CIRED
17th International Conference on Electricity Distribution
Barcelona, 12-15 May 2003
EFFECT ON THE DYNAMICS OF THE POWER SYSTEM OF A LARGE PENETRATION
OF PHOTOVOLTAIC GENERATION
Yun Tiam TAN, D. S. KIRSCHEN, N. JENKINS
UMIST - United Kingdom
y.tan@stud.umist.ac.uk, daniel.kirschen@umist.ac.uk, jenkins@fs5.ee.umist.ac.uk
SUMMARY
As the concern over global warming increases, renewable
energy sources have become a more significant source
generation of electrical energy. Among these renewable
energy sources, photovoltaic (PV) generation is attracting a
growing amount of political and commercial interest. For
example, the European Commission’s White Paper on
renewable energy sets an indicative objective of 3GW of
installed photovoltaic generation in Western Europe by 2010.
Such a large penetration of distributed PV generation would
have far reaching consequences on the power system. The
effect of a large penetration of PV generation on the stability
and security of the power system must therefore be
considered carefully.
The first part of this paper describes a model of PV
generation suitable for integration in a power system stability
program. This model was developed on the basis of
experimental results. It was found that the maximum power
point tracking technique is the crucial element in the dynamic
behaviour of the PV generation. Experimental results show
that the model gives reasonably accurate results when used to
predict the PV response following small changes in
irradiance, sudden large changes in irradiances and sudden
large changes in grid ac voltage.
characteristic of the PV array. The other input to this block is
the irradiance Ir and the output is Vpv. The block representing
the MPPT has two inputs, Vpv and Ipv, and one output,
∆IpvMPPT. Finally, two blocks are used to represent the effect
of sudden changes in irradiance and voltage. They take the
magnitude of these sudden changes as their input and produce
∆IpvIr and ∆IpvVac respectively.
Flow Chart
While Figure 1 represents the interactions of the different
parts of the model, the flow chart of Figure 2 illustrates
software implementation of this model. Following the
initialization of the variables Ipv, Ir, and Vpv, the model enters
a loop with a cycle time of 0.2s. The first step in this loop is
to determine whether there has been a sudden change in
irradiance and the magnitude of the change ∆IpvIr. The
Initialisation
k=k+1
∆Ir
Calculate ∆IpvIr
∆Vac
Calculate ∆IpvVac
The second part of this paper describes how the PV
generation model has been used to analyse the impact on the
power system of incorporating a significant amount of PV
generation. It discusses the slow transient in bus voltages
corresponding to fluctuation in photovoltaic generation
resulting from the passage of clouds.
Ipv (k)=Ipv (k)+ ∆IpvIr (k)+ ∆IpvVac (k)
PV Array Equation
PV GENERATOR MODEL
MPPT : Calculate ∆IpvMPPT
I.
ss
Initialisation
Figure 1 gives an overview of the proposed PV generator
model. Ipv is the control variable and is calculated at each time
step as the sum of four components:
• The value of Ipv at the previous step
• The change ∆Ipvmppt that reflects the action of the
Maximum Power Point Tracking (MPPT) controller
• The change ∆Ipv that represents the effect of variations in
irradiance
• The change ∆IpvVac that represents the effect of sudden
variations in ac grid voltage
Ipv (k+1)=Ipv (k)+ ∆IpvMPPT(k)
Read Ir(k)
= sudden decrease
∆Ir(k)=Ir (k)-Ir (k-
magnitude of the change ∆IpvVac is calculated if necessary.
Ipv
changes to
The new value of Ipv is calculated by adding these
-0.08<∆I (k)<0.08 B
Ipv
Ir(k)
Ir(k)the PV
Ipv(k) of Ipv and this new
value
is fed
into
thePV
current
= slow
change
Equation value
V (oc)(k)=f(I I(k),I
=0)
(k-1)
pv
A
array equation to determine
IpvMPPT is
I (k)= I ∆
(k-1)
pv and
(k)=V
(k-1)Ppv. Finally,
∆V V
Ir
∆
I
(k)
due
to
slow
(k-1)
I
pv
r
calculated by comparing the current and previous values of
change in Ir
PpvNew Operating Point with
r
pv
r
pv
pv
pv
pv
Ir(k1)
PV Equation
pv(k-1),
Ipv(k)=f(IrI(k),V
pv (k))
A
Ipv(k)
Session 4 Paper No 84
pv
PV Equation
Ipv(k)=f(Ir (k),Vpv (k))
Vpv(k)=0.92 Vpv(oc)(k)
Ipv is one of the inputs to the block representing the non-linear
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∆Ir(k)>0.08
= sudden increase
(k)<-0.08
∆IrFlow
Figure 2:
Chart of PV generation model
B
Vpv(k-1)
Vpv
Vpv(k)
(k)- Ipv (k-1)
∆
Vpv(k) Vpv
-Vpv
1(k-1)
Fig 4: Path of operating point for slow change in Ir
5: Path
ofof
operating
point for sudden increase in Ir
Fig. Fig.
3: Flow
chart
∆I Ir calculation
IpvIr(k)=Ipv
pv
CIRED
17th International Conference on Electricity Distribution
Figure 3 shows the flow chart for the calculation of ∆IpvIr.
This calculation depends on whether there has been a small
change in irradiance, a sudden large decrease in irradiance or
a sudden large increase in irradiance.
Barcelona, 12-15 May 2003
∆IpvIr (k) = Ipv (k) - Ipv (k-1)
Effect of Changes in irradiance
Figure 4, 5, 6 and 7 show how the operating point of the PV
generator changes as the operating condition change. The
nature of these changes was derived from experimental
results.
Figure 4 shows the path of the operating point following a
small change in irradiance. The operating point of the PV
array is assumed to be initially at A. on the curve
corresponding to Ir (k-1). If |Ir (k-1) - Ir (k)| is sufficiently
small (e.g. |Ir (k-1) - Ir (k)| < 8%), it was observed that the
operating point is assumed to move from point A to point B.
The dc voltage across the PV array is assumed to remain
constant:
Vpv (k) = Vpv (k-1)
Effect of Change in ac Grid Voltage
Figure 7 illustrates the modeling of the effects of changes in
the ac grid voltage. If A is the operating point before the
voltage disturbance, B is assumed to be the operating point
immediately after an increase in voltage and C the operating
point immediately after a decrease in voltage. While the
behavior of the system is qualitatively similar for both cases,
experimental results suggest that the quantitative effects are
different. The changes in PV array currents are:
∆IpvVac = -G×∆Vac for an increase in voltage
∆IpvVac = -0.25×G×∆Vac for a decrease in voltage
where G is a constant number equal to 2.875 for the generator
studied in this paper.
Ipv
Ipv (k) is calculated using the equation of the PV array with Ir
(k) and Vpv (k) as the inputs. Hence, for a small change in
irradiance:
I r (k )
A
B
∆IpvIr (k) = Ipv (k) - Ipv (k-1)
C
Figure 5 shows the path of the operating point following a
sudden large increase in irradiance. Immediately after the
sudden large increase in irradiance from Ir (k-1) to Ir (k), the
operating point moves from point A to point B. Hence, the
model assumes that:
Fig. 7: Path of operating point for sudden increase and decrease in Vac
Ipv (k) = Ipv (k-1) or ∆IpvIr(k)= 0
Figure 6 shows the path of the operating point following a
sudden large decrease in irradiance. Immediately after the
sudden large decrease in irradiance from Ir (k-1) to Ir (k), the
operating point moves from point A to point B along a
straight line. Point B is such that
Vpv (k) = 0.92 . Vpv (oc)
where Vpv (oc) is the open circuit voltage of the PV array for
these conditions, i.e. the value of Vpv for Ir (k) and Ipv (k)=0.
Ipv (k) is then calculated using the characteristics of the PV
array with Vpv (k) and Ir (k) as input. Hence, for a large
decrease in irradiance:
Ipv
Ir(k-1)
Ipv(k-1)
A
∆ IpvI r(k) due to sudden
decrease in Ir
Ir (k)
MPPT
This PV generation model assumes that the MPPT technique
used is the Perturb and Observe (P&O) method. Instead of
monitoring and controlling VPV, this model adjusts IPV in its
search for the maximum power point. The input to the MPPT
model are IPV and VPV. These two quantities are multiplied to
obtain P(k), which is compared to P(k-1), i.e. the value
obtained during the previous cycle. If the dc power delivered
by the array has increased since the last measurement, the
output of the MPPT will have the same sign as in the last
cycle. On the other hand, if the power has decreased, the
output of the MPPT will have the opposite sign to the last
cycle. This output (+1 or –1) is multiplied by the IPV step
value, IpvMPPT and added with the other components of the
current IPV. The value of IpvMPPT was determined by trial and
error. If the cycle time is small, the IpvMPPT will be relatively
small. If the cycle time is big, the IpvMPPT will be larger. In this
model, the cycle time used is 0.2s, and the IpvMPPT value
obtained is 0.085A.
CASE STUDIES
Ipv(k)
UMI_Tan_A1
V pv
These case studies illustrate the response of the system when
B
V pv(k-1)
V pv
V pv(k)
Session
4 Paper No 84
Fig. 6: Path of operating point for sudden decrease in Ir
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CIRED
17th International Conference on Electricity Distribution
Barcelona, 12-15 May 2003
subjected to a sudden change in irradiance caused by a
passing cloud. Figure 8 is the diagram of the test system used
in these examples. The system consists of a local area
connected to a remote area by five 500kV transmission lines.
All the loads (6668MW, 1910Mvar) are in the local area.
Without PV generation, the local generator at bus 3 generates
1154 MW, and the remaining power is supplied by the two
remote generators (bus 1 and bus 3) through five 500 kV
transmission lines. Shunt capacitors are connected at various
buses in the local area.
7
1
5
3
6
12
13
14
9
10
11
2
Figure 12(a): Irradiance data for the 5 PV generators
Figure 12(b): Total PV active power in bus 14
Figure 12(c): Bus voltage at Bus 1, Bus 3 and Bus 14
Figure 8: Test System with PV Generation allocated at Bus 11 and Bus 14
Table 1: Generations produced by both the conventional generators and PV
generation in the case of 10%, 20% and 30% level of PV penetration
Bus
Five PV generators are connected to the local area of 13.8kV
distribution circuit (bus 11 and bus 14) as shown in Figure 9.
External
Network
PV generation connection
point
P
PV 1
PV 2
PV 3
PV 4
PV 5
P (MW)
1
10%
Penetration
3291
20%
Penetration
2581
30%
Penetration
1876
2
1736
1736
1736
3
1154
1154
1154
11
335
670
1005
14
335
670
1005
Different amounts of PV penetration are considered in these
case studies. Table 1 shows both the power produced by the
conventional generators and the peak power of the PV
Figure 9: Diagram of 5 PV generators connected in a single bus
UMI_Tan_A1
Session 4 Paper No 84
Figure 10(a): Irradiance data
Figure 10(b): Total PV active power in bus 14
Figure 10(c): Bus voltage at Bus 1, Bus 3 and Bus 14
-3Figure 13(a):
11(a): Irradiance
Irradiance data
data for the 5 PV generators
Figure
Figure 13(b):
11(b): Total
PV active
powerpower
in busin14bus 14
Figure
PV active
Figure 13(c):
11(c): Bus
Bus voltage
voltage at
at Bus
Bus 14
14
Figure
CIRED
17th International Conference on Electricity Distribution
generators for 10%, 20% and 30% penetration of PV
generation. This system was simulated over a 60 seconds
period on a typical partly cloudy day. In case study 1, all the 5
PV generators are assumed to receive the same irradiance,
which is shown in Figure 10(a). The sampling rate of the
irradiance data is 1 sample/seconds. A plot of the generation
versus time for 10% PV penetration is shown in Figure 10(b).
Figure 10(c) shows the bus voltage versus time profile for a
few selected buses within the system. Figures 11(b) and 11(C)
show respectively the PV generation and bus voltages at bus
14 respectively for the three levels of penetration. Similar
simulations were carried out in case study 2. However, as
shown in Figure 12(a), the irradiance is shifted by 3 seconds
for each of the 5 PV generators. Figure 12(b) shows the total
amount of active power generated by the 5 PV generators into
Bus 14. Figure 12(c) shows the bus voltages on busses 3 and
14. The comparisons between the PV generations and the bus
voltages at bus 14 for the 3 levels of PV penetration are
shown in Figures 13(b) and 13(c) respectively.
ANALYSIS
Figure 10 shows that the amount of power produced by the
PV generators follows the pattern of irradiance. This is
because the MPPT controller keeps the PV systems operating
at their maximum power point despite the large fluctuations in
irradiance that take place over the 60 seconds. Figures 10(c)
and 12(c) confirm that the voltage at the bus with
conventional generators (Bus 3) is not affected by the
fluctuation in PV output because of the action of the
automatic voltage regulators. Bus 14 is connected to a PV
generator. Its bus voltage fluctuates during the large change in
irradiance level (between 3s and 25s). Its change follows the
pattern of change in the total power at the bus. The PV
generator is modelled as a P injector without a voltage
regulator.
Figure 11 shows that when the amount of PV penetration is
high, the amount of voltage fluctuation due to irradiance
change becomes more significant. As shown in figure 11(c) at
t=0s, all the bus are at the same voltage (0.948 p.u).
However, at t=60s, when the irradiance level is low, the
voltage for bus 14 settles at 0.925 p.u. for the 10% penetration
case, 0.90 p.u. for the 20% case and at 0.88 p.u. for the 30%
case. Figure 13 shows that similar results were obtained for
case study 2.
Barcelona, 12-15 May 2003
REFERENCE
[1] W. T. Jewell, R. Ramakumar and S.R. Hill, "A study of
dispersed photovoltaic generation on the PSO system",
IEEE Transaction on Energy Conversion, Vol. 3, No. 3,
September 1988.
[2] E. C, Kern, E. M. Gulachenski and G.A. Kern, " Cloud
effects on distributed photovoltaic generation: slow
transients at the Gardner, Massachusetts photovoltaic
experiment", IEEE Transaction on Energy Conversion,
Vol. 4, No. 2, June 1989.
[3] D. L. Garrett and S. M. Jeter, "A photovoltaic voltage
regulation impact investigation technique: Part 1 - Model
development,” IEEE Transaction on Energy Conversion,”
Vol. 4, No. 1, pp. 47-53, March 1987
[4] O. Wasynczuk, "Modelling and dynamic performance of a
self-commutated photovoltaic inverter system," IEEE
Transaction on Energy Conversion, Vol. 4, No. 3, pp.
322-328, September 1989
[5] O. Wasynczuk, "Modelling and dynamic performance of a
line-commutated photovoltaic inverter system," IEEE
Transaction on Energy Conversion, Vol. 4, No. 3, pp.
337-343, September 1989
[6] L.Wang, Y. H. Lin, "Dynamic stability analysis of a
photovoltaic array connected to a large utility grid, " IEEE
PES Winter Meeting, 2000 Vol. 1, pp. 476-480
[7] Energy for the Future: Renewable Sources of Energy White Paper for a Community Strategy and Action Plan,
pp. 599, 26 November 1997
[8] K.H. Hussein, L.Muta, T. Hoshino, M. Osakada,
"Maximum photovoltaic power tracking: an algorithm for
rapidly changing atmospheric conditions," an algorithm
for rapidly changing atmospheric conditions," IEE Proc.
on Generation, tranmission and distribution, Vol 142, No.
1, January 1995
[9] J.H.R Enslin, M.S. Wolf, D.B. Snyman, W. Swieger,
"Integrated photovoltaic maximum power point tracking
converter," IEEE Trans. on Industrial Electronics, Vol. 44,
No. 6, December 1997
CONCLUSION
A dynamic model of a PV generator has been developed and
incorporated in a power system stability program. Using this
model, it is possible to investigate the impact on the system of
the fluctuating PV generation resulting from changes in
irradiance caused by passing clouds. As the penetration of
PV generation increases, it could have a significant effect on
bus voltages. Without proper voltage control, it is unlikely
that PV generation will satisfy grid regulations and this could
hamper its adoption. Further research on the voltage control
of PV generation is therefore needed.
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