The state equation of the augmented-state system which consists of internal model and plant is
0
0
WT WT WT WT
W WT
R T RWT WT RWT RWT
x A x B
x B C A x u (6.13)
wherexWTis the states of plant (6.4),xRWTis the states of internal model. The feedback controllers, KPWTandKRWTcan be got by minimizing the performance index
0 WT T WT WT T W
RWT RWT WT T WT
J x x Q x x u R u dt (6.14)
whereuWTis the input of the argument-state system. A dual system of the plant is shown as
( )= ( )+ ( )
( )= ( )
T T
LWT WT LWT WT LWT
LWT T
WT LWT
dx t A x t C u t
dt
dy t B x t
dt
(6.15)
The state observe gain, WT, is designed by minimizing the performance index
0 TLWT( ) LWT LWT( ) TLWT( ) LWT LWT( )
J x t Q x t u t R u t dt (6.16)
The design method of the parameters in Fig. 6-6 (b) is the same.
TABLE6-1 PARAMETERS OF THE SIMULATION CIRCUIT OF GRID-CONNECTED MICROGRID
Rated voltage of load 40 / 2 V Voltage of utility grid,Rf 55 V Frequency of utility grid,Lf 50 Hz SPWM switching frequency
of PWM inverters 10 kHz
DC-link voltage 100 V
Filter inductance,Lf 10 mH Filter capacitor,Cf 3.3 uF Filter resistance,Rf 0.3 Chock coil inductance,Lt 3 mH
Chock coil resistance,Rt 10 mH Grid inductance,Lg 3 mH
Grid resistance, Rg 10 Load inductance,Ll 3 mH
Load resistance, Rl 10
6.4.1 Calculation of Control Parameters of the Two TLPFC Systems
For the TLPFC system for WT-DG system, we choose the parametersQMT,RMT,QLMT, andRMTin (6.14) and (6.16) as follows
diag 1 1 1015 10
QMT , RMT diag 1 ,
diag 10 103
QLMT , RLMT diag 1
Then, we got the state-feedback controller,KPMTandKRMT, and the state observer gain, MT ,as 103 0.6402 1.9598
KPMT , KRMT 107 3.1622 6.3142 ,
105 1.3726 0.3107T
MT
The parameter MT in (6.16) is chosen as 106.
For the PV DG system, we use the same calculation methods by using
5 6
diag 1 10 10
QPV , RPV diag 1 ,
Then, the state-feedback controller,KPPVandKRPV, and the state observer gain, PV ,are obtained as
1.3248
KPPV , KRPV 104 0.0258 5.7313 , 105 3.1613
PV
The parameter PVin (6.16) is chosen as 1012.
The H norm of the TLPFC system for inverter of WT-DG system is
=0.1445<1
dWT dWT
G F
so, the control system is stable. The H norm of the TLPFC system for inverter of PV DG system is
= 0.9903 < 1
dPV dPV
G F
so, this control system is also stable.
6.4.2 Analysis of Simulation Results
We did two simulations to test the effectiveness of the TLPFC systems. One is on the condition that 40% voltage sag occurs. Another is on the condition that 40% voltage swell occurs. We assume that the active power that generated by the PV DG system is 20 W.
First, a 40% voltage sag of the utility grid starts at 0.1 s and lasts for 0.1 s is considered. From Fig. 6-7, we can see that the load voltage follows the reference voltage closely, which is the rated voltage of the sensitive local load, and utility grid only supply active power to the load during all the simulation process. Before the voltage sag, utility grid and the PV DG system supply active power to the load together (Fig. 6-7(a)), while only the WT-DG system supplies reactive power to the load (Fig. 6-7(b)). After the voltage sag occurred, the PV DG system still outputs its maximum active power to the load, while the utility grid no longer has enough active power. So, the WT-DG system begins to supply enough active and reactive power to the load. After the voltage returns to the normal value, the utility grid begins to supply power to the load again. There is a drop in output active power of utility grid at 0.1 s, but it brought back at 0.2 s. When without the disturbance compensator, the response time of regulating active and reactive power of WT-DG system and PV DG system is slower than the response time with the disturbance compensator.
The TLPFC system is effective on regulating active and reactive power flow in the grid-connected microgrid when voltage sag occurs.
(a) Performance of active power flow
(b) Performance of reactive power flow
Fig. 6-7 Performances of the TLPFC systems when 40% voltage sag occurs in utility grid (Black lines: TLPFC systems with disturbance compensator, Grey lines: TLPFC systems without
disturbance compensator)
0.05 0.1 0.15 0.2 0.25
-100 0 100
0.05 0.1 0.15 0.2 0.25
60 80 100
0.05 0.1 0.15 0.2 0.25
0 50 100
0.05 0.1 0.15 0.2 0.25
10 20 30
0.05 0.1 0.15 0.2 0.25
0 50 100
t (s)
0.050 0.1 0.15 0.2 0.25
10 20
0.05 0.1 0.15 0.2 0.25
-20 0 20 40
0.05 0.1 0.15 0.2 0.25
-20 0 20
0.05 0.1 0.15 0.2 0.25
-20 0 20
t (s)
(a) Performance of active power flow
(b) Performance of reactive power flow
Fig. 6-8 Performances of the TLPFC systems when 40% voltage swell occurs in utility grid (Black lines: TLPFC systems with disturbance compensator, Grey lines: TLPFC systems without
disturbance compensator)
0.05 0.1 0.15 0.2 0.25
-100 0 100
0.05 0.1 0.15 0.2 0.25
60 80 100
0.05 0.1 0.15 0.2 0.25
-150 -100 -50 0
0.050 0.1 0.15 0.2 0.25
10 20 30
0 0.05 0.1 0.15 0.2 0.25
0 100 200
t (s)
0.050 0.1 0.15 0.2 0.25
10 20
0.05 0.1 0.15 0.2 0.25
-20 0 20 40
0.05 0.1 0.15 0.2 0.25
-10 0 10
0.05 0.1 0.15 0.2 0.25
-20 0 20
t (s)
First, a 40% voltage sag of the utility grid starts at 0.1 s and lasts for 0.1 s is considered. From Fig. 6-7, we can see that the load voltage tracks the reference voltage, which is the rated voltage of the sensitive local load, so that the sensitive local load can operate well. The utility grid only supply active power to the load during all the simulation process. Before the voltage swell, utility grid and the PV DG system supply active power to the load together (Fig. 6-7(a)). Only the WT-DG system supplies reactive power to the load (Fig. 6-7(b)). After the voltage swell occurred, the PV DG system still outputs its maximum active power to the load, and the utility grid output much more active power to the load. The PV DG system and utility grid supply enough active power to the load. So, the WT-DG system still only supplies reactive power to the load. After the voltage returns to the normal value, the PV DG system and the utility grid still supply active power to the load. When without the disturbance compensator, the response time of regulating active and reactive power of WT-DG system and PV DG system is slower than the response time with thedisturbance compensator. The TLPFC system is effective on regulating active and reactive power flow in the grid-connected microgrid when voltage swell occurs.