Zeszyty Problemowe – Maszyny Elektryczne Nr 3/2014 (103)
41
Dariusz Borkowski
Cracow University of Technology
OPTIMIZING CONTROL ALGORITHM OF ENERGY CONVERSION
SYSTEM FOR SMALL HYDROPOWER PLANT WORKING AT
VARIABLE SPEED
Abstract: The paper presents the control algorithm dedicated to a variable speed energy conversion system in
a small hydropower plant. The energy conversion system consists of propeller water turbine, permanent
magnet synchronous generator and power electronic converter.
The main purpose of the algorithm, apart from the water level controlling, is to achieve the highest possible
efficiency of the system. The changeable hydrological conditions, in the form of significant variations in a
river’s flow and head throughout the year, requires to operate in a wide water flow and head range. Applied
optimizing techniques guarantee maximal average efficiency independently of hydrological condition changes,
by constant searching of the optimal operation parameters.
The presented control method is implemented and tested in the energy conversion model, created in the
Matlab/Simulink software. All characteristics and parameters were identified on the real small hydropower
plant and on the special laboratory model.
Keywords: small hydro power plant, variable speed, control algorithm, PM generator
1. Introduction
Small Hydropower Plants (SHP), as a
decentralized energy sources located close to
their customers, improve grid stability by
diversifying the electricity system and reducing
transmission losses. In Poland a fast
development of SHP, from 400 objects in year
2000 to 700 power plants in year 2010, has
been registered. Moreover, according to the
“Energy policy of Poland until 2030 year” the
threefold increase of installed capacity is
planned. Production of energy from renewable
sources has a key importance for the energy
security of Poland and European Union policy.
According to 2009/28/EC [1] directive the
European Union (Poland) should produce 20%
(15%) of electrical energy from renewable
energy sources by the end of year 2020, while
the current share of this sources is estimated at
12.7% (9.5%) [2].
SHPs are objects rated up to 10 MW. The main
division criterion is the type of energy
conversion system, that is elements complex
used to convert energy from water through
mechanical energy (water turbine) into
electrical
energy
(electrical
generator)
supplying power system. Traditional solutions
of energy conversion system for SHP are based
on the water turbines working at constant speed
(synchronous generators) or almost constant
speed (asynchronous generators).
An interesting solution is to apply the system
used in wind power plants, which due to the
huge wind variations works with variable
rotational speed. This design significantly
simplifies the mechanical system but requires a
Power Electronic Unit (PEU) in the energy
conversion system to match the load and
control the power flow from the generator to
the grid [3], [4]. The Permanent Magnet
Synchronous Generator (PMSG) is the most
likely candidate from among the generator
types used in SHPs because of its potential for a
high pole number (a gearbox is not needed for
variable speeds) and a high efficiency under a
wide range of loads. The PEU, which control
the turbine load torque by setting a given
generator current, allows to operate the turbine
in a wide range. In Europe and particularly in
Poland that type of solutions are rare and have
mainly the prototype character [5]. However,
significant and promising features following
from applying variable speed operation as well
as accessibility of high power electronic
converters cause increasing interests of such
solutions in SHPs.
In the recent years some innovative solutions
integrating the propeller turbine and the
synchronous generator have appeared on the
market. It eliminates the complexity of
designing and maintaining mechanical systems
for gearbox, shaft and rotor blade control.
Applying the variable speed operation in this
42
Zeszyty Problemowe – Maszyny Elektryczne Nr 3/2014 (103)
system improves its features and makes it more
attractive nowadays [6].
The profitability of SHPs depends largely on
their
location
and
the
hydrological
characteristics at that location [7]. SHPs are
primarily “run-of-the-river” plants, defined as
providing little or no water storage. Thus, the
operation state of the power plant (e.g.
generating power) depends on the actual
hydrological conditions. Due to the changeable
hydrological conditions throughout the year, it
is recommended to operate in a wide water flow
and head range [8]. It significantly increases the
annual average efficiency of generation system.
Using variable speed operation allows to work
in a such changeable conditions with high
efficiency of the turbine. Management of the
energy conversion system with the PEU, due to
the specific features of water turbine (quite
different then wind turbine), should be based on
the dedicated control strategies ensuring proper
exploitation and the optimal parameters of
turbine operation. Desirable regulation has to
adjust the operation parameters due to the
actual conditions in order to obtain the highest
possible efficiency of the whole energy
conversion system. Dedicated optimization
algorithm presented in this paper fulfils this
requirements. It is implemented and tested on
the simulation model created in the
Matlab/Simulink
software.
The
energy
conversion model is based on the real system
installed in the SHP of 150 kW nominal
power [6]. All characteristics and parameters
are identified in this object and in the 30 kW
laboratory model [9].
2. Energy conversion system structure
The energy conversion system, analysed in this
paper, contains guide vanes, which control the
water quantity flowing through the turbine,
propeller turbine integrated with permanent
magnet synchronous generator (PMSG) and the
power electronic unit (PEU). The block
diagram of the system is presented in Fig. 1.
The controller adjust the guide vanes angle α
limit
and current limits of the PEU (I DC
, I slimit )
depending on the actual measuring parameters:
water head H, rotational speed n as well as
current and voltage of the grid (I s , U s ) .
Is
Us
α
Ig
r
I DC
I gr
Fig. 1. Block diagram of the energy conversion in SHP
3. Identification of elements features and
system parameters
In order to create the simulation model of
energy conversion system all elements have to
be analysed and represented by its essential
features. Due to the fact, that this model will be
using to test the control method, particular
elements will be represented by a steady state
characteristics, time constants and efficiency
function. This simplification is necessary to
accelerate the simulation calculations.
3.1. Power electronic unit
Applied Power Electronic Unit (PEU) is the
full-scale
AC/DC/AC
power
converter
consisting of: an uncontrolled rectifier, DC-DC
boost converter which increases the DC voltage
and the DC/AC converter with DPC-SVM
algorithm (Virtual Flux – Direct Power Control
with SVM modulator) [4], [6]. The main
limit
controlling parameter is I DC
which tunes the
DC current by the PI-IDC regulator (Fig. 2).
Zeszyty Problemowe – Maszyny Elektryczne Nr 3/2014 (103)
D
LDC
TDC
CR
CF
iDC
u DC
r
U DC
+
limit
I DC
r
i DC
Fig. 2. Block diagram of AC/DC/AC converter
Thus the generator current I g can be controlled
limit
by the I DC
with relation:
2 limit
I DC
3
Ig =
(1)
Fig. 3 presents real operation points of the
converter compared with relation (1).
43
It is also changing depending on the generator
speed but in a small range, thus this variation
has been neglected.
The second controlling parameter – limit of the
grid current I slimit , which limits the generated
output power, is set to the value that
corresponds to the maximum power to protect
the PEU and turbine against a runaway speed
condition [6].
3.2. PM synchronous generator
The synchronous generator can be treated as an
inertial object of a first order, where the
generator current can be regarded as the system
input, to which turbine torque is the system
output. Taking into account linear relations
between stator current and electromagnetic
torque the object gain is constant and
independent on the generator speed. The delay
and inertia of this object can be neglected
comparing to the dynamic parameters of the
PEU, see Fig. 5. The PMSG efficiency is
relatively constant over a wide range of loads,
what is visible in Fig. 4.
Ig
1.5
I gN
I DC
I DCN
1
0.5
0
I DC
0
0.5
1
1.5
2
2.5
3
3.5
4
t[s]
I gN
Fig. 3. Steady state characteristic of converter
PI-IDC regulator
Dynamic characteristic of the PEU in the form
of current step response was shown in [9]. The
time constant ToPEU were estimated to be about 1
second. The efficiency of the PEU is sensitive
to the value of the transferred power (Fig. 4).
1.5
T
TN
1
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
t[s]
Ig
I gN
1.5
1
0.5
0
-0.5
-1
-1.5
0
0.5
1
1.5
2
2.5
3
3.5
4
t[s]
PMSG
η
[%]
Fig. 5. IDC step response of generator
parameters: generator torque and stator
current
PEU
P
PN
Fig. 4. Measured efficiencies of the PEU and
PM synchronous generator in power domain
3.3. Propeller turbine
Turbine properties can be visualised by a
universal characteristic (known as a hill chart)
that presents efficiency isolines on a water
flow-speed plane. The real characteristic has
been identified in the power plant and
approximated [9] (Fig. 6).
Zeszyty Problemowe – Maszyny Elektryczne Nr 3/2014 (103)
44
tests of real turbine operation have allowed to
identify this parameter estimated at 3,5
seconds [9].
1.4
1.2
1
n
nN
4. Simulation model of SHP implemented
in Matlab/Simulink software
0.8
0.6
0.4
0.2
0.2
0.4
0.6
0.8
Q / QN
1
1.2
1.4
Fig. 6. Universal characteristic of the real
propeller turbine (guide angle line – solid,
efficiency isoline – dashed)
Dynamic behaviour of the turbine is caused by
many elements, but the most significant is
dynamic of the water mass. This time constant,
marked by the Tow is a function of the water
head and the volume of the inlet channel. The
All features described in the previous chapter
have been implemented in the Matlab/Simulink
software (Fig.7). In addition the water tank
model [9] and guide vanes model, which limits
the speed of position changing, have been
created. The main task of the regulation system
is to maintain a constant hydrological
conditions i.e., maintain the upper water Hg at a
fixed level. Usually this is realizing by negative
feedback control system. The regulator (usually
PI) adjusts the control input (the angle α of the
guide vanes) based on the actual error ε. The
DC current is the parameter that controls the
speed by setting the generator torque. Its value
is set depending on the hydrological conditions
in order to obtain the desirable operation point.
Fig. 7. Block diagram of SHP simulation model
5. Optimizing algorithm
The main criterion of a control parameter, i.e.
the DC current, from the economic point of
view, is the maximum efficiency of the whole
energy conversion system. The control of “runof-the-river” plants is difficult due to the
continuously
changeable
hydrological
conditions as well as turbine features caused by
silt deposited in channels. Algorithms basing on
the fixed settings and operation characteristics
are ineffective [10]. From that reason, the
special methods which will be adapting control
parameter automatically to the actual conditions
have to be defined. It can be done by the using
of the optimizing nonlinear algorithms. The
procedure starts from non-optimal current
value and tries to improve the production
efficiency η by applying the gradient method.
Zeszyty Problemowe – Maszyny Elektryczne Nr 3/2014 (103)
∆I DC = k ⋅
∂η
∂I DC
(2)
The efficiency of energy conversion system is
defined by following formula:
η=
where:
3 ⋅U s ⋅ Is
9.81 ⋅ Q ⋅ H
(3)
U s - grid voltage, I s - grid current,
Q - water flow, H - water head
Using the discretization Euler method of an
order one the formula (2) may be written as
follow:
η − η( −1)
I DC (1) = I DC ( 0 ) + k ⋅ ( 0 )
(4)
I DC ( 0 ) − I DC ( −1)
45
The procedure changes the initial values of
current IDC following the direction of the
gradient components multiplied by a positive
factor k. The optimizing algorithm is activating
only in a steady state of the system, which is
obtained by the PI regulator.
The example operation of the algorithm is
presented in Fig. 8. Simulated situation assume
nominal water head and zero initial parameters.
The water flow characterises step change from
90% to 100% of nominal value in the 20th
algorithm step. After each algorithm step,
resulting in new DC current value, the system is
tuned by PI regulator in order to obtain the
steady state condition and desired upper water
level (Fig. 9).
step 23
Ts
step 24
1.002
Hset= 1
where, the subscript brackets indicate the step
number of optimizing algorithm l.
Hr
0.998
t [s]
a)
Q
QN
1.1
1
1
α
0.9
0.9
t [s]
0.8
5
10
15
20
25
30
35
b)
l
40
o – Ig
x – n 1.1
□–α 1
1.1
Qin = 1
Qr
0.9
0.9
t [s]
0.8
5
10
15
20
25
30
35
1.1
l
c)
η
ηN
40
n
1
1
0.9
0.95
0.9
5
d)
ε
x 10
10
15
20
25
30
35
l
40
-3
4
2
0
5
10
15
20
25
30
35
l
40
Fig. 8. Relative system parameters: a) water
flow b) generator current (circle), speed (cross)
and guide angle (square), c) total efficiency, d)
regulator error; for a certain algorithm step
Tg
Tt
t [s]
Fig. 9. Time domain system parameters during
the example inter-optimizing period (Ts=200s)
tuned by PI regulator
The optimizing method fulfils the main
criterion of control algorithm by obtaining the
maximum efficiency of the whole system for a
given hydrological conditions. This feature can
be seen in Fig. 8 c) and in the efficiency
characteristic presented below (Fig. 10). The
maximal efficiency is achieved after several
algorithm steps. Continuous seeking process
provide optimal operation parameters also after
changes of the water flow value.
Zeszyty Problemowe – Maszyny Elektryczne Nr 3/2014 (103)
46
Spr(n,Q)
1.1
1.05
1
0.95
Q
Q
QN
0.9
0.85
starting point
0.8
0.75
0.7
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
n / nn N
Fig. 10. Steady state algorithm steps (square
markers) on the water flow – rotational speed
plane (total efficiency isolines – solid line,
guide angle lines – dashed line, maximal
efficiency line – dash-dot line)
6. Summary
The changeable hydrological conditions and
variable turbine parameters due to the ageing
process as well as river pollution requires
adaptive control. This paper presents the
procedure based on gradient method which
tunes the generator current, through the DC
current of the PEU, in order to obtain the
highest possible efficiency. The controller uses
the standard PI regulator which provide desired
upper water level and the steady state
conditions in which the optimizing algorithm is
activated.
The gradient descent method, applied in this
paper, can provide small step changes resulting
in short periods of unsteady states. Thus the
optimal operation point may be obtained
relatively fast. The drawback of this technique
is the limitations of target to the local extreme
(minimum or maximum). Fortunately, the
efficiency characteristic (quality function) of
the investigated system is the convex function
which means that any local extreme is the
global extreme.
Presented simulation results confirm the
algorithm effectiveness and application
possibility on the real system.
7. Bibliography
[1]. Directive 2009/28/ec of the european parliament
and of the council of 23 April 2009 on the
promotion of the use of energy from renewable
sources and amending and subsequently repealing
Directives 2001/77/EC and 2003/30/EC. [Online].
Available:http://eurlex.europa.eu/LexUriServ/LexUr
iServ.do?uri=Oj:L:2009:140:0016:0062:en:PDF
[2]. Report from the commission to the european
parliament, the Council, the european economic and
social committee and the Committee of the regions,
Brussels, 27.3.2013, [Online]. Available:
http://eurlex.europa.eu/LexUriServ/LexUriServ.do?u
ri=COM:2013:0175:FIN:EN:PDF
[3]. Fraile-Ardanuy J., Wilhelmi J.R., Fraile-Mora
J.J., Perez J.I.: Variable-Speed Hydro Generation:
Operational
Aspects
and
Control,
IEEE
Transactions on Energy Conversion, vol. 21, no. 2,
June 2006
[4]. Kaźmierkowski M., Krishnan R., Blaabjerg F.,
Irwin J.: Control In Power Electronics,
ACADEMIC PRESS, 2003, ISBN: 0-12-402772-5
[5]. Status report on variable speed operation in
small hydropower Austria: Energie publication,
2000. [Online]. Available:
http://ec.europa.eu/energy/res/sectors/doc/small_hyd
ro/statusreport_vspinshp_colour2.pdf
[6]. Borkowski D., Węgiel T.: Small Hydropower
Plant with Integrated Turbine-Generators Working
at Variable Speed. IEEE Transactions on Energy
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[7]. G. A. Aggidis, E. Luchinskaya, R. Rothschild,
and D. C. Howard, The costs of small-scale hydro
power production: Impact on the development of
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2632–2638, 2010
[8]. A. Wijesinghe and L. Lei Lai, Small hydro
power plant analysis and development, in Proc. 4th
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[9]. Borkowski D.: Laboratory model of small
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Zeszyty Problemowe – Maszyny Elektryczne Nr
3/2013 (100), pp. 27-32
[10]. Borkowski D., Węgiel T.: Optymalizacja
przetwarzania energii dla małych elektrowni
wodnych z generatorami pracującymi ze zmienną
prędkością obrotową. Zeszyty Problemowe Maszyny Elektryczne Nr 92/2011, pp. 121-126
Author
Dariusz Borkowski, Ph.D.
Cracow University of Technology,
Faculty of Electrical and Computer Engineering,
Institute of Electromechanical Energy Conversion,
31-155 Kraków, Warszawska 24 St.
tel. +48 12 628-26-59, email: [email protected]
Acknowledgement
This work was supported by the Research
and Development Centre „Rader Bis”.