Page 143 - Hybrid-Renewable Energy Systems in Microgrids

Study of control strategies of power electronics during faults in microgrids 127

 k 1− k   k 1− k 
I qL = Q *  v q + + v − q  I , qS = Q *  v q + − v − q  (7.42) IqL=Q*kqv⊥++1−kqv⊥−, IqS=Q*kqv




⊥
⊥
⊥
⊥
⊥+−1−kqv⊥−
+
φ − φ − φ − φ − π φ − φ − π
+
+
γ = , γ = + , γ = − (7.43) γa=φ+−φ−2, γb=φ+−φ−2+π3, γc=
a
2 b 2 3 c 2 3 φ+−φ−2−π3
where Î m represents the peak current in each phase; I pL and I pS are the values of the
long and short axes of the active current ellipse; I qL and I qS are the values of the long
+
and short axes of the reactive current ellipse; φ and φ are the phase angles of posi-
−
tive- and negative-sequence voltage respectively. Take phase-A as an example, by sub-
stituting Eqs. (7.41)–(7.43) into Eq. (7.40), the relationship among the peak current of
phase-A Î a and the power references can be expressed as:
q)
 k v − 2 + 1 ( − k ) 2 v + 2 − k 2 ( 1− k cos(2 ) vγ + ⋅ v − 
2
0 = Q  q q q a 
*2
 v + 2 ⋅ v − 2 
 
pq)
 k 2 ( + k 2 − 4 kk sin(2 ) vγ + ⋅ v 
−
− PQ  p q a 
*
*
  v + 2 ⋅ v − 2  
p)
 k v − 2 + 1 ( − k ) 2 v + 2 + k 2 ( 1− k cos(2 ) vγ + ⋅ v − 
2
+ P  p p p a  − Î 2 (7.44) 0 = Q * 2 k q 2 v − + 1 − k q v + − 2 k q 1 − k q
2
2
2
*2
 v + 2 ⋅ v − 2  a 2 2
  cos (2 γ a )v+ ⋅ v − v+ ⋅ v − − P * Q *2
2
kp+2kq−4kpkqsin(2γa)v+⋅v−v+ ⋅v−-
2
2
2 + P *2 k p 2v − +1 − k p v+ +2 k p 1 − k
2
∗
Given the values of Q , k and k , the expression in Eq. (7.44) can be regarded as a pcos(2γa)v+⋅v−v+ ⋅v− −Îa2
2
2
q
p
∗
quadratic equation with P as an unknown variable. The solution of this quadratic equa-
tion gives the maximum allowed active power P a lim to comply with the current limit of
phase-A. With γ changed to γ and γ , the maximum allowed active power to guarantee
a
c
b
a safe current in phase-B and phase-C, namely P b lim and P c lim , can be obtained using the
same procedure. Finally, the limit on active power under fault conditions is restricted by:
lim
lim
lim
P max = min{ P , P , P } (7.45) Pmax=minPalim,Pblim,Pclim
c
b
a
To illustrate the effectiveness of this current limitation method, the short-circuit
response of a VSI to a phase A-B fault with 0.1 Ω fault resistance is plotted in Fig. 7.6
∗
for the same scenarios of Fig. 7.5. With Q set to zero, the current in each phase is
restricted within 61.23 A.
3.4.2 Flexible oscillating power control
The current limitation method presented above is only valid for flexible positive- and
negative-sequence power control because current references Eqs. (7.28) and (7.29)