This paper introduces a novel topology and an effective control strategy for a shunt hybrid power filter (SHPF) to simultaneously compensate harmonic currents and reactive power. The proposed SHPF topology is composed of an
LC
passive filter tuned to the 7
^{th}
harmonic frequency and a smallrated active filter connected in parallel with the inductor
L_{pf}
of the
LC
passive filter. Together with the SHPF topology, we also propose a control strategy, which consists of a proportionalintegral (PI) controller for DClink voltage regulation and a PI plus repetitive current controller, in order to compensate both the harmonic current and the reactive power without the need for additional hardware. Thanks to the effectiveness of the proposed control scheme, the supply current is sufficiently compensated to be sinusoidal and inphase with the supply voltage, regardless of the distorted and phase lagging of the load current. The effectiveness of the proposed SHPF topology and control strategy is verified by simulated and experimental results.
1. Introduction
Nowadays, the use of power electronics devices such as diode rectifiers, adjustable speed drives, power supplies, and large air condition systems, are becoming increasingly popular. These devices are nonlinear loads that generate harmonic currents and reactive power in distribution power systems. High current harmonic distortion leads to various problems in both distribution systems and consumer products, including equipment and transformer overheating, malfunction of protection devices, reducing power system efficiency. High reactive power consumed by loads may increase power losses and lower network stability. Therefore, compensation for harmonic current and reactive power is a mandatory requirement for system operators and end users.
Traditionally,
LC
passive filters have been used to suppress current harmonics in distribution power systems due to their low cost and simplicity. However, they have many problems, such as low dynamic performance and resonance problems, and their filtering characteristics can be easily affected by system parameters
[1]
. Active power filters (APFs) have been developed to overcome the disadvantages of
LC
passive filters
[2

5]
. APFs can offer flexible control functionalities, but their high initial and operational costs are the main barriers that limit their application in practice.
To provide a costeffective solution for harmonic current compensation in power distribution systems, various shunt hybrid power filter (SHPF) topologies composed of active and passive parts have been introduced
[6

15]
. Among these approaches, SHPFs with tuned passive filters connected in series with a smallrated active filter are popularly utilized for harmonic current compensation. The main advantages of these SHPF topologies are the low operating DClink voltage, reduced number of passive components, and small size and volume thanks to the absence of coupling transformers
[6

9]
. Unfortunately, due to the series connection of passive and active parts, this type of SHPF can supply only a fixed amount of reactive power; it is unable to perform a dynamic reactive power compensation function when the load changes. To overcome this limitation, several novel SHPF topologies have been proposed to simultaneously take into account the harmonic currents and the reactive power
[10

14]
. In
[10

12]
, additional passive components, such as capacitors, inductors, or coupling transformers, were inserted into the typical SHPF to improve harmonic current and reactive power compensation capability. However, these approaches required additional hardware, which degraded the costeffective advantage of the SHPF. In
[13]
, an enhanced control algorithm for SHPF was proposed to compensate harmonic current and reactive power. The suggested control method was able to fulfill the control target, but the control algorithm was very complex with many control stages. A combination of an SHPF and a thyristorcontrolled reactor was introduced to perform both harmonic current and reactive power compensation functions
[14]
. The control method was simple and effective, but the demand of extra hardware was again a drawback of this method.
To overcome the limitations of previous SHPF topologies, this paper proposes a new SHPF topology and an effective control strategy, introduced succinctly in
[15]
, to simultaneously achieve the harmonic current and reactive power compensation. The proposed SHPF is composed of an
LC
passive filter tuned at the 7
^{th}
harmonic frequency and a smallrated APF, where the APF is connected in parallel with the inductor
L_{pf}
of the
LC
passive filter. In the proposed configuration, the control strategy is developed to compensate both the harmonic current and the reactive power without the need for additional hardware. The proposed algorithm applied to the SHPF consists of a proportionalintegral (PI) controller for DClink voltage regulation and a PI plus repetitive current controller for harmonic current and reactive power compensation. The supply current after compensation is almost sinusoidal with very low THD and is inphase with the supply voltage with an almost unity power factor (PF). In this paper, we present the analysis and design of the proposed SHPF topology and the proposed control strategy in detail. The effectiveness of the proposed SHPF topology and control strategy is verified through comparative simulations and experimental results.
2. Proposed Control Strategy for SHPF
 2.1 Configuration of a typical SHPF
Fig. 1
shows the configuration of a typical SHPF topology. The SHPF is composed of an
LC
passive filter connecting in series with a smallrated APF. This type of SHPF is popularly used because it requires a small number of passive components and it can lessen the DClink voltage of the APF, which results in a lower system cost for the SHPF system. However, due to the series connection of the passive and active parts, the APF can only supply a fixed amount of reactive power, so dynamic compensation of reactive power with load changes is unable to be achieved.
Typical shunt hybrid power filter
 2.2 The proposed SHPF
To overcome the limitation to reactive power compensation of the typical SHPF configuration, shown in
Fig. 1
, this paper develops a new SHPF topology, shown in
Fig. 2
. In this SHPF topology, the active part is connected in parallel with the inductor
L_{pf}
. Thanks to the parallel connection of passive and active parts, dynamic compensation for the reactive power of the SHPF can be achieved. In addition, low DClink voltage of the APF is still realized because of the APF connected with the system through the capacitor
C_{pf}
.
The proposed shunt hybrid power filter
3. Analysis and Control of the Proposed SHPF
 3.1 Equivalent circuit of proposed SHPF
In the equivalent model of the proposed SHPF, illustrated in
Fig. 3
, the APF is considered as a controllable voltage source
v_{APF}
, and the load is regarded as a current source
i_{L}
. From
Fig. 3
, the voltage and current equations of the system are determined as
Control strategy for proposed SHPF
From (1), the harmonic components in the supply current can be determined from the load current and supply voltage as
where
and
Z_{HPF}
=
X_{Cpf}
+
X_{Lpf}
/ /
X_{Laf}
.
From (2) and (3), assuming that the supply voltage harmonics are very small, the supply current waveform mainly depends on the parameters of the passive filters and the controller function of the APF,
K_{p}
. As a consequence, to compensate the harmonic components in the supply current, the designs of the passive components and the controller play equally vital roles.
 3.2 Design of passive components
In the SHPF,
C_{pf}
and
L_{pf}
together operate as a passive filter to sink a specific, e.g., the 5
^{th}
or 7
^{th}
, harmonic current generated by the nonlinear loads. In this paper,
C_{pf}
and
L_{pf}
are tuned to absorb the 7
^{th}
order harmonic current (
h_{1}
=7). The reason we select the 7
^{th}
harmonic is that the volume and cost of
C_{pf}
and
L_{pf}
are lower for the 7
^{th}
than for the 5
^{th}
harmonic frequency
[6]
.
where
f_{s}
denotes the fundamental frequency of the system, which is 60 Hz in this paper.
In addition,
C_{pf}
can also supply a part of the reactive power demanded by the load, which is calculated as
where V
_{ll(RMS)}
=208 V is the RMS value of the linetoline voltage in this paper.
From (5), we can see that a higher value of
C_{pf}
will compensate a larger amount of reactive power. However, since reactive power can also be compensated by an active filter, in order to reduce the volume of capacitor
C_{pf}
, we choose
C_{pf}
to be only 50% of the base capacitance of the system
C_{b}
[6]
, where
C_{b}
is defined as
where
P_{L}
= 5 kW is the rating power of load.
Therefore,
The closest commercial capacitance is chosen, i.e.,
C_{pf}
= 75
μF
.
From (4), we can obtain
L_{pf}
as
 3.3 Control strategy for proposed SHPF
In the previous section, the passive filter was designed to compensate the 7
^{th}
harmonic and a fixed amount of the reactive power demanded by the load. The other harmonic components and the remaining reactive power should be compensated by the APF. The proposed control strategy, shown in
Fig. 4
, consists of four parts: DClink voltage control, harmonic compensation, reactive power compensation, and current regulation. In this case, the SHPF is operated autonomously without an external power supply. Therefore, a DClink voltage controller developed based on a proportionalintegral (PI) controller is used to regulate the DClink voltage of the APF. The output of this control loop is the reference current in the daxis
. This reference current is added to the reference current of the harmonic compensation scheme. Meanwhile, in the harmonic compensation block, the threephase supply current is measured and transformed to the synchronous (
dq
) reference frame through an
abcdq
transformation, as follows
Control strategy for proposed SHPF
Then, the highpass filter (HPF) given in (10) is applied to extract the harmonic components from the supply current, which becomes the reference current signal
.
where
ω_{p}
= 2
π
⋅10 (rad/s) is the selected passing frequency of the HPF.
Reactive power compensation can be achieved easily by using a reference current along the qaxis of
. After finding the reference current for the current controller, the measured supply current is compared with its reference value, and the error is fed into the PIrepetitive controller (RC) to generate the control signal for the APF. The transfer functions of the RC in continuous and discrete time are
where
N
=
T_{d}
/
T_{s}
is the number of delay samples, which is an integer,
T_{s}
is the sampling period,
Q
(
z
) is a filter transfer function,
K_{r}
is the RC controller gain, and
z^{k}
is a phase lead term to compensate the phase lag caused by plant
G_{p}
(
z
).
 3.4 Design of repetitive current controller
To design the RC in (11), three components are considered: the filter
Q
(
z
), the phase lead term
z^{k}
, and the RC controller gain
K_{r}
. First, we have to determine the filter
Q
(
z
) that is used to improve the system stability by reducing the peak gain of the RC in the highfrequency range. Then, the phase lead term
z^{k}
is designed to compensate the phase lag caused by the control plant to achieve better harmonic compensation performance of the RC. Finally, the RC’s controller gain
K_{r}
is chosen based on the system stability condition in (14).
3.4.1 Selection of the filter Q(z):
Q
(
z
) is used to improve the system stability by reducing the peak gain of the RC in the highfrequency range. There are two popular methods used in previous studies to employ
Q
(
z
): a closed unity gain
Q
(
z
)=0.95 and a zerophase LPF
Q
(
z
) = (
z
+ 2 +
z
^{−1}
) / 4
[16]
,
[17]
. In this study, these two types of
Q
(
z
) are also adopted, and the Bode diagrams of the RC for each
Q
(
z
) are plotted in
Fig. 5
in order to determine a suitable
Q
(
z
) for the RC. In
Fig. 5
, when
Q
(
z
)=0.95, the RC provides high gain over the entire frequency range, so the system becomes unstable due to the high gain in the highfrequency region. In contrast, for
Q
(
z
) = (
z
+ 2 +
z
^{−1}
) / 4, the gain of the RC is high at loworder harmonics, but it reduces to significantly less than 0 dB in the highfrequency range (above 2 kHz). It is wellknown that a low peak gain in the highfrequency range can ensure a robust system. Furthermore, in contrast to the typical firstorder LPF, a zerophase LPF does not shift to the original position of the RC peak gain. Therefore, the use of this zerophase LPF does not have an impact on the RC accuracy; thus, we choose
Q
(
z
) = (
z
+ 2 +
z
^{−1}
) / 4.
Bode diagram of the PIRC controller with Q(z) = 0.95 and Q(z) = (z + 2 + z^{−1}) / 4.
3.4.2 Determination of the phaselead term z^{k}
:
Because the control plant
G_{p}
(
z
) commonly acts as a lowpass filter, which introduces some phase lag, a phaselead term
z^{k}
is needed to compensate the phase lag of
G_{p}
(
z
), and
k
is selected to minimize the phase displacement of , where
G_{p}
(
z
) is the inductor
L_{af}
.
Fig. 6
shows the Bode diagram of
G_{p}
(
z
)
z^{k}
with respect to different values of
k
. From
Fig. 6
, we select
k
=5 because it provides the minimum phase displacement near the dominant harmonics, such as the 5
^{th}
, 7
^{th}
, 11
^{th}
, and 13
^{th}
, and system stability is guaranteed up to the 37
^{th}
harmonic component at a frequency of 2.22 kHz. Furthermore, to remove the effect of delay time due to digital control in the experimental implementation,
k
=6 is used.
Phaselag compensation for different values of k.
3.4.3 Determination of the controller gain K_{r}:
To investigate the stability condition of the RC and to determine the controller gain
K_{r}
, the tracking error of the RC with respect to the reference value is defined as
Let
H
(
z
) =
Q
(
z
) −
K_{r}z^{k}G_{p}
(
z
). Based on the small gain theorem
[17]
, the repetitive control system is sufficiently stable if the vector
H
(
e^{jωTs}
) locates within the unity circle. Consequently, the stability condition of the repetitive control system is given as
ω
∈ [0,
π
/
T_{s}
], where
π
/
T_{s}
is the Nyquist frequency
The controller gain
K_{r}
is determined to satisfy the stability condition given in (14). To select the proper value for
K_{r}
, the loci of the vector
H
(
e^{jωTs}
) is shown in
Fig. 7
with respect to different values of
K_{r}
. It can be observed that the vector
H
(
e^{jωTs}
) is located inside the unity circle; i.e., the system is stable if
K_{r}
is less than 1.2. In fact, a large
K_{r}
offers a better steadystate performance as well as faster response but limits the stability margin of the system at the same time. Therefore, to guarantee a sufficient stability margin, we select
K_{r}
=0.8.
Loci of the vector H(e^{jωTs})
4. Simulation results
To verify the effectiveness of the proposed control strategy for the SHPF, a simulation model is built in the PSIM software. The system parameters are given in
Table 1
. In the simulation system, the load consists of a threephase diode rectifier (nonlinear load) and a threephase
RL
(linear load) with total harmonic distortion (THD) and power factor (PF) of the load current of about 17.4% and 0.746, respectively. The SHPF is installed to compensate the harmonic current and the reactive power, and so the supply current can be compensated so that it is sinusoidal and inphase with the supply voltage.
System parameters
Fig. 8
shows the simulation results of the traditional SHPF topology using the control strategy introduced in
[6]
, where reactive power compensation is not considered. It can be observed in
Fig. 8
that the supply current can be compensated for such that it is almost sinusoidal despite the distorted load current waveform. The THD of the supply current after compensation is about 3.27%. However, because the reactive power is not considered and compensated for, the supply current is lagged compared to the supply voltage with a power factor (PF) of 0.85. The THD of the supply current is greatly reduced, but its PF cannot be significantly improved because the reactive power is not taken into account in the conventional control system.
Simulation results of traditional SHPF without reactive power compensation
These limitations of the traditional control method can be overcome by the proposed SHPF topology and control strategy, as demonstrated by the simulation results shown in Fig. 9. In Fig. 9, the supply current after compensation is almost sinusoidal and is inphase with the supply voltage. The THD and PF of the supply current after compensation are about 1.47% and 0.997, respectively. These results verify the feasibility of the proposed SHPF scheme for harmonic current and reactive power compensation.
In addition to a good steadystate performance, a dynamic response of the SHPF to load changes is also an important factor. To assess the dynamic performance of the SHPF, simulation results of the supply current under load changing is shown in
Fig. 10
. As shown in
Fig. 10(a)
, when the load current has a step increase, the SHPF quickly responds to compensate the load change and maintain the supply current as sinusoidal and inphase with the supply voltage. During a load increase, the DClink voltage suffers a small reduction, but it restores to the initial value within a short period of time. A similar dynamic performance of the SHPF is shown in
Fig. 10(b)
when the load current is reduced. Finally, we can conclude that the supply current is effectively compensated to be sinusoidal and inphase with the supply voltage regardless of the load current conditions.
Dynamic response of the proposed SHPF under load changing (a) load increase, (b) load decrease
Table 2
shows a comparison for operation current, voltage, and power of the active filter in a pure shunt APF
[5]
, a typical SHPF
[6]
, and the proposed SHPF under a 5 kVA load condition. From
Table 2
, it can be observed that the active filter in the proposed SHPF demands lower current, voltage, and power compared to both the pure shunt APF and the typical SHPF. Therefore, the proposed SHPF scheme can be regarded as a costeffective solution for harmonic current and reactive power compensation.
Comparisons of different active power filter topologies
Comparisons of different active power filter topologies
5. Experimental Verifications
To experimentally verify the effectiveness of the proposed scheme, we built an experimental system in the laboratory with the same parameters used in the simulation, as shown in
Fig. 11
. The proposed SHPF was composed of a passive part consisting of an
LC
filter and an active part. The active part of the proposed SHPF was implemented with three IGBT modules (FMG2G50US60 from Fairchild). The control strategy was realized by a 32bit floatingpoint DSP (TMS320F28335 of Texas Instruments). The supply voltage was generated by a programmable AC power source (Chroma 61704). The THD values of the load voltage and the supply current were measured using a power analyzer (HIOKI 3193).
Experimental system for the proposed SHPF
In the experimental tests, due to the unavailability of inductive loads in the laboratory, only a threephase diode rectifier was used in the load side. In this case, the THD and PF of the load current were about 30.2% and 0.85, respectively. The steadystate performance of the proposed SHPF with the proposed control strategy is illustrated in
Fig. 12
. It can be seen that the supply current was effectively compensated to be sinusoidal and inphase with the supply voltage even though the load current was highly distorted with poor PF. The THD and PF of the supply current after compensation were about 2.17% and 0.995, respectively. These experimental results completely verify the validity of the proposed SHPF topology and control strategy.
Steadystate performance of the proposed SHPF
The dynamic response of the proposed SHPF with respect to load change is illustrated in
Fig. 13
. It is obvious that the supply current is quickly compensated to be sinusoidal within three fundamental cycles after a sudden load change. The supply current is always compensated to be sinusoidal and inphase with the supply voltage, regardless of the load current condition. The proposed SHPF scheme provides good steadystate performance as well as robust and fast dynamic response.
Dynamic response of the proposed SHPF with increasing load
6. Conclusions
This paper proposes a new control strategy for a novel SHPF to simultaneously compensate the harmonic current and the reactive power. The design of the passive components and the current controller for the SHPF were presented in detail. The effectiveness of the proposed topology is verified through simulated and experimental results: the supply current after compensation is almost sinusoidal with a very low THD of about 2.17% and is inphase with the supply voltage with an almost unity power factor, regardless of the distorted load current condition. The proposed SHPF provides good steadystate performance and fast dynamic performance. Moreover, the proposed SHPF has a lower power rating requirement compared to pure shunt APF and typical SHPF topology. Thanks to its lowcost and highperformance qualities, the proposed SHPF topology is suitable to apply in highvoltage highpower applications.
Acknowledgements
This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF20100025483).This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF2013R1A2A2A01016398).
BIO
HongHee Lee received his B.S., M.S., and Ph.D. in Electrical Engineering from Seoul National University, Seoul, Korea, in 1980, 1982, and 1990, respectively. From 1994 to 1995, he was a Visiting Professor at the Texas A&M University. He has been a Professor in the School of Electrical Engineering in the Department of Electrical Engineering, University of Ulsan, Ulsan, Korea since 1985. He is also the Director of the Networkbased Automation Research Center (NARC), which is sponsored by the Ministry of Trade, Industry and Energy. His research interests include power electronics, networkbased motor control, and renewable energy. Dr. Lee is a member of the Institute of Electrical and Electronics Engineers (IEEE), the Korean Institute of Power Electronics (KIPE), the Korean Institute of Electrical Engineers (KIEE), and the Institute of Control, Robotics and Systems (ICROS).
QuocNam Trinh was born in Vietnam, in 1985. He received the B.S. degree from Ho Chi Minh City University of Technology, Vietnam, in 2008 and the Ph.D degree from University of Ulsan, Korea in 2014 both in Electrical Engineering. Currently, he is a postdoctoral research fellow at Energy Research Institute @ NTU, Nanyang Technological University, Singapore. His research interests are active power filters, harmonic compensation, distributed generation, and gridconnected inverters.
Rivas D.
,
Moran L.
,
Dixon J. W.
,
Espinoza J. R.
2003
“Improving passive filter compensation performance with active techniques”
IEEE Trans. Ind. Electron.
50
(1)
161 
170
DOI : 10.1109/TIE.2002.807658
Lee W.C.
2015
“CostEffective APF/UPS System with Seamless Mode Transfer”
Journal of Electrical Engineering & Technology
10
(1)
195 
204
DOI : 10.5370/JEET.2015.10.1.195
Jung Y.G.
2013
“Graphical Representation of the Instantaneous Compensation Power Flow for SinglePhase Active Power Filters,”
Journal of Electrical Engineering & Technology
8
(6)
1380 
1388
DOI : 10.5370/JEET.2013.8.6.1380
Yi Hao
,
Zhuo Fang
,
Li Yu
,
Zhang Yanjun
,
Zhan Wenda
2013
“Comparison Analysis of Resonant Controllers for Current Regulation of Selective Active Power Filter with Mixed Current Reference”
Journal of Power Electronics
13
(5)
861 
876
DOI : 10.6113/JPE.2013.13.5.861
Trinh Q. N.
,
Lee H. H.
2013
“An Advanced Current Control Strategy for ThreePhase Shunt Active Power Filters,”
IEEE Trans. Ind. Electron.
60
(12)
5400 
5410
DOI : 10.1109/TIE.2012.2229677
Tangtheerajaroonwong W.
,
Hatada T.
,
Wada K.
,
Akagi H.
2007
“Design and performance of a transformerless shunt hybrid filter integrated into a threephase diode rectifier,”
IEEE Trans. Power Electron.
22
(5)
1882 
1889
DOI : 10.1109/TPEL.2007.904166
Rahmani S.
,
Hamadi A.
,
Mendalek N.
,
AlHaddad K.
2009
“A new control technique for threephase shunt hybrid power filter,”
IEEE Trans. Ind. Electron.
56
(8)
2904 
2915
DOI : 10.1109/TIE.2008.2010829
Rahmani S.
,
Hamadi A.
,
AlHaddad K.
2012
“A LyapunovFunctionBased Control for a ThreePhase Shunt Hybrid Active Filter,”
IEEE Trans. Ind. Electron.
59
(3)
1418 
1429
DOI : 10.1109/TIE.2011.2163370
Corasaniti V.F.
,
Barbieri M.B.
,
Arnera P.L.
,
Valla M.I.
2009
“Hybrid Power Filter to Enhance Power Quality in a MediumVoltage Distribution Network,”
IEEE Trans. Ind. Electron.
56
(8)
2885 
2893
DOI : 10.1109/TIE.2009.2014369
Li Yan
,
Li Gang
2013
“A Novel Hybrid Active Power Filter with a HighVoltage Rank”
Journal of Power Electronics
13
(4)
719 
728
DOI : 10.6113/JPE.2013.13.4.719
Chau MinhThuyen
,
Luo An
,
Shuai Zhikang
,
Ma Fujun
,
Xie Ning
,
Chau Van Bao
2012
“Novel Control Method for a Hybrid Active Power Filter with Injection Circuit Using a Hybrid Fuzzy Controller”
Journal of Power Electronics
12
(5)
800 
812
DOI : 10.6113/JPE.2012.12.5.800
Luo An
,
Tang Ci
,
Shuai Zhi Kang
,
Zhao Wei
,
Rong Fei
,
Zhou Ke
2009
“A Novel ThreePhase Hybrid Active Power Filter With a Series Resonance Circuit Tuned at the Fundamental Frequency,”
Industrial Electronics, IEEE Transactions on
56
(7)
2431 
2440
DOI : 10.1109/TIE.2009.2020082
Lam C.S.
,
Wong M.C.
,
Choi W.H.
,
Cui X.X.
,
Mei H.M.
,
Liu J.Z.
2014
“Design and Performance of an Adaptive LowDCVoltageControlled LCHybrid Active Power Filter With a Neutral Inductor in ThreePhase FourWire Power Systems,”
IEEE Trans. Ind. Electron.
61
(6)
2635 
2647
DOI : 10.1109/TIE.2013.2276037
Rahmani S.
,
Hamadi A.
,
AlHaddad K.
,
Dessaint L.A.
2014
“A Combination of Shunt Hybrid Power Filter and ThyristorControlled Reactor for Power Quality,”
IEEE Trans. Ind. Electron.
61
(5)
2152 
2164
DOI : 10.1109/TIE.2013.2272271
Trinh Q. N.
,
Lee H. H.
“Harmonic Current and Reactive Power Compensation with Novel Shunt Hybrid Power Filter”
Proc. The 20th International Conference Electrical and Electronics Engineering
1 
6
Trinh Q. N.
,
Lee H. H.
2013
“An Advanced Repetitive Controller to Improve the Voltage Characteristics of Distributed Generation with Nonlinear Loads”
J. Power Electronics
13
(3)
409 
418
DOI : 10.6113/JPE.2013.13.3.409
Zhang K.
,
Kang Y.
,
Xiong J.
,
Chen J.
2003
“Direct repetitive control of SPWM inverters for UPS purpose,”
IEEE Trans. Power Electron.
18
(3)
784 
792
DOI : 10.1109/TPEL.2003.810846