DEVELOPMENT AND APPLICATION OF THE ADJUSTABLE LOAD SHARING COEFFICIENTS METHOD FOR LOAD SHARING CONTROL BETWEEN PARALLEL OPERATING GENERATORS IN ISOLATED POWER GENERATION SYSTEMS
An isolated hydroelectric power-generating system of 400 V/50 Hz is studied. The system is built using hydroelectric units equipped with regulated hydraulic turbines and induction generators, a power electronic AC/DC voltage converter, a dump load and a bank of compensating capacitors. The stator wi...
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| author | Mazurenko , L. Dzhura , O. Shykhnenko , M. |
| author_facet | Mazurenko , L. Dzhura , O. Shykhnenko , M. |
| author_institution_txt_mv | [
{
"author": "L. Mazurenko ",
"institution": "Institute of Electrodynamics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine."
},
{
"author": "O. Dzhura ",
"institution": "Institute of Electrodynamics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine."
},
{
"author": "M. Shykhnenko ",
"institution": "Institute of Electrodynamics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine."
}
] |
| author_sort | Mazurenko , L. |
| baseUrl_str | https://ve.org.ua/index.php/journal/oai |
| collection | OJS |
| datestamp_date | 2026-07-18T06:32:22Z |
| description | An isolated hydroelectric power-generating system of 400 V/50 Hz is studied. The system is built using hydroelectric units equipped with regulated hydraulic turbines and induction generators, a power electronic AC/DC voltage converter, a dump load and a bank of compensating capacitors. The stator windings of the generators in the system under consideration were connected in parallel. The power electronic converter, implemented on fully controlled semiconductor switches, performs the functions of a static synchronous compensator and an active rectifier in the system. A new method for frequency, voltage and load sharing control between generators is proposed. Based on the proposed method, frequency, voltage and load sharing controllers for the discussed system are developed. The converter control is implemented using stator voltage oriented vector control technique and space-vector pulse-width modulation of stator voltage. Verification of the proposed method for frequency, voltage and load sharing control between generators is carried out using the developed dynamic simulation model of the system under consideration. The obtained simulation results were analyzed and further research directions were formulated. Bibl. 23, Fig. 3, Table.  |
| doi_str_mv | 10.36296/1819-8058.2025.3(82).184-192 |
| first_indexed | 2025-10-01T01:30:54Z |
| format | Article |
| fulltext |
184
Відновлювана енергетика. № 3/2025 | Гідро-воднева енергетика
UDC 621.313.332 https://doi.org/10.36296/1819-8058.2025.3(82).184-192
DEVELOPMENT AND APPLICATION OF THE ADJUSTABLE LOAD SHARING COEFFICIENTS METHOD
FOR LOAD SHARING CONTROL BETWEEN PARALLEL OPERATING GENERATORS IN ISOLATED
POWER GENERATION SYSTEMS
Received Sept. 01, 2025; accepted Sept. 22, 2025
Available online Sept. 30, 2025
Mazurenko L.1, Dzhura O.2, Shykhnenko M.3
Author for correspondence: Mazurenko Leonid,
e-mail: 3662491@gmail.com
An isolated hydroelectric power-generating system of 400 V/50
Hz is studied. The system is built using hydroelectric units
equipped with regulated hydraulic turbines and induction gen-
erators, a power electronic AC/DC voltage converter, a dump
load and a bank of compensating capacitors. The stator windings of the generators in the system under consider-
ation were connected in parallel. The power electronic converter, implemented on fully controlled semiconductor
switches, performs the functions of a static synchronous compensator and an active rectifier in the system. A new
method for frequency, voltage and load sharing control between generators is proposed. Based on the proposed
method, frequency, voltage and load sharing controllers for the discussed system are developed. The converter
control is implemented using stator voltage oriented vector control technique and space-vector pulse-width mod-
ulation of stator voltage. Verification of the proposed method for frequency, voltage and load sharing control
between generators is carried out using the developed dynamic simulation model of the system under considera-
tion. The obtained simulation results were analyzed and further research directions were formulated. Bibl. 23,
Fig. 3, Table.
Keywords: isolated hydroelectric power generating system, hydraulic turbine, active power; load sharing coeffi-
cients, parallel operating generators, voltage source converter, regulated dump load, transients.
РОЗРОБКА ТА ЗАСТОСУВАННЯ МЕТОДУ ЗМІННИХ КОЕФІЦІЄНТІВ ДОЛЬОВОЇ УЧАСТІ
ДЛЯ РЕГУЛЮВАННЯ РОЗПОДІЛУ НАВАНТАЖЕННЯ МІЖ АВТОНОМНИМИ
ПАРАЛЕЛЬНО ПРАЦЮЮЧИМИ ГЕНЕРАТОРАМИ
Отримано 01 вер. 2025 р.; рекомендовано до публікації 22 вер. 2025 р.
Доступно онлайн 30 вер. 2025 р.
Мазуренко Л. І.1, Джура О. В.2, Шихненко М. О.3
Автор для кореспонденції: Мазуренко Леонід,
e-mail: 3662491@gmail.com
Розглянуто автономну гідравлічну електрогенерувальну
систему 400 В/50 Гц, яка побудована на основі регульова-
них гідроагрегатів з асинхронними генераторами, напів-
провідникового AC/DC перетворювача напруги, регульо-
ваного баластного навантаження і батареї компен-
саційних конденсаторів. Обмотки статора генераторів у розглянутій системі були з’єднані парале-
льно. Напівпровідниковий перетворювач, що реалізований на повністю керованих напівпровідникових
ключах, у системі виконує функції синхронного статичного компенсатора та активного випрямляча.
Запропоновано новий метод регулювання частоти, напруги і розподілу навантаження між генерато-
рами. На основі положень запропонованого методу розроблено алгоритми регулювання частоти,
1 Dr. of Tech. Sciences, prof.
https://orcid.org/0000-0002-7059-249Х
2 Cand. of Tech.Science
https://orcid.org/ 0000-0002-0224-3351
3 Cand. of Tech.Science
https://orcid.org/0000-0003-4012-1731
1, 2, 3 Institute of Electrodynamics of the National
Academy of Sciences of Ukraine, Kyiv, Ukraine.
1 д-р. тех. наук, проф.
https://orcid.org/00000-0002-7059-249Х
2 канд. техн. наук, ст. наук. співр.
https://orcid.org/0000-0002-0224-3351
3 канд. техн. наук, наук. співр.
https://orcid.org/0000-0003-4012-1731
1, 2, 3 Інститут електродинаміки НАН України,
м. Київ, Україна.
185
Відновлювана енергетика. № 3/2025 | Гідро-воднева енергетика
напруги та розподілу навантаження в системі. Керування перетворювачем реалізовано на основі век-
торного алгоритму з орієнтацією за результуючим вектором напруги статора та з застосуванням
просторово-векторної широтно-імпульсної модуляції статорної напруги. Верифікацію запропонова-
ного методу регулювання частоти, напруги і розподілу навантаження між генераторами проведено з
використанням розробленої імітаційної динамічної моделі розглянутої системи. Проведено аналіз
отриманих результатів моделювання та визначено подальший напрям досліджень. Бібл. 23, рис. 3,
табл. 1.
Ключові слова: автономна гідравлічна електрогенерувальна система, гідравлічна турбіна, активна по-
тужність; дольові коефіцієнти, паралельно працюючі генератори, напівпровідниковий перетворювач,
регульоване баластне навантаження, перехідні процеси.
Використані позначення та скорочення
IHPGS – isolated hydroelectric power generation system
BCC – battery of compensating capacitors
AC load – alternating current load
RDL – regulated dump load
GV – guide vane
STATCOM – static synchronous compensator
SVPWM – space vector pulse width modulation
ALSCM – adjustable load sharing coefficients method
SG – synchronous generator
IG – induction generator
VSC – voltage source converter
DC load – direct current load
INDM – imaginary no-droop method
CSM – curve shifting method
DM – droop method
MSM – master-slave method
THD –total harmonic distortion
Introduction. Isolated power generation systems (IPGSs)
and microgrids for improving technical and economic per-
formance, using standard equipment, and providing power
reserve are typically designed based on more than one
source of electrical energy operating in parallel on a direct
or alternating current bus [1, 2]. When designing, the pos-
sibility of further increasing the IPGS power rating at the
modernization stage due to the integration of additional
electric power-generating units is also laid down.
Accordingly, experts and scientists, among other things,
need to solve the problems of improving the energy effi-
ciency of parallel operating generators and systems [3-7].
IPGSs are built using various energy sources, both renewable
and conventional. A stable power supply to local consumers
can be provided by IPGSs that have at least one source of
stable power generation. Diesel, gas, gasoline, and hydroe-
lectric power units are capable of providing stable and con-
tinuous power generation. The construction of isolated hy-
droelectric power generation systems (IHPGS) requires
greater capital investment than diesel power plants and die-
sel-battery power plants of comparable capacity.However, if
sufficient water resources and stable electricity consumption
are available, preference should be given to IHPGSs due to
their independence from fossil fuels [8].
One way to reduce capital investment in the construction
and maintenance of IHPGSs is to use induction generators
(IGs), which are less expensive than synchronous genera-
tors (SGs) and easier to maintain.
A number of methods have been developed to regulate
parallel-operating AC generators. Among them, the droop
method (DM), the Curve Shifting Method (CSM), also
known as the Droop Compensation Method, and the mas-
ter-slave method (MSM) should be noted [9-12]. These
methods ensure the stabilization of the electrical frequency
and voltage in the system, as well as the needed load dis-
tribution between the units.
CSM (Droop Compensation Method) was developed to reg-
ulate the frequency and voltage of SGs within a power plant
operating on a centralized network and to regulate the load
sharing between several plants. The advantages of this
method are its relative simplicity of implementation and
the ability to isochronous (no-droop) frequency and voltage
control. CSM can also be used in isolated power systems.
According to CSM, the frequency of parallel-operating units
is regulated using properly shifted droop characteristics.
However, it is also theoretically possible to regulate the fre-
quency of one of the units according to the law f=const,
similar to MSM. CSM is considered as a modification of DM.
This is explained by the fact that the basis of both DM and
CSM is frequency and voltage droop control. But in the case
of CSM, droop characteristics are shifted due to additional
(secondary) control when the load of the generators
changes [13]. Due to this, such shifted droop characteristics
are sometimes called imaginary droop characteristics.
The advantage of CSM is the absence of steady state volt-
age and frequency control errors. Among the disad-
vantages of CSM, the first one is the no-zero steady state
error when at least one of the units is disconnected from
the system. Another disadvantage of this method is that its
use leads to long-term transients. If these disadvantages
are eliminated, the quality of control and, accordingly, the
energy conversion efficiency of isolated hydroelectric
power generation systems can be improved.
186
Відновлювана енергетика. № 3/2025 | Гідро-воднева енергетика
The aim of the work. The aim of the work is to expand the
control theory of renewable energy isolated power-gener-
ating systems.
Presentation of the main material
1. Schematic solution. The proposed configuration of the
IHPGS is shown in Fig. 1. The system shown in Fig. 1 con-
tains hydroelectric power units with regulated hydraulic
turbines (HT1, HT2, ... HTn) driving IGs G1, G2, …Gn. The
mechanical torque of the HTs is regulated by the control
systems of the servo motors of the guide vanes (GVs) GV1,
GV2, ... GVn by adjusting the angle references of the GV
blades. The stator windings of the generators are con-
nected in parallel. The reactive power required for excita-
tion of the IGs is supplied from two sources, one of which
is a battery of compensating capacitors (BCC), and the
other is an AC/DC semiconductor voltage source converter
(VSC). The VSC acts as a static synchronous compensator
(STATCOM) and an active rectifier. A regulated dump load
(RDL) is connected to the DC-side of the VSC. The RDL is
formed by a series-connected resistor DR1 and transistor
VT. A DC load shown as a current source is also connected
to the DC terminals.
The three-phase AC load of local 400 V/50 Hz electricity
consumers is supplied from the stator windings of parallel-
operating generators.
The main functions and equations of the VSC, GVs, and the
RDL electronic controllers are discussed below.
2. Modification of the curve shifting method
2.1. Development of the adjustable load sharing coeffi-
cients method (ALSCM). It should be noted that the above-
mentioned CSM was originally called the imaginary no-
droop method (INDM), and CSM was just a modification of
CSM in [14]. Let’s assume that the power generation in an
isolated system is equal to the power consumption. Then,
under the condition of parallel operation of n electric
power units equipped with SGs and operating in an IHPGS,
in accordance with CSM, load sharing between generators
and no-droop frequency and voltage control are obtained
when the control law is used according to the following
equations [14, 15]
( )
( )
( )
=−+
=−+
=−+
0
0
0
22
11
LsumnPnP
LsumPP
LsumPP
PPnsf
PP2sf
PP1sf
*
*
*
...........
, (1)
( )
( )
( )
=−+
=−+
=−+
0
02
01
22
11
LsumnQnQg
LsumQQg
LsumQQg
QQnsU
QQsU
QQsU
*
*
*
...........
, (2)
where 0jPs , 0jQs - droop coefficients of “active
power-frequency” and “reactive power-frequency” droop
characteristics of the j-th unit;
*Pj , *Qj - active and
reactive power reference of the j-th unit;
Pj
ff
s
jj
jP
−
=
12
;
Qj
UU
s
gjgj
jQ
−
=
12
; 1jf , 2jf , 1gjU , 2gjU - the values of fre-
quency and voltage at two arbitrary points 1 and 2 of the
above-mentioned static characteristics of the j-th unit;
Pj ; Qj - the difference in the values of active and re-
active powers between points 1 and 2 of the static charac-
teristics of the j-th unit; nj ,1= ; jP , jQ - active and re-
active power sharing coefficients of the j-th unit;
1
1
=
=
n
j
jP ; 1
1
=
=
n
j
jQ ; LsumP , LsumQ - total active and
reactive load of all units of the system; fff −= *
- the
system output electrical frequency error;
*f - frequency
reference; ggg UUU −= *
- the system output AC voltage
error value.
In order to eliminate the above-mentioned shortcomings of
CSM, the authors of this article developed an improved
method based on CSM for isolated power generation sys-
tems built with parallel-operating IGs (Fig. 1). The method
was called the adjustable load sharing coefficients method
(ALSCM). The essence of the proposed method is that all
units of the system participate in the load sharing similar to
the CSM, but instead of performing the function of fre-
quency control in the system, they control the power of the
regulated dump load. At the same time, the above-men-
tioned function is assigned to the RDL control system. In ad-
dition, in order to eliminate the frequency droop in the sys-
tem resulting from the failure/disconnection of one or
more units, the active load sharing coefficients of the units
are properly adjusted.
Provided that n electric power units equipped with IGs op-
erate in parallel in an isolated power generation system, in
accordance with the ALSCM, proper load distribution be-
tween generators and no-droop speed and voltage control
are obtained by using the control law described by the fol-
lowing equations
( ) ( )dtPP
P
k
PP
P
Pj EXDLn
j
Nj
Ij
EXLsum
Nj
jP
pu
−−+=
=
***
1
; (3)
*
max
max
*
~~
EX
mm
sumDL P
dtkk
dt
d
k
JP +
−−
=
−
1
21
; (4)
constUg =
*
, (5)
where Ik , k , 1k , 2k are amplification coefficients;
( )mnmm ....,maxmax 21= is the highest rotor speed
187
Відновлювана енергетика. № 3/2025 | Гідро-воднева енергетика
among all generators in the system;
=
=
n
j
jsum JJ
1
is the
sum of the moments of inertia of all units;
*
EXP is the fre-
quency-responsive fast reserve reference of active power
in the system;
*
gU is the output AC voltage reference of the
system; max
*~ −= mm ;
*
m - angular speed reference
of the generator of the unit with the highest rotor speed;
*
puPj - IG active power reference of the j-th unit, p.u.; NjP
- IG rated power of the j-th unit;
*
DLP , DLP - RDL power
reference and actual power values; j - RDL quasi-steady
state power sharing control coefficient of the j -th unit
in the system, nPnPP /....// === 2211 ;
VSCLdcLacLsum PPP /+= ; LacP , LdcP - active power of AC
load and DC load of consumers; VSC - efficiency of the
VSC; nj ,1= .
Since IG does not generate reactive power but instead con-
sumes it, there are no equations similar to (2) in the system
of equations (3)-(5). The constUg =
*
law is performed by
the dIi current controller of the VSC control system. The
equation of this controller is given below. The power elec-
tronic converter VSC in the system of Fig. 1 performs the
functions of a STATCOM [16-18].
In equation (4), instead of the highest rotational speed er-
ror, to reduce the number of sensors, the control action can
also be the error in the electrical frequency at the system
AC output or the error in the angular speed of any unit.
Let us assume that PB1 , PB2 , …. nPB are the basic ac-
tive load sharing coefficients of the units in the system, pro-
vided that all n units are operating and 1
1
=
=
n
j
jPB . Let’s
also introduce logical signals “j-th unit is ON/OFF”
−
−
= startedunitofOFFswitching,
startedunitofONswitching,
thj
thj
kGUj 0
1
. (6)
Then the nPPP ,...., 21 values, provided that the ratio
of active load sharing coefficients must be equal to the ratio
of basic active load sharing coefficients, will be evaluated
as follows
=
=
n
j
GUjjPB
GUj
jPBjP
k
k
1
, nj ,1= . (7)
From (7) it can be seen that if all units are operating, then
jPBjP = , nj ,1 , and if at least one unit is stopped,
then jPBjP . Due to the insertion of the adjustable
coefficients nPPP ,...., 21 , the power balance between
consumption and generation is maintained, and thus, the
no-droop in frequency or speed control is achieved.
The system of equations (3)-(7) is the theoretical basis of
the proposed ALSCM method.
If the units are driven by regulated HTs, the GV blades angle
reference of the j-th unit can be approximately computed
from the following equation
tjGj
pu
j
A
Pj
c
*
* = , nj ,1= , (8)
where tjA is the ratio of HT rated power and IG rated
power of the j-th unit; Gj is the IG efficiency of j-th unit.
2.2. Example. For example, let us assume that there are
four units in the IHPGS and 201 .=PB , 202 .=PB ,
2503 .=PB , 3504 .=PB . Let us assume that during the
operation of the system, the 1st unit was stopped. Then,
Fig. 1. Schematic diagram of the isolated hydroelectric power generation system
188
Відновлювана енергетика. № 3/2025 | Гідро-воднева енергетика
after its shutdown, from (7) we obtain 01 =P ,
( ) 25035025020202 ..../. =++=P ,
31250802503 ../. ==PB , 43750803504 ../. ==PB .
Thus, as a result of the shutdown of the first unit, the active
power load sharing coefficients of the second, third, and
fourth units will be increased by 1.25 times. Due to this, the
active power balance between consumption and genera-
tion in the system configurations using four and three op-
erating units will be the same.
3. Control of the VSC. The VSC converter control system
(Fig. 2b) provides independent DC voltage control of the
VSC and the AC stator winding voltage control of the gen-
erators. The VSC control algorithm shown in Fig. 2b is simi-
lar to that discussed in [19]. The angular position of the IG
voltage vector is computed in the PLL (phase-locked loop)
block. The equations of the DC voltage controller, AC volt-
age controller, q-axes, and d-axes VSC current controllers
are as follows:
321
10
0 kdtukuku
RC
u
Ci dcdcdc
D
VTdc
qI /)~~( *
*
*
+++−=
; (9)
( )
1
11
21
−
−−
++
+
++
=
ph
g
dI
ph
gq
qI
uu
ph
phqIqI
qI
L
i
L
v
i
dtkk
L
Ri
dt
di
u
~
**
*
; (10)
+= dtukuki ggdI
~~*
54 ; (11)
( )
1
11
43
−
−−
−+
+
++
=
ph
g
qI
ph
gd
dI
uu
ph
phdIdI
dI
L
i
L
v
i
dtkk
L
Ri
dt
di
u
~
**
*
, (12)
where
*
VT – duty cycle reference of the VT control signal;
dcdcdc uuu −= *~ ; qIqIqI iii −= *~ ; dIdIdI iii −= *~ ; qIi , dIi , gqv ,
gdv are q-axes and d-axes components of the VSC current
and AC load voltage; g – angular frequency of the AC load
voltage; 1k , 2k , 3k , 4k , 5k , 1uk , 2uk , 3uk , 4uk are con-
stants. The logic signals for the VSC transistors control are
formed by a space vector pulse width modulation (SVPWM)
unit.
4. RDL control. The block diagram of the RDL control algo-
rithm for n=2 units is shown in Fig. 2c. As a control action
of the RDL controller, it was decided to use the angular
speed error of the generator of the unit with the highest
rotor speed in the system. The duty cycle reference *
VT of
the VT control signal is computed as the ratio of the dump
load power reference (continuously computed) to its rated
power. The RDL power reference is obtained using equa-
tion (4).
5. HT control. The block diagram of the HT power control
algorithm for n=2 units is shown in Fig. 2a. Low-pass filters
LPF1, LPF2 are used to attenuate the high-frequency com-
ponent of the output signal. As can be seen from Fig. 2a,
the GV blades angle control in HT1 and HT2 hydro turbines
is implemented using equations (3), (6), (7) and (8).
6. Digital simulation settings. Complex mathematical mod-
els of electromechanical systems are often implemented in
simulation environments, such as MATLAB. This computing
platform is considered a powerful and effective tool for the-
oretical investigations [20].
The proposed IHPGS (Fig. 1) was numerically investigated
using the MATLAB/Simulink software environment in con-
figuration with n=2 units.
Generators G1 and G2 were represented by a fourth-order
dynamic model during the numerical studies [21].
HT1 and HT2 were modeled without a surge tank by a dif-
ferential-algebraic system of equations [22].
mjjjjnljjtjpuHTj cDqqhAP −−= )(, ; (13)
Fig. 2. Block diagram of the HT power control (a), the VSC control (б), the HT speed control (в)
189
Відновлювана енергетика. № 3/2025 | Гідро-воднева енергетика
Wj
jljj
T
hh
dt
dq −−
=
1
, (14)
( ) ( )AjAjAjRjjSj kTpkpxcpW //// 211 ++== , (15)
where puHTjP , is HTj power, p.u.; jh is pressure head, p.u.;
jq and jnlq are flow rate and no load flow, p.u.; ljh – head
loss due to friction in theconduit, p.u.; 1−= mjmj is
the HT speed deviation from 1 p.u.; WjT is time constant of
the conduit, s; jjj hcq = ; jc is the GV blades angle; jD
is the HT damping coefficient; ( )pWSj is the GV servo mo-
tor transfer function; dtdp /= ; Rjx – input signal of the
servo motor formed by the HT speed controller; Ajk , AjT –
gain coefficient and time constant of the servo motor and
GV blades; 21,=j .
The characteristics and parameters of the electromechani-
cal systems of unit 1 and unit 2 were assumed to be identi-
cal.
Hydro turbines HT1, HT2
Nominal power: 30 kW; time constant of the conduit 1WT
= 2WT =1 с; 1tA = 2tA =1.073; 1D = 2D =0; 1Ak = 2Ak = 3.33;
1AT = 2AT =0.07 s; no load flow nlq1 = nlq2 =0 p.u.; head loss
due to friction in the conduit 1lh = 2lh =0 p.u.; GV blades
speed limits: 0.2 p.u./s.
Generators G1 and G2
Rated power/voltage (connection): 30 kVA/400 V (Y); rated
speed/number of pole pairs: 1500 rpm/2; active resistance
of stator/rotor phase: 0.143 Ω/0.08 Ω; stator and rotor
leakage inductance: 0.00115 H; IG and HT rotating mass in-
ertia constant: 2 s; friction factor: 0.027 N∙m∙s/rad. The
magnetization characteristic of IGs is shown in the table be-
low.
Table. Magnetization characteristic of IGs
Phase
current, A
3 6 11 15 20 30 44 62 120
Line
voltage, V
192 270 345 384 422 460 498 536 600
Load, inductors and capacitors
The DC side dump load resistance 191 =DR Ω; VT re-
sistance in ON/OFF state = 0.001 Ohm / 100 kOhm; AC load
is resistive symmetrical; DC load power = 0.02 kW; active
resistance of inductors 0410.=phR Ω; inductance of in-
ductors 000680.=phL H; 0400 .=C F; rated
power/rated voltage/connection of compensating capaci-
tors: 8 kVA/400V/Yn.
Base quantities of power, voltage, current, frequency and
speed for Fig. 3 transients
30 kVA = 1 p.u. of power; 230 V = 1 p.u. of root mean square
voltage; 2261 /. A = 1 p.u. of IG rms phase current; 770
V = 1 p.u. of DC side voltage; 50 Hz = 1 p.u. of electrical fre-
quency; 1500 rpm = 1 p.u. of speed.
SVPWM vector control system of the VSC
Carrier frequency = 9 kHz; 1k =60; 2k =900; 3k =1.5;
4k =10 , 5k =25; 1uk =1540; 2uk =640000; 3uk =1540;
4uk =640000; RMS phase voltage reference of IGs = 1.04
p.u.; DC side voltage reference of the VSC = 1 p.u.
Controllers of GVs of hydraulic turbines
Ik =2; P1 = PB1 =0.767; P2 = PB2 =0.233; 1 =0.256;
2 =0.0778; 1G = 2G =0.9; the values of the
( )dtPPPk EXDL
n
j
NjIj −
=
*/
1
component in equation
(3) were limited by the range 12501250 .,.− .
RDL control system
Switching frequency = 2 kHz; differential, proportional, and
integral gain of the frequency controller: k =0.68, 1k =
272, 2k = 5.1; the frequency-responsive fast reserve of ac-
tive power reference in the system
*
EXP = 8.7 kW;
*
m
=1.02 p.u.
7. Analysis of simulation results. Simulation results of the
Fig. 1 system are shown in Fig. 3.
As can be seen from Fig. 3a, until the moment of time
ct 44.= the IHPGS operated in a quasi-steady state. The
total active load of consumers was 0.108 p.u. = 3.24 kW and
the RDL power was 0.29 p.u. = 8.7 kW. The values of active
power generated by IGs G1 and G2 were equal 0.344 p.u.
and 0.09 p.u. (Fig. 3b), respectively. Thus, the ratio of the
active powers of the IGs was 3.82, while the ratio of the ac-
tive power sharing reference coefficients of the units was
slightly lower, namely: P1 : P2 =0.767:0.233=3.29. The
difference in ratio values is due to the low load power and
the influence of losses in the IGs (the actual efficiencies of
G1 and G2 differed due to their different loadings) on the
precision of load sharing. The VSC active power corre-
sponded to the active power of the RDL.
The speeds of IGs G1 and G2 were 1.02 p.u. and 1.0155 p.u.,
respectively, and the electrical frequency in the system was
1.0137 p.u. (Fig. 3d).
The reactive power consumption of IG G1 and IG G2 did not
differ significantly and amounted to 0.467 p.u. and 0.435
p.u., respectively (Fig. 3c). Most of the reactive power that
had been consumed by both IGs came from the VSC (0.604
p.u. = 18.12 kVA), and the rest was provided by the BCC.
190
Відновлювана енергетика. № 3/2025 | Гідро-воднева енергетика
The GV blades’ angle reference (Fig. 3e) in unit 1 was 0.351
p.u., in unit 2 – 0.107 p.u., and their ratio was 3.28, being
close to the ratio reference P1 : P2 .
The RMS phase current value of the IG G1 stator winding
was 0.543 p.u., that is 0.122 p.u. higher than in G2 due to
the different loadings of the generators.
The RMS value of the IGs phase voltage and the rectified
voltage magnitude of the VSC were equal to the reference
values of 1.04 p.u. = 239.2 V and 1 p.u. = 770 V, respectively
(Fig. 3f).
The THD coefficient of the IGs phase voltage was around
2% (Fig. 3h).
At the moment of time ct 44.= , the admittance of the AC
load increased. Due to this, AC load active power reached a
value of 0.324 p.u. = 9.73 kW.
As a result of the rapid increase in the AC load, the mechan-
ical rotational speed in both units and the electrical fre-
quency of the system began to decrease (Fig. 3d), as well as
the power of the RDL (Fig. 3a).
The GV blades’ angle reference (Fig. 3e) in unit 1 was in-
creased by the GV controller of HT1 to 0.537 p.u. with a
subsequent slow decrease to 0.517 p.u. In unit 2, the GV
blades’ angle reference was increased to 0.164 p.u. and
then slightly reduced to 0.157 p.u. as a result of adjusting
the ( )dtPPPk EXDL
n
j
NjIj −
=
*/
1
component in equa-
tion (3) of the HT power controller (Fig. 2a).
At the end of the transient process caused by the increase
in consumer load, the ratio of active powers of IG G1 and
IG G2 settled at 0.520 p.u./ 0.1435 p.u. = 3.62. Comparing
this value with the corresponding value of 3.82 at the inter-
val before load increase, it can be seen that the active load
sharing between IGs became more approximate to the ra-
tio reference value of 3.29.
As can be seen from Fig. 3d, the speed and frequency tran-
sients in the system faded away in 1.5–1.6 s, that is nearly
10 times quicker than that of an isolated hydroelectric unit
equipped with a SG and speed control using solely the GV
controller [23].
Figure 1. Fig. 3. Electromechanical transients in the system of Fig. 1 for two isolated hydroelectric power units
operating in parallel
191
Відновлювана енергетика. № 3/2025 | Гідро-воднева енергетика
The maximum RMS phase voltage error of IGs during the
transient process in the system was 0.29% of the rated volt-
age value, and the VSC maximum rectified voltage error
was 0.23% of the DC voltage reference.
The power of the RDL at the end of the simulation interval
was nearly equal to the RDL power magnitude that was be-
fore the increase in consumer load (Fig. 3a).
As a result of performing by GVs and RDL controllers their
control actions, the IG G1 speed settled at the value that
was before AC load increase, that is 1.02 p.u. At the same
time, the IG G2 speed and the electrical frequency in the
system decreased slightly to 1.0134 p.u. and 1.0106 p.u. re-
spectively in accordance with equation (4).
The value of the IGs output voltage THD did not change sig-
nificantly with an increase in load (Fig. 3h).
Conclusions. A new adjustable load-sharing coefficients
method for frequency and voltage control in IHPGSs using
parallel operating induction generators has been devel-
oped. Due to this, further advancement in control theory of
renewable energy isolated power-generating systems was
attained. The results of numerical simulation of the pro-
posed isolatedpower generation system built with two par-
allel-operating hydroelectric power units equipped with IGs
of 30 kVA rated power, allowed for preliminary verification
of the proposed adjustable load sharing coefficients
method. The implementation of the control strategy for HT
guide vanes, regulated dump load, and voltage source con-
verter based on the statements of the proposed method al-
lowed to achieve no-droop control of voltage, the rota-
tional speed of one of the units, and quasi-steady state
power of the regulated dump load in the system.
Based on the analysis of the electromechanical transients
of the system obtained during a stepwise increase in the
load of consumers by 11% of the total rated power of the
generators, it was specified that the decay time of speed
and frequency transients did not exceed 1.5–1.6 s. This is a
good result due to a 10 times shorter transient time com-
pared to an isolated hydroelectric unit investigated by
other scientists, equipped with an SG and speed control im-
plemented solely with the GV controller.
It was also found that the implementation of the proposed
adjustable load sharing coefficients method led to active
load sharing between generators with an error. The magni-
tude of this error for a consumer load of 3.24 kW (5.4% of
the total rated power of the generators) was 16%, and for
a consumer load of 9.73 kW (16.2% of the total rated power
of the generators), it was 10%. This error is explained by the
fact that the proposed method provides control of the ratio
of the mechanical powers of the generators in accordance
with the load-sharing reference coefficients. As a result,
losses in the IGs in load sharing control are not taken into
account, thus affecting the accuracy of the active load shar-
ing between the units.
Further investigations are planned to focus on more thor-
ough studies of the considered isolated hydroelectric
power generation system with two or more units and on
improving the accuracy of load sharing between units.
This work was supported by the NATIONAL RESEARCH
FOUNDATION OF UKRAINE [PROJECT "Electromechanical
systems of increased energy efficiency for energy, technol-
ogies and transport", № 2023.04/0075].
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|
| id | veorgua-article-562 |
| institution | Vidnovluvana energetika |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-19T01:16:59Z |
| publishDate | 2025 |
| publisher | Institute of Renewable Energy National Academy of Sciences of Ukraine |
| record_format | ojs |
| resource_txt_mv | veorgua/fa/88a1525fee6abe50cabe94714803d6fa.pdf |
| spelling | veorgua-article-5622026-07-18T06:32:22Z DEVELOPMENT AND APPLICATION OF THE ADJUSTABLE LOAD SHARING COEFFICIENTS METHOD FOR LOAD SHARING CONTROL BETWEEN PARALLEL OPERATING GENERATORS IN ISOLATED POWER GENERATION SYSTEMS РОЗРОБКА ТА ЗАСТОСУВАННЯ МЕТОДУ ЗМІННИХ КОЕФІЦІЄНТІВ ДОЛЬОВОЇ УЧАСТІ ДЛЯ РЕГУЛЮВАННЯ РОЗПОДІЛУ НАВАНТАЖЕННЯ МІЖ АВТОНОМНИМИ ПАРАЛЕЛЬНО ПРАЦЮЮЧИМИ ГЕНЕРАТОРАМИ Mazurenko , L. Dzhura , O. Shykhnenko , M. isolated hydroelectric power generating system, hydraulic turbine, active power; load sharing coefficients, parallel operating generators, voltage source converter, regulated dump load, transients. автономна гідравлічна електрогенерувальна система, гідравлічна турбіна, активна потужність; дольові коефіцієнти, паралельно працюючі генератори, напівпровідниковий перетворювач, регульоване баластне навантаження, перехідні процеси. An isolated hydroelectric power-generating system of 400 V/50 Hz is studied. The system is built using hydroelectric units equipped with regulated hydraulic turbines and induction generators, a power electronic AC/DC voltage converter, a dump load and a bank of compensating capacitors. The stator windings of the generators in the system under consideration were connected in parallel. The power electronic converter, implemented on fully controlled semiconductor switches, performs the functions of a static synchronous compensator and an active rectifier in the system. A new method for frequency, voltage and load sharing control between generators is proposed. Based on the proposed method, frequency, voltage and load sharing controllers for the discussed system are developed. The converter control is implemented using stator voltage oriented vector control technique and space-vector pulse-width modulation of stator voltage. Verification of the proposed method for frequency, voltage and load sharing control between generators is carried out using the developed dynamic simulation model of the system under consideration. The obtained simulation results were analyzed and further research directions were formulated. Bibl. 23, Fig. 3, Table.  Розглянуто автономну гідравлічну електрогенерувальну систему 400 В/50 Гц, яка побудована на основі регульованих гідроагрегатів з асинхронними генераторами, напівпровідникового AC/DC перетворювача напруги, регульованого баластного навантаження і батареї компенсаційних конденсаторів. Обмотки статора генераторів у розглянутій системі були з’єднані паралельно. Напівпровідниковий перетворювач, що реалізований на повністю керованих напівпровідникових ключах, у системі виконує функції синхронного статичного компенсатора та активного випрямляча. Запропоновано новий метод регулювання частоти, напруги і розподілу навантаження між генераторами. На основі положень запропонованого методу розроблено алгоритми регулювання частоти, напруги та розподілу навантаження в системі. Керування перетворювачем реалізовано на основі векторного алгоритму з орієнтацією за результуючим вектором напруги статора та з застосуванням просторово-векторної широтно-імпульсної модуляції статорної напруги. Верифікацію запропонованого методу регулювання частоти, напруги і розподілу навантаження між генераторами проведено з використанням розробленої імітаційної динамічної моделі розглянутої системи. Проведено аналіз отриманих результатів моделювання та визначено подальший напрям досліджень. Бібл. 23, рис. 3, табл. 1.      Institute of Renewable Energy National Academy of Sciences of Ukraine 2025-09-28 Article Article application/pdf https://ve.org.ua/index.php/journal/article/view/562 10.36296/1819-8058.2025.3(82).184-192 Vidnovluvana energetika ; No. 3(82) (2025): Scientific and applied Journal renewable energy ; 184-192 Возобновляемая энергетика; ##issue.no## 3(82) (2025): Scientific and applied Journal renewable energy ; 184-192 Відновлювана енергетика; № 3(82) (2025): Науково-прикладний журнал Відновлювана енергетика; 184-192 2664-8172 1819-8058 10.36296/1819-8058.2025.3(82) en https://ve.org.ua/index.php/journal/article/view/562/473 Copyright (c) 2025 L. Mazurenko , O. Dzhura , M. Shykhnenko https://creativecommons.org/licenses/by-nc-nd/4.0 |
| spellingShingle | isolated hydroelectric power generating system hydraulic turbine active power; load sharing coefficients parallel operating generators voltage source converter regulated dump load transients. Mazurenko , L. Dzhura , O. Shykhnenko , M. DEVELOPMENT AND APPLICATION OF THE ADJUSTABLE LOAD SHARING COEFFICIENTS METHOD FOR LOAD SHARING CONTROL BETWEEN PARALLEL OPERATING GENERATORS IN ISOLATED POWER GENERATION SYSTEMS |
| title | DEVELOPMENT AND APPLICATION OF THE ADJUSTABLE LOAD SHARING COEFFICIENTS METHOD FOR LOAD SHARING CONTROL BETWEEN PARALLEL OPERATING GENERATORS IN ISOLATED POWER GENERATION SYSTEMS |
| title_alt | РОЗРОБКА ТА ЗАСТОСУВАННЯ МЕТОДУ ЗМІННИХ КОЕФІЦІЄНТІВ ДОЛЬОВОЇ УЧАСТІ ДЛЯ РЕГУЛЮВАННЯ РОЗПОДІЛУ НАВАНТАЖЕННЯ МІЖ АВТОНОМНИМИ ПАРАЛЕЛЬНО ПРАЦЮЮЧИМИ ГЕНЕРАТОРАМИ |
| title_full | DEVELOPMENT AND APPLICATION OF THE ADJUSTABLE LOAD SHARING COEFFICIENTS METHOD FOR LOAD SHARING CONTROL BETWEEN PARALLEL OPERATING GENERATORS IN ISOLATED POWER GENERATION SYSTEMS |
| title_fullStr | DEVELOPMENT AND APPLICATION OF THE ADJUSTABLE LOAD SHARING COEFFICIENTS METHOD FOR LOAD SHARING CONTROL BETWEEN PARALLEL OPERATING GENERATORS IN ISOLATED POWER GENERATION SYSTEMS |
| title_full_unstemmed | DEVELOPMENT AND APPLICATION OF THE ADJUSTABLE LOAD SHARING COEFFICIENTS METHOD FOR LOAD SHARING CONTROL BETWEEN PARALLEL OPERATING GENERATORS IN ISOLATED POWER GENERATION SYSTEMS |
| title_short | DEVELOPMENT AND APPLICATION OF THE ADJUSTABLE LOAD SHARING COEFFICIENTS METHOD FOR LOAD SHARING CONTROL BETWEEN PARALLEL OPERATING GENERATORS IN ISOLATED POWER GENERATION SYSTEMS |
| title_sort | development and application of the adjustable load sharing coefficients method for load sharing control between parallel operating generators in isolated power generation systems |
| topic | isolated hydroelectric power generating system hydraulic turbine active power; load sharing coefficients parallel operating generators voltage source converter regulated dump load transients. |
| topic_facet | isolated hydroelectric power generating system hydraulic turbine active power; load sharing coefficients parallel operating generators voltage source converter regulated dump load transients. автономна гідравлічна електрогенерувальна система гідравлічна турбіна активна потужність; дольові коефіцієнти паралельно працюючі генератори напівпровідниковий перетворювач регульоване баластне навантаження перехідні процеси. |
| url | https://ve.org.ua/index.php/journal/article/view/562 |
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