A Controllably Inductive Power Filtering Method For ...

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College of Electrical and Information Engineering, Hunan University, Changsha 410082, China. 2. School of Information ... csuliufang@csu.edu.cn and [email protected]. Abstract—This ... the hybrid active power filtering technology. First, the ...
A Controllably Inductive Power Filtering Method For Large-Power Industrial Rectifier System Qianyi Liu1, Yong Li1, Fang Liu2, Sijia Hu1, Bin Xie1, Longfu Luo1, Yijia Cao1 1. College of Electrical and Information Engineering, Hunan University, Changsha 410082, China 2. School of Information Science and Engineering, Central South University, Changsha 410082, China [email protected] and [email protected] Abstract—This paper proposes a new controllably inductive power filtering (CIPF) method to solve the power quality issues of the large-power industrial DC power supply system. This method is based on the theory of magnetic potential balance and combined with the hybrid active power filtering technology. First, the system topology and the wiring scheme are proposed, and the equivalent circuit model and the mathematical model of the new system are established. Then, the technical features, such as the harmonic suppression nearby the nonlinear loads and the harmonic resonance damping for the grid side, are revealed by means of mechanism analysis. Furthermore, to achieve a better filtering performance, an improved control method is discussed in detail. Finally, according to the design parameters of a practical DC power supply system for electrolytic aluminum loads, the simulation model of the new system is established. The research results validate the theoretical analysis, and indicate that the proposed CIPF method can effectively dampen the parallel/series harmonic resonance at the grid side, and has a better filtering performance than the traditional filtering method. Keywords—Inductive power filtering; harmonic suppression; resonance damping; sensitivity; power quality.

I. INTRODUCTION Due to the technical limitations of the power quality (PQ) management of the chemical industry, metallurgy and other energy-intensive enterprises with nonlinear power loads [1], [2], there are a series of PQ issues to public grid, such as harmonic pollution, low power factor and high operating loss. The passive power filter (PPF) is generally considered as an economic choice for PQ improvement [3], [4] because of its low investment cost. But it can only filter out the considered order harmonics, and the filtering performance will be seriously affected when the harmonic source changes dynamically. By adopting active power filter (APF) method, it can realize the real-time tracking and suppression of harmonic currents [5]-[10]. However, the large-capacity APF has disadvantages of higher investment cost and much maintenance workload to be widely used. In the recent years, an inductive power filtering (IPF) method was proposed for industrial DC power supply system [11]-[13]. The IPF method not only suppresses the harmonic currents but also prevents harmonic current from flowing into the primary winding of the rectifier transformer, which means that it can reduce the effects of harmonic components on the transformer. However, it can be found in practice that the filtering performance is easily affected because of the disturbance and the change of the filtering system parameters.

In order to solve these problems, this paper proposes a controllably inductive power filtering (CIPF) method with a new filtering mechanism. By adding a filtering winding in the rectifier transformer, the harmonic magnetic potential can be balanced between the valve and the filtering winding, and the harmonic leakage flux in the transformer can be reduced greatly. Thus, the effects of the harmonic currents on transformer can be mitigated effectively. Furthermore, the proposed CIPF method can realize the bi-directional suppression of the harmonic currents from the nonlinear load side and the grid side, respectively. This paper is structured as follows. Section II describes the main circuit topology of the new DC power supply system and analyzes the technical features of the proposed the CIPF method. In section III, the special benefits of the CIPF method on harmonic suppression and resonance damping are revealed based on the established equivalent circuit model and the mathematical model. An improved controller is also designed in the section. A detailed case study on a practical system is carried out in Section IV. Finally, the conclusion is given in Section V. II. SYSTEM TOPOLOGY WITH CIPF METHOD Fig. 1 shows the topology of large-power industrial system based on the proposed CIPF method. For each phase, the rectifier transformer consists of a primary (grid) winding with the on-load tap changer (OLTC), a delta (valve) winding, a star (valve) winding and a filtering winding. Both the delta and the star windings of the rectifier transformer adopt co-phase counter parallel wiring scheme, and are connected with the thyristor bridges. All of them constitute the 12-pulse rectifier unit and provide power to the DC load. The filtering winding is connected to the fully-tuned (FT) branches and the voltage-source inverter (VSI) in series. The new industrial DC power supply system with the proposed CIPF has the following technical features: • The harmonic currents flowing into the valve winding from the nonlinear loads and the induced harmonic current on the filtering winding meet the principle of magnetic potential balance at the harmonic frequencies. Hence, there are few harmonic currents in the grid winding, and the harmonic flow path can be limited. • By the virtual impedance control of the VSI, the filtering performance can be further improved and the harmonic resonance at the grid side can be damped.

This work was supported in part by the national Natural Science Foundation of China (NSFC) under Grant 61304092, 51377001 and 51520105011, in part by the Research Fund for the Doctoral Program of Higher Education of China under Grant 20130162120022, and in part by the Innovation Driven Foundation of Central South University under Grant 2016CX013.

978-1-5090-2320-2/16/$31.00 ©2016 IEEE

• Since the FT branch at the fundamental frequency is capacitive, it can nearby compensate the reactive power consumption of the rectifier bridges. The commutation reliability of the rectifiers can be enhanced and the power factor at the grid side can be improved. • To select a reasonable voltage level of the filtering winding, the investment costs of the FT branches, the VSI and the rectifier transformer should be taken into account. Therefore, it has a certain degree of flexibility.

where Ii, Vi (i=1, 2, 3, 4) are the currents or voltages of the primary (grid), the delta (valve), the star (valve) and the filtering winding, respectively; and Zi are the related equivalent impedance. I1 I 2

Zs

VS V1

35kV

N1

Nonlinear load

I3

IL3 N3 V3

N 4 V4

Is

11th 13th

Zf

I4 Rectifier transformer with OLTC

IL2

N 2 V2

FT Branches

If

VSI

VC

FT Branches

Fig. 2. Equivalent circuit model of the new DC supply system

According to the principle of transformer magnetic potential balance and ignoring the transformer exciting current, we can obtain that N1I1+N2I2+N3I3+N4I4=0

VSI

(3)

where Ni (i=1, 2, 3, 4) are the numbers of turns of the primary (grid), the delta (valve), the star (valve) and the filtering winding, respectively.

DC Load

According to Kirchhoff’s voltage law (KVL) and current law (KCL), the following voltage and current equations can be obtained:

Fig. 1. Topology of the new DC power supply system with CIPF method

III. MECHANISM OF CIPF METHOD A. System Modeling Fig. 2 shows the single phase equivalent circuit model of the new industrial DC power supply system. In the model, Is, Vs and Zs are the grid voltages, the system impedance and the grid-side currents, respectively; ILi (i=2, 3) are the load currents; Zf is the parallel equivalent impedance of 11th, 13th FT branches. VC is the AC port voltage of the inverter, which can be expressed as follows: ∞

VC = K ⋅ ¦ I Sn + K R11 ⋅ I f 11 + K R13 ⋅ I f 13

­V1 = Vs − Z s I s ® ¯V4 = Z f I f + KI s

(4)

­ I1 = I s °I = I ° 2 L2 ® I I = L3 ° 3 °I 4 = − I f ¯

(5)

(1)

Equations (1)-(5) construct the mathematical model based on the relationship among voltage, current and impedance of the system with CIPF method.

where K is the harmonic damping control coefficient, which can be equivalent to a virtual resistor in series with the grid; KR11 and KR13 are the zero-impedance control coefficient. The subscript n represents the n-order harmonic.

B. Filtering Characteristics Analysis Converting the load currents of the delta and the star winding to the primary side, it can be obtained that

n=2

According to the theory of multi-winding transformer, the voltage transfer equations of four winding transformer can be obtained as follows

­V1 − V2′ = Z12 I1 + Z2 I3′ + Z2 I 4′ ° ®V1 − V3′ = Z13 I1 + Z3 I 2′ + Z3 I 4′ °V − V ′ = Z I + Z I ′ + Z I ′ 14 1 4 2 4 3 ¯ 1 4

(2)

I L′ =

N N2 I L 2 + 3 I L3 N1 N1

(6)

When considering the filtering characteristics for ILn at valve winding and the harmonic voltage Vsn at grid side, the grid side harmonic current ISn can be expressed as follows

I Sn =

′ ( Z 4 n + Z ′fn ) I Ln Vsn − Z ′fn + Z sn + Z14 n + k14 K Z ′fn + Z sn + Z14 n + k14 K

(7)

From the above (7) it can be found that the grid side harmonic current Isn highly depends on the filtering winding’s impedance parameter Z4n, the FT branches’ total impedance parameter Zfn and the harmonic damping control coefficient parameter K. When there is only FT branches in operation, it can be equivalent to that K=0. If the system parameters changes due to the disturbance, the resonance will be excited easily at norder harmonic frequency. The denominator of formula (7)’s preceding fraction will get a smaller value at n-order harmonic frequency. Then it just only applies a small amount of background harmonic voltage, a lot of grid side harmonic current will be generated. For the latter fraction by the action of ILn, the denominator gets smaller in the same way, which causes the Isn to increase exponentially. If the system adopts the proposed CIPF method and selects an appropriate value of K to make it much larger than the sum of several other denominator, the value of Isn will not change greatly, even though the several other impedance values get smaller because of resonance

To reach resonance state at the considered harmonic order (11th, 13th), the FT branches’ quality factor should be as high as possible, which means the internal resistance of reactance must be approximately equal to zero. It can be achieved by adjusting the zero-impedance control coefficient KRn. C. Sensitivity Performance Analysis The sensitivity functions, which represent the grid side harmonic current against the grid side harmonic voltage or against the valve side harmonic current, can be expressed as ∂I sn 1 = ′ ∂Vsn Z fn + Z sn + Z14 n + k14 K

(10)

( Z 4 n + Z ′fn ) ∂I sn =− ′ ∂I Ln Z fn + Z sn + Z14 n + k14 K

(11)

It can be found from (8) and (9) that the control coefficient K has a great impact on the filtering performance. Fig. 3 shows the spectrums after the implementation of the traditional method (K=0) or the proposed CIPF method (K=20, 40), according to the parameters of a practical DC power supply system for electrolytic aluminum loads.

Without considering the harmonic voltage components at the grid side (Vsn=0), the harmonic current at the grid side can be further simplified, that is I Sn = −

′ ( Z 4 n + Z ′fn ) I Ln Z ′fn + Z sn + Z1n + Z 4 n + k14 K

(8) (a)

From (7), it can be observed that, to eliminate harmonic currents at the grid side, it should satisfy that Z4n+Zfn=0, i.e., Z4n=0, Zfn=0, or K is as large as possible. In the practical transformer’s impedance (Z4=R4+jX4) design, it needs to increase the cross-sectional area of the wire or improve the conductivity of the material to sufficiently decrease the resistance value of R4. By adjusting the short-circuit impedance, the value of X4 can be equal or approximately equal to 0 and a good filtering performance can be guaranteed. Hence, the progress to make Z4 close to 0 needs to adjust and optimize the structure parameters of the transformer. Since the main characteristic harmonics order of the 12pulse rectifier system is 11th and 13th, the corresponding FT branches are designed. Considering the filtering performance, the device configuration and the capacity of inverter, the FT branches can be designed as follows ­ (n 2 − 1)QC °C f = (V 2ω1 )n 2 ° ® 1 °L = °¯ f n 2ω12C f

(9)

where Ȧ1 is the fundamental angle frequency; V is the input voltage of the FT branches; and QC is the capacity of the reactive power compensation.

(b) Fig. 3. Sensitivity analysis of the system with or without CIPF method. (a) Considering Isn against the load side harmonic current ILn; (b) Considering Isn against the grid side harmonic voltage Vsn.

As shown in Fig. 3(a), the sensitivity of the system with the CIPF method is far below the system with the traditional method. The system (K=0) cannot effectively filter out the harmonics far beyond the tuning point. However, the system (K=20, 40), for the harmonic frequency deviating from the tuning point, still presents a low impedance. With the increase of K, the filtering performance will get better, which indicates that the CIPF method can significantly improve the filtering performance of the traditional passive filter. From Fig. 3(b), it can be seen that the sensitivity of Isn against Vsn has been maintained at a low level when adopting CIPF method (K=20, 40). That is to say, the harmonic resonance is hardly excited. Besides, we can also find that the higher the K increases, the lower the percentage of the grid side harmonic current Isn is. On the contrary, the system without the CIPF method (K=0) has an obviously sensitive areas. The harmonic resonance is easily excited and it may cause harmonic current amplification.

Therefore, the CIPF method can effectively reduce the effect of the background harmonic voltage Vsn on the system filtering performance. In general, the impact of system and filter parameters on the CIPF method’s filtering performance is much less than those on the traditional filtering method. D. Control Strategy Fig. 4 shows a block diagram of the control strategy for the CIPF method. It consists of two parts: one for extracting the harmonic component from the grid side current and the other one for extracting the harmonic component at the considered frequency from the passive filter current If. The control object is to regulate the inverter’s output voltage to satisfy the control law (1). Harmonic Damping Control

ω1t

iS a

abc to dq

iS b iSc

id iq

ω1t

_

LPF

id

dq to abc

_

LPF

iq

11ω1t i fa

Vsa Vsb Vsc i fb i fc

PLL

abc to dq

id11 iq11

_

LPF

id11 _

LPF

i q11

iS aiS bi S c -

+

-

ĂĂ

+

VCb

+

-

11ω1t

+

+

VCc

+

+

+

KR11

As described in the section of passive filter parameters design, the n-order FT branch has been well tuned at the norder harmonic frequency, the voltage can be simplified to that

V fn = (rfn + K Rn ) ⋅ I fn

(13)

If KRh is controlled to be equal to -rfn, the voltage on the passive filter is 0, which means the total impedance of the FT branches is 0. The zero-impedance coefficient KRn can be regarded as a virtual negative resistor connected with the reactance in series. In this way, the FT branches’ quality factor is infinite and the filtering performance can be further improved. IV. CASE STUDY To validate the above theoretical analysis, according to the topology and the design parameters of the industrial DC power supply system with the proposed CIPF method, as shown in Fig. 1, the simulation model is established in the environment of MATLAB/SIMULINK.

+

dq to abc

+ + + + +

13ω1t

ω1t i ,i ,i fa fb fc

VCa

K

+

where rfn is a internal resistance of the reactance in the corresponding passive filter.

Zero-Impedance Control

KR11 ⋅ i f 11 KR13 KR13 ⋅ i f 13

(a)

Fig. 4. Block diagram of control strategy for the CIPF method

1) Harmonic damping control Three phase currents (ISa, ISb, ISc) and voltages (VSa, VSb, VSc) at grid side are detected through three AC-CTs. Based on the measured VSa, VSb and VSc, Ȧ1t can be calculated by means of a phase locked loop (PLL), which is used as a reference phase angle in the dq-transformation. As shown in [14] and [15], the dq-transformation is used to real-time calculate the fundamental current component. Then, the detected harmonic components are multiplied with the harmonic damping control coefficient K, a part of the reference voltage can be obtained. The coefficient K can be regarded as a virtual resistor connected with system impedance Zs in series. In this way, the equivalent impedance at grid side is increased, thus the harmonic resonance can be damped. 2) Zero-impedance control Three phase currents (Ifa, Ifb, Ifc) at filtering winding are measured on-line. Using the same way as above, 11- and 13order harmonic components existed in the current flowing into passive filters can be calculated. Then other part of the reference voltage can be obtained by amplifying Ifn with a gain KRn (n=11,13). At h-order harmonic, the voltage on the passive filter is given by

V fn = ( jωn L fn − j

1

ωnC fn

+ rfn ) ⋅ I fn + K Rn ⋅ I fn

(12)

(b)



(c)

(d) Fig. 5. Dynamic responses of the industrial DC supply system with the CIPF method. (a) Grid side current IS ; (b) Load side current IL2 (delta winding); (c) Load side current IL3 (star winding); and (d) Filtering winding side current.

Fig. 5 shows the simulation results. From Fig. 5(a) and (b), it can be seen that the, in the large-power industrial rectifier

system, there are large number of harmonic components on the load winding of the rectifier transformer, due to the nonlinear characteristics of the rectifier bridges. When implementing the CIPF method at 0.2 s, as shown in Fig. 5(c), the content of the harmonic current on the grid winding is reduced significantly, which indicates that the CIPF method can prevent harmonic currents from flowing into the grid winding, thus the current waveform at the grid represents a good sinusoid. Meanwhile, the FT branches with VSI can attract most of the harmonic components from the nonlinear load side, as shown in Fig 5(d). It can be seen from Table I that the current’s total harmonic distortion (THD) has dropped from 10.09% to 0.53% after the implementation of the CIPF method. Therefore, the filtering performance of the CIPF method is outstanding. TABLE I. Condition 6-pulse load 12-pulse load PPF PPF+APF

HARMONIC CONTENT OF THE SYSTEM IN DIFFERENT CONDITIONS I5/% 23.86 0.19 0.28 0.07

I7/% 10.62 0.22 0.59 0.03

I11/% 8.83 8.41 0.35 0.00

I13/% 5.80 4.80 0.12 0.01

THD/% 29.41 10.09 1.82 0.53

Table I gives the corresponding fast Fourier transform (FFT) results. From Table I, it can be seen that the contents of main-order (11th, 13th) harmonic currents are reduced greatly after the implementation of passive filter. On the other hand, the contents of 5th, 7th harmonic currents are increased 1.47 times and 2.68 times at the same time, respectively. It indicates that the harmonic resonance between the grid’s and the filter’s impedance is excited. Further, when using the CIPF method after 0.2s, this phenomenon is obviously disappeared. The content of the 5th, 7th, 11th, 13th harmonic currents are reduced by more than 60%, especially the 11th and 13th harmonic current. The simulation results are consistent with the theoretical analysis (see section III). The new DC supply system with proposed CIPF method can dampen the harmonic resonance effectively. V. CONCLUSION In this paper, a CIPF method is proposed to improve the power quality of the large-power industrial DC power supply system. Based on the proposed method, a new main circuit topology for the DC power supply system is presented, which mainly includes a new rectifier transformer integrated FT branches with a controlled VSI in series. The equivalent circuit model and the mathematical model of the new system are established to obtain the realization condition of the CIPF method and reveal the mechanism of harmonic suppression and harmonic resonance damping. In order to achieve the aim of harmonic resonance damping and zero-impedance design, a special control strategy is presented. Both the theoretical and the simulation results indicate that, by means of the CIPF method, the harmonic currents can be greatly suppressed nearby the nonlinear load side, and there are few harmonic components in the primary winding and at the grid side. Moreover, by means of the VSI control, the filtering performance of the inductive filtering can be further improved

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