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Titre: Design of integrated synergetic controller for the excitation and governing system of hydraulic generator unit
Auteur: Wenlong Zhu

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Engineering Applications of Artificial Intelligence 58 (2017) 79–87

Contents lists available at ScienceDirect

Engineering Applications of Artificial Intelligence
journal homepage: www.elsevier.com/locate/engappai

Design of integrated synergetic controller for the excitation and governing
system of hydraulic generator unit

MARK



Wenlong Zhua, , Yang Zhengb, Jisheng Daia, Jianzhong Zhoub
a
b

CRRC Zhuzhou Electric Locomotive Research Institute Co., Ltd., Huazhong University of Science and Technology, Wuhan 430074, China
School of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

A R T I C L E I N F O

A BS T RAC T

Keywords:
Hydraulic generator unit
Hydraulic generator governing system
Voltage regulation
Excitation control
Synergetic control

Synergetic control theory is introduced into hydraulic generator excitation system (HGES) and hydraulic
generator governing system (HGRS) in this paper. Synergetic excitation controller (SEC), synergetic governing
controller (SGC) of HGU have been designed. In order to enhance the terminal voltage control and mechanical
power tracking performances simultaneously, the integrated synergetic controller (ISC) is also proposed. ISC
implements synergetic control of terminal voltage, rotor speed, mechanical input power and guide vane
opening. Namely, the ISC is considering both of the excitation system and governing system of hydraulic
generator unit (HGU), which can provide control function instead of SEC and SGC. In addition, the control rules
of the aforementioned three controllers are deduced from the nonlinear mathematical analytic model of
hydroelectric generator unit. At the end of this paper, comparative case studies between the proposed SGC, SEC,
ISC and classic PID controller are presented. The results show that the proposed ISC improves the nonlinear
HGU system performance with a more accurate precision and shorter settling time in different operating
conditions.

1. Introduction
Hydroelectric generator unit (HGU) is the key equipment of
hydroelectric energy conversion system with complex transient characteristics influenced by hydraulic, mechanical and electrical factors. In
this system, turbine governor and generator exciter are utilized to
control the active power and terminal voltage of HGU. The design of
controller for the excitation and governing system of HGU will directly
influence the utilization efficiency of hydroelectric energy, the security
and stabilization of power plant operation and the power quality sent to
the grid (Chen et al., 2014a). However, hydraulic generator governing
system (HGRS) and hydraulic generator excitation system (HGES) are
complex nonlinear, time-variant and non-minimum phase control
system, the control performances of which are affected by nonlinear
plant characteristics, load changes and uncertain disturbance. It is still
a challenging and important problem to model a suitable prototype and
design proper control rules (Yuan et al., 2016). In this regard, a special
kind of nonlinear control technique, synergetic control theory, is
introduced into the control design of HGRS and HGES of HGU in
the paper.
In the past decades, many advanced control techniques have been
applied in controller design of HGRS and HGES, such as predictive



control (Jones and Mansoor, 2004; Nilsson et al., 2015), robust control
(Singh et al., 2013; He et al., 2015), adaptive control (Liu et al., 2016),
fuzzy control (Kishor, 2008; Nagode and Škrjanc, 2014), sliding mode
controller (Yuan et al., 2015) or H_∞ robust control (Mei et al., 2007).
However, there are still some practical problems for the strategies
mentioned above to overcome the long-term operation of power
systems in real-time applications (Yuan et al., 2016). For instance, it
will result in low control accuracy since the chattering phenomenon of
sliding mode controller. The classic PID controller has been designed
specifically for a certain operating condition, which is not suited to the
whole condition of HGU. In addition, existing control models of HGRS
and HGES are often isolated from each other. HGRS controller ignores
the transient changing of power angle and terminal voltage, and HGES
regards load variation as a sudden step in the mechanical input power
of the synchronous generator. Thus, a well-known nonlinear control
strategy, synergetic control is introduced into the design of an
integrated controller considering both of the excitation and governing
system of HGU in this paper.
To remedy this chattering phenomenon of sliding mode controller,
synergetic control is proposed (Kolesnikov, 2000; Kolesnikov et al.,
2000), it has the advantages of order reduction and is similar to sliding
mode control but without the disadvantage of chattering (Zhao et al.,

Corresponding author.
E-mail address: z.huw@hotmail.com (W. Zhu).

http://dx.doi.org/10.1016/j.engappai.2016.12.001
Received 3 May 2016; Received in revised form 31 October 2016; Accepted 1 December 2016
0952-1976/ © 2016 Published by Elsevier Ltd.

Engineering Applications of Artificial Intelligence 58 (2017) 79–87

W. Zhu et al.

Nomenclature

Ty
uf
ω
ex

ey
eh

eqx
eqy

eqh

Ef
Vref
ωref
Pmref
yref
xq ∑
xt
xL

xq
vf
T′d0
y
h
Pm
δ
H
D
Pe
E′q
xd
x′d
xd ∑
x′d ∑
Eq
Vs
ω0

Ka
Ta
Vt
Id
Iq

Relay connecter response time of servomotor
Guide vane opening control signal
Rotor speed
Partial derivatives of turbine torque with respect to the
rotor speed
Partial derivatives of turbine torque with respect to the
guide vane opening
Partial derivatives of turbine torque with respect to water
head
Partial derivatives of turbine flow with respect to the guide
vane opening
Partial derivatives of turbine flow with respect to guide
vane opening
Partial derivatives of turbine flow with respect to water
head
Excitation voltage of the generator
Reference value of terminal voltage
Reference value of rotor speed
Reference value of rotor speed
Reference value of guide vane opening
Total synchronous reactance of q-axis
Short circuit reactance of transformer
Reactance of transmission lines

Synchronous reactance of q-axis
Excitation voltage control signal
Time constant of field windings
Guide vane opening
Water head
Mechanical input power
Rotor angle of generator
Inertia time constant of generator
Damping coefficient of generator
Electrical power of generator
Transient potential of q-axis
Synchronous reactance of d-axis
Transient reactance of d-axis
Total synchronous reactance of d-axis
Total transient reactance of d-axis
Potential of q-axis
Voltage of the infinite bus
Synchronous angular speed
Water inertia time constant
Magnification
Time constant of excitation
Terminal voltage of generator
Stator current of d-axis
Stator current of q-axis

frequency control, the terminal voltage, rotor speed, mechanical power,
and guide vane opening are included in the manifold for the purpose of
achieving global asymptotic stability and voltage regulation, mechanical power regulation simultaneously in ISC controller. To the best of
authors’ knowledge, this is the first paper to investigate the integrated
nonlinear control system contained both of the excitation system and
governing system of HGU using synergetic control theory, and additionally, standard third-order synchronous generator model is taken
into consideration in HGRS model. At the end of this paper, comparative cases between proposed SGC, SEC, ISC and classic PID controller
are presented, the results of numerical simulation experiments indicate
that the proposed SGC, SEC and ISC generally respond more quickly
than PID, and ISC has little overshoot as a whole. It means that ISC has
a superior performance compared with SEC, SGC and PID controller.
For a clear presentation, the remainder of this paper is structured
as follows. In Section 2, theory of synergetic control is introduced.
Section 3 briefly presents the modeling of the excitation and governing
system of HGU. In Section 4, SEC, SGC and ISC controller are
designed. Meanwhile, the control rules of the SEC, SGC and ISC are
deduced from mathematical analytic model of HGRS and HGES. Then,
comparative experiments are designed and the results are discussed in
Section 5. Finally, conclusions are presented in Section 6.

2015). The comparison results indicate that synergetic control theory is
purely analytical and nonlinear, which provides asymptotic stability
and reduces the chattering phenomenon compared to sliding mode
control (Bounasla et al., 2015). Synergetic control is ideal for digital
control implementation with a fairly low bandwidth (Santi et al., 2004).
In recent years, with the mature of synergetic control theory in
engineering practice, which has been successfully applied designing
controllers for power electronics (Jiang and Dougal, 2004), synchronous generator (Ademoye and Feliachi, 2012), permanent magnet
synchronous motor (Bastos et al., 2004), power system stabilizers
(Zhao et al., 2014; Jiang, 2009). For instance, Bouchama et al. (2016)
proposed an adaptive fuzzy power system stabilizer using robust
synergetic control theory and terminal attractor techniques. Variable
speed synergetic control is introduced into eliminating the chaotic
oscillation of power system in paper (Ni et al., 2014). Also, synergetic
control theory was satisfactorily applied in asynchronous electric
traction drives of locomotives (Veselov et al., 2014).
In this paper, synergetic control theory is introduced into the HGRS
and HGES, synergetic excitation controller (SEC), synergetic governing
controller (SGC) and integrated synergetic controller (ISC) of HGU
have been designed, and the control rules of them are deduced from
nonlinear mathematical analytic model, which can guarantee the
macro-variables run into the constructed manifold in a finite time. In
order to closely reflect the transient process of voltage control and load

Fig. 1. Block diagram of hydraulic turbine governing system and excitation system.

80

Engineering Applications of Artificial Intelligence 58 (2017) 79–87

W. Zhu et al.

considered in the model of penstock system. And the relationship of
water head h and flow q is stated in Eq. (7).

2. Synergetic control theory
The basic principles of synergetic control theory are shown below.
The initial statement of the control system is described by the
differential equation of the object (Kolesnikov, 014).

h = −Tω

where x (t ) is the state coordinate vector, u is the control vector, q is the
setting state, M is the potential disturbing action.
The synergetic control of the above system is based on a macrovariable which is a function of state of coordinate vector, and it is
expressed by Eq. (2).

⎧ Pm = ex *ω + ey *y + eh *h

⎩ q = eqx *ω + eqy *y + eq h *h

(2)

φ = φ (x )

When the system is motivated by the potential disturbing action M,
the synergetic control objective is to force and restrict the system to
operate on the manifold φ (x ) = 0 and the setting state q (Taoridi and
Feliachi, 2012).
The constructed manifold φ (x ) = 0 is evolved by introducing a
constraint, and then the macro variable run into the constructed
manifold. The constraint function is given as:

T


+ φ = 0, T > 0
dt

(7)

where Tω is water inertia time constant.
Water turbine is a very complicated nonlinear system, and do not
have any analytic expression until now. In actual project, it is usually
described as moment-flow function of y , x and h . The model of water
turbine can be expressed by Eq. (8) (Yuan et al., 2016).

(1)

x ̇ (t ) = f (x , u , q , M )

dq
dt

(8)

where
ex = ∂mt /∂ω, ey = ∂mt /∂y, eh = ∂mt /∂h, eqx = ∂q /∂ω, eqy = ∂q /∂y, eqh , Pm is

= ∂q /∂h
mechanical input power, ω is rotor speed. Rotor speed had less impact
for the Pm and q since HGU is involved as a part of power system,
namely, ex = 0 , eqx = 0 .
According to Eqs. (6)–(8), the differential equations of hydraulic
turbine governing is deduced out, and it is shown in Eq. (9).

(3)

⎧ ẏ = 1 (−y + y + u )
f
0
Ty







⎪ Pṁ = 1 ⎢ −Pm + ey y − ⎜ eqy eh − eqh⎟ ey Tω y⎥̇
eqh Tω
ey







where T is controller parameter which decides the converging speed of
the closed-loop system to the constructed manifold specified by that the
micro variable equals to zero (Zhang et al., 2008). According to chain
rule of differentiation, dφ is deduced, and it is shown in Eq. (4).

(9)

dt


dφ (x, t )
∂φ (x, t ) dx (t )
=
=
dt
dt
∂x
dx

The guide vane opening y is controlled by guide vane opening
control signal u f , furtherly, adjusting the mechanical power for meeting
the need of load power of the power system.
Excitation system of HGU constitutes a synchronous generator and
an excitation device. The standard third-order synchronous generator
model is stated in Eq. (10).

(4)

Then, the control law of synergetic controller can be found as
follows.

u = g (x, t , φ (x, t ), T )

(5)

From Eq. (5), it is obviously drawn a conclusion that output of
synergetic controller system depends on state vector, macro variable
and controller parameter T . Then, selecting a suitable macro variable
and controller parameter T is crucial aspects in design of synergetic
controller.

⎧ δ ̇ = (ω−1) ω0

⎪ ω̇ = 1 [Pm − D (ω−1) ω0 − Pe (δ, Eq′)]
2H



xd ∑
xd − xd′
1 ⎛
̇

⎪ Eq = T ′ ⎜Ef − x ′ Eq′ + x ′ Vs cos δ ⎟
d0 ⎝

d∑
d∑


3. Model of excitation and governing system of HGU

where δ is rotor angle of generator, H is inertia time constant of
generator, D is damping coefficient of generator, Pe electrical power of
generator, E′q is transient potential of q-axis, xd , x′d , xd ∑ and x′d ∑ are
synchronous reactance of d-axis, transient reactance of d-axis, total
synchronous reactance of d-axis and total transient reactance of d-axis,
respectively. Ef is excitation voltage of the generator, Vs is voltage of the
infinite bus, T′d0 is time constant of field windings.
The model of excitation system is shown in Eq. (11).

HGU is the most important equipment of energy conversion which
can convert kinetic and potential energy of water into electric power, it
has strong ability of peak regulation and frequency adjustment in
power grid contained various renewable energy generator units.
Hydraulic turbine governing system and excitation system of HGU
provide the effective control strategy to ensure the security and stability
of the power grid. The hydraulic turbine governing system is used to
control the mechanical power through guide value opening, while
excitation system is employed to control the terminal voltage of the
generator through excitation voltage. The block diagram of a hydraulic
turbine governing system and excitation system is to be depicted in
Fig. 1.
As is shown in Fig. 1, the hydraulic turbine governing system is
composed of servomechanism, penstock and water turbine. The
servomechanism is the actuator of guide vane opening. The model of
servomechanism is always simplified as one-order system and described by Eq. (6).

Ty

dy
+y=u
dt

Eḟ =

1
(Ka vf − Ef )
Ta

(10)

(11)

where vf is excitation voltage control signal, Ka is magnification, Ta is
time constant of excitation.
The excitation voltage can be controlled via excitation voltage
control signal vf , furtherly, terminal voltage of synchronous generator
is adjusted. In this paper, we suppose Ka = 1, Ta = 0 for simplifying
calculating, so the expression of synchronous generator model considered excitation system can be simplified as follows.

⎧ δ ̇ = (ω−1) ω0

⎪ ω̇ = 1 [Pm − D (ω−1) ω0 − Pe (δ, Eq′)]
2H



xd ∑
xd − xd′
1 ⎛
⎪ Eq̇′ = T ′ ⎜vf − x ′ Eq′ + x ′ Vs cos δ ⎟
d0 ⎝

d∑
d∑


(6)

where Ty is major relay connecter response time of servomotor, y is
guide vane opening, u is the output signal of guide vane opening of
servomotor.
The rigid water hammer effect in water diversion system is

Electric power of synchronous generator is shown in Eq. (13).
81

(12)

Engineering Applications of Artificial Intelligence 58 (2017) 79–87

W. Zhu et al.

Pe (δ, Eq′) =

Eq′ Vs sin(δ )

+

xd′ ∑

Vṫ can be expressed as follow.

Vs2 xd′ ∑ − xq ∑
sin(2δ )
2 xd′ ∑ xq ∑

(13)

Vṫ =

Terminal voltage of synchronous generator is stated in Eq. (14).

Eq2 xs2 + Vs2 xd2 cos2 (δ ) + 2xd xs Eq Vs cos(δ )

Vt =

+

xd2∑

xq2∑

⎧ m = a cos2 (δ ) + be 2 − c cos(δ ) e + d sin2 (δ )

⎨ n = 2be + c cos(δ )
⎪ l = 2(d − a )cos(δ )sin(δ ) − ce sin(δ )


(14)

xd ∑
xd − xd′
Eq′ −
Vs cos(δ )
xd′ ∑
xd′ ∑

Vs2 xq2 sin2 (δ )
xq2∑

xs

xd ∑ Vt2 +

vf =

xd′ ∑

Vs2 xq2 sin2 (δ )
− Vs xd cos(δ )
x2
q∑

xs

,c =

xd − xd′
xd′ ∑

2xd xs Vs
,xd ∑ xd′ ∑



Vs cos(δ ) ⎥.



(21)

+

φ2 = ( y − yref ) + k3 (Pm − Pmref ) − k 4 (ω − ωref )

(22)

(23)

The partial derivatives of φ2 can be deduced, and it is shown in Eq.
(24).

φ2̇ = y ̇ + k3 Pṁ − k 4 ω̇

⎛ E ′ Vs

x ′ − xq ∑
⎜⎜ q cos(δ ) + Vs2 d ∑
cos(2δ ) ⎟⎟ δ ̇ = oEq̇′ + pδ ̇
xd ∑ xq ∑
⎝ xd′ ∑


xd′ ∑ xq ∑

xd2 xs2

⎞2
⎜xd′ ∑⎟



In the hydraulic turbine governing system, the guide vane opening,
mechanism power and rotor speed are chosen as macro variable
expressed as follows.

where

+

,b =

4.2. Design of SGC

(18)

xd′ ∑

xd2∑ xd′ ∑

(17)

φ1̇ = Vṫ + k1 Pė − k2 ω̇

p=

2Vs2 xd xs (xd − xd′ )


1
̇
− ( 2 m−1/2l + k1 p ) δ ⎬


where Vref , Peref and ωref are the reference value of terminal voltage,
electrical power and rotor speed, respectively.
The partial derivatives of φ1 can be deduced, and it is shown in Eq.
(18).

where 0 =



⎧ 1
Td′ 0
⎨− [(Vt − Vref ) − 2k1 Hω̇ − k2 (ω − ωref )] + k2 ω̇
1
T1m−1/2n + k1o ⎩ T1
2

According to synergetic control theory, the macro variable which is
often selected as a linear combination of state variables should be
determined, the terminal voltage, electrical power and rotor speed are
selected as macro variable. The expression of macro variable is shown
in Eq. (17).



Vs2 cos(2δ ) ⎜xd′ ∑ − xq ∑⎟



xd2∑

Substituting Eqs. (12), (18) and (19) into (21), In addition,
Pe − Pref = −2Hω̇ , the detailed deducing formula is presented in paper
(Zhao et al., 2014). Thus, the control law of the SEC can be obtained as
follows.

4.1. Design of SEC

Eq′ Vs cos(δ )

Vs2 xd2

T1 (Vṫ + k1 Pė − k2 ω̇ ) + (Vt − Vref ) + k1 (Pe − Pref ) − k2 (ω − ωref ) = 0

4. Design of synergetic controller for the excitation and
governing system

Vs sin(δ )
,
xd′ ∑

+


Vs2 xq2 sin2 (δ )
− Vs xd cos(δ )
⎢ xd ∑ Vt2 + x 2
q∑
d = 2 ,e = x ⎢
+
x
xq ∑
s
d∑ ⎢


According to Eq. (3), we can obtain

(16)

V sin(δ ) ̇′
Pė = s
Eq +
xd′ ∑


⎞2
⎜xd′ ∑⎟



Vs xq2



xd − xd′

Vs cos(δ ) ⎥
+
xd′ ∑

⎥⎦

φ1 = Vt − Vref + k1 (Pe − Peref ) − k2 (ω − ωref )

xs2 (xd − xd′ )2Vs2

a=

(15)

− Vs xd cos(δ )

(20)

where

E′q is deduced by Eqs. (14) and (15), and it is described as follow.

⎢ xd ∑ Vt2 +
xd′ ∑ ⎢
Eq′ =
xd ∑ ⎢⎢
⎢⎣

(19)

where

Vs2 xq2 sin2 (δ )

where xq , xq ∑ are synchronous reactance of q-axis and total synchronous reactance of q-axis, respectively. xs = xt + 0.5xL , xt , xL is short
circuit reactance of transformer and reactance of transmission lines.
xd ∑ = xd + xs , xd′ ∑ = xd′ + xs , xq ∑ = xq + xs . Eq is potential of q-axis, it
can be expressed by Eq. (15).

Eq =

1 −1/2
m
(nEq̇′ + lδ )̇
2

(24)

Suppose

T2 φ2̇ + φ2 = 0
we can obtain

.

Fig. 2. Block diagram of SGC.

82

(25)

Engineering Applications of Artificial Intelligence 58 (2017) 79–87

W. Zhu et al.

T2 ( ẏ − k3 Pṁ − k 4 ω̇ ) + ( y − yref ) + k3 (Pm − Pmref ) − k 4 (ω − ωref ) = 0

Thus, an ISC model, which considers the effects of both governing
system and generator excitation, is proposed. The macro variables are
expressed in Eq. (29).

(26)
and

⎧ φ1 = (Vt − Vref ) − k2 (ω − ωref )

⎩ φ2 = ( y − yref ) + k3 (Pm − Pmref ) − k 4 (ω − ωref )


⎧ 1
* ⎨− [( y − yref ) + k3 (Pm − Pmref )
ẏ =
⎞ ⎩ T2
k 3 ey ⎛ eqy eh
1 − e ⎜ e − eqh⎟
qh ⎝ y


k3
− k 4 (ω − ωref )] + k 4 ω̇ −
(−Pm + ey y) ⎬
eqh Tω

Ty



The constructed manifold is shown in Eq. (30).

⎧ φ1 = 0

⎩ φ2 = 0

(27)

Ty
1−

k 3 ey ⎛ eqy eh
eqh




ey


− eqh⎟


⎧T1 φ1̇ + φ1 = 0

⎩T2 φ2̇ + φ2 = 0



(31)

Thus, the excitation voltage control signal vf is deduced, and it is
shown in Eq. (32).

⎧ 1
⎨− [( y − yref ) + k3 (Pm − Pmref ) − k 4 (ω − ωref )] + k 4 ω̇
⎩ T2

k3

(−Pm + ey y) ⎬
eqh Tω


(30)

The constraint function is expressed as follows.

Thus, the control law of SGC can be expressed as follows.

μf = y − y0 +

(29)

xd ∑ Vt2 +

vf =

(28)

Vs2 xq2 sin2 (δ )
− Vs xd cos(δ )
x2
q∑

xs

+

⎧ 1

Td′ 0
̇
⎨− [(Vt − Vref ) − k2 (ω − ωref )] + k2 ω̇ − 1 m−1/2lδ ⎬
1
T
2
−1/2
1
T1m
n⎩

2

The block diagram of SGC is shown in Fig. 2.
4.3. Design of ISC

(32)

Guide vane opening control signal μf is deduced, and it is shown in
Eq. (33).

First-order generator model and second-order generator model are
commonly used in governing system control model of HGU (Yuan
et al., 2016b; Fang et al., 2011; Chen et al., 2013, 2014b; Jiang et al.,
2006). However, the first-order generator model ignores the changing
of power angle and terminal voltage (Abdelaziz and Ali, 2015; Shiva
et al., 2015), the second-order generator ignores the changing of
terminal voltage. Both of them cannot meet the requirement of modern
power system simulation. In addition, synchronous generator is
regarded as constant mechanical power model in most of the existing
excitation control model (Zhao et al., 2015; Yao et al., 2014). These two
control models mentioned above cannot get a satisfactory result which
reflects the realistic dynamic process of HGU. The integrated model of
excitation system and governing system of HGU is described as follows.

Ty

μf = y − y0 +
1−

k 3 ey ⎛ eqy eh
eqh




ey


− eqh⎟




⎧ 1
⎨− [( y − yref ) + k3 (Pm − Pmref ) − k 4 (ω − ωref )] + k 4 ω̇
⎩ T2

k3

(−Pm + ey y) ⎬
eqh Tω


(33)

The block diagram of ISC of HGU is shown in Fig. 3.
5. Numerical simulations

⎧ ẏ = 1 (−y + y + u )
f
0
Ty




⎪ P ̇ = 1 ⎢ −P + e y − ⎛⎜ eqy eh − e ⎞⎟ e T y⎥̇
y
qh y ω
⎪ m eqh Tω ⎣ m

⎝ ey


⎨ δ ̇ = (ω−1) ω
0

⎪ ω̇ = 1 [Pm − D (ω−1) ω0 − Pe (δ, Eq′)]
2H


xd ∑
xd − xd′
⎪ ̇′
1 ⎛
⎪ Eq = Td′ 0 ⎜⎝Ef − x ′ ∑ Eq′ + x ′ ∑ Vs cos δ ⎟⎠
d
d


The topology of the simulation system is shown in Fig. 4. From
Fig. 3, it is found that the simulation system is a single machine infinite
bus power system. In this system, the geode vane opening and rotor
speed deviations are used to sustain the mechanical power of hydraulic
turbine which is connected with generator, the terminal voltage of
generator is adjusted with excitation voltage of exciter to satisfy its
terminal voltage to the given level. The initial parameters of the
simulation system are shown as follows. ey = 1.0 , eh = 1.5, eqh = 0.5,
eqy = 1.0 , eqx = 0 , ex = 0 , bp = 0.05xd = 0. 95, xq = 0. 57, x′d = 0. 24 ,
′ = 0. 13, xT′ 2 = 0. 11,
H = 4. 1, D = 0. 1, T′d0 = 5. 2 , ω0 = 100π , xT1

Fig. 3. Block diagram of ISC of HGU.

83

Engineering Applications of Artificial Intelligence 58 (2017) 79–87

W. Zhu et al.

Fig. 4. Topology of simulation system and its interconnected power grid.

Time(s)

Time(s)

Time(s)

Time(s)

Fig. 5. Responses to synergetic controller and comparative schemes in load disturbance condition: (a) Guide vane opening response; (b) Mechanical power response; (c) Rotor angle
response; (d) Rotor speed response.

effectiveness of ISC controller.

xl = 0. 59 , Tw = 0. 68, Ty = 0. 25, U0 = 1. 0 , P0 = 0. 9956 , cos(φ0 ) = 0. 24 ,
δ 0 = 38. 94°, Ut0 = 1. 2901, E′q0 = 1. 46 , ω0 = 1. 0 , Uf 0 = 2. 09,
y0 = 0. 9956 , xs = 0. 535, xds = 1. 485, x′ds = 0. 775, xqs = 1. 105,
Pm0 = 0. 9956 , Ka = 1, Ta = 0. 000 .
In experiments, three simulation experiments have been conducted
in the power system shown in Fig. 4. SGC, ISC and classic PID
controller of governing system are employed under step disturbance
of load condition to validate the superiority of the proposed synergetic
control scheme used in power control condition. PID controller of
excitation system, SEC and ISC are applied in terminal voltage step
condition to show control performance of ISC used in voltage control
condition. And the integrated PID controller and ISC of hydro turbine
are applied in three-phase short circuit fault condition to validate the

5.1. Step disturbance of load
In this part of experiments, SEC, ISC and classic PID controller are
employed to act on the HGU system for a better dynamic performance
with a step disturbance of load under load running condition.
Simulation results of +50% step disturbance of load at 5 s are shown
in Fig. 5. Reference values in this case are given as follows, ωref = 1,
Pmref = 0.5, yref = 0.5, Vref = 1.2901. Controller parameters of ISC are
given as follows, T1 = 0.0739 , k1 = 0 , k2 = 0.7026 , T2 = 2.7542 , k3 = 0.217,
k 4 = 15.7317. Controller parameters of SGC are given as follows,
T2 = 4.7304 , k3 = 0.312 , k 4 = 14.9897. Controller parameters of classic

Table 1
Quantitative analysis of regulating performance with different controller under step disturbance of load condition.
Mechanical power

Overshoot (pu)
Settling time(s)
Oscillation times

Rotor speed

Guide vane opening

PID

SGC

ISC

PID

SGC

ISC

PID

SGC

ISC

0.1746
14.66
1

0.097
4.482
1

0.0567
8.25
1

0.0019
0
2

0.0008
0
1

0.0004
0
1

0
13.68
0

0
3.616
0

0
7.29
0

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W. Zhu et al.

Table 2
Quantitative analysis of regulating performance with different controller under step
disturbance of terminal voltage condition.
Rotor speed

Overshoot
Settling time(s)
Oscillation times

Terminal voltage

PID

SEC

ISC

PID

SEC

ISC

0. 0044
0
8

0.0021
0
3

0. 0004
0
1

0.2287
2.3771
11

0
2.3677
0

0
2.25
0

Fig. 8. Short circuit fault happens in the system.
Fig. 6. Phase trajectory of the control system under step disturbance of load condition.

manifold. In the Fig. 6, the zero of space axes represents the manifold
φ (x ) = 0 . The synergetic controller will restrict the system to operate
on the manifold when the system was motivated by the step disturbance of load, and the cyan dotted line reflects the control process
curve of synergetic controller. From the Fig. 6, it can be seen that the
trajectory of the three variables is restricted to a plane defined by the
manifold and from the original disturbance point to the new equilibrium point of the system. And additionally, rotor speed ω appears
weak oscillation near the new equilibrium point of system in SGC and
PID controller, while rotor speed ω is restricted to the new equilibrium
point of system in ISC controller, which means ISC controller has
shown the better performance of rotor speed regulating and stronger
damping under step disturbance of load condition, and has no
chattering phenomenon.

PID controller are given as follows, kp = 12.4595, ki = 1.7283,
kd = 3.3779 .
It is found that ISC and SGC are more rapid than PID to calm down
in Fig. 5(a)–(d). The synergetic control policies of ISC and SGC have
rapid response rate. In order to compare control performance achieved
by different controllers, the results on overshoot, settling time and
oscillation times are listed in Table 1. In Table 1, it is shown that,
compared with PID, SGC and ISC have the advantage of fast response,
and ISC has smallest overshoot. It can be concluded that ISC can
provide better regulating performance under step disturbance of load
condition than SGC and PID controller of HGRS.
To exhibit the regulating performance of the proposed ISC controllers, we investigate the phase trajectory of all the three control
models under step disturbance of load condition. Fig. 6 is the phase
trajectory of variables guide vane opening y , mechanism power Pm and
rotor speed ω after the system operating point has converged to the

5.2. Step disturbance of terminal voltage
Simulation results of −20% terminal voltage step disturbance at 5 s

Time(s)

Time(s)

Time(s)

Time(s)

Fig. 7. Responses to synergetic controller and comparative schemes in terminal voltage step condition: (a) Rotor angle response; (b) Rotor speed response; (c) Terminal voltage
response; (d) Mechanical power response.

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Engineering Applications of Artificial Intelligence 58 (2017) 79–87

W. Zhu et al.

Time(s)

Time(s)

Time(s)

Time(s)

Fig. 9. Responses to synergetic controller and comparative schemes under three-phase short circuit fault condition: (a) Terminal voltage response; (b) Rotor speed response; (c) Rotor
angle response; (d) Mechanical power response.

of the parallel lines, namely the point of high voltage side of the
boosting transformer T-1 in Fig. 9.
When a three-phase short circuit fault is set on the point of the high
voltage side of the transmission line (seen from Fig. 8) at 1 s and the
faulted line is cut-off after 0.2 s. Controller parameters of ISC are given
as follows, T1 = 2.997, k1 = 0 , k2 = 14.095, T2 = 2.025, k3 = 2.176 ,
k 4 = 0.47. Controller parameters of PID controller of excitation system
are given as follows, kp = 50 , ki = 10 , kd = 1. Controller parameters of
PID controller of governing system are given as follows, k2p = 12.4595,
k2i = 1.7283, kd = 3.3779. The transient process of this system under the
given case with the utility of ISA and PID are shown in Fig. 9, which
exhibits the dynamic response curves of 10 s under three-phase short
circuit fault, it is seen that ISC the overshoots of terminal voltage, rotor
speed and mechanical power of the ISC controller are significantly less
than that of PID controller.
To furtherly compare the control performance, the quantitative
analysis results of regulating performance with different controller are
listed in Table 3. In Table 3, it is shown that, compared with PID, ISC
has the control nimbly, fast response, small overshoot. It means that
ISC can provide better regulating performance under three-phase short
circuit fault condition than PID controller.

Table 3
Quantitative analysis of regulating performance with different controller under threephase short circuit fault condition.

Overshoot
Settling time(s)
Oscillation times

Mechanical power

Rotor speed

Terminal voltage

PID

ISC

PID

ISC

PID

ISC

0.0832
1. 27
3

0.0002
1.21
0

0. 005
1.21
3

0. 0038
1.21
2

0.0896
1. 21
2

0. 0049
1.21
2

are shown in Fig. 7. Reference values in this case are given as follows,
ωref = 1, Pmref = 0.9956 , yref = 0.9956 , Vref = 1.05. Controller parameters
of ISC are given as follows, T1 = 1.7778, k1 = 0 , k2 = 3.1529 , T2 = 2.6079,
k3 = 5, k 4 = 0.0000001. Controller parameters of SEC are given as
follows, T1 = 0.2276 , k1 = 0.4367, k2 = 21.9102 . Controller parameters of
PID controller of excitation system are given as follows, kp = 15,
ki = 10 , kd = 1.
Seen from Fig. 7, the rotor angle, rotor speed and terminal voltage
of the ISC controller totally lies inside the concave portion of that of
PID controller. In addition, ISC controller shows weaker oscillations
that PID and SEC. It is proved that ISC provides better voltagefollowing capability and excellent regulating performance under voltage step disturbance condition than SEC. In order to compare the
control performance of this three controllers, the results on overshoot,
settling time and oscillation times are listed in Table 2. In Table 2, it is
shown that, compared with PID and SEC, ISC has smallest overshoot
and oscillation times. It means that ISC can provide better regulating
performance under step disturbance of terminal voltage condition than
the SEC and PID controller.

6. Conclusion and discussion
In this paper, the synergetic excitation controller, synergetic
governing controller and integrated synergetic controller of HGU have
been designed with their synergetic control rules deduced, respectively.
In HGRS model, the third-order synchronous generator model is
adopted, which means the transients of power angle and terminal
voltage are taken into consideration. In the HGES model, the mechanical power input of the synchronous generator is also considered. Thus,
the adopted mathematical model in this paper can closely reflect the
transient process of both voltage and frequency controls.
In addition, synergetic control theory is introduced into HGES and

5.3. Three-phase short circuit fault
In this paper, the fault location is set on the high voltage side of one
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HGRS, and SEC, SGC and ISC of HGU have been designed. The
proposed ISC implements synergetic control of terminal voltage, rotor
speed, mechanical input power and guide vane opening. Namely, the
ISC is considering both of HGRS and HGRS of HGU. Furthermore, the
control rules of the three controllers are deduced from nonlinear
mathematical analytic model.
In the end of this paper, control performances of the proposed
controllers have been studied in various simulation conditions. The
results of the experiments show that the proposed SGC, SEC and ISC
generally respond more quickly than PID, and ISC has little overshoot
as a whole. It means that ISC achieves a superior performance
compared with SEC, SGC and PID controller. The numerical simulations have proved that ISC provides better voltage-following capability
and excellent regulating performance under all of the above cases
compared with SEC, SGC and PID. It is shown that the synergetic
controller design technique is more befitting to handle the affine
nonlinear model of HGU and may serve as a potential alternative for
the design of next-generation controllers for HGU.
Synergetic control theory is first introduced to the modeling of a
hydro-turbine governing system and excitation system, although this
paper studied only by designing the controller and its numerical
simulations. In the future, the robustness analysis of a hydropower
plant will be studied to prove the control performance of the ISC, such
as its robustness analysis when load changes are unknown. In addition,
over the course of the study, we found that the parameters (T1, k1, k2 , T2 ,
k3, k 4 ) of ISC have a significant impact on control performance, and the
optimal parameters varies under different working conditions.
Therefore, we will attempt to establish the self-adaption synergetic
controller suited for the whole condition of hydro-turbine.
Acknowledgements
The authors would like to acknowledge the National Natural
Science Foundation of China (Nos. 51579107 and 51239004) and the
Specialized Research Fund for the Doctoral Program of Higher
Education of China (No. 20100142110012).
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