Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 88 (2016) 349 – 355
CUE2015Applied Energy Symposium and Summit 2015: Low carbon cities and urban energy systems
Optimized secondary control for distributed generation under unbalanced conditions Peng Jina, Yang Lib,* a State grid customer service center, Tianjin 300140, P.R. China School of Electrical Engineering, Northeast Dianli University, Jilin 132012, Jilin, P.R. China
b
Abstract Control structure have a critical influence on converterinterfaced distributed generations (DG) under unbalanced conditions. In this paper, the relationship between amplitude of active power oscillations and reactive power oscillations is firstly deduced and the hierarchical control of DG is proposed to reduce power oscillations. Current references are generated in the primary control level and active power oscillations can be suppressed by the dual current controller. The secondary control reduces active power and reactive power oscillations by optimal model aiming at minimum amplitude of oscillations. The simulation results show that the proposed scheme with less injecting negative sequence current than traditional control method can effectively suppress oscillations of both active power and reactive power. © Published by Elsevier Ltd. This © 2016 2015The TheAuthors. Authors. Published by Elsevier Ltd.is an open access article under the CC BYNCND license (http://creativecommons.org/licenses/byncnd/4.0/). Selection and/or peerreview under responsibility of CUE Peerreview under responsibility of the organizing committee of CUE 2015
Keywords: distributed generation; secondary control; power oscillations suppression; dual current controller
1. Introduction Voltagesourced converter (VSC) now appears to be one of the most promising integration modes of static energy conversion systems for DGs [1]. Most DGs are located at the terminals of distribution network or microgrid where unbalanced conditions exist owing to singlephase loads and asymmetrical faults. Grid imbalance in a threephase system leads to 100Hz power oscillations. Active power oscillations have negative effects on dc link of converters and reactive power oscillations causing high power loss and overcurrent stress [23]. Consequently, various control structures have been proposed in recent years whose aim is improving VSC operation under unbalanced conditions.
* Corresponding author. Tel.: +86043264806066; fax: +86043264806066. Email address:
[email protected] .
18766102 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BYNCND license (http://creativecommons.org/licenses/byncnd/4.0/). Peerreview under responsibility of the organizing committee of CUE 2015 doi:10.1016/j.egypro.2016.06.137
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Peng Jin and Yang Li / Energy Procedia 88 (2016) 349 – 355
Control structures have critical influence on the DG’s behavior under unbalanced conditions. Notch filters are adopted to separate the components of positive and negative sequences, and the dual PI current controllers are proposed to control positive sequence and negative sequence components respectively [4]. The dclink voltage ripple and active power oscillations can be suppressed, but reactive power oscillations are significantly amplified and system dynamics are limited by notch filters. Alternatively, delay signal cancellation (DSC) is adopted for realtime symmetrical component extraction which is based on a combination of timedelayed synchronous frame magnitudes and permits a fixed 5 ms delay sequence extraction time [5]. As discussed in [6], it is possible to change the relative amplitudes of oscillating active and reactive power smoothly through an adjustable parameter of current reference. Previous studies mainly focus on reduction of active power oscillations, but the analytic relationship between active and reactive power oscillations is still unclear. In this paper, the mechanism of power oscillations is revealed from the viewpoint of positive and negative sequence current injection. Furthermore, an optimization model aimed at power oscillations suppression is established, and a secondary control is proposed to simultaneously reduce both active and reactive power oscillations. 2. Mechanism of power oscillations under unbalanced conditions VT1 A
Udc
VT3 VD1
VD3 B
Ceq VT4
VT5
VT6 VD 4
C VT2 VD6
VD L ia 5 ib
R PCC
ic VD2
Fig. 1. Equivalent circuit of DG converter
An unbalanced threephase input voltage { Ea , Eb , Ec } at the PCC causes 100Hz power oscillations, and instantaneous power of a DG can be expressed as P(t )
P0 Pc 2 cos(2Zt ) Ps 2 sin(2Zt )
(1)
Q(t )
Q0 Qc 2 cos(2Zt ) Qs 2 sin(2Zt )
(2)
where P0 , P1 , Pc 2 , Ps 2 , Qc 2 , Qs 2 can be expressed as
P0 ° ® Pc 2 °P ¯ s2
Ed I d Eq I q Ed I d Eq I q
Q0 ° ®Qc 2 °Q ¯ s2
Eq I d Ed I q Eq I d Ed I q
Ed I d Eq I q Ed I d Eq I q d q
E I
q d
E I
d q
E I
E I
Eq I d Ed I q Eq I d Ed I q d d
E I
q q
E I
d d
E I
(3)
q d
(4)
q q
E I
Based on (3) and (4), the relationship between active and reactive power oscillations can be derived as followed:
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Peng Jin and Yang Li / Energy Procedia 88 (2016) 349 – 355
Pv2 +Qv2 =Ps22 +Pc22 +Qs22 +Qc22 =( Ed I q Eq I d Ed I q Eq I d )2 ( Ed I d Eq I q Ed I d Eq I q )2 d d
q q
d d
2 q q
q d
d q
q d
(5)
2 d q
+( E I E I E I E I ) +( E I E I E I E I )
The
structure of (5) is complex, assume , , , and we can simplify the A E I E I B Ed I d Eq I q C Ed I q Eq I d D Eq I d Ed I q d d
q q
resultant to Pv2 +Qv2 =(C D) 2 +(A+B) 2 ( A B) 2 (C D) 2
2( A2 B 2 C 2 D 2 )=2 ^( Ed I d ) 2 + ( Eq I q ) 2 +( Ed I d ) 2
(6)
( Eq I q ) 2 ( Ed I q ) 2 +( Eq I d ) 2 ( Eq I d ) 2 + ( Ed I q ) 2 `
where Pv
Ps22 Pc22 , Qv
Qs22 Qc22 , E
Ed++ 2 +Eq++ 2 , E
Ed 2 +Eq 2 , I
I d++ 2 +I q++ 2 , I
I d 2 +I q 2 .
Equation (6) can be simplified as
Pv2 Qv2
2( E I )2 2( E I )2
(7)
In normal state, the amplitude of negative sequence electric quantity is much less than that of positive sequence electric quantity. Consequently, the positive sequence current can be written as ª I d º ª Ed « »« ¬« I q ¼» ¬« Eq
1
Eq º ª P0 º » Ed ¼» «¬Q0 »¼
(8)
Equation (8) indicates that positive sequence current can be approximately regarded as constant if P0 and Q0 are determined. Accordingly, 2( E I )2 in (7) can also be regarded as constant and Pv2 Qv2 reaches the minimum when I d  and I q  are set to zero. 3. Hierarchical control of dg converter 3.1. Primary control of dg converter The hierarchical control consists of the primary control and the secondary control, which are different in current references of the controller. Active power oscillations can be suppressed in the primary level by matrix as follow [4]. ª I d º « » « Iq » « I d » « » «¬ I q »¼
ª Ed « « Eq « Eq « «¬ Ed
Eq
Ed
Ed
Eq
Ed
Eq
Eq
Ed
Eq º » Ed » Ed » » Eq »¼
1
ª P0 º « » « Q0 » (9) « Ps2 » « » ¬ Pc2 ¼
where Ps2 =Pc2 =0 . Active power oscillations can be eliminated in ideal state. Once active power oscillations is suppressed in primary control, but negative sequence current can lead to additional power oscillations term 2( E I )2 and reactive power oscillations are enlarged. 3.2. Secondary control of dg converter
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Peng Jin and Yang Li / Energy Procedia 88 (2016) 349 – 355
When voltage of PCC is unbalance, primary control adjusting current reference in (9) starts to reduce power oscillations at the beginning. Once the primary control achieves stable and reactive pulse exceeds a certain range, the secondary control starts. By resetting current references, the secondary control corrects power quality, and current references can be obtained as followed: min F Ps22 Pc22 Qs22 Qc22 ° P0 Pref ° s.t. ° Q0 Qref ® ° 2 2 Ps 2 Pc 2 Qs22 Qc22 ° =0 ° Pref2 Qref2 ¯
(10)
where Pref and Qref are power references of the DG. The aim of (10) is to reduce amplitudes of active and reactive power oscillations simultaneously. Power coefficients in (10) are functions of [ I d , I q , I d , I q ] , and optimized current references can be obtained by the optimization. The original optimization that contains equality constraints can be transformed into unconstrained problem by Lagrange multiplier method as follow G
F O1 ( P0 Pref ) O2 (Q0 Qref )+O˄ 3
Ps22 Pc22 Qs22 Qc22 ˅ Pref2 Qref2
(11)
where O1 , O2 and O3 are the Lagrange multipliers, respectively. The optimal references of sequence current can be obtained by solving unconstrained problem. 4. Control structure of dg converter
E
d
E
q
I d +
PI
dm qm
I I Pref
Qref
I q+
Current reference of primary control and secondary control
ωL Z0 L ωL 
PI

I qm
E
q
I
q
+
PI
+ +dq
Sa
+ +
S P W M
+ 
E
q

ωL
I dm
Ed
+
+ I d
Ed +

abc +
+
Sb Sc
+
Ed +

dq
ωL 
+ PI
Eq
abc +
Fig. 2. Control structure of the dual current controller
As illustrated in Fig. 2, the dual current controller adjusts positive sequence and negative sequence electrical quantity separately. The current commands appear as DC in rotate frame, so dual current controller is suit for hierarchical control of DG converter. 5. Case studies
Peng Jin and Yang Li / Energy Procedia 88 (2016) 349 – 355
In order to verify the performance of proposed scheme, simulation studies are carried out in MATLAB environment. Unbalanced threephase input voltage at PCC is [ Ea , Eb , Ec ] ª¬341sin(Zt 90 ),291sin(Zt 30 ),311sin(Zt 210 )º¼ . The process of stabilizing active and reactive power oscillations is illustrated in Fig. 3. Active and reactive power references of DG are Pref = 8 kW and Qref 6 kVar . At the beginning of the simulation, primary control starts to eliminate active power oscillations. As illustrated in Fig. 3(a), active power oscillations are effectively suppressed, but the amplitude of reactive power oscillations is up to 780 Var. The large amplitude oscillations of reactive power can be explained by the special reciprocal relationship between active and reactive power oscillations in (7). 8000
P [W]
6000
4000
2000
0 0
0.3
0.6
0.9
1.2
Time [s]
(a) Dynamic active power response of DG 8000
Q [Var]
6000
4000
2000
0 0
0.3
0.6
0.9
1.2
Time [s]
(b) Dynamic reactive power response of DG Fig. 3. Dynamic power response transformed from primary control to secondary control
The secondary control is activated until t =0.77s . As shown in Fig. 3(b), amplitudes of active and reactive power oscillations are less than 450VA by the secondary control. Furthermore, amplitudes of active and reactive power oscillations are proportional to respective power references and the power oscillations rate is limited at 5.6%. In addition, the injection of negative sequence current is significantly reduced as illustrated in Fig. 4. Negative sequecne current [A]
2
Iq 
1.5 1 0.5 0
Id
0.5 1 0
0.3
0.6
Time [s]
0.9
(a) Negative sequence dq current
1.2
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Peng Jin and Yang Li / Energy Procedia 88 (2016) 349 – 355
Positive sequence current [A]
20 15
Iq+
10 5 0 5
Id+
10 15 20 25 0
0.3
0.6
Time [s]
0.9
1.2
(b) Positive sequence dq current Fig. 4. Positive and negative sequence dq current
The positive and negative sequence dq current reflect characteristics of power oscillations amplitude. The positive sequence current is mainly proportional to the average output active power and reactive power, so it changes slightly when the control mode switches. Variation of negative sequence current mainly determines the change of power oscillations amplitude. 6. Conclusion This paper focuses on power oscillations of DGs under unbalanced voltage. The analysis results reveal analytic relationship between active and reactive power oscillations, and a secondary control based on an optimization model is also proposed. The simulation results show that both active and reactive power oscillations of DG can be effectively suppressed and the injection of negative sequence current is reduced. Therefore, the proposal befits power oscillations reduction of DGs operating on fix power control mode. 7. Copyright Authors keep full copyright over papers published in Energy Procedia Acknowledgements This research is supported by the Doctor Scientific Research Foundation of Northeast Dianli University under Grant No. BSJXM201407. References [1] IEEE guide for design, operation, and integration of distributed resource island systems with electric power systems, IEEE Std. 1547.4. [2] Moran L, Ziogas P, Joos G. Design aspects of synchronous PWM rectifier—inverter systems under unbalanced input voltage conditions. IEEE Trans. Ind. Applicat. 1992; 28:1286–93. [3] Sannino A, Bollen M, Svensson J. Voltage tolerance testing of threephase voltage source converters. IEEE Trans. Power Del. 2005; 20(2):1633–39. [4] Song HS, Nam K. Dual current control scheme for PWM converter under unbalanced input voltage conditions. IEEE Trans. Ind. Electron. 1999; 46(5):9539.
Peng Jin and Yang Li / Energy Procedia 88 (2016) 349 – 355
[5] Saccomando G, Svensson J. Transient operation of gridconnected voltage source converter under unbalanced voltage conditions. Proc. IEEE Ind. Appl. Conf. 2001; p. 2419–2424. [6] Wang F, Duarte J, Hendrix M. Design and analysis of active power control strategies for distributed generation inverters under unbalanced grid faults. IET Gener., Transmiss. Distrib. 2010; 4(8):905–16.
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