DC power transmisson system of voltage source converter using pulse-interleaving auxiliary circuit

Abstract

A DC power transmission system of a voltage source converter using a pulse-interleaving auxiliary circuit is disclosed.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrating a conventional multi-pulse DC power transmission system disclosed in Korean Patent No. 10-034614.

FIG. 2 is a diagram illustrating a conventional 36-step converter using a DC auxiliary circuit.

FIG. 3 is a schematic diagram illustrating a back-to-back system.

FIG. 4 is a diagram illustrating a 36-step converter using a DC auxiliary circuit in accordance with the present invention.

FIG. 5 is a graph illustrating a result of a simulation of an operation of a 36-step converter using a PSCAD/EMTDC software in accordance with the present invention.

FIG. 6 is a graph illustrating a result of an experiment according to circuit parameters of table 1 using a DSP TMS320VC33 for a control of entire system and a generation of a gate pulse in order to verify an operation and a performance of a 36-step converter in accordance with the present invention.

FIG. 7 is a diagram schematically illustrating a back-to-back HVDC system in accordance with the present invention.

FIG. 8 a illustrates a single-phase equivalent circuit of the back-to-back HVDC system of FIG. 7 in accordance with the present invention, and FIG. 8b illustrates a vector diagram illustrating a source voltage, an output voltage of each converter, and a resulting output voltage of the converter, when the upper and lower firing angles of a voltage source converter.

FIG. 9 is a graph illustrating a variation of α₁ and α₂ with respect to P of table 2 as a function of Q.

FIG. 10 is a block diagram illustrating a configuration of a controller of each converter.

FIG. 11 is a graph illustrating a result of a simulation for verifying an operation of an entire system in accordance with the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention will now be described in detail with reference to the accompanied drawings.

FIG. 4 is a diagram illustrating a 36-step converter system using a DC auxiliary circuit in accordance with the present invention.

The 36-step converter system shown in FIG. 4 comprises a first converter 110 connected to a Y-Y transformer 160, a second converter 120 connected to a Y-Δ transformer 170, an injection transformer 130, first and second DC capacitors 140 and 140′, and a 3-level half bridge circuit 150.

A ground terminal of the first converter 110 and an output terminal of the second converter 120 are connected to a first terminal of a primary winding of the injection transformer 130, and a connecting point of the first and second DC capacitors 140 and 140′ serially connected between an output terminal of the first converter 110 and a ground terminal of the second converter 120 is connected to a second terminal of the primary winding of the injection transformer 130.

A first terminal of a secondary winding of the injection transformer 130 is simultaneously connected to the second terminal of the primary winding of the injection transformer 130 and the 3-level half bridge circuit 150, and a second terminal of the secondary winding of the injection transformer 130 is connected to the 3-level half bridge circuit 150.

The 3-level half bridge circuit 150 comprises first through fourth switching elements S1, S2, S1′ and S2′, using an IGBT for instance, connected to the first and second DC capacitors in parallel, and a clamping diode D1 connected between a connection point of the first and second switching elements S1 and S2 and a connection point of the second terminal of the primary winding and the first terminal of the secondary winding of the injection transformer 130, and a clamping diode D2 connected between a connection point of the third and fourth switching elements S1′ and S2′ and a connection point of the second terminal of the primary winding and the first terminal of the secondary winding of the injection transformer 130.

A characteristic of the converter described above will be described in detail below.

When a bridge of the first and second converters 110 and 120 is assumed to be ideal, voltages of the first and second DC capacitors 140 and 140′ of upper and lower bridges are the same. Therefore, DC voltages of the first converter 110 connected to the Y-Y transformer 160 and the second converter 120 connected to the Y-Δ transformer 170 of FIG. 4 may be expressed as equations 1 and 2 where V_dc/2 is the voltage of the first and second DC capacitors 140 and 140′ and V_aux is an injection voltage of the 3-level half bridge circuit 150.

V _Y =V _dc/2+V_aux  [Equation 1]

V _Δ =V _dc/2−V_aux  [Equation 2]

An output AC voltage of each converter from above equations may be controlled simultaneously by the injection voltage V_aux. On the other hand, the injection voltage V_aux is determined by a switching pattern of the 3-level half bridge circuit 150 and a winding ratio of the injection transformer 130. Therefore, the injection voltage V_aux may have three levels of zero, k*V_dc, −k*V_dc, where k is the winding ratio of the injection transformer 130.

Two converter systems connected to the Y-Y transformer 160 and the Y-Δ transformer 170 shown in FIG. 4 generate 12 steps by making a phase voltage of an AC side to have a phase difference of 30°, and the injection voltage V_aux forms a step corresponding to a frequency six times larger than a fundamental frequency since the 3-level half bridge circuit 150 operates at every 30°. The winding ratio k of the injection transformer 130 used in the 3-level half bridge circuit 150 should be determined such that a harmonic of an output voltage waveform is minimized.

FIG. 5 is a graph illustrating a result of a simulation of an operation of a 36-step converter using a PSCAD/EMTDC software in accordance with the present invention.

FIG. 5 a illustrates a voltage injected through the transformer from the 3-level half bridge circuit 150, FIG. 5b illustrates an A-phase voltage V_YA of an upper bridge of the first converter 110, and FIG. 5c illustrates an A-phase voltage V_ΔA of a lower bridge of the second converter 120. In accordance with the present invention, a 36-step waveform shown in FIG. 5d is obtained by combining a waveform of the upper bridge of FIG. 5b and a waveform of the lower bridge of FIG. 5c.

The multi-step output voltages V_YA and V_ΔA may be expresses as equations 3 and 4 using a Fourier series.

$\begin{array}{cc}{V}_{\mathrm{YA}}\left(\omega t\right)=\sum _{n=1}^{\infty }\frac{4}{3}{\cos }^2\left(\frac{n\pi }{6}\right)b_nV_{\mathrm{dc}}\sin \left(n\omega t\right)& \left[\mathrm{Equation}3\right]\\ V_{\Delta A}\left(\omega t\right)=\sum _{n=1}^{\infty }\frac{2}{\sqrt{3}}\cos \left(\frac{n\pi }{6}\right)b_nV_{\mathrm{dc}}\sin \left(n\omega t\right),\mathrm{where}b_n=\frac{\left[1-{\left(-1\right)}^n\right]}{n\pi }\left\{1+k\left[8\sin \frac{n\pi }{6}\sin \frac{n\pi }{12}\cos \frac{n\pi }{36}-1\right]\right\}& \left[\mathrm{Equation}4\right]\end{array}$

An AC voltage V_A(ωt) of a primary winding of the transformer is a sum of V_YA(ωt) and V_ΔA(ωt). Therefore, a total RMS value of an output phase voltage is expressed as equation 5.

$\begin{array}{cc}{V}_{\mathrm{ARMS}}=\frac{V_{\mathrm{dc}}}{9}\sqrt{36+15\sqrt{3}+\left(24-12\sqrt{3}\right)k^2}& \left[\mathrm{Equation}5\right]\end{array}$

A fundamental wave peak value is expressed as equation 6.

$\begin{array}{cc}{V}_{A1}=\frac{4V_{\mathrm{dc}}}{\pi }\left[1+\left(4\cos \frac{\pi }{36}\sin \frac{\pi }{12}-1\right)k\right]& \left[\mathrm{Equation}6\right]\end{array}$

Therefore, a THD_v of the output phase voltage is expressed as equation 7.

$\begin{array}{cc}{\mathrm{THD}}_v=\sqrt{\frac{2V_{\mathrm{ARMS}}^2}{V_{A1}^2}-1}& \left[\mathrm{Equation}7\right]\end{array}$

The winding ratio k of the injection transformer is determined by

$k=1.5\left(7+4\sqrt{3}\right)\left(4\cos \frac{\pi }{36}\sin \frac{\pi }{12}-1\right)\approx 0.6547$

at a minimum value of 5.09% of THD_v, which is about 0.6547.

FIG. 6 is a graph illustrating a result of an experiment according to circuit parameters of table 1 using a DSP TMS320VC33 for a control of entire system and a generation of a gate pulse in order to verify an operation and a performance of a 36-step converter in accordance with the present invention.

TABLE 1
Source Voltage    3Φ 220 V
Frequency         60 Hz
Source Inductance 2 mH
Power Factor      0.73
Load (R, L)       20 Ω, 50 mH
Load Capacity     2 kVA

FIG. 6 a illustrates a waveform of an injection voltage of the 3-level half bridge circuit 150, FIG. 6b illustrates a waveform of the A-phase voltage V_YA of the upper bridge of the first converter 110, and FIG. 6c illustrates a waveform of the A-phase voltage V_ΔA of the lower bridge of the second converter 120. FIG. 6d illustrates a combination waveform of the waveform of the A-phase voltage V_YA of the upper bridge of the first converter 110 and the waveform of the A-phase voltage V_ΔA of the lower bridge of the second converter 120.

As shown in waveforms of FIG. 6, the entire voltage waveform is very similar to the wave forms of the simulation, and the entire waveform of the output voltage of the converter is close to a sinusoidal wave in spite of a small irregularity.

FIG. 7 is a diagram schematically illustrating a back-to-back HVDC system in accordance with the present invention.

As shown in FIG. 7, in accordance with the present invention, a back-to-back converter comprising two 36-step converter wherein the AC side thereof is connected in serial and a DC side thereof is connected in parallel.

FIG. 8 a illustrates a single-phase equivalent circuit of the back-to-back HVDC system of FIG. 7 in accordance with the present invention. The back-to-back converter 200 independently controls effective/reactive powers of an interconnected AC system by operating a firing angle α₁ of an upper converter 210 and a firing angle α₂ of a lower converter 220 differently.

FIG. 8 b illustrates a vector diagram illustrating a source voltage, a voltage of each converter, and a total voltage of the converter when the upper and lower firing angles of the voltage source converter are different. As shown in FIG. 8b, when the firing angle α₁ of the upper converter 210 and the firing angle α₂ of the lower converter 220 are properly adjusted, an output voltage vector Vc of the converter forms a power angle δ with the source voltage Vs and a magnitude thereof may be adjusted. Therefore, the upper firing angle α₁ and the lower firing angle α₂ may be adjusted in order to independently control the effective/reactive powers of the interconnected AC system.

Equation related to the firing angles α₁ and α₂ may be obtained using the vector diagram of the output voltage vector Vc and the power angle δ.

Since V_C=V₁+V₂=V∠α₁+V∠α₂ in accordance with the vector diagram, and from

V_C=2V cos ρ  [Equation 8]

ρ=α₁−δ=δ−α₂, where ρ denotes an angle between Vc and V₁ or Vc and V₂  [Equation 9]

δ is express as equation 10.

$\begin{array}{cc}\delta =\frac{{\alpha }_1+{\alpha }_{\mathrm{2`}}}{2}& \left[\mathrm{Equation}10\right]\end{array}$

When a maximum value of Vc assumed to be 1.15 times the Vs, Vc may be expressed as equation 11.

$\begin{array}{cc}{V}_C=1.15V_S\cos \left(\frac{{\alpha }_1-{\alpha }_{\mathrm{2`}}}{2}\right)& \left[\mathrm{Equation}11\right]\end{array}$

The firing angles α₁ and α₂ of the converters 210 and 220, which are expressed in equations 12 and 13, are obtained by combining equations 10 and 11 with respect to δ and Vc.

$\begin{array}{cc}{\alpha }_1=\delta +{\cos }^{-1}\left(\frac{V_C}{1.15V_S}\right)& \left[\mathrm{Equation}12\right]\\ {\alpha }_2=\delta -{\cos }^{-1}\left(\frac{V_C}{1.15V_S}\right)& \left[\mathrm{Equation}13\right]\end{array}$

The effective/reactive powers in the vector diagram of FIG. 8b are expressed as equations 14 and 15.

$\begin{array}{cc}P=\frac{3V_CV_S}{X_C}& \left[\mathrm{Equation}14\right]\\ Q=\frac{3\left(V_S^2-V_CV_S\cos \delta \right)}{X_C}& \left[\mathrm{Equation}15\right]\end{array}$

By combining equations 14 and 15 with respect to effective/reactive powers and using a solution formula of a second order equation, Vc and δ may be expressed as equations 16 and 17.

$\begin{array}{cc}{V}_C=\sqrt{\frac{P^2X_C^2+{\left(3V_S^2-{\mathrm{QX}}_C\right)}^2}{9V_S^2}}& \left[\mathrm{Equation}16\right]\\ \delta ={\sin }^{-1}\left(\frac{{\mathrm{PX}}_C}{3V_SV_C}\right),\mathrm{where}a=\frac{V_S}{X_C}\mathrm{and}b=\frac{1}{X_C}& \left[\mathrm{Equation}17\right]\end{array}$

Therefore, the firing angles α₁ and α₂ for given P and Q may be determined by obtaining values of Vc and δ using equations 16 and 17, and substituting the values into equations 12 and 13.

Table 2 shows the values of Vc and δ with respect to P and Q when a line-to-line voltage is assumed to be 154 kV and a coupling inductance is assumed to be 15% at the base rating of 200 MVA. FIG. 9 is a graph illustrating a variation of α₁ and α₂ with respect to P of table 2 as a function of Q. As shown in FIG. 9, as the reactive power Q shifts from inductive to capacitive value, the values of α₁ and α₂ moves close to 0o axis.

	TABLE 2
	50 MW	100 MW	150 MW
−150	MVar	1.114Vs ∠1.93°	1.120Vs ∠3.84°	1.129Vs ∠5.72°
−75	MVar	1.058Vs ∠2.03°	1.064Vs ∠4.04°	1.074Vs ∠6.01°
0	MVar	1.002Vs ∠2.14°	1.008Vs ∠4.27°	1.019Vs ∠6.34°
75	MVar	0.946Vs ∠2.27°	0.953Vs ∠4.52°	0.964Vs ∠6.70°
150	MVar	0.890Vs ∠2.42°	0.897Vs ∠4.80°	0.909Vs ∠7.11°

As described above, the back-to-back converter 200 consisting of two 36-step converter in accordance with the present invention allows the effective/reactive powers of the interconnected AC system to be controlled independently.

A system operation characteristic and a performance analysis of a controller will now be described using PSCAD/EMTDC for the embodiment of FIG. 7 in accordance with the present invention.

A power circuit in accordance with the embodiment is embodied using circuit elements, switches and transformers. The controller, which is shown in FIG. 10, is embodied using a built-in controller module. Table 3 shows circuit parameters used in the simulation for the embodiment.

TABLE 3
Source Voltage        3Φ 154 kV, 60 Hz
Source Inductance     15.7 mH
DC capacitor          1500 uF
Phase transformer     40 kV/20 kV(Y—Y)
                      40 kV/34.64 kV(Y-Δ)
Auxiliary transformer 32.7 kV/50 kV
System rating         200 MVA

A voltage source HVDC system operates by adjusting a magnitude of a terminal voltage applied to both terminals of the converter for controlling the firing angles, and changing a direction of power. That is, when the power is transmitted from the converter A 200 to the converter B 300 in FIG. 7, the converter A constantly performs a DC voltage control and a reactive power control. When the power is transmitted from the converter B 300 to the converter A 200, an opposite control scheme is performed. Therefore, the controller of each converter has an identical configuration as shown in FIG. 10.

When the converter A 200 transmits the power to the converter B 300, a measured value of DC voltage v_dc follows a reference value v_dc*. A reference value of an effective current I_dA* is obtained from a measured value of an effective current I_dB in the converter B. Measured values of a reactive current I_qA and an effective current I_dB follow a reference value I_qA* and I_dB* through a control algorithm. An AC current controller has an identical configuration to that of the converter generally used in the controller. Reference values of a d-q transformed AC system voltage v_dA* and v_qA* are used to determine the values of V_C and δ. The values of α₁ and α₂ are obtained from V_C and δ using the relationship described in equations 12 and 13.

Table 4 shows a simulation scenario used in an operation analysis of the back-to-back converter in accordance with the present invention.

	TABLE 4
	Mode
	M1	M2	M3	M4	M5	M6	M7	M8	M9
Time(sec)	0.5~1.0	1.0~1.5	1.5~2.0	2.0~2.5	2.5~3.0	3.0~3.5	3.5~4.0	4.0~4.5	4.5~5.0
Vdc*[kV]	60
idA*[A]	Vdc control	330	660
iqA*[A]	0	−500	500
idB*[A]	0	330	330	660	660	990	990	Vdc control
iqB*[A]	0	−950	950	950	−500	−500	500	0
PA[MW]	0	−50	−50	−100	−100	−150	−150	50	100
QA[Mvar]	0	−75	75
PB[MW]	0	50	50	100	100	150	150	−50	−100
QB[Mvar]	0	−150	150	150	−75	−75	75	0

The controller is in operation in 0.5 sec after the simulation starts. It is assumed that the direction of the power is from the system A 200 to the system B 300 between 0.5 sec and 4.0 sec, and the direction is changed from the system B 300 to the system A 200 at 4.0 sec. In addition, the reference values of effective and reactive power are varied according to each of the operation modes from M1 to M9 shown in Table 4 in order to analyze a control performance of the effective and reactive powers.

FIGS. 11 a through 11g illustrate a result of the simulation for verifying the operation of the entire system in accordance with the present invention.

The controllers of the system A 200 and the system B 300 have the same structure, and the control parameters have same values with opposite sign. FIG. 11a shows variations of the power angle δ, the upper firing angle α₁ and the lower firing angle α₂ of the output voltage of the converter A 200, while FIG. 11b shows variations of the power angle δ, the upper firing angle α₁ and the lower firing angle α₂ of the output voltage of the converter B 300. The values of α₁ and α₂ correspond with those shown in FIG. 9 and the value of δ corresponds to that shown in Table 2.

FIG. 11 c shows a variation of an RMS value of the output voltage and a superposed output voltage of the converter A 200, and FIG. 11d shows a variation of an RMS value of the output voltage and a superposed output voltage of the converter B 300. The value of Vc, which is a vector sum of V₁ and V₂, corresponds with that of Table 2. FIG. 11e shows the control performance of a DC link voltage. The DC link voltage is initially charged to 60 kV so that the system may be in operation at 0.5 sec. A measured value of DC link voltage tracks a reference value of 60 kV without excessive transients. FIG. 11f shows a variation of the effective and reactive powers transmitted from the converter B 300 to the AC system B. It is verified that the effective and reactive powers to the system B may be independently controlled. FIG. 11g shows a variation of the effective and reactive powers transmitted from the AC system A to the converter A 200. The value of the effective power is the same as that of FIG. 11f, while the reactive power has a different value since each controller carries out the independent control. Therefore, it may be verified that the DC transmission system in accordance with the present invention is capable of the independent control for the effective and reactive powers.

While the DC transmission system in accordance with the present invention has been particularly shown and described with reference to the preferred embodiment thereof, it will be understood by those skilled in the art that various changes in form and details may be effected therein without departing from the spirit and scope of the invention.

As described above, in accordance with the present invention, the normal transformer is used instead of a tapped transformer to reduce the size thereof and to obtain an accurate transformer ratio, the 3-level half bridge is used instead of the H-bridge to reduce the switching loss in order to increase the number of pulses of the output waveform by superposing the voltage in the form of the pulse using the auxiliary transformer and the bridge circuit.

Moreover, the back-to-back converter system consisting of two 36-step converters allows the independent control of the effective and reactive powers of the connected AC systems.

Claims

1. A converter system comprising: an IGBT converter for converting an AC power to a DC power or the DC power to the AC power;an open Y-Y transformer and a Y-Δ transformer for stepping up or stepping down the AC power having a predetermined magnitude;a capacitor for dividing a DC voltage; anda transformer and a half-bridge auxiliary circuit for overlapping a pulse type input voltage to increase a number of pulses of an output waveform.

2. The converter system in accordance with claim 1, wherein the IGBT converter comprises a first converter connected to the Y-Y transformer and a second converter connected to the Y-Δ transformer, and wherein the capacitor comprises a first DC capacitor connected to a primary side terminal of a transformer of the half-bridge auxiliary circuit and an output terminal of the first converter, and a second DC capacitor connected to the primary side terminal of the transformer of the half-bridge auxiliary circuit and a ground terminal of the second converter.

3. The converter system in accordance with claim 2, wherein a half-bridge of the half-bridge auxiliary circuit comprises a 3-level half-bridge consisting of first through fourth switching elements connected to the first DC capacitor and the second DC capacitor in parallel using an IGBT.

4. The converter system in accordance with claim 3, wherein the transformer of the half-bridge auxiliary circuit comprises a primary side coil and a secondary side coil, the primary side coil being connected between a point where a ground terminal of the first converter and an output terminal of the second terminal are connected and a point where the output terminal of the first converter and the ground terminal of the second converter are connected, and the secondary side coil being connected to the half-bridge such that a difference of output voltages are provided, and wherein the half-bridge of the half-bridge auxiliary circuit comprises a first clamping diode and a second clamping diode, the first clamping diode being connected between a connection point of the first and the second switching elements and a connection point of a second terminal of the primary side coil and a first terminal of the secondary side coil, and the second clamping diode being connected between a connection point of the third and the fourth switching elements and the connection point of the second terminal of the primary side coil and the first terminal of the secondary side coil,whereby a 36-step waveform output voltage is obtained according to a level of a voltage inputted to the transformer of the half-bridge auxiliary circuit.

5. A DC transmission system comprising a back-to-back converter wherein the back-to-back converter includes two of the converter systems in accordance with claim 4, the two of the converter systems being connected to an AC voltage side in serial and connected to a DC voltage side in parallel.