كتاب Design and Development of Model Predictive Primary Control of Micro Grids - Simulation Examples in MATLAB
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 كتاب Design and Development of Model Predictive Primary Control of Micro Grids - Simulation Examples in MATLAB

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Design and Development of Model Predictive Primary Control of Micro Grids - Simulation Examples in MATLAB
Puvvula Vidyasagar, K. Shanti Swarup

كتاب Design and Development of Model Predictive Primary Control of Micro Grids - Simulation Examples in MATLAB  M_d_a_18
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Contents
1 Micro-grid Introduction and Overview . 1
1.1 Conventional Power Systems Review . 1
1.2 Concept of Distributed Generation . 4
1.3 Necessity of Distributed Generation 5
1.4 Single DG Challenges 7
1.5 Concept of Micro-grid and Definitions . 8
1.6 General Constituents of a Micro-grid . 11
1.7 Advantages of a Micro-grid . 16
1.8 Micro-grid Challenges . 16
1.9 Micro-grid Operational Modes 17
1.10 Key Takeaways . 18
References . 18
2 An Overview of Micro-grid Control 21
2.1 Control Objectives in a Micro-grid . 21
2.2 Control Architectures in a Micro-grid 23
2.3 Hierarchical Control of a Standalone Micro-grid . 25
2.3.1 Primary Control 26
2.3.2 Secondary Control 30
2.3.3 Tertiary Control 33
2.4 Key Takeaways . 33
References . 34
3 Mathematical Modelling of a Micro-grid . 37
3.1 Micro-grid Description and Reference Frames . 37
3.2 Synchronous-DG Model 40
3.3 EI-DG Model . 43
3.3.1 AC Side Dynamics of the EI-DG in abc Frame 43
3.3.2 AC Side Dynamics of the EI-DG in Its Local d3-q3
Frame . 45
3.3.3 Phase-Locked Loop Dynamics 45
3.3.4 DC Side Dynamics of the EI-DG 46
vvi Contents
3.4 Load Modelling in the Micro-grid . 48
3.5 Network Modelling in the Micro-grid 49
3.6 Complete Model of the Grid-Connected Micro-grid 50
3.7 Complete Model of the Standalone Micro-grid . 51
3.8 Key Takeaways . 52
References . 52
4 Introduction to Model Predictive Control . 53
4.1 MPC Description 53
4.2 Advantages of MPC . 54
4.3 MPC Types . 54
4.4 Linear Model-Based MPC/Linear-MPC/L-MPC . 56
4.4.1 Augmented Model 57
4.4.2 Prediction Vector Within the Prediction Horizon . 58
4.4.3 Optimal Control Problem Formulation . 59
4.5 Nonlinear Model-Based MPC/Nonlinear-MPC/N-MPC . 60
4.6 Brief Review of MPC in Power Engineering . 61
4.7 Micro-grid MPC Methodologies Discussed in the Book . 63
4.8 Key Takeaways . 65
References . 66
5 LTI-MPC for the Micro-grid Control 69
5.1 Mathematical Formulation of the LTI-MPC . 69
5.1.1 Augmented Model 70
5.1.2 Prediction Vector Within the Prediction Horizon . 71
5.1.3 Optimal Control Problem Formulation . 72
5.2 LTI-MPC for the Micro-grid Control . 74
5.2.1 Role of Each DG Unit in the Micro-grid Control 74
5.2.2 Operational Constraints 75
5.2.3 Choice of the Controller Parameters . 75
5.3 Performance Analysis 78
5.4 Key Takeaways . 89
References . 89
6 LTV-MPC with Extended “TAIL” . 91
6.1 Mathematical Formulation of the LTV-MPC . 91
6.1.1 Prediction of the Forced Response . 92
6.1.2 Prediction of the Natural Response 94
6.1.3 Optimal Control Problem Formulation . 95
6.1.4 Choice of the Input Reference Trajectories Vref (t) . 96
6.2 Performance Analysis 97
6.3 Key Takeaways . 104
References . 107Contents vii
7 Special Functions in the MPC Formulation . 109
7.1 Role of Orthonormal Special Functions in the MPC 109
7.2 Approximation of the Original Control Trajectories 110
7.2.1 Laguerre Functions 110
7.2.2 Kautz Functions 111
7.3 Mathematical Formulation of the LTI-MPC Using Special
Functions 114
7.3.1 Augmented Model 114
7.3.2 LTI-MPC Using Special Functions 115
7.4 Mathematical Formulation of the LTV-MPC Using Special
Functions 117
7.4.1 Augmented Model 117
7.4.2 Prediction of the Natural Response 120
7.4.3 LTV-MPC Using Special Functions 120
7.4.4 Choice of the Input Reference Trajectories Vref (t) . 122
7.5 Performance Analysis 123
7.5.1 Choice of the Laguerre and Kautz Network
Parameters . 123
7.6 Key Takeaways . 124
References . 131
8 Auxiliary Requirements for Real-Time Implementation 133
8.1 Scalability 133
8.2 Harmonics . 134
8.3 State Estimation . 135
8.4 Choice of a Particular MPC Formulation 135
8.4.1 Computational Complexity . 135
8.4.2 Performance Point of View . 136
8.5 Robustness . 136
8.5.1 Disturbance Compensator 136
8.5.2 Mathematical Formulation of the Robust LTI-MPC 138
8.5.3 Mathematical Formulation of the Robust LTI-MPC
with Special Functions . 141
8.6 Performance Analysis of the Robust LTI-MPC . 143
8.7 Key Takeaways . 146
References . 148
9 Conclusion and Future Scope 149
9.1 Summary of the Book 149
9.2 Novel Concepts in the Book 151
9.3 Limitations . 152
9.4 Future Scope . 153
Appendix 1 . 153
Appendix 2 . 155
Abbreviations
AC Alternating Current
DC Direct Current
DER Distributed Energy Resource
DG Distributed generator
DMC Dynamic Matrix Control
FIR Finite Impulse Response
GPC Generalized Predictive Control
IM Induction Motor
kVb Base kV
L-MPC Linear model-based MPC
LQR Linear Quadratic Regulator
LTI Linear Time-Invariant
LTI-MPC Linear Time-Invariant Model Predictive Controller
LTV Linear Time-Variant
LTV-MPC Linear Time-Variant Model Predictive Controller
MPC Model Predictive Controller
MPPT Maximum Power Point Tracking
MVAb Base MVA
N-MPC Nonlinear model-based MPC
OAT One At a Time
PCC Point of Common Coupling
P-f Active power versus Frequency
PI Proportional Integral
PID Proportional Integral Derivative
PLL Phase Locked Loop
PR Proportional Resonant
PV Photovoltaic
PV-DG Photovoltaic Distributed Generator
PWM Pulse Width Modulator
Q-V Reactive power versus Voltage
R-L Impedance load
xixii Abbreviations
SG-DG Synchronous Generator based Distributed Generation
SHE Selective Harmonic Elimination
VSC Voltage Source Converter
VSI Voltage Source Inverter
ZOH Zero-Order Hold
Nomenclature
B1 Bus number 1
B2 Bus number 2
B3 Bus number 3
B4 Bus number 4
B5 Bus number 5
B6 Bus number 6
B7 Bus number 7
B8 Bus number 8
L2 Impedance load at bus B2
L5 Impedance load at bus B5
L6 Induction motor load at bus B6
L7 Impedance load at bus B7
L8 Impedance load at bus B8
ωb Angular speed of the global reference frame D-Q (rad/s)
VG1 Voltage space vector of the bus B1
ωr Angular speed of the SG-DG rotor reference frame d1-q1 (rad/s)
ω3 Angular speed of the PV-DG local reference frame d3-q3 (rad/s)
VG3 Voltage space vector of the bus B3
δ0 Torque angle or power angle of the SG-DG (rad)
δ1 Rotor reference frame angle of the SG-DG (rad)
δ3 Local reference frame angle of the PV-DG (rad)
f Any arbitrary quantity (either voltage or current)
f abc Vector of instantaneous values of the quantity f in stationary abc reference
frame
f dq0 Vector of instantaneous values of the quantity f in rotating d-q reference
frame
T
abc-dq0 Park’s transformation matrix
θc Angle between d-q reference frame and abc reference frame
Id1 d1-axis component of the SG-DG output current
Iq
1 q1-axis component of the SG-DG output current
Vd1 d1-axis component of the bus B1 voltage
xiiixiv Nomenclature
Vq
1 q1-axis component of the bus B1 voltage
E'
d1 d1-axis component of the SG-DG stator induced voltage
E'
q1 q1-axis component of the SG-DG stator induced voltage
Ψ ad1 d1-axis component of the damper winding flux linkage
Ψ
aq2 q1-axis component of the damper winding flux linkages
Ψ d1 d1-axis component of the armature flux linkage
Ψ
q1 q1-axis component of the armature flux linkage
T '
do d1-axis transient open circuit time constant
T '
qo q1-axis transient open circuit time constant
T ''
do d1-axis sub-transient open circuit time constant
T ''
qo q1-axis sub-transient open circuit time constant
Rs Stator resistance
Xls Leakage reactance
X ''
d1 d1-axis sub-transient reactance
X ''
q1 q1-axis sub-transient reactance
X '
d1 d1-axis transient reactance
X '
q1 q1-axis transient reactance
Xd1 d1-axis synchronous reactance
X
q1 q1-axis synchronous reactance
Efd Field voltage
H Inertia constant
T e Electrical torque
T m Mechanical torque
RD Droop constant of the governor
Pref Load reference set-point or turbine reference set-point
P
sv Steam valve output
T
sv Steam valve time constant
T CH Time constant of the steam chest
V t Terminal voltage of the SG-DG
KE Exciter gain
T E Exciter time constant
KA Amplifier gain
T A Amplifier time constant
V in Voltage regulator input
V R Voltage regulator output
rf Per phase resistance of the filter
lf Per phase inductance of the filter
cf Per phase capacitance of the filter
rt Per phase resistance of the interfacing transformer
lt Per phase inductance of the interfacing transformer
Cdc DC link capacitor
V dc Voltage across Cdc
I
cap Current through Cdc
I
pv Output current from the photovoltaic array
Idc DC link currentNomenclature xv
e3abc abc frame components (3-ϕ instantaneous values) of the VSI output
voltage
v3fabc abc frame components (3-ϕ instantaneous values) of the filter voltage
v3abc abc frame components (3-ϕ instantaneous values) of the bus B3 voltage
i
3fabc abc frame components (3-ϕ instantaneous values) of the filter current
i3abc abc frame components (3-ϕ instantaneous values) of the PV-DG current
E
3abc p.u abc frame components of the VSI output voltage for d3-q3 conversion
V
3fabc p.u abc frame components of the filter voltage for d3-q3 conversion
V3abc p.u abc frame components of the bus B3 voltage for d3-q3 conversion
I
3fabc p.u abc frame components of the filter current for d3-q3 conversion
I
3abc p.u abc frame components of the PV-DG current for d3-q3 conversion
Rf p.u resistance of the filter
Xf p.u inductive reactance of the filter
XCf p.u capacitive reactance of the filter
Rt p.u resistance of the interfacing transformer
Xt p.u inductive reactance of the interfacing transformer
Ed3 d3-axis component of the VSI output voltage
V fd3 d3-axis component of the voltage across the filter capacitor
V d3 d3-axis component of the bus B3 voltage
Ifd3 d3-axis component of the filter current
Id3 d3-axis component of the PV-DG current
E
q3 q3-axis component of the VSI output voltage
V fq3 q3-axis component of the voltage across the filter capacitor
V
q3 q3-axis component of the bus B3 voltage
Ifq3 q3-axis component of the filter current
I
q3 q3-axis component of the PV-DG current
K
p PLL proportional gain
Ki PLL integral gain
ϕPLL PLL intermediate state variable
G Solar irradiance (W/m2)
T Surface temperature (0C)
q Electron charge (Coulombs)
A Diode quality factor
K Boltzmann’s constant
N
pa Number of parallel rows in each module
N se Number of series cells in each parallel row of a module
Isc Short circuit current of the module (A)
Iscn Short circuit current of the module at nominal conditions (A)
KI Temperature coefficient of the short circuit current (A/°C)
T n Nominal temperature (°C)
V oc Open circuit voltage of the module (V)
V ocn Open circuit voltage of the module at nominal conditions (V)
KV Temperature coefficient of the open circuit voltage (V/°C)
I0 Dark saturation current of the diode (A)
Rse Equivalent series resistance of each module (Ω)xvi Nomenclature
Rsh Equivalent shunt resistance of each module (Ω)
Iph Photo generated current of each solar cell (A)
Gn Nominal irradiance (W/m2)
N
pp Number of parallel rows of modules in the PV array
Nss Number of series modules in each parallel row of the PV array
V D
i D-axis component of ith bus voltage
V Q
i Q-axis component of ith bus voltage
I D
li D-axis component of ith bus load current
I Q
li Q-axis component of ith bus load current
Rli Resistance of the load at ith bus
Xli Reactance of the load at ith bus
I D
mi D-axis component of ith bus induction motor load current
I Q
mi Q-axis component of ith bus induction motor load current
E D
mi D-axis component of the induced voltage of the induction motor at ith bus
E Q
mi Q-axis component of the induced voltage of the induction motor at ith bus
Rmi Stator resistance of the induction motor at ith bus
X '
mi Transient reactance of the induction motor at ith bus
Xmi Synchronous reactance of the induction motor at ith bus
T mi Transient open circuit time constant of the induction motor at ith bus
Smi Slip of the induction motor at ith bus
Hmi Inertia constant of the induction motor at ith bus
T emi Electrical torque of the induction motor at ith bus
T mmi Mechanical torque of the induction motor at ith bus
I D
i j D-axis component of the line current between buses i and j
I Q
i j Q-axis component of the line current between buses i and j
Rij Resistance of the line between buses i and j
Xij Inductance of the line between buses i and j
NB Number of buses in the micro-grid
I D
i D-axis component of the generator injected current at ith bus
I Q
i Q-axis component of the generator injected current at ith bus
XCi Shunt capacitance at ith bus
X Continuous-time state vector
N Number of states
V Input vector
nip Number of inputs
Y Output vector
n
op Number of outputs
PG3 Active power injected at bus B3 by the PV-DG
V 1 Voltage at generator bus B1
V 3 Voltage at generator bus B3
ts Present time moment (seconds)
T s Sampling time of the controller (seconds)
t Continuous-time (seconds)
k Discrete-time (samples)Nomenclature xvii
ki Present sample
N
p Length of the prediction horizon in samples
N c Length of the control horizon in samples
U Vector with incremental control trajectories within the control horizon
YE Vector with micro-grid outputs predicted within the prediction horizon
U
opt Vector with optimal incremental control trajectories within the control
horizon
W Vector with future set-points for the outputs within the prediction horizon
R Positive definite weight matrix on input increments
PG1 Active power output of the SG-DG
QG1 Reactive power output of the SG-DG
QG3 Reactive power output of the PV-DG
PG1,min Minimum active power of the SG-DG
PG1,max Maximum active power of the SG-DG
QG1,min Minimum reactive power of the SG-DG
QG1,max Maximum reactive power of the SG-DG
PG3,min Minimum active power of the PV-DG
PG3,max Maximum active power of the PV-DG
QG3,min Minimum reactive power of the PV-DG
QG3,max Maximum reactive power of the PV-DG
V
mppt Voltage of the PV module corresponding to the maximum power point
P3,nom Nominal output of the PV-DG
RD3 Droop constant of the PV-DG
ε Error between the predicted and actual response of the micro-grid output
yactual Actual response of the micro-grid output
ypredicted Predicted response of the micro-grid output
X
ref Reference trajectory of the state vector
V
ref Reference trajectory of the input vector
Y
ref Reference trajectory of the output vector
ΔY
p Vector with forced response of the micro-grid within the prediction
horizon
Y
p Vector with natural response of the micro-grid within the prediction
horizon
V
opt Optimal value of the input vector
Vtail Tail of the input vector
ci ith coefficient in the special function network of N functions
oi ith special function in the special function network of N functions
li ith Laguerre function in a Laguerre network of N functions
p Real pole of the Laguerre network
Lag Laguerre network of N functions
N s Number of special functions to approximate the control trajectory of sth
input
Lags Laguerre network to approximate sth input
ηS Coefficient vector of sth input
L Complete Laguerre matrixxviii Nomenclature
η Complete coefficient vector
p1 Complex pole of the Kautz network with N functions
p1 Complex conjugate pole of the Kautz network with N functions
Ki ith Kautz function in a Kautz network of N functions
Kat Kautz network of N functions
KatS Kautz network to approximate sth input
K Complete Kautz matrix
O Complete special function matrix
w Vector having set-points for each output in the output vector
r Vector having penalties on each input increment in the incremental input
vector
Rw Penalty matrix on input increments
ηopt Optimal coefficient vector
C Complexity factor
N
sg Number of synchronous generators
N
pv Number of PV generators
Υ Disturbance vector
ɅΥ
Estimated disturbance vector from the compensator
α Gain matrix of the compensator
B9 Bus number 9
B10 Bus number 10

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