Distributed Cooperative Control of Micro-grids

Transcription

1 Distributed Cooperative Control of Micro-grids

2 F.L. Lewis, National Academy of Inventors Moncrief-O Donnell Endowed Chair Head, Controls & Sensors Group UTA Research Institute (UTARI) The University of Texas at Arlington F. Lewis and A. Davoudi Work of A. Bidram and V. Nasirian Supported by ONR, NSF Distributed Synchronization Control of Micro-grids Talk available online at

3 Invited by Tom Field 5

4 F.L. Lewis, H. Zhang, A. Das, K. Hengster-Movric, Cooperative Control of Multi-Agent Systems: Optimal Design and Adaptive Control, Springer-Verlag, 2013 Key Point Lyapunov Functions and Performance Indices Must depend on graph topology H. Zhang, F.L. Lewis, and Z. Qu, "Lyapunov, Adaptive, and Optimal Design Techniques for Cooperative Systems on Directed Communication Graphs," IEEE Trans. Industrial Electronics, vol. 59, no. 7, pp , July Hongwei Zhang, F.L. Lewis, and Abhijit Das Optimal design for synchronization of cooperative systems: state feedback, observer and output feedback, IEEE Trans. Automatic Control, vol. 56, no. 8, pp , August 2011.

5 Outline Synchronization in Nature Cooperative Control Electric Power Microgrids Cooperative Control for Synchronization in Microgrids

6 Patterns in Nature and Society

7 1. Natural and biological structures Some of these beautiful pictures are from a lecture by Ron Chen, City U. Hong Kong Pinning Control of Graphs

8 Distribution of galaxies in the universe

9 Airline Route Systems

10 2. Motions of biological groups Fish school Birds flock Locusts swarm Fireflies synchronize

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12 Herd and Panic Behavior During Emergency Building Egress Helbring, Farkas, Vicsek, Nature 2000

13 Communication Graph G=(V,E) N nodes x () t i State at node i is xi () t Synchronization problem x () t x () t 0 i j

14 The Power of Synchronization Coupled Oscillators Diurnal Rhythm

15 Electric Power Microgrids

16 An introduction on micro grids: Why micro grid? US power grid interconnections: 27

17 An introduction on micro grids: Why micro grid? Blackouts all around the world 1. India blackout, 2012, 670 millions affected. 2. Indonesia blackout, 2005, 100 millions affected. 3. Brazil blackout, 1999, 97 millions affected. 4. Brazil and Paraguay blackout, 2009, 87 millions affected. 5. US blackout, 2003, 55 millions affected. 28

18 What is a microgrid? o Department of Energy: Microgrid, as the main building block of smartgrids, is a group of interconnected loads and distributed energy resources. o Microgrid has the ability to work in both grid-connected and islanded modes. Microgrid applications: o o o Rural plants. Business buildings, hospitals, and factories Forward operating bases Photo from: 5

19 An introduction to micro grids: Micro grid applications The main building block of smart-grids Rural plants Business buildings, hospitals, and factories Smart grid photo from: sphere.com

20 Non-renewables Distributed Generators (DG) Distributed Energy Resources (DER) Internal combustion engine Micro-turbines Fuel cells Renewables Photovoltaic Wind Biomass 32

21 Mobile applications Micro grid applications High saving in diesel fuel consumption, Providing more reliable power to the consumers. Photos from: 33

22 Micro grid Advantages Micro-grid provides high quality and reliable power to the critical consumers During main grid disturbances, micro-grid can quickly disconnect form the main grid and provide reliable power for its local loads DGs can be simply installed close to the loads which significantly reduces the power transmission line losses By using renewable energy resources, a micro-grid reduces CO2 emissions 34

23 An introduction to micro grids: Micro grid Objectives Voltage and frequency synchronization for both grid-connected and islanded operating modes Proper load sharing and DG coordination Power flow control between the microgrid and the main grid Optimizing the microgrid operating cost Hierarchical control structure 35

24 Micro grid Control Challenges In Grid-connected mode, the main grid has rotating synchronous generators that provide a frequency reference In Grid-connected mode, the main grid provides voltage support and power quality During grid disturbances, micro-grid goes to islanded mode to provide the power for its local loads In islanded mode, there is no frequency reference In islanded mode, microgrid controller must provide voltage support and power quality 36

25 Back to Synchronization Communication Structures

26 Flocking Reynolds, Computer Graphics 1987 Reynolds Rules: Alignment : align headings a ( ) i ij j i jn Cohesion : steer towards average position of neighbors- towards c.g. Separation : steer to maintain separation from neighbors i

27 Distributed Adaptive Control for Multi Agent Systems

28 Communication Graph Strongly connected if for all nodes i and j there is a path from i to j. Diameter= length of longest path between two nodes N Volume = sum of in-degrees Vol di i1 Tree- every node has in-degree=1 Leader or root node 1 Followers Spanning tree Root node

29 Dynamic Graph- the Distributed Structure of Control x u Each node has an associated state i i j Standard local voting protocol ui aij( xj xi) jn 1 u x a a x d x a a i i ij ij j i i i in jn jn i i i x x 1 N x i u u u 1 N D d 1 d N A [ a ij ] u DxAx( DA) xlx L=D-A = graph Laplacian matrix x Lx Closed-loop dynamics If x is an n-vector then x ( LI ) x n

30 Graph Eigenvalues for Different Communication Topologies Directed Tree- Chain of command Directed Ring- Gossip network OSCILLATIONS

31 Synchronization on Good Graphs Chris Elliott fast video

32 Synchronization on Gossip Rings Chris Elliott weird video

33 Synchronization of Chaotic node dynamics Ron Chen Pinning control of largest node (for increasing coupling strengths) c=0 c=10 Chen s attractor node dynamics c=20 c=15

34 Back to Microgrid 52

35 Bidram, A., & Davoudi, A. (2012). Hierarchical structure of microgrids control system. IEEE Transactions on Smart Grid, vol. 3, pp , Dec Micro grid Hierarchical Control Structure Optimal operation in both operating modes Power flow control in grid-tied mode Tertiary Control Voltage deviation mitigation Frequency deviation alleviation Secondary Control Do coop. ctrl. here to Synchronize frequency and voltage Voltage stability provision Frequency stability Plug and preserving play capability for DGs Primary Control Maintains Stability Microgrid Tie Main grid

36 Micro grid Primary Control Primary control: The primary control maintains voltage and frequency stability Conventional primary control: Droop techniques nmp P Ev V n Q mag n Q m P m P P1 max1 PN maxn n Q n Q Q1 max1 QN max N v o i o Microgrid load conditions Power calculator Q P Resulting Power Droop Control E ω Q P E ω Reference voltage 2 Esin(ωt) * v o Required voltage and frequency To maintain stability

37 Design of Droop Control Parameters n n mp P min mp1 DG1 mp2 DG2 Pick slopes so that P P max1 max 2 P Then mp1 ( )/P n min max1 mp2 ( n min )/Pmax 2 m P m P P1 max1 PN maxn Balanced Load sharing 55

38 Micro grid primary control 1. Connected to Main Power Grid Load is 7kW Grid supplies 1kW Primary control (frequency droop) Before islanding occurs 2.5kW v o1 v b1 Maingrid 1kW DG1 nominal power, Pmax1= 4 kw DG2 nominal power, Pmax2= 6 kw m P m P P1 max1 P2 max2 DG1 3.5kW v o2 Rc1 L c 1 3.5kW 1 v b2 R line L line1 n ref DG2 R c2 L c2 min DG1 DG2 3.5kW 2.5kW 3.5kW P 56

39 Micro grid Primary Control 2. After Islanding DGs must make up an extra 1kW Pload= 7kW New P1 + P2= 2.8kW + 4.2kW n ref new DG1 DG2 Makes frequency decrease n mp P min P1old P 1new P2 old P 2 new Increase n to restore frequency to ref value P (kw ) 57

40 Secondary Frequency Control New Secondary Control Input for Frequency Synchronization Secondary Control input Prescribed frequency e.g. 60 Hz ni i i ni Pi i m Pi m P Change ni To synchronize i P i P max i Existing power conditions in the microgrid

41 Micro grid secondary control Secondary control: The secondary control restores the voltage and frequency of the micro-grid to their nominal value. Current Secondary control implementation: Centralized structure Low reliability Requires a Central control authority Requires too many communication links V n KPE ( vref vmag ) K IE ( vref vmag ) dt n KP( ref ) K I ( ref ) dt We want to develop a new Distributed Control structure Highly reliable Uses sparse communication network 60

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43 Micro grid secondary control: Distributed CPS structure Work of Ali Bidram With Dr. A. Davoudi DG 8 DG 7 Communication link DG 6 DG 5 Cyber layer A sparse, efficient communication network to allow cooperative control for synchronization of voltage and frequency DG 1 DG 2 DG 3 DG 4 Cyber communication framework Cyber Physical System (CPS) DG 1 DG 8 DG 2 DG 3 Microgrid DG 7 DG 6 DG 4 DG 5 Physical Layer The interconnect structure of the power grid 64

44 Inverter-based DGs in a microgrid Voltage Controlled Voltage Source Inverter VCVSI Primary control Main grid Primary control Load 1 CCVSI Load 2 Current Controlled Voltage Source Inverter 9

45 Dynamical model of a DG Primary Control Structure Renewable DER Provides DC voltage VSC Voltage source converter Power electronics Voltage controller i * Ld i od, i oq, i * Lq Current controller i Ld, i Lq v i abc/dq VSC i L LC filter R f L f C f v o i o Output connector R c L c v b Microgird Network Load disturbances v* od, v* oq v od, v oq ω Power controller Primary Control ω n V Droop control is here n * * Given load conditions v, i pick, v, v using Droop to maintain stability 0 0 od oq 69

46 From adaptive voltage ctrl Trans CST paper The nonlinear dynamics of the i th DG, while neglecting the fast dynamics of voltage and current controllers x i,1 ni mpixi,2 com x i,2 ci( xi,6 xi,8 xi,7 xi,9 xi,2 ) x i,3 ci( xi,6 xi,9 xi,7 xi,8 xi,3 ) r V n x x x x x rfi xi,7 x i,5 xi,5 comxi,4 Lfi Lfi xi,4 xi,8 x i,6 comxi,7 C fi xi,5 xi,9 x i,7 comxi,6 C fi rci xi,6 vbdi x i,8 xi,8 comxi,9 Lci L ci r x ci i,7 vbqi x i,9 xi,9 comxi,8 Lci Lci fi ni Qi i,3 i,6 i,4 i,4 com i,5 Lfi Lfi x [ P Q i i v v i i ]. i i i i Ldi Lqi odi oqi odi oqi T 74

47 Synchronization in Microgrid of Interconnected DG Voltage synchronization DG 1 DG 2 DG 3 DG 4 DER 1 v o1 R c1 L c1 R line1 L line1 DER 2 v o2 R c2 L c2 R line2 L line2 DER 3 v o3 R c3 L c3 R line3 L line3 R c4 L c4 DER 4 v o4 P load4 +jq load4 P load3 +jq load3 R line4 P load1 +jq load1 P load2 +jq load2 L line4 L c8 R line7 L line7 R line6 L R line6 line5 L line5 L c7 L c6 L c5 R c8 R R c7 c6 R c5 v o8 v o7 v o6 v o5 DER 8 DER 7 DER 6 DER 5 DG 8 DG 7 DG 6 DG 5 Frequency synchronization Voltage synchronization (per unit) y m P i i ni Pi i E vmag Vn nqq 2 2 o, magi odi oqi v v v

48 Secondary Control Synchronization Objectives Renewable DER Provides DC voltage VSC Voltage source converter Power electronics Voltage controller i * Ld i od, i oq, i * Lq Current controller i Ld, i Lq abc/dq VSC i L LC filter R f L f C f v o i o Output connector R c L c v b Microgird Network Load disturbances v* od, v* oq v od, v oq ω Power controller Voltage synchronization (per unit) ω n V n Frequency synchronization Secondary Control Inputs Change Droop control parameters to get synchronization

49 DG Microgrid Model and Synchronization Control Objectives Heterogeneous Agent Dynamics different dynamics 13 i i i i i i i i i x i x f ( x ) k ( x ) D g ( x ) u yi hi( xi) diui 1. For secondary frequency control: y u i i ni Pi i i ni m P di 0 2. For secondary voltage control: Evmag Vn nqq y u i i v V odi ni di 0 78

50 1. Distributed secondary frequency control of micro-grids 2. Distributed secondary voltage control of micro-grids Work of Ali Bidram With Dr. A. Davoudi

51 1. Secondary Frequency Control New Secondary Control Input for Frequency Synchronization Secondary Control input Prescribed frequency ni i m P i ni Pi i m Pi Change ni To synchronize i i ref, i P i P max i Existing power conditions in the microgrid For example ref 50Hz

52 Droop control relationship i ni Pi i 1. Secondary Frequency Control m P Using input-output feedback linearization i ni mpip i u i u c e i i i ei aij( i j) gi( i ref ) jn i Theorem. Let the digraph of the communication network have a spanning tree and the pinning gain be nonzero for at least one DG placed on a root node. u i Let the auxiliary control be chosen as above. Then, the global neighborhood error is asymptotically stable. Moreover, the DG frequencies synchronize to ref 83

53 1. Secondary Frequency Control Restores Frequency Synchronization after islanding i ni mpip i u i ref j j a ( ) g( ) ij i j i i ref e i c i u i 1 s ni x i fi( xi) gi( xi) ui y h( x) du i i i i i i x i jn i m pi calculating P i Feedback Linearization Inner Loop 85

54 1. Secondary frequency control Simulation Example Physical Microgrid Network DG 1 DG 2 DG 3 DG 4 DER 1 v o1 R c1 L c1 R line1 L line1 DER 2 v o2 R c2 L c2 R line2 L line2 DER 3 v o3 R c3 L c3 R line3 L line3 R c4 L c4 DER 4 v o4 P load4 +jq load4 P load3 +jq load3 R line4 P load1 +jq load1 P load2 +jq load2 L line4 L c8 R line7 L line7 R line6 L R line6 line5 L line5 L c7 L c6 L c5 R c8 R R c7 c6 R c5 v o8 v o7 v o6 v o5 DER 8 DER 7 DER 6 Cyber communication network sparse DER 5 DG 8 DG 7 DG 6 DG 5 DER 8 DER DG 7 DER DG 6 DER DG 5 DER 4 DER 3 DER 2 DER 1 DG 8 DG 4 DG 3 DG 2 DG 1 Leader

55 1. Secondary frequency control Ref. Frequency Is 50 Hz f (Hz) DG 1 DER1 DER2 DG 2 DER3 DG 3 DER4 DG 4 DG 5 DER5 DER6 DG 6 DG 7 DER7 DER8 DG t (s) Islanding Turn on Coop secondary control 87

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57 New Secondary Control Input for Frequency Synchronization AND Balanced Power Sharing Secondary Control input ni i m P i ni Pi i m Pi Change ni To synchronize i P i P max i And enforce balanced power sharing P P 1 max1 P P N max N

58 Secondary frequency and power control Differentiating the frequency droop characteristic yields: m P u ni i Pi i i For N DGs: 1mP 1P 1 u1 2 mp2p 2 u2 m P u N PN N N m P i ni Pi i The auxiliary controls are chosen based on each DG s own information, and the information of its neighbors in the communication digraph DG 1 ref 3, P 3 DG 2 1, P 1 2, P 2 DG 3 Local neighborhood tracking errors u c( a ( ) g ( ) a ( m P m P )) i ij i j i i ref ij Pi i Pj j jn jn i TWO CONTROL OBJECTIVES WITH ONE CONTROL INPUT i 91

59 Secondary frequency and power control ω ref ω j j N i Σ j a ij ( ω i -ω j )+g i (ω i -ω ref ) Cooperative tracker Cooperative regulator Σ m P u ni i Pi i i c u i 1 s ω ni DG i ω i P i P j Σ j a ij ( m Pi P i -m Pj P j ) j N i TWO CONTROL OBJECTIVES WITH ONE CONTROL INPUT 92

60 Secondary frequency and power control The local neighborhood tracking error control u c( a ( ) g ( ) a ( m P m P )) i ij i j i i ref ij Pi i Pj j jn jn i Guarantees that c(( LG)( ) Lm P) 0. This does not guarantee synchronization of freq. and power separately There is another relation between power and frequency in the microgrid DGs Write the output active power as P i ref v v oi bi i i i i X ci So that approximately P h ( ), P i i i ref sin( ) h sin( ), In global form P h( ref ), Therefore at steady state all frequencies synchronize to the reference frequency So that G( ) Lm P 0 ref P

61 Simulation results Physical Microgrid Network Cyber communication network sparse Reference value DG 1 DG 4 DG 2 DG 3 17

62 Simulation results 50.5 DG1 DG2 DG3 DG4 f(hz) 50 (a) time (s) D P *P (b) time (s) 18

63 Distributed secondary control Objectives: o o Voltage and frequency control. Share P and Q among VCVSIs based on their ratings. Objectives: o Share P and Q among CCVSIs based on their ratings. o Provide P and Q support for VCVSIs 33

64 Case studies VCVSI PCC VCVSI CCVSI CCVSI VCVSI CCVSI CCVSI 15

65 Case studies v c,mag (pu) (a) n q *Q (b) t(s) t(s) 50.1 DG1 DG5 DG7 P/P max (a) Q/Q max (b) DG2 DG3 DG4 DG t(s) t(s) f(hz) (a) DG1 DG5 DG t(s) 1 ω ref v ref α P α Q m p *P 0.5 (b) t(s) VCVSIs CCVSIs 16

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