Chaudhary, Sanjay

Guerrero, Josep M.

Li, Chendan

Vasquez, Juan Carlos

Chendan Li

Sanjay K. Chaudhary

Juan C. Vasquez

Josep M. Guerrero

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Power flow analysis for droop controlled LV hybrid AC-DC microgrids with virtual impedance

The AC-DC hybrid microgrid is an effective form of utilizing different energy resources and the analysis of this system requires a proper power flow algorithm. This paper proposes a suitable power flow algorithm for LV hybrid AC-DC microgrid based on droop control and virtual impedance. Droop and virtual impedance concepts for AC network, DC network and interlinking converter are reviewed so as to model it in the power flow analysis. The validation of the algorithm is verified by comparing it with steady state results from detailed time domain simulation. The effectiveness of the proposed algorithm makes it a potential method for planning, dispatching and operation of droop controlled LV hybrid AC-DC

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    Aalborg UniversitetPower flow analysis for droop controlled LV hybrid AC-DC microgrids with virtualimpedanceLi, Chendan; Chaudhary, Sanjay K.; Quintero, Juan Carlos Vasquez; Guerrero, Josep M.Published in:Proceedings of the IEEE Power &amp; Energy Society General Meeting, PES 2014DOI (link to publication from Publisher):10.1109/PESGM.2014.6939887Publication date:2014Document VersionEarly version, also known as pre-printLink to publication from Aalborg UniversityCitation for published version (APA):Li, C., Chaudhary, S., Vasquez, J. C., & Guerrero, J. M. (2014). Power flow analysis for droop controlled LVhybrid AC-DC microgrids with virtual impedance. In Proceedings of the IEEE Power & Energy Society GeneralMeeting, PES 2014 (pp. 1-4). IEEE Press. DOI: 10.1109/PESGM.2014.6939887General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            ? Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            ? You may not further distribute the material or use it for any profit-making activity or commercial gain            ? You may freely distribute the URL identifying the publication in the public portal ?Take down policyIf you believe that this document breaches copyright please contact us at vbn@aub.aau.dk providing details, and we will remove access tothe work immediately and investigate your claim.Downloaded from vbn.aau.dk on: April 24, 2017MainUtility GridEV chargingPCCBatteriesDC LoadEV charging FlywheelInterlinkingconverterPVWTIBSDC microgridDC microgridAC microgridAC LoadFigure 1.    Structure of an example of hybrid AC-DC microgrid  Power flow analysis for droop controlled LV hybrid AC-DC microgrids with virtual impedanceChendan Li, Sanjay K. Chaudhary, Juan C. Vasquez, and Josep M. Guerrero Department of Energy Technology, Aalborg University Aalborg, Denmark  {che , skc , juq , joz}@et.aau.dk    Abstract— The AC-DC hybrid microgrid is an effective form of utilizing different energy resources and the analysis of this system requires a proper power flow algorithm. This paper proposes a suitable power flow algorithm for LV hybrid AC-DC microgrid based on droop control and virtual impedance. Droop and virtual impedance concepts for AC network, DC network and interlinking converter are reviewed so as to model it in the power flow analysis. The validation of the algorithm is verified by comparing it with steady state results from detailed time domain simulation. The effectiveness of the proposed algorithm makes it a potential method for planning, dispatching and operation of droop controlled LV hybrid AC-DC.   Index Terms—hybrid AC-DC microgrid, droop control, virtual impedance, power flow.  I. INTRODUCTION Recent technology development and practice in power system has witnessed increasing interests on the concept of “direct DC”, from the adoption of High-voltage direct-current (HVDC) transmission  systems  when connecting offshore wind farms or large distance interconnected grids, to energy efficient applications in distribution system that utilize DC power directly from the source residentially or commercially for the purpose of avoiding DC-AC-DC power conversions. Among these applications, DC microgrid, which comprises distributed generation, energy storage systems  and local  loads  as a local grid, is gaining more interests due to its potential to integrate increasing DC renewable source and load, such as , electrical  vehicles,  photovoltaic  systems,  fuel  cells,  or  LEDs , with high efficiency. The application of DC microgrids have increasingly been found its way in data centers, telecom system, and some buildings and offices.     DC microgrids are, however, not likely to fully replace an existing AC microgrid due to the long historical development of the AC power system.  The architecture of the coexistence of AC and DC subgrids intertied by an electronically controlled power converter is here to stay [1]-[5]. The structure of an example of hybrid AC-DC microgrid is shown in Fig. 1.  This hybrid network consists of two DC subgrids and one AC subgrid, and the main grid is connected with it by an intelligent bypass switch.  One of the main purposes of the management for the microgrid is the control of the power flow. To achieve this goal, among many control strategies, hierarchical control methodology is proposed in [1] as a generalized and even standard way for AC microgrid and DC microgrid. The steady state power distribution is the direct control outcome of the primary control of the hierarchical control. To make the planning, dispatch and operation more economical and reliable, a steady state power flow analysis for a microgrid is always desired.  For this purpose, a lot of work has been done [6]−[8], but they all aimed at the AC microgrid only. Moreover, to a certain extent, none of them is suitable for Low voltage AC microgrid, either because they use conventional  concepts of PQ, PV and slack buses in the modelling or due to that they overlooked the effect of the virtual impedance[7].  Power flow analysis for AC-DC power system is not a new topic, yet many of them are addressed for HVDC system thus not suitable for a hybrid microgrid with its unique power flow control based on droop and virtual impedance[9]-[11]. This paper, a power flow for hybrid AC-DC microgrid is proposed considering the droop control with virtual impedance and power flow among microgrids through interlinking converter control. The paper is organized as follows. In the second section, power flow control strategy based on the droop control and virtual impedance for single microgrid and intertied microgrids are reviewed as background knowledge to justify the choice of modelling method in the next section. In the third section, mathematical model of proposed power flow analysis is presented based on the control discussed previously. The verification of the proposed algorithm by comparing the results from calculation and the steady state results from time domain simulation is AC source generation using virtual impedance control  Virtual impedanceAC Bus i AC Bus i+1Virtual Droop Bus v v vZ R j L  lineZdroopV- +GVLine impedancelineIFigure 2. Concept of   droop control with virtual impedance in a single AC microgrid  DC source using virtual impedance control  Virtual resistanceDC Bus i DC Bus i+1DR lineR0(DC)V (DC)GVLine resistancelineI+- Figure 3. Concept of  droop control using virtual impedance in a single DC microgrid   AC Bus iInterlinking convertersAC microgrid DC microgrid DC Bus k1CP 2CP1CQFigure 4. Concept of   droop control with virtual impedance in a single AC microgrid  provided in the fourth section which shows the effectiveness of the algorithm.  Finally, section five gives the conclusions and the future work. II. DROOP CONTROL AND VIRTUAL IMPEDANCE SCHEME IN MICROGRIDS A.  For a single LV AC microgrid The concept of the droop control with virtual impedance is illustrated in Fig.2. As is shown in it, when the virtual impedance Zv equals zero, i.e., virtual impedance is not used, the output characteristic of generation is controlled by the droop equation as (1) and (2) to mimic the synchronous generator in the bulk grid.   * 0i Pi Gif f K P    (1)  0| | | |Gi G i Qi GiV V K Q    (2) Being f0i, KPi, PGi,VG0i, KQi, QGi the nominal frequency, proportional frequency droop parameter, real power generation, nominal voltage, proportional voltage amplitude droop parameter, and reactive power at generator i, respectively. But when the virtual impedance is added in the control so as to decouple real and reactive power when the line impedance is not inductive enough, it changes the output voltage characteristics of the generation as is shown in (3).  ( )G droop G vdroop Gbus G vV V I ZV Y V Z    (3) Where the droopV is the voltage matrix of the virtual droop bus, GlineI  the injection current matrix in the generation bus, GbusY  the admittance matrix of the network directed connected to the generation buses, vZ  the virtual impedance matrix of the controller and GV  the voltage matrix of generation bus (assume all the generation buses are droop controlled). B. For a single  LV DC microgrid The principle of the droop control for LV DC microgrid is illustrated in Fig. 3. In fact, the realization of droop control in DC microgrid is through the use of the virtual resistance RD. DC sources in a network cannot work as stiff voltage sources for there will be circulating current. The droop concept has thus come into being by multiplication of measured voltage deviation to a value reciprocal to the virtual resistance. The concept is illustrated by (4).   (DC) 0 (DC) (DC)Gi i Di GiV V R i    (4) Where VGi(DC) is the voltage reference to DC source which should be equal to the measured voltage value in a stable system in the steady state, 0 (DC)iV  is the output reference at no load which is usually modified from secondary control to achieve voltage regulation, DiR is the virtual impedance of the droop controller, and (DC)Gii is the output current of the DC source.  C. For intertied microgrids Droop concepts can also be applied to two different microgrids by controlling the interlinking converter as are proposed in [1]-[4].  Although the droop concept is used in the control of the interlinking converter, the interlinking converter cannot be seen as a droop controlled converter to each interconnected side as in a single microgrid. There are mainly two control objectives which are realized by using droop concepts. One is aiming at making the two intertied connected microgrids being studied share all the load equally [2], another is aiming at making the two intertied microgrids equally stressed and minimize the interlinking energy flow by controlling the power transferred according to the load condition of the two microgrids [3]. Despite different control objectives, to make the droop coefficients comparable, the variables used for sharing the real power as the signals need to be normalized to common per unit range. Moreover, despite different control strategy the ultimate given to the interlinking converter is the transferred power through it. To make the model of the interlink converter control strategy independent, the generalized form of the power flow control in the interlinking converter can be show in fig. 4. The direction of the arrow indicates the positive direction of the power. Reactive power cannot be transferred through the interlinking converter and that is why there is only Qc1 in the AC side. The transferred real power satisfies the following equations consider the converter power loss and the possible energy storage system in the DC link of the converter.                      2 1c c loss storageP P P P                            (5)   AC Load 2AC Bus 1AC Bus 2AC Bus 3AC Bus 4AC Bus 5AC Bus 6AC source 1Interlinking Converter 2Interlinking Converter 1 DC Bus 1DC source 1DC Bus 4DC Bus 2AC Load 1AC Load 3DC Bus 3DC source 2DC Load 1 DC Load 2AC source 3AC source 2 Figure 5. Single line diagram of test hybrid micogrid   III. MATHEMATICAL MODEL OF POWER FLOW IN LV HYBRID AC-DC MICROGRID For the AC buses, taking into account that the frequency is a global variable for all the DG buses throughout the microgrid, from (1) we can obtain:  0 0i Pi Gi g Pg Ggf K P f K P     (6) where i=1,…, g-1, being g the number of the buses. The network equations that all buses should obey are given by: ( cos sin )i i j ij ij ij ijP V V G B     (7)  ( cos sin )i i j ij ij ij ijQ V V G B          (8) Where θij，Gij and Bij are the bus admittance angle, the conductance and the susceptance, respectively.  For DC buses, it is possible to assume the network is pure resistive in its steady state model. According to the Kirchhoff's current law, that current injected at the bus i equals to the current flowing to other buses, the network equation can be written as follows:  (DC) (DC) (DC) (DC)1( )ni ij i jjj iI Y V V    (9)   Where (DC)iI  is the DC injection current in bus i, (DC)ijY  is the admittance between the bus i and bus j, and (DC)iV is the voltage magnitude in bus i;  (DC)(DC) (DC) (DC)1(DC)(V )niij i jjij iPY VV         (10)  Additionally, for the Droop-buses, there is one more constraint they have to follow:  (DC) 0 (DC) (DC)Gi i Di GiV V R i    (11) Where  (DC)Gii  can be written as,   (DC)(DC)(DC)GiGiGiPiV    (12)       Considering the virtual impedance constraint (3) for AC buses, and assuming there is no energy storage in the DC link and the power loss in the converter is not significant which is reasonable in LV small microgrid system, the overall mathematical model of power flow analysis for a hybrid microgrid is as follows:      0 0 0i g Pi Gi Pg Ggf f K P K P     (13)  0| | | | 0G i Gi Qi GiV V K Q     (14)  1 0Gi Di i cP P P P      (15)  1 0Gi Di i cQ Q Q Q      (16)  ( ) 0G droop Gbus G vV V Y V Z     (17)  ,, , ,1,( )ndc idc ij dc i dc jjdc ij iPY V VV    (18)  (DC)(DC) 0 (DC)(DC)GiGi i DGiPV V RV    (19)  (DC) (DC) , 2 0Gi Di dc i cP P P P      (20)        IV. ALGORITHM VERIFICATION ON A TEST HYBRID MICROGRID   The validity of the algorithm is verified using a 10-bus hybrid microgrid by comparing the results from calculation and the steady state results from time domain simulation with the toolbox SimPowerSystems of Matlab as is shown in Fig.5. According to [3], it defines four basic rules for the control of transferred power, the real power flow will have three different cases: scenario 1, real power flows from AC side to DC side; scenario 2, real power flows form DC side to AC side; and scenario 3, no power flows in between. Since the last case is equivalent to calculate two separated AC network and DC network, only first two cases are tested. The network data and control parameters are listed in Table I.  TABLE I.  THE NETWORK DATA AND CONTROL PARAMETERS OF TEST HYBRID MICROGRID paramaters symbol value  units frequency droop for DG1 KP1 0.001 rad/(W · s) amplitude droop for DG1 KQ1 0.02 V/Var frequency droop for DG2 KP2 0.0005 rad/(W · s) amplitude droop for DG2 KQ2 0.01 V/Var frequency droop for DG3 KP3 0.004 rad/(W · s) amplitude droop for DG3 KQ3 0.002 V/Var Virtual resistor  Rv_i(i=1,2,3) 0.1 Ω Virtual inductor Lv_i(i=1,2,3) 0.004 H reference voltage in DC bus 1 Vref1 48 V reference voltage in DC bus 2 Vref2 48 V Virtual resistance for DC source 1 Rd1 0.2 Ω Virtual resistance for DC source 2 Rd2 0.5 Ω bus number Rload(Ω) Lload(mH)  DC bus 2 5 0  DC bus 4 3 0  AC bus 4 100 0  AC bus 5 100 0  AC bus 6 100 0.25136H  from bus to bus Line resistance(Ω) line inductance(mH) DC bus 1 DC bus 2 0.05 0 DC bus 2 DC bus 3 0.04 0 DC bus 3 DC bus 4 0.08 0 DC bus 4 DC bus 1 0.03 0 AC bus 1 AC bus 4 0.15 0. 062 AC bus 2 AC bus 5 0.21 0.096 AC bus 3 AC bus 6 0.11 0.048 AC bus 4 AC bus 5 0.12 0.031 AC bus 5 AC bus 6 0.15 0.062 In scenario 1, real power 200W and 300W is flowing from AC network to DC network through interlinking converter 1 and 2 respectively. The comparison results of generation buses are shown in Table II. TABLE II.  COMPARISON RESULTS WHEN REAL POWER FROM AC TO DC Node SimPowerSystem results Power Flow Results Mag.(p.u.) Power(W) Mag.(p.u.) Power(W) DC bus 1 0.99541 525.76 0.99993 520.79 DC bus 3 0.99597 184.812 0.99994 182.4 AC bus 1 0.97680 1289.07 0.97661 1287.94 AC bus 2 0.97947 2578.13 0.97921 2575.87 AC bus 3 0.97562 644.532 0.97547 643.97       In scenario 2, the real power 200W and 300W is flowing from DC network to AC network. The comparison results of generation buses are shown in Table III. TABLE III.  COMPARISON RESULTS WHEN REAL POWER FROM DC TO AC Node SimPowerSystem results Power Flow Results Mag.(p.u.) Power(W) Mag.(p.u.) Power(W) DC bus 1 0.99035 1100.73 0.99986 1094.29 DC bus 3 0.98693 594.441 0.99981 593.08 AC bus 1 0.98891 1023.02 0.99009 1023.03 AC bus 2 0.99090 2046.04 0.99211 2046.07 AC bus 3 0.98839 511.513 0.98957 511.52 From these two sets of power flow results comparisons for the generation buses, it shows that the calculated values are close to the simulation thus verifies the effectiveness of the proposed algorithm. V. CONCLUSION A power flow algorithm suitable for droop controlled LV hybrid AC-DC microgrid has been proposed where the virtual impedance is used in both the AC network, DC network and the interlinking converter.  The validation of the proposed power flow algorithm is verified by comparing the results from time domain simulation and that from calculation through this algrothm. Coincidence of the results shows that this power flow algorithm can be used as a tool to analyze the steady state response of the hybrid microgrid which uses droop and virtual impedance as its control strategy. REFERENCES  [1] Guerrero, J.M.; Poh Chiang Loh; Tzung-Lin Lee; Chandorkar, M., "Advanced Control Architectures for Intelligent Microgrids—Part II: Power Quality, Energy Storage, and AC/DC Microgrids," Industrial Electronics, IEEE Transactions on , vol.60, no.4, pp.1263,1270, April 2013 [2] Poh Chiang Loh; Ding Li; Yi Kang Chai; Blaabjerg, F., "Autonomous Control of Interlinking Converter With Energy Storage in Hybrid AC–DC Microgrid," Industry Applications, IEEE Transactions on , vol.49, no.3, pp.1374,1382, May-June 2013  [3] Loh, Poh Chiang, et al. "Autonomous operation of ac–dc microgrids with minimised interlinking energy flow." IET Power Electronics 6.8 (2013): 1650-1657.  [4] Nutkani, Inam Ullah, Poh Chiang Loh, and Frede Blaabjerg. 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Power flow analysis for droop controlled LV hybrid AC-DC microgrids with virtual impedance

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