Damped-Type Double Tuned Filters Design for HVDC Systems M. A. Zamani Faculty of Engineering Islamic Azad University of Abadan Abadan, Iran
[email protected] Abstract- The ac/dc filters are always needed in HVDC converter stations to suppress harmonic currents/voltages. The ac side filters are also employed to compensate network requested reactive power. Among different types of filters, double tuned passive filters have been widely utilized in HVDC stations, yet these filters are still not considered well developed. This paper presents an algorithm for design of the conventional and damped-type double tuned filters to reduce harmonic distortion and improve power factor in electrical systems. Firstly, the conventional double tuned filters are comprehensively studied, and an algorithm for precisely determining the parameters of this type of filters is presented. Next, the proposed design algorithm is developed for damped-typed double tuned filters. Using this method, the parameters of damped-type double tuned filters are calculated based on the tuned frequencies, the parallel resonance frequency, and the reactive power compensation capacity etc. Finally, the performance of the design algorithm is tested for a 6-pulse HVDC converter simulated on the MATLAB. The results clearly show the effectiveness of proposed design method in harmonics elimination and power factor correction. Keywords- HVDC converters, harmonics, filter design, dampedtype double tuned filters.
I. INTRODUCTION HVDC converter stations usually require ac/dc filters, the main purpose of which is to mitigate current/voltage distortion in the connected networks. In addition, the ac side filters significantly compensate the network demanded reactive power [1-2]. Recently, the passive double tuned filters are widely used as ac/dc side filters. The main advantages of employing double tuned filters over the single tuned filters are one reactor subjected to full line voltage, occupying less space, and needing to only one switchgear etc [2-3]. Two different types of double tuned filters are the conventional type and the damped-types, as respectively shown in Fig. 1 and Fig. 2. Several methods have been proposed for passive harmonic filters design. Turkey suggested a simple method for designing
M. Mohseni Department of Electrical Engineering Shahid Chamran University Ahvaz, Iran
[email protected] of passive filters and tested them in a cement factory [4]. Makram presented the application of the Z-bus method for economic passive filter design and analyzed the steady and transient states of filters [5]. Chang introduced three NLP mathematical formulations for designing a group of single tuned filters for both harmonic current/voltage reduction and power factor correction [6]. Joorabian proposed an algorithm for designing single tuned and high pass filters with considering several different criteria [7]. Nevertheless, most of literatures mainly focused on single tuned passive filters, and the double tuned filters are still not considered well developed. Lastly, a simple method of double tuned filter design is presented by Yao, but this method does not consider several practical constraints of passive filters design [8]. This paper is divided into six sections. In Section II, the essential equations of HVDC converters needed for the filter design are established. Section III and IV respectively presents the design algorithm of conventional and damped-type double tuned filters. The proposed design algorithm is oriented to improve both power quality and power factor of electrical network. Furthermore, some design considerations such as the reduction of resonance probability, permitted individual harmonic voltage, and minimum power losses are considered in this design algorithm. In Section V, the design method is assessed for a typical HVDC converter simulated on the MATLAB. The results confirm great performance of the design algorithm in power quality and power factor improvement. Finally, the paper is concluded in section VI. C1 L1 C2
L2
Fig.1 Conventional double tuned filter
C1
C1
C1
L1
R
L1
C2
L2
L1 R
R
C2
L2
C2
L2
(a)
(b)
(c)
C1
C1
C1
L1
C2
L1
L1
R1
R1
L2
C2
R (d )
L2 R2
(e)
C2
L2 R 2 (f)
Fig.2 Different configurations of damped-type double tuned filters
II. HVDC EQUATIONS Basically, an HVDC system consists of two converter stations connected by a dc overhead line or an underground (or submarine) cable. During the operation of converters (rectifiers or inverters), harmonic voltages and currents will be flowed on dc and ac sides, respectively. A converter of pulse number P generates harmonic currents/voltages of order Pk ± 1 / Pk , k = 1, 2, 3, ... . The current harmonics on the ac side of a 6-pulse converter will be of orders n= 5, 7, 11, 13, … , which called characteristic harmonics. These current harmonics flow through the plant and utility power system and cause voltage distortion and power losses in the system. They also interact with power factor correction capacitor banks leading to equipment failures. Besides, the non-ideal conditions may lead to the generation of another harmonics with different orders, but these non-characteristic harmonics cannot significantly affect the power quality. Fortunately, the amplitudes of generated characteristic current harmonics decrease with increasing harmonic order. It can be shown that the amplitude of an ac harmonic current of order n , i.e. In is less than I1/n, where I1 is the amplitude of the fundamental current [2]. The exact rms value of In with considering overlap is equal to F ( n) In = I1 (1) nD where (2) D = cos(α ) − cos(u ) sin[(n − 1)u / 2 2 sin[(n + 1)u / 2] 2 ) ) +( F (n) = {( n −1 n +1 (3) sin[(n − 1)u / 2]. sin[(n + 1)u / 2] 12 ). cos( 2 α )} u + − 2( n 2 −1
, and α and u are the control and overlap angles. Eq. (1) is valid only for characteristic harmonic orders when the overlap angle does not exceed 60o . In the case of 60 o < u < 120 o , α > 30 o , and u + α < 150o , α and u in (1) - (3) are replaced by α ′ and u′ , where , α ′ = α − 30 u′ = u + 60 (4) If internal converter losses are ignored ( Pdc = Pac ) , the amplitude of I1 in (1) is equal to Pdc Vd I d I1 = = (5) 3VL cos ϕ 3VL cos ϕ where, Pdc is the dc side power (MW), Vd and Id are the average dc voltage (kV) and current (kA), respectively. Also, VL and cos ϕ are the line-to-line ac voltage (kV) and power factor of the network. The demanded reactive power of an HVDC converter is often expressed in terms of the active power of dc side, i.e. Q = Pdc . tan ϕ (6) where ϕ is the phase difference between the fundamental frequency voltage and current components, so tan ϕ is equal to sin(2α + 2u ) − sin( 2α − 2u ) (7) tan ϕ = cos(2α ) − cos(2α + 2u ) Using (6)-(7), the demanded reactive power of HVDC converters can be calculated. III. CONVENTIONAL DOUBLE TUNED FILTER DESIGN The conventional double tuned filters comprise a series resonance circuit and a parallel resonance circuit, as shown in Fig.1. The series circuit impedance is 1 ) (8) Z s (ω ) = J ( L1ω − C1ω where ω=2πf is the angular frequency in radian. Hence, the series resonance frequency will be equal to 1 (9) Z (ω s ) = 0 ⇒ ω s = L1C1 On the other hand, the parallel circuit impedance is 1 Z p (ω ) = ( − JC2ω ) −1 (10) JL2ω and the parallel resonance frequency will be 1 (11) Z (ω p ) = 0 ⇒ ω p = L2 C 2 The Thevenin impedance of a conventional double tuned filter is, thereby, calculated through the summation of series and parallel circuits’ impedances. This Thevenin impedance is a function of frequency, and it will be equal to zero for tuned frequencies. Consequently, the tuned frequencies (ω1 , ω 2 ) are derived from
Providing a part of the demanded reactive power is another purpose of the double tuned filters application in HVDC converter stations [7,9]. The generated reactive power of double tuned filter is V2 (19) Q= Z (ω0 )
Fig.3 The characteristic of the conventional double tuned filter
Z (ω0 ) = Z s (ω0 ) + Z p (ω0 )
Z (ω ) = Z s (ω ) + Z p (ω ) = J ( L1ω −
1 1 )+( − JC 2ω ) −1 = 0 C1ω JL2ω
(12)
Eq. (12) can be rewritten as ω 4 L1L2C1C2 − ω 2 ( L2C1 + L1C1 + L2C2 ) + 1 = 0 (13) Using Vida's theory, the of (13) can be calculated by 1 1 ω1 .ω 2 = . = ω s .ω p (14) L1C1 L2 C 2 The filter impedance versus frequency curve Z(ω) for a conventional double tuned filter is illustrated in Fig.3 [8]. It is clear that the characteristic of the double tuned filter is capacitive over the some frequencies e.g. fundamental frequency, and filter can provide reactive power in these frequencies. Since the filter Thevenin impedance at the tuned frequencies is zero, the harmonic currents of tuned frequencies orders (ω1, ω2) will be suppressed by filter. These tuned frequencies are determined based on the filtering project requirements. Further, the filter impedance is infinite at the parallel frequency (ωp), so engineer should take account of the network characteristics and select a parallel resonance frequency properly in designing procedure to prevent some harmonic current near ωp from being amplified. Once ω1, ω2 and ωp are determined, ωs can be precisely calculated by (14). Substituting (9) and (11) into (13) yields C 1 ω4 1 1 (15) −( 1 . + 2+ )ω 2 + 1 = 0 2 2 2 C2 ω ωs ω 2 ω .ω s
p
p
p
The ω1 is one of the roots of (15), so replacing ω by ω1 leads to the following equation between C1 and C2 2 2 2 C1 ω1 + ω 2 − ω p = −1 (16) C2 ω s2 Also, using (9) and (11) yield two other equations for L1 and L2 parameters calculation as ωp 2 1 (17) L1 = ( ) . ω1.ω2 C1 and
L2 =
ω12 + ω22 − ω 2p 1 1 = 2 ( − 1) ω p C2 ω p .C1 ωs2 1
. 2
where V is the network fundamental rated ac voltage, ω0 is the fundamental frequency in radians and Z(ωo) is the filter impedance at the fundamental frequency. According to (12), Z(ωo) is equal to
(18)
1 1 −1 ) − J (ω0C2 − ) ω0C1 ω0 L2 From (19)-(20), the C1 parameter is obtained by = J (ω0 L1 −
(20)
⎛ ω p 2 1 ω0 (ω12 + ω22 − ω 2p )ω 2p − ω12ω22 ⎞⎟ Q + C1 = ⎜ ω0 ( ) − ⎜ ⎟U2 ω1ω2 ω0 ω12ω22 (ω 2p − ω02 ) ⎝ ⎠ (21) To summarize, in HVDC stations with known network voltage (V) and demanded reactive power (Q), when tuned frequencies (ω1, ω2) and the parallel resonance frequency ωp are determined, the parameters of the conventional double tuned filter, (L1, L2) and (C1, C2), can be designed based on (17, 18) and (16, 21).
IV. DAMPED-TYPE DOUBLE TUNED FILTER DESIGN Thevenin impedance of conventional double tuned filters is almost devoid of resistance component. Thus, if the power system reactance and the filter impedance are conjugate, the network resonance will take place. This phenomenon causes severe overvoltage harmonics on the filter and other power system components. To prevent network elements from exposing to this harsh condition, damping resistors are added to the conventional double tuned filter in different configurations. This type of filters, as shown in Fig. 2, is called damped-type double tuned filter. The comprehensive study of all damped-type configurations is presented in [8] thus not repeated here. The most widely-used configuration of damped-type filters is shown in Fig. 2(a). Although this configuration is considered for filter design in this study, the proposed design method can be successfully applied for design of all filter configurations depicted in Fig. 2. In other word, the proposed method is not restricted by the configuration of installed damped-type double tuned filter. The characteristics of different damped-type double tuned filters are almost alike, and all of them avoid harmonic voltages from being rigorously amplified during the network resonance situations. In fact, since the impedance of this type of filters at parallel resonance frequency ωp is finite, the network resonance is prevented form happening. The harmonic impedance Zn for configuration Fig. 2(a) is
Y /∆
Fig. 4 Simulated HVDC converter on the MATLAB
Z n (ω ) =
R ( L2nω ) 2 ( L2nω ) + R 2 (1 − L2C2n 2ω 2 ) 2 2
1 L2nωR 2 ) + J ( L1nω − + 2 C1nω ( L2nω ) + R 2 (1 − L2C2n 2ω 2 ) 2
(22)
Through studying impedance-frequency characteristic of this double tuned filter and also other configurations, it is observed there are three pairs of tuned frequencies in this type of filters, which are: i. The minimum impedance frequencies, ωz1 and ωz2; ii. The zero reactance frequencies, ωx1 and ωx2; iii. The desired tuned frequencies of the double tuned filter by ignoring the resistance R component, ω1 and ω2. Indeed, while ω1 and ω2 are used to calculate the filter parameters, the damped-type double tuned filter practically suppresses ωz1 and ωz2 or ωx1 and ωx2 frequencies components. The proposed filter design algorithm for damped-type double tune filter is graphically represented in Appendix A. According to that diagram, the resistance R is initially assumed regarding to the network data and demanded reactive power compensation capacity. The sort of tuned frequencies are then chosen between the minimum impedance and zero reactance tuned frequencies. Next, filter parameters, (L1, L2) and (C1, C2), are calculated based on the chosen tuned frequencies (ω1, ω2) and (16-18, 21). In the following step, the practical tuned frequencies of filter, ( ω z1, ω z 2 ) or ( ω x1, ω x 2 ), are calculated when the resistance R is take into account. If the difference between the practical and desired tuned frequencies is more than the permitted design error, the filter parameters are recalculated by modifying tuned frequencies (ω1 , ω2). Afterwards, the design procedure is pursued by n’th filter individual harmonic voltage calculation as Vh = Vn2 + V(2n + 2)
, V n = Z n .I n
(23)
where, In is n’th harmonic current given by (1). The value of R will be changed if individual harmonic voltages (Vh) are
more than the permitted level of IEEE Std. 519 [10]. Finally, the performance of filter design is inspected by considering the network characteristics and other installed filters. If the results are not satisfying, the resistances should be modified and the algorithm will be repeated for new R values. V. SIMULATION RESULTS In this section, a 6-pulse HVDC converter with Y / ∆ transformer connection is simulated on the MATLAB, as shown in Fig. 4. The system parameters are given in Table. I. Considering (6)-(7), the total demanded reactive power of the simulated converter is equal to 72.3 MVar. Fig. 5 shows the ac current/voltage waveforms of the simulated system when the requisite reactive power is completely supplied by compensators and no passive filter is installed. The harmonic spectral diagram of the resulted current is shown in Fig. 6. It is clearly seen that the harmonic components of the current signal are considerable. Next, two damped-type double tuned filters are employed for harmonic suppression and power factor correction. While two filters tuned frequencies are (5,7) and (11,13), the compensated reactive power of each filter is considered equal to 24MVar. Except 48Mvar supplied by two double tuned filters, the high-pass filter is designed to provide 12MVar fundamental reactive power [7]. Rest of the demanded reactive power is provided by compensators. The parameters of two damped-type double tuned filters are calculated by the proposed algorithm and based on the above data, as given in Table II. After the designed filters installation, current/voltage harmonics components are majorly suppressed. The resulted current/voltage waveforms and spectral diagram of current under these circumstances are shown in Fig. 7 and Fig. 8. Fig. 8 also depicts the IEEE Standard allowable amplitude of all individual harmonic components. Further, the practical generated reactive power by double tuned filters is almost 47.4MVar, which implies only %0.75 deviations from the desired value.
TABLE I SIMULATED SYSTEM SPECIFICATION
Line Voltage of the AC network (KV) Frequency (Hz) Commutation reactance (P.U.) Control angle α (deg.) Maximum freq. Deviation (δ m )
132 50 0.12 5 0.01
TABLE II THE DOUBLE TUNED FILTERS PARAMETERS (R=2740 Ω ) Filter order
L1 (mH )
L2 (mH )
C1 ( µ f )
C2 ( µ f )
5,7 11,13
70.21 16.39
7.75 0.455
4.24 4.35
36.32 154.7
Fig.8 Spectral diagram of AC current with filters
VI. CONCLUSION
Fig.5 AC current/voltage waveform without filters
Due to the merits of the double tuned filters, these filters are widely used in HVDC filtering projects. After a short discussion on HVDC system, this paper firstly presents a simple and precise design algorithm for determining the parameters of conventional double tuned filters. Then, the proposed design algorithm is developed for damped-type double tuned filters. In this algorithm, the filter parameters are calculated based on tuned and parallel resonance frequencies, requested power factor correction, permitted individual harmonics voltage etc. Lastly, the proposed filter design method is used for harmonic elimination and reactive power compensation of a 6-pulse HVDC converter. Simulation results show the significant improvement of both power quality and power factor achieved by appropriate passive filters design. REFERENCES
Fig.6 Spectral diagram of AC current without filters
Fig. 7 AC current/voltage waveforms with filters
[1] CIGRÉ WG 14-30. “Guide to the Specification and Design Evaluation of AC Filters for HVDC Systems,” Technical Brochure 139, April 1999. [2] E. W. Kimbark, Direct Current Transmission, John wiley & Sons, 1971 [3] J. Arrillaga, D. A. Bradley, and P. S. Bodger, power system harmonics, John Wiley & Sons, 1985. [4] B. Turkay, “Harmonic filter design and power factor correction in a cement factory”, IEEE Porto power tech conference, Sep. 2001. [5] E. B. Makram et al, “Harmonic filter design using actual recorded data”, IEEE Trans. on Indusry Applications, Vol.29, No.6, Nov./Dec. 1993 [6] H. Cheng, H. Sasaki and N. Yorino, “A new method for both harmonic voltage and harmonic current suppression and power factor correction in industrial power system”, IEEE paper 1995, Serial No. 0-7803-2479-x/95/. [7] M. Joorabian, S. GH. Seifossadat and M. A. Zamani, “An algorithm to design harmonic filters based on power factor correction for HVDC systems”, Proc. IEEE International Conference on Industrial Technology, India, Dec. 2006. [8] Xia Yao, “algorithm for the parameters of double tuned filter”, IEEE International Conference on Harmonic and Quality of Power, Greece, Oct. 1998. [9] J. C. Dos, “Passive Filters-Potentialities and limitations”, IEEE Trans. on Industry Applications, Vol. 40, No. 1, Jan./Feb. 2004. [10] IEEE Std 519-1992, “IEEE Recommended and Requirements for Harmonic Control in Electrical Power Systems”.
Appendix A. Algorithm of the damped-type double tuned filters design
Select the damped-type double tuned filter configuration and inputs: - The rated system voltage ( V ) - The compensated reactive power of filter (Q) - The filter parallel resonance frequency (ωp ) - The filter desired tuned frequencies (ω2, ω1) - Permitted design error ( εm ) - The filter resistance(s) value
- Select the pair of tuned frequencies between (ωx1,ωx2) and (ωz1,ωz2) - Suppose ω1(1)=ω1 and ω2(1)=ω2
- Calculate double tuned filter parameters, (L1, L2) and (C1, C2), based on (17, 18) and (16, 21)
- Calculated the practical tuned frequencies (ωx1,ωx2) or (ωz1,ωz2) with taking into account the resistance R
⎧∆ω1( j ) = ω1 − ω(z1j ) and ∆ω(2j ) = ω2 − ω(z2j ) ⎪ −⎨ or ⎪ ( j) ( j) ( j) ( j) ⎩∆ω1 = ω1 − ωx1 and ∆ω2 = ω2 − ωx2
ω1(j+1) =ω1(j)+∆ω1(j) ω2(j+1) =ω2(j)+∆ω2(j)
{
− ε = max ∆ω1( j ) , ∆ω(2j )
No
}
ε < εm Yes
- Calculate all individual harmonic voltage
- Modify the resistance(s) value
Vn = Z n I n , Vh =
No
V n2 + V (n2 + 2)
Vh < Vh(std) Yes
- Check the filter band pass and other performances by considering the network characteristics and other installed filters
No
Confirmed ?
Yes Stop
