harmonic injection problem can be avoided. The i.sub.cx*is calculated by applying the i.sub.d-i.sub.q method [7] because it is valid for different voltage and current conditions.

(56) The calculated i.sub.cx*contains reactive power, unbalanced power, and current harmonic components. By controlling the compensating current i.sub.cx to track its reference i.sub.cx*, the active inverter part can compensate for the load harmonic current and improve the reactive power compensation ability and dynamic performance of the TCLC part under different voltage conditions. The i.sub.cx*can be calculated as:

(57) $\begin{array}{cc}\left[\begin{array}{c}{i}_{\mathrm{ca}}^{*}\\ i_{\mathrm{cb}}^{*}\\ i_{\mathrm{cc}}^{*}\end{array}\right]=\sqrt{\frac{2}{3}}.Math.\left[\begin{array}{cc}1& 0\\ -1/2& \sqrt{3}/2\\ -1/2& -\sqrt{3}/2\end{array}\right].Math.\left[\begin{array}{cc}\cos {}_a& -\sin {}_a\\ \sin {}_a& \cos {}_a\end{array}\right].Math.\left[\begin{array}{c}{\tilde{i}}_d\\ i_q\end{array}\right]& \left(20\right)\end{array}$
where i.sub.d and i.sub.q are the instantaneous active and reactive current, which include DC components .sub.d and .sub.q, and AC components .sub.d and .sub.q. .sub.d is obtained by passing i.sub.d through a high-pass filter. i.sub.d and i.sub.q are obtained by:

(58) $\begin{array}{cc}\left[\begin{array}{c}{i}_d\\ i_q\end{array}\right]=\left[\begin{array}{cc}\cos {}_a& \sin {}_a\\ -\sin {}_a& \cos {}_a\end{array}\right].Math.\left[\begin{array}{c}{i}_{}\\ i_{}\end{array}\right]& \left(21\right)\end{array}$

(59) In (21), the current (i.sub. and i.sub.) in - plane are transformed from a-b-c frames by:

(60) $\begin{array}{cc}\left[\begin{array}{c}{i}_{}\\ i_{}\end{array}\right]=\left[\begin{array}{ccc}1& -1/2& -1/2\\ 0& \sqrt{3}/2& -\sqrt{3}/2\end{array}\right].Math.\left[\begin{array}{c}{i}_{\mathrm{La}}\\ i_{\mathrm{Lb}}\\ i_{\mathrm{Lc}}\end{array}\right]& \left(22\right)\end{array}$
where i.sub.Lx is the load current signal.

(61) The TCLC part has two back-to-back connected thyristors in each phase that are triggered alternately in every half cycle, so that the control period of the TCLC part is one cycle (0.02 s). However, the hybrid-STATCOM structure connects the TCLC part in series with an instantaneous operated active inverter part, which can significantly improve its overall response time. With the controller, the active inverter part can limit the compensating current i.sub.cx to its reference value i.sub.cx*via pulse width modulation (PWM) control, and the PWM control frequency is set to be 12.5 kHz. During the transient state, the response time of hybrid-STATCOM can be separately discussed in the following two cases: a.) if the load reactive power is dynamically changing within the inductive range (or within the capacitive range), the response time of hybrid-STATCOM can be as fast as traditional STATCOM; and b.) in contrast, when the load reactive power suddenly changes from capacitive to inductive or vice versa, the hybrid-STATCOM may take approximately one cycle to settle down. However, in practical application, case b.) described above seldom happens. Therefore, based on the above, the hybrid-STATCOM can be considered as a fast-response reactive power compensator in which the dynamic performances of hybrid-STATCOM are proved by the simulation result shown in FIG. 4 and the experimental results shown in FIGS. 5, 6, and 10.

(62) Simulation Results

(63) In the following, the simulation results among traditional STATCOM, C-STATCOM, and the hybrid-STATCOM are discussed and compared. The previous discussions of the required inverter voltage (or DC-link voltage V.sub.DC={square root over (2)} .Math.{square root over (3)} .Math.V.sub.invx) for these three STATCOMs are also verified by simulations. The STATCOMs are simulated with the same voltage level as in the experimental results. The simulation studies are carried out with PSCAD/EMTDC. Table III shows the simulation system parameters for traditional STATCOM, C-STATCOM, and hybrid-STATCOM. In addition, three different cases of loading are built for testing: a.) inductive and light loading, b.) inductive and heavy loading, and c.) capacitive loading. These three testing cases are also represented by points A, B, and C in FIG. 2. The detailed simulation results are summarized Table II.

(64) With the consideration of IEEE standard 519-2014 [23], total demand distortion (TDD)=15% and I.sub.SC/I.sub.L in 100<1000 scale at a typical case, the nominal rate current is assumed to be equal to the fundamental load current in the worst-case analysis, which results in THD=TDD=15%. Therefore, this paper evaluates the compensation performance by setting THD<15%.

(65) a.) Inductive and Light Loading

(66) When the loading is inductive and light, traditional STATCOM requires a high DC-link voltage (V.sub.DC>{square root over (2)}.Math.V.sub.L-L=269V, V.sub.DC=300V) for compensation. After compensation, the source current i.sub.sx is reduced to 5.55 A from 6.50 A and the source-side displacement power factor (DPF) becomes unity from 0.83. In addition, the source current total harmonics distortion (THD.sub.isx) is 7.22% after compensation, which satisfies the international standard [23] (THD.sub.isx<15%).

(67) For C-STATCOM, the coupling impedance contributes a large voltage drop between the load voltage and the inverter voltage so that the required DC-link voltage can be small (V.sub.DC=80V). The i.sub.sx, DPF and THD.sub.isx are compensated to 5.48 A, unity, and 2.01%, respectively.

(68) For the hybrid-STATCOM, the i.sub.sx, DPF, and THD.sub.isx are compensated to 5.48 A, unity, and 1.98%, respectively. As discussed in the previous part, a low DC-link voltage (V.sub.DC=50V) of hybrid-STATCOM is used to avoid mistuning of firing angles, prevent resonance problems, and reduce the injected harmonic current.

(69) b.) Inductive and Heavy Loading

(70) To compensate for the inductive and heavy loading, traditional STATCOM still requires a high DC-link voltage of V.sub.DC=300V for compensation. Traditional STATCOM can obtain acceptable results (DPF=1.00 and THD.sub.isx=6.55%). The i.sub.sx is reduced to 5.95 A from 8.40 A after compensation.

(71) With a low DC-link voltage (V.sub.DC=50V), C-STATCOM cannot provide satisfactory compensation results (DPF=0.85 and THD.sub.isx=17.5%). However, when the DC-link voltage is increased to V.sub.DC=300V, the compensation results (DPF=1.00 and THD.sub.isx=7.02%) are acceptable and satisfy the international standard [23] (THD.sub.isx<15%). The i.sub.sx is reduced to 5.90 A from 8.40 A after compensation.

(72) On the other hand, the hybrid-STATCOM can still obtain acceptable compensation results (DPF=1.00 and THD.sub.isx=3.01%) with a low DC-link voltage of V.sub.DC=50V. The i.sub.sx is reduced to 5.89 A from 8.40 A after compensation.

(73) c.) Capacitive Loading

(74) When the loading is capacitive, with V.sub.DC=250V (V.sub.DC<{square root over (2)}.Math.V.sub.L-L=269V), the compensation results of traditional STATCOM are acceptable, in which the DPF and THD.sub.isx are compensated to unity and 7.61%. The i.sub.sx is also reduced to 3.67 A from 4.34 A after compensation.

(75) For C-STATCOM with V.sub.DC=50V, the i.sub.sx increases to 7.10 A from the original 4.34 A. The compensation performances (DPF=0.57 and THD.sub.isx=23.5%) are not satisfactory, which cannot satisfy the international standard [23] (THD.sub.isx<15%). When V.sub.DC is increased to 500V, the DPF is improved to 0.99 and the THD.sub.isx is reduced to 10.6%, which can be explained by its V-I characteristic. However, the compensated i.sub.sx=5.02 A is still larger than i.sub.sx=3.73 A before compensation.

(76) With the lowest DC-link voltage (V.sub.DC=50V) of the three STATCOMs, hybrid-STATCOM can still obtain the best compensation results with DPF=1.00 and THD.sub.isx=3.01%. In addition, the i.sub.sx is reduced to 3.41 A from 4.34 A after compensation.

(77) Dynamic Response of Hybrid-STATCOM

(78) FIG. 4 shows the dynamic performance of hybrid-STATCOM for different loadings compensation. When the load reactive power changes from capacitive to inductive, hybrid-STATCOM takes about one cycle to settle down. However, when the load reactive power is changing within the inductive range, the transient time is significantly reduced and the waveforms are smooth. Meanwhile, the fundamental reactive power is compensated to around zero even during the transient time. In practical situations, the load reactive power seldom suddenly changes from capacitive to inductive or vice versa, and thus hybrid-STATCOM can obtain good dynamic performance.

(79) TABLE-US-00002 TABLE II Simulation Results for Inductive and Capacitive Reactive Power Compensation of Traditional STATCOM, C-STATCOM and Hybrid-STATCOM Loading Without and With THDi.sub.sx V.sub.DC Type STATCOM Comp. i.sub.sx(A) DPF (%) (V) Case A: Before Comp. 6.50 0.83 0.01 inductive Trad. STATCOM 5.55 1.00 7.22 300 and light C-STATCOM 5.48 1.00 2.01 80 loading Hybrid STATCOM 5.48 1.00 1.98 50 Case B: Before Comp. 8.40 0.69 0.01 inductive Trad. STATCOM 5.95 1.00 6.55 300 and heavy C-STATCOM 6.30 0.85 17.5 50 loading C-STATCOM 5.90 0.98 7.02 300 Hybrid STATCOM 5.89 1.00 2.10 50 Case C: Before Comp. 4.34 0.78 0.01 capacitive Trad. STATCOM 3.67 1.00 7.61 250 loading C-STATCOM 7.10 0.57 23.5 50 C-STATCOM 5.02 0.99 10.6 500 Hybrid STATCOM 3.41 1.00 3.01 50

(80) According to the above simulation results, Table II verifies the V-I characteristics of the traditional STATCOM, C-STATCOM, and hybrid-STATCOM, as shown in FIG. 2. With similar compensation performance, the capacity of the active inverter part (or DC-link voltage) of the hybrid-STATCOM is only about 16% of that of traditional STATCOM under wide range compensation (both inductive and capacitive). According to the cost study in [14] and [17], the average cost of traditional STATCOM is around USD $60/kVA, whereas that of SVC is only approximately $23/kVA. Therefore, by rough calculation, the average cost of the hybrid-STATCOM is just about $33/kVA (=$60/kVA*16%+$23/kVA), which is 55% of the average cost of traditional STATCOM. Moreover, because the hybrid-STATCOM can avoid the use of multilevel structures in medium-voltage level transmission system in comparison to traditional STATCOM, the system reliability can be highly increased and the system control complexity and operational costs can be greatly reduced.

(81) Based on the simulation results, a summary can be drawn as follows: The traditional STATCOM can compensate for both inductive and capacitive reactive current with a high DC-link operating voltage due to a small coupling inductor. Due to its high DC-link voltage, the traditional STATCOM obtains the poor source current THD.sub.isx (caused by switching noise) compared with hybrid-STATCOM. C-STATCOM has a low DC-link voltage characteristic only under a narrow inductive loading range. However, when the loading current is outside its designed range, the C-STATCOM requires a very high DC-link operating voltage due to a large coupling capacitor. The hybrid-STATCOM obtains the best performances among the three STATCOMs under both inductive and capacitive loadings. The hybrid-STATCOM has a wide compensation range with low DC-link voltage characteristic and good dynamic performance.

(82) Experimental Results

(83) The objective of the experiment is to verify that the hybrid-STATCOM has the characteristics of a wide compensation range and low DC-link voltage under different voltage and current conditions, such as unbalanced current, voltage dip, and voltage fault. In the experiment, a 110-V, 5-kVA experimental prototype of the three-phase hybrid-STATCOM is constructed in the laboratory. The control system has a sampling frequency of 25 kHz. The switching devices for the active inverter are Mitsubishi IGBTs PM300DSA060. The switching devices for the TCLC are thyristors SanRex PK110FG160. Moreover, the experimental parameters of the hybrid-STATCOM are the same as those for the simulation listed in Table III. The experimental prototype's DC-link voltage is maintained at V.sub.DC=50V for all experiments.

(84) TABLE-US-00003 TABLE III Simulation and Experimental Parameters for Traditional STATCOM, C-STATCOM and Hybrid-STATCOM Parameters Physical values System parameters v.sub.x, f, L.sub.s 110 V, 50 Hz, 0.1 mH Traditional STATCOM L 5 mH C-STATCOM L, C 5 mH, 80 uF Hybrid-STATCOM L.sub.c, L.sub.PF, C.sub.PF 5 mH, 30 mH,160 uF Case A. Inductive and L.sub.L1, R.sub.L1 30 mH, 14 light loading Case B. Inductive and L.sub.L2, R.sub.L2 30 mH, 9 heavy loading Case C. Capacitive loading C.sub.L3, R.sub.L3 200 uF, 20

(85) FIGS. 5 and 6 show the dynamic compensation waveforms of load voltage v.sub.x, source current i.sub.sx, and reactive power Q.sub.sa of phase a by applying hybrid-STATCOM for inductive load and capacitive load compensation. FIG. 7 provides the corresponding source current harmonic spectrums for inductive and capacitive reactive power compensations.

(86) FIG. 5 clearly shows that after hybrid-STATCOM compensation, the source current i.sub.sx and the load voltage v.sub.x are in phase with each other. The source displacement power factors (DPFs) are compensated to 1.00 from the original 0.69 (for inductive loading) and 0.64 (for capacitive loading). The worst phase source current THD.sub.isx are 3.5% and 5.4% after compensation, which satisfy the international standard [23] (THD.sub.isx<15%). The source current i.sub.sx are also significantly reduced after compensation. In FIGS. 5a and 5b, the hybrid-STATCOM obtains a good dynamic compensation performance. In FIG. 5c, the response time is longer than expected by one cycle because the inductive loads and capacitive loads are manually switching on and off.

(87) FIGS. 8 and 10 illustrate dynamic compensation waveforms of load voltage v.sub.x and source current i.sub.sx by applying hybrid-STATCOM under unbalanced loads and voltage fault situations, which clearly verify its good dynamic performance. FIGS. 9 and 11 provide their corresponding source current harmonic spectrums.

(88) FIGS. 8 and 9 show that the hybrid-STATCOM can compensate for and balance the source current even under unbalanced loads with low V.sub.DC=50V. The unbalanced i.sub.sx are compensated from 4.80 A, 3.83 A, and 5.74 A to 2.94 A, 2.79 A, and 2.86 A, respectively. The DPF and THD.sub.isx are compensated to unity and lower than 9.0%, which satisfy the international standard [23]. From FIGS. 10 and 11, it can be seen that the hybrid-STATCOM can still obtain satisfactory performances even under asymmetric grid fault. During the voltage fault, the i.sub.sx can be compensated to be approximately balanced with DPF1 and THD.sub.isx<10.0%.

(89) FIG. 12 also provides the dynamic compensation waveforms of load voltage v.sub.x and source current i.sub.sx by applying hybrid-STATCOM during a sudden voltage dip. It is found that hybrid-STATCOM can obtain good dynamic and reactive power compensation performances.

(90) Table IV summarizes the hybrid-STATCOM experimental results. The experimental results confirm that the hybrid-STATCOM has a wide reactive power compensation range and low DC-link voltage characteristics with good dynamic performance even under different voltage and current conditions.

(91) TABLE-US-00004 TABLE IV Experimental Compensation Results by Hybrid-STATCOM (V.sub.DC = 50 V) under Different System and Loading Situations Different i.sub.sx (A) DPF THDi.sub.sx (%) Situations Comp. A B C A B C A B C Inductive Before 7.13 7.14 7.34 0.69 0.70 0.70 1.1 1.2 1.2 load After 4.79 4.97 4.95 1.00 1.00 1.00 3.5 3.3 3.3 Capacitive Before 3.60 3.63 3.65 0.65 0.64 0.64 3.1 2.9 2.8 load After 2.92 2.80 2.85 1.00 1.00 1.00 5.4 5.4 5.2 Unbalanced Before 4.80 3.83 5.74 0.36 0.69 0.64 2.0 1.4 1.2 loads After 2.94 2.79 2.86 1.00 1.00 1.00 5.9 8.7 8.1 Voltage Before 5.57 4.18 7.06 0.67 0.38 0.87 2.3 2.5 1.6 fault After 4.30 3.98 4.00 0.99 1.00 0.99 4.7 9.3 6.2

(92) The embodiments disclosed herein may be implemented using general purpose or specialized computing devices, computer processors, or electronic circuitries including but not limited to digital signal processors (DSP), application specific integrated circuits (ASIC), field programmable gate arrays (FPGA), and other programmable logic devices configured or programmed according to the teachings of the present disclosure. Computer instructions or software codes running in the general purpose or specialized computing devices, computer processors, or programmable logic devices can readily be prepared by practitioners skilled in the software or electronic art based on the teachings of the present disclosure.

(93) In some embodiments, the present invention includes computer storage media having computer instructions or software codes stored therein which can be used to program computers or microprocessors to perform any of the processes of the present invention. The storage media can include, but are not limited to, floppy disks, optical discs, Blu-ray Disc, DVD, CD-ROMs, and magneto-optical disks, ROMs, RAMs, flash memory devices, or any type of media or devices suitable for storing instructions, codes, and/or data.

(94) The foregoing description of the present invention has been provided for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many modifications and variations will be apparent to the practitioner skilled in the art.

(95) The embodiments were chosen and described in order to best explain the principles of the invention and its practical application, thereby enabling others skilled in the art to understand the invention for various embodiments and with various modifications that are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the following claims and their equivalence.