A Frequency Control Method for Isolated Photovoltaic-diesel Hybrid Power System with Use of Full Renewable Energy
Abstract -- In this paper, a frequency control method is introduced for photovoltaic-diesel hybrid system by using a load estimator and an energy storage system. The proposed method is compared with a fuzzy based frequency control method.
Simulation results show that the proposed method is feasible to reduce the frequency deviations of the isolated power utility and delivers maximum power compared to the fuzzy based method.
Index Terms—Frequency control, photovoltaic-diesel hybrid power system, load estimator, energy storage system, frequency deviation.
I. I NTRODUCTION
Most small islands around the world are still dependent on imported fossil fuels for most of their energy requirements.
The electricity of these islands is exclusively produced by diesel generators. The use of diesel generators to provide electricity is one of the most expensive and environmentally detrimental ways of generating electricity [1]. Although these islands produce only a tiny fraction of global green house gas emissions, they are amongst the most vulnerable to the effects of climate change. So, there is a need to introduce renewable energy in isolated islands to reduce the diesel consumption.
Global photovoltaic (PV) production has been doubling every two years, increasing by an average of 48% each year since 2002, making it the world’s fastest growing energy technology [2]. One of the most promising applications of photovoltaic power system is the installation of PV-diesel hybrid systems in isolated islands where the cost of grid extension is prohibitive and the price for fuel increases drastically with the remoteness of the location. It is reported that in sunny locations, PV generators compare favorably with wind generators [3].
To date it has not been necessary for PV power systems to provide frequency control services to the isolated power utility. In the future, with an increasing penetration of PV generation, their impact upon the overall control of the power system will be significant [4]. This will lead to a situation where the PV generators will be required to share some of the duties, such as frequency control. Therefore, for the penetration of large PV power in the isolated utility without reducing the reliability of the utility, suitable measures must be applied to the PV systems side.
Fig. 1. Block diagram of the isolated power system.
Several studies have been carried out for reducing the harmful effect of large PV power penetration. Power characteristics of PV ensembles are presented in [5] where monitored data from 100 PV systems were used to study effects of combined power generation of these systems, compared to the characteristics of an individual system. It was claimed that a significant amount of power fluctuations disappeared, however, large amount of short term power fluctuations are remained. In addition, when the numbers of PV power systems were decreased, the power fluctuations increased. Smoothing of PV system output by tuning maximum power point tracking (MPPT) control is demonstrated in [6]. In this method, when the insolation increases rapidly, the operating MPPT point changes to a new point where the maximum power is not generated with the current insolation. It was reported that this method can be applied to several PV power generation systems to achieve a combined output power fluctuations smoothing. However, the condition of power utilities like frequency deviation is not considered for tuning the MPPT and for limiting the new output voltage. Moreover, none of the above methods is used for frequency control purpose.
Recently, a fuzzy based frequency control method for PV- diesel hybrid system is introduced in [7]. Insolation, change of insolation, and frequency deviation are used as inputs for fuzzy controlled output power command system which decides the required PV output power to reduce frequency deviations.
In this paper, we introduce a frequency control method for PV-diesel hybrid system by using a load power estimator [8]
Manoj Datta, Tomonobu Senjyu, Atsushi Yona
Student Member, IEEE, Senior Member, IEEE, Member, IEEE University of the Ryukyus
Okinawa 903-0213, Japan
[email protected], [email protected]
Toshihisa Funabashi
Senior Member, IEEE Meidensha Corporation Tokyo 141-6029, Japan [email protected]
MPPT Control
PV Array Bi-directional
Inverter
Energy
Storage Bi-directional Inverter
Diesel Generator
Load
AC Bu s
PEDS2009
and an energy storage system (ESS) [9]. Our method is compared with the method described in [7] and is found effective in following key features: supplying MPPT generated PV power, reducing required diesel power so as the CO2 emission, and reducing frequency deviations.
1 R
5 T S + 1
d1 MS +D K
s
1 T S + 1
gΔf
Governor Diesel generator Power system
insolation
Load
S
iLoad power
estimator P
dP
LP
LΔf
u
u
Bi-directional Inverter MPPT
control EDLC
P
max*P
ESSPV Inveter
P
ESS*P
LP
pvP
ESSP
pvOutput power command generation and ESS charging system
Fig. 2. The isolated power system model.
D
R
R V R
Io
o o
sh s
Irsh
Ig
Id
Fig. 3. Equivalent circuit of a solar module.
0 5 10 15 20 25 30 35 40
0 1 2 3 4 5 6 7 8 9
T=25 C
1000 W/m2
800 W/m2
600 W/m2
Module Volatge [v]
Module Current [A]
(a)
0 5 10 15 20 25 30 35 40
1000 W/m2
800 W/m
600 W/m
Module Volatge [v]
Module Power [W]
0 50 100 150 200 250
T=25 C 2
2
(b)
Figure 4. Solar module characteristic curves. (a) Current-voltage curves. (b) Power –voltage curves. The discrete data points shown are taken from the manufacturer’s curves [11], and show excellent correspondence with the model.
II. M ODEL OF I SOLATED P OWER SYSTEM
The block diagram of the isolated power utility used in this paper is shown in Fig. 1. The isolated power utility consists of a diesel generator, a PV system, and an ESS that generate power to supply the load demand.
The detail model of the isolated power system consisted of a diesel generator, a PV generator, a load estimator, an ESS and load is shown in Fig. 2, where, S is the insolation, i P pv is the PV power, P max * is the MPPT power, P d is the generated diesel power, R is the speed regulation, T g is the governor time constant, T d is the diesel generator time constants, P is the load, L P ˆ is the estimated load power, L M is the inertia constant, D is the damping constant, P ESS and P ESS * is the actual ESS power and command ESS power, u is the governor input, and Δ f is the frequency deviation.
As the design of power converter and the control system is significantly influenced by the PV module characteristics, these will briefly reviewed here. The PV module is a nonlinear device and can be represented as a current source model, as shown in Fig. 3. The traditional I- V characteristics of a PV module are given by the following equation [10]:
rsh p
s s a
sat p g
p I
N I R V N AKT I qV
N I N
I −
⎪⎭
⎪ ⎬
⎫
⎪⎩
⎪ ⎨
⎧ ⎟ ⎟ −
⎠
⎞
⎜ ⎜
⎝
⎛ +
−
= exp 0 0 0 1
0 (1)
where I 0 and V 0 are the output current and output voltage of the PV module, respectively, I g is the generated current under a given insolation, I sat is the reverse saturation current, q is the charge of an electron, K is the Boltzmann’s constant, A is the ideality factor, T a is the temperature of the PV array (K), N p is the number of cells in parallel, N s is the number of cells in series and I rsh is the current due to intrinsic shunt resistance of the PV module.
The saturation current ( I sat ) of the PV module varies with temperature according to the following equation [10]:
⎥ ⎥
⎦
⎤
⎢ ⎢
⎣
⎡
⎟ ⎟
⎠
⎞
⎜ ⎜
⎝
⎛ −
⎥ ⎥
⎦
⎤
⎢ ⎢
⎣
= ⎡
a ref a g ref
or a
sat KT T T
qE T
I T
I exp 1 1
3
(2)
[ sc t ( a ref ) ] 1000 i
g
T S T I I
I = + − (3) where I is the saturation current at or T ref , T ref is the
reference temperature, E is the band gap energy, g I is t the short circuit current temperature coefficient, and I is sc the short circuit current of PV module. The current due to the shunt resistance is given by the following equation [10]:
ESS
T a
T a
PEDS2009
sh s
s
rsh N R s
R I N
I = V 0 + 0 (4) where R sh is the internal shunt resistance of the PV module. The PV module output power is given by the following equation:
0 0
0 V I
P = (5) For PV module, (1)-(5) are used in the development of MATLAB/SIMULINK based computer simulations. Figs.
4(a) and (b) show the simulated ampere-volt and power-volt curves for the PV module. Here, the discrete data points shown are taken from the manufacturer’s data sheet [11] for validating the model. From these curves, it is observed that the output characteristics of the PV array are nonlinear and are vitally affected by the variation of insolation.
III. L OAD P OWER E STIMATOR D ESIGN
First, a minimal-order observer is designed to estimate the load power by using the power system parameters. A simple minimal-order observer [12] is shown in Fig. 5. The state space representation of the plant is obtained by
) ( ) ( )
( t Ax t Bu t
x = + (1) )
( ) ( t Cx t
y = (2) where x ( t ) is an n × 1 state vector, y ( t ) is an l × 1 output vector, u(t) is an m × 1 input vector, A is an n × system n matrix, B is an n × input matrix, and C is an m n × output l matrix.
From [12] and Fig. 6, the minimal-order state observer can be written as
) ˆ ( ) ( ) ˆ ( )
( t = A ω t + Ky t + B u t
ω (3) )
( ) ( )
ˆ ( t D t Hy t
x = ω + (4) where ) ω (t is the n − l × 1 state variable of the observer,
( n n l )
D × − , H ( ) n × l , A ˆ ( n − l × n − l ) , K ( n − l × l ) , and ( n l m )
B ˆ − × are design co-efficients in the minimal-order observer, and A ˆ = A 22 − LA 12 , K = A ˆ L + A 21 − LA 11 ,
ˆ LB 1
B = − + B , 2 ⎥
⎦
⎢ ⎤
⎣
= ⎡
−
− l I n S
D 1 0
, and ⎥ ⎦
⎢ ⎤
⎣
= − ⎡ L S I
H 1 l .
B
K
H u
A D
x
y ω . ω
x=Ax+Bu y=Cx
Plant
Minimal order observer Fig. 5. Structure of a typical minimal order observer.
1 R
5 T S + 1
d1 MS +D K
s
1 T S + 1
gΔf Governor Diesel generator Power system
Load
P
DP
Lx .
1x .
2x .
3u
Fig. 6. Power system model for observer
PV array Model and MPPT Control
S i
insolation
estimated load power
P max
P dreq P L
required diesel power
Average of
20 seconds P ESS *
P dlevel
Fig. 7. ESS charging/discharging command system.
The power system model used to design the observer is shown in Fig. 6. From Fig. 6, after using the state space manipulation given in [12], the coefficients of the minimal- order state observer can be found as
, 265 . 5
4538 . 15
3748 . 1 ,
9 0 9
75 . 9 10 75 . 9
95 . 1 2 . 0 75 . 1 ˆ
⎥ ⎥
⎥
⎦
⎤
⎢ ⎢
⎢
⎣
⎡
−
=
⎥ ⎥
⎥
⎦
⎤
⎢ ⎢
⎢
⎣
⎡
−
−
−
−
= K
A
⎥ ⎥
⎥ ⎥
⎦
⎤
⎢ ⎢
⎢ ⎢
⎣
⎡
−
= −
⎥ ⎥
⎥ ⎥
⎦
⎤
⎢ ⎢
⎢ ⎢
⎣
⎡
=
⎥ ⎥
⎥
⎦
⎤
⎢ ⎢
⎢
⎣
⎡
=
9 . 0 975 . 0
195 . 0
1 and
, 1 0 0
0 1 0
0 0 1
0 0 0 , 0 10
0
ˆ D H
B , and the
minimal-order observer can be written as (see the Appendix)
u y
⎥ ⎥
⎥
⎦
⎤
⎢ ⎢
⎢
⎣
⎡ +
⎥ ⎥
⎥
⎦
⎤
⎢ ⎢
⎢
⎣
⎡
− +
⎥ ⎥
⎥
⎦
⎤
⎢ ⎢
⎢
⎣
⎡
−
−
−
−
=
⎥ ⎥
⎥
⎦
⎤
⎢ ⎢
⎢
⎣
⎡
=
0 10 0 265 . 5
4538 . 15
3748 . 1 9
0 9
75 . 9 10 75 . 9
95 . 1 2 . 0 75 . 1
3 2 1
ω ω ω ω
(5)
y x
x x x x
⎥ ⎥
⎥ ⎥
⎦
⎤
⎢ ⎢
⎢ ⎢
⎣
⎡
− + −
⎥ ⎥
⎥ ⎥
⎦
⎤
⎢ ⎢
⎢ ⎢
⎣
⎡
=
⎥ ⎥
⎥ ⎥
⎦
⎤
⎢ ⎢
⎢ ⎢
⎣
⎡
=
9 . 0 975 . 0
195 . 0
1
1 0 0
0 1 0
0 0 1
0 0 0
4 3 2 1
ω
(6)
PEDS2009
IV. O UTPUT P OWER C OMMAND S YSTEM
After estimating load power, Pˆ , the required diesel power L can be found by the following equation.
max *
ˆ P
P
P dreq = L − (7) where P max * is the MPPT command power. The leveling diesel power can be obtained by the following equation.
∫
−
=
t T t
dreq
dlevel T P dt
P 1 (8) where T is the sampling time. Now the ESS charging/discharging power command is generated by the following equation.
dlevel dreq
ESS P P
P * = − (9) If the sign of P ESS * is negative, ESS is in discharging mode. On the other hand, if the sign of P ESS * is positive, ESS is in charging mode. The ESS charging/discharging command system is shown in Fig. 7.
V. S IMULATION R ESULTS
Effectiveness of the proposed frequency control method is examined by simulation with system model and parameters mentioned in [10], [11], [13], and [14]. In order to use the parameters of real systems given in [13], [14], the rated output powers of the PV generator and the diesel generator are 225 kW and 450 kW respectively. The rating of the ESS is 135 kW. Simulation parameters of power system, PV array, and power converter are shown in TABLE III. Integral time T is 100s, and sampling time T s to obtain discrete value of output power command is 10s. Simulation time is 30 minutes.
0 200 400 600 800 1000 1200 1400 1600 1800
0.65 0.7 0.75 0.8 0.85 0.9
Actual Estimated
Time t, s
P [pu]L(a) Load power estimation
0 200 400 600 800 1000 1200 1400 1600 1800
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Time t, s
Estimation error [%]
(b) Load power estimation error
Fig. 8. Load power estimation
Fig. 8(a) shows the actual load and estimated load by solid line and dotted line respectively. Fig. 8(b) shows the percentage of estimation error. The load estimator works well as the estimated values are in accordance with the actual values and the estimation error is less than 1%. Fig. 9 shows the comparative simulation results of the proposed method and the method given in [7]. Fig. 9(a) shows insolation which is pretty fluctuating with time. Figs 9 (b), (c), (d), and (e) show the comparative simulation results where results of the proposed method are shown by solid line and results of the fuzzy based method [7] are shown by dotted line respectively.
Fig. 9(b) shows PV power where the power produced by the fuzzy based method is less than the power produce by the proposed method as proposed method supplies MPPT controlled PV power to the utility. Fig. 9(c) shows the diesel power where diesel power produced with the proposed method is less fluctuating than the diesel power produced with fuzzy based method. Moreover, lesser amount of diesel power is required with the proposed method; therefore, proposed method can reduce usage of heavy oil compared to the fuzzy based method. Fig. 9(d) shows frequency deviation where frequency deviation with the proposed method is almost zero. Fig. 9(e) shows ESS charging and discharging power.
TABLE III S IMULATION P ARAMETERS
Parameters of isolated power system
Inertia constant, M 0.150 puMW.s/Hz
Damping constant, D 0.008 puMW/Hz
Governor time constant, T
g0.10 s
Time constant, T
t0.25 s
Time constant, T
r8.0 s
Speed regulation, R 2.5 Hz/puMW
Parameters of PV module
Rated output power 216 W
Open circuit voltage, V
oc36.50 V Short circuit current, I
sc8.10 A
Shunt resistance, R
sh50 Ω
Series resistance, R
s5 Ω
Ideality factor, A 1.450
Inverse Saturation Current, I
or3.047e-07 A S.C. current temperature constant, I t 1.73e-03 A/
0K Number of cells in series, N
s60
Dimension 0.75 m
3Parameters of PV array
Rated output power 225 kW
Open circuit voltage 584 V
Short circuit current 526.50 A
Number of modules in series 16 Number of modules in parallel 65
Total number of cells 62,400
Parameters of Power converter
Inverter power rating 225 kW
Nominal ac output voltage 480 V (3-φ)
Nominal ac output frequency 50 Hz
Maximum ac line current 271 rms Maximum dc input voltage 600 V Maximum dc input current 781 A
Efficiency 94.5%
PEDS2009
0 200 400 600 800 1000 1200 1400 1600 1800 400
500 600 700 800 900 1000
Time t, s Si[W/m ]2
(a) insolation
0 200 400 600 800 1000 1200 1400 1600 1800
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
PV output power,P [ pu]A
Time t, s Fuzzy Proposed
(b) PV power
0 200 400 600 800 1000 1200 1400 1600 1800
0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Diesel power,P [pu]d
Time t, s Fuzzy Proposed
(c) Diesel generated power
0 200 400 600 800 1000 1200 1400 1600 1800
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
Fuzzy Proposed
Frequency deviation,Δf [Hz]
Time t, s
(d) Frequency deviations
0 200 400 600 800 1000 1200 1400 1600 1800
-0.15 -0.1 -0.05 0 0.05 0.1 0.15
Time t, s Fuzzy Proposed ESS charging/discharging power, Pess[pu]
![Fig. 9. Comparative simulation results of the proposed method and the method described in [7]](https://thumb-ap.123doks.com/thumbv2/9libinfo/9125068.409488/5.918.89.444.105.906/fig-comparative-simulation-results-proposed-method-method-described.webp)
