Engineering, 2009, 2, 117-126
doi:10.4236/eng.2009.12014 Published Online August 2009 (http://www.SciRP.org/journal/eng/).
Hierarchical Coordinated Control for Power System
Voltage Using Linear Temporal Logic
Hongshan ZHAO, Hongliang GAO, Yang XIA
Department of Electrical Engineering, North China Electric Power University, Baoding, 071003, China.
Received May 18, 2009; revised July 3, 2009; accepted July 10, 2009
Abstract
The paper proposed an approach to study the power system voltage coordinated control using Linear Tem-
poral Logic (LTL). First, the hybrid Automata model for power system voltage control was given, and a hi-
erarchical coordinated voltage control framework was described in detail. In the hierarchical control struc-
ture, the high layer is the coordinated layer for global voltage control, and the low layer is the power system
controlled. Then, the paper introduced the LTL language, its specification formula and basic method for con-
trol. In the high layer, global voltage coordinated control specification was defined by LTL specification
formula. In order to implement system voltage coordinated control, the LTL specification formula was
transformed into hybrid Automata model by the proposed algorithms. The hybrid Automata in high layer
could coordinate the different distributed voltage controller, and have constituted a closed loop global volt-
age control system satisfied the LTL specification formula. Finally, a simple example of power system volt-
age control include the OLTC controller, the switched capacitor controller and the under-voltage shedding
load controller was given for simulating analysis and verification by the proposed approach for power system
coordinated voltage control. The results of simulation showed that the proposed method in the paper is feasible.
Keywords: Power Systems Voltage Control, Linear Temporal Logic, Hierarchical Coordinated Control,
Hybrid Automata
1. Introduction
Power systems voltage control involves many distributed
continuous controllers such as the generator excitation
controller and discrete controllers such as the OLTC, the
capacitor banks switching and load shedding, so power
system is a classical hybrid dynamic control system. At
present, the common methods of power system voltage
control are the optimal control method based on optimi-
zation theory [1-3], the VQC method [4,5] and the
Multi-Agent control method [6-8]. Substation is the
main node of power system voltage control, particularly
most voltage controllers in substation present the discrete
dynamic. How to coordinate these controllers that have
different functions is crucial to power system voltage
control. In order to ensure the voltage security control, it
is necessary to prevent redundancy and disorderly action
and regulation, moreover the disturbances exacerbated
the power system operation should be avoided [9].
In the light of the hybrid characteristics of power
sys-tem voltage control, a method using the Linear
Temporal Logic (LTL) is proposed to study the coordi-
nated control problem of the multiple discrete voltage
controllers in substation [10-12]. The main ideas: A hi-
erarchical method is adopted for voltage control. The
upper layer is voltage coordinated controller and the
lower layer is composed by the physics equipments and
their local controllers. In the high layer, Linear Temporal
Logic (LTL) is used to describe power system coordi-
nated voltage control specification [13], and then the
LTL specification formula is converted into hybrid
automata [14]. The hybrid automata effectively imple-

H. S. ZHAO ET AL.
118
ment the coordinated voltage control with multiple
specifications and multiple controllers. The most impor-
tant feature of this approach is that hybrid automata of
the coordinated controller can be designed automatically
though LTL specification formula. If the detailed LTL
specification formula is given, the hybrid automata
model can automatically be derived using the algorithms
in [14]. In particular, for complex systems, this method
greatly reduced the miscellaneous design and deductive
inference of the complexity control logic. Moreover, it is
easy to be extended to large-scale power system coordi-
nated voltage control.
2. Hierarchical Control Structure of Power
System
2.1. Hybrid Dynamic of Power System
Power system hybrid dynamics can be described by the
following equations:
(,,,)
x
fxqvt
，, (1)
(, ,,)0
j
sxqvt1, ,jn
() (,,,)
j
txqv 

t
(,,,) 0
j
sxqvt
,， (2)
{1,, }jn
(,,,)zhxqvt (3)
where Equation (1) describes the continuous dynamics of
power system, which are differential equations.
When the system continuous dynamics trajectory
passes through discontinuous plane Sj(·)=0,a discrete
event will occur. That is to say,Sj(·)=0 is the condition of
events occurred. Equation (2) describes the subsequence
change of continuous state vector when events occurred.
Equation (3) describes the output of hybrid power sys-
tem.
In order to facilitate modeling and analysis, we ex-
press the mathematical description of the hybri dynamics
system by nine-tuple a hybrid automata model [16],
(,,, ,,,,,)inv fsXQV IFj= (4 )
where is the continuous state space of the sys-
tem, ; is the set of discrete state,
n
XR
()xt Xm QN q

Q
()vt
;
is the set of discrete event input,
m
NV

V
00
( ))t
;
is the system initial state,
IXQ (( )xt ,q

I;
include dimensions continuous state output
ZXQ p
x
zand dimensions discrete state output , that is,
rq
z
() xpr
q
z
zt z



ZR N
(5)
and is produced by function
()zt :hXQVR pr
RN
The vector field:n
f

QXVR R
:2
X
inv V
q
describes con-
tinuous dynamics, and assigns an invariant
set to each location, the continuous part of the state.
The function :
j
s

XQVRR
(, ,
j
, de-
scribes the condition of events occurred. As long as the
discontinuous plane function
1, ,jn
,,) 0,
s
xyuqvt

is satis-
fied, the system trajectory makes the continuous dynamic
evolve according to Equation (1).
The function :XQVRXQ


 is the reset
map, describes the change of continuous state vector
after discrete events occurred, that is, subsequence
state ()t


.
()
() ()
T
n
xt
tqt




 l

 


XQ RN
(6)
Note that in the hybrid automata that we use in this paper
all the reset maps are defined to be the identify function.
We assume that the switching conditions and the location
invariants are connected sets. Also we let

XQHto
denote the state space of hybrid automata. 
The trajectory of the hybrid automataconsist of
combinations of the continuous state and discrete transi-
tions. A trajectory ofcan start at a location, then it
evolves under the gradient of vector field whose values is
constraint by the set

qt
()
(, )
f
q

while the state()
x
tremain
always within the invariant set. When continuous
state of trajectory satisfies the switching conditions, the
system instantaneously switches to the new -
tion ()qt
()inv q
loca

. The new state of the systell bem wi(,qx)

.

Formally, the semantics of hybrid automata are given
in term of generalized transition systems. A generalized
transition system is a tuple 0, where
(,, )
H
THH
0
H
is the set of initial condition and is a transition rela-
tion. We define a trajectory

0
:R

X of the transi-
tion system. The set of all trajectories
H
T

of that
start from a state in is the language of the
generalized transition system.
H
T
)
0
HH
(T
H
T
2.2. Hierarchical Voltage Control Structure
From the hybrid dynamics above, we know that it needs
complex logic analysis and effective coordination among
the dispersed controllers to implement global voltage
safety control for the power system with both continuous
control input and discrete control input.
We adopted hierarchical method to research the volt-
age control problem, as shown in Fig.1. The upper layer
is the voltage coordinated control model, and a global
control specification in this layer is defined by the LTL
formula to coordinate the action of multiple voltage con-
trollers to ensure the global voltage control safety. The

H. S. ZHAO ET AL.
119
Figure 1. A hierarchical control structure of power system.
lower layer is local closed loop control system composed
by the physics equipments and their continuous control-
lers or discrete controllers. Moreover, the coordinated
controller in upper layer and the physics system in lower
layer also consist of a global closed loop control system
satisfied LTL specification formula.
For the power system hybrid voltage control, how to
carry on logic analysis and coordination based on the
system running status is the main content of this paper.
The aim is mainly focused on:
- The control inputs should ensure the security and
stability of the system voltage;
- The results of coordination control should ensure that
the actions of the multiple discrete controllers are
reasonable, and the number of action is minimum;
- Avoid aggravating the deterioration of the power
system state due to disorder regulation of controllers.
3. Linear Temporal Logic and Controller
Synthesis
3.1. Linear Temporal Logic
LTL is a mathematical language based on the set of
propositions 01
{,,, }
n

   and provides a succinct
expression to describe the temporal and logic identity of
dynamic control system. The denotation
is a mapping function and represents a subset of .
For any
:(
k
PR
n
R
)

 , it is n



R. denotes the
power set of a set .
()P
LTL includes traditional logic operators, such as con-
junction (), disjunction () and negation (


), and
temporal operators such as eventually (), always ()
and until (


). For

, the set of all well formed
LTL overis constructed using the grammar.


::|||||

 



(7)
Let be a function fromtoand be the set
of atoms. For
()yt
Rn
R
,ts R


, the semantics of any formula



can be recursively defined as
- (, )|y


 , iff


(0)y

.
- (, )|y


 , iff


(0)y

.
- 12
(, )|y



 , if 1 (, )|y

 or 2 (, )|y

 .
- 12
(, )|y



 , if 1 (, )|y

 and 2 (, )|y


 .
- 1
(, )|y




2

, if there exists 0tsuch that
2
(|,)|
t
y


 and for all s such that 0
s
t

 we
have )|
s1
(|,y



Note that the path formula 1


2

intuitively ex-
presses the property that over the trajectory ,
()yt1

is
true until 2

becomes true. Here the semantics of until
requires that 1

holds when 2

become true. The for-
mula


indicates that over the trajectory the
subformula
()yt

becomes eventually true, that is, it de-
scribes the reachability properties for control problems,
whereas the formula

 or

denotes that

is
always true over, and it describes the safety proper-
ties for control problems.
()yt
Beyond the usual properties, LTL can capture se-
quences of events and certain infinite behaviors. For
example,
- Coverage: The formula

12 m

   
reads as the system will eventually reach 1


and
eventually 2


and ... eventuallym


, requiring
the system to eventually visit all regions of interest
without any particular ordering.
- Reachability while avoiding regions: The formula


12 n

 



1n

 expresses the
property that eventually 1n

 will be true, and until
1n


is reached, we must avoid all unsafe sets i


,
1, ,in

.
- Sequencing: The requirement that we must visit 1


,
2


and 3


in that order is naturally captured
by the formula



123



 .
- Recurrence: The formula


12 m

 


requires that the trajec-
tory does whatever the coverage does and, in addition,
will force the system to repeat the desired objective infi-
nitely often.
More complicated control specification can be com-
posed from more basic specifications using the logic
operators.
For a hybrid control system, we can define LTL seman-
tics over abstractions of the output trajectories of discrete
set

. Let (,)|y


 to denote the satisfaction of the

H. S. ZHAO ET AL.
120
LTL formula

over the output trajectory start-
ing at time t = 0 with respect to the atom mapping
()yt

. If
all the output trajectories of system driven by a
controller are such that
()yt
(,y

C)|

 , then we write
([ ,],H)|

 
and we say that [, ]
H
 satisfies LTL
formula

.
3.2. From LTL to Hybrid Automata
In this section, we describe an algorithmic procedure for
deriving a hybrid automata whose transition system gen-
erates the models of certain fragments of LTL using the
framework presented in [15]. In the following, we intro-
duce the algorithm for the (,,)LTL

, (,LTL ,)


and (,, , )LTL

fragments of the logic.
The fragment(,LTL ,)

contains the Boolean op-
erators of conjunction and disjunction and until temporal
operator. According to the three propositions 1-3 in [15],
the algorithm of(,LTL ,)

c
(,,
an be described as fol-
lows:
Algorithm1: the)LTL

fragment
Input: A formula (,LTL ,)Îf

Output: the Hybrid Automata
f
H
)
procedure (HA
u
LTLto

if then
f=
H
LT
p
return p
else if then 12
f
1
()
ff=
return u
L toHA

Ç2
()
u
LTL toHA

else if then 12
f
1
()
ff =
return u
L toHALT

È2 ()
u
LTL toHA

else if fp=


then
¬H
()y
u
L toHALT
(,
y
LTL
return
f
H
end if
end procedure
Algorithm 1 presents the procedure for the synthesis of
hybrid automata that generate the models of a specifica-
tion in
f,)

, hence we have the following the
proposition:
Let f(,,)LTLÎ 

and letbe the output of algo-
rithm 1, then
f
H

f
hÎ(T)implies . |hf=
, )
For the fragment(,LTL


(,LTL

,) 
, its algorithm is
similar to algorithm 1 of

. The algorithm of
the captures both reachability and safety proper-
ties, that is, it is combinations of
U
LTL
(,LTL ,)

and . Therefore, we can take
advantage of these algorithms to synthesize the controller
satisfied the reachability and safety properties.
(, L,) LT
3.3. Coordinated Controller Synthesis Based on
LTL
The problem of synthesizing a coordinated controller can
be described by the following:
If there is a dynamic systemand LTL formula


on
set

, we construct a coordinated controllerfor the
system
C

, such that its trajectories generated by the
close-loop control system should satisfy the LTL speci-
fication

.
Coordinated controller synthesis includes two parts: (a)
define LTL specification formula; (b) the design of coor-
dinated controller satisfied LTL formula.
The LTL specification formula described the global
control behavior, through coordinating the lower layer
controller to achieve the global system stability control.
The step of coordinated controller design is as follow:
First, transform the LTL formulas into hybrid auto-
mata by using these algorithms mentioned above. Then,
construct a closed-loop control system combined the
objects controlled in lower layer with their coordinated
hybrid automata in top layer.
Hybrid automata can satisfy the requirements of
reachability and safety from any state driving system
trajectory. In fact, this control behavior is to simplify the
entire system to combinations of a series of control con-
trollers, that continuous trajectory produced by these
controllers should satisfy the LTL formula.
4. Coordinated Controller Synthesis to Power
System Substation
4.1. Hybrid Model of Power System
We make use of a substation which including OLTC
controller, load shedding relay and capacitor bank
switching to research the coordinated voltage control.
The generator bus is modeled as an ideal voltage source.
The load is modeled as a dynamic exponential recovery
load, as shown in Figure 2. The voltage safe operating
region is ±10％ of the rating voltage.
The hybrid dynamic model of system above power
system is,
1
02 2
((
st
p
T
ppL
xxkPVV

 
))
(8)
1
02 2
((
st
q
T
qqL
xxkQVV

 
))
(9)

H. S. ZHAO ET AL.
121
S
Slack
V=1,th...
V0 V1
T
V2
jx 1 + j 0.
2
j0.1 j0.1
Figure 2. A simple power system.
02
()
02
0(1 )()sin
t
T
VV
kiX
Lp
kx PV


  (10)
2
20 2
2
2
() 02 02
()
0(1 )()cos
t
TT
VV V
kiX Lq C
kiX
kxQV kBV

  (11)
where are the active power recovery time con-
stant and reactive power recovery time constant respec-
tively,
,
pq
TT
,
s
t
VV


are the steady-state dependency,
,
s
t
VV

are the transient dependency. []
T
pq
x
xx
T
represents the load internal states, and[]
y
V
]
is alge-
braic variables. represents the dis-
crete control input included the OLTC ratio, load shed-
ding ratio and capacitor banks switching ratio.
[T
TLC
vkkk
Discrete control input depends on all discrete con-
troller action. When does not change, Equation
(8)-(11) will evolve continuously. In order to describe
the discrete dynamic behavior of each voltage controllers,
their hybrid automata models are given in next section.
v
v
4.2. The Automata Model of OLTC Controller
The control behavior of OLTC can be described by the
following mathematical model:
()(1)()
TT
kikidf V
(12)
where is the OLTC ratio of the ith regulation; is
the OLTC regulation step, is the voltage
deviation, is reference voltage;
()
T
ki
V
d
r
VVV
(
r)
f
V denotes up
or down of OLTC regulation, its expression is
1max
2
1min
2
1()(
() 1()()(
0others
Brtd T
Brtd T
VD tTkn
fVVDt Tkn
 


 




（） )
)
4
(13)
where, is the sum of OLTC timer delay and me-
chanical delay, are the maximum and mini-
mum regulation tap respectively.
td
T
max min
,nn
The OLTC control behavior described by model (12)
can be described by a hybrid automata model, as shown
Figure.3. The regulation condition of up or down of
OLTC regulation is as follows
13up ttt

  (14)
0
q
1
q
2
q
dn

up

rt

rt

Figure 3. Automata model of OLTC controller.
23dn ttt5



 (15)
6rt t



(16)
where, atomic proposition 1 12
()
t
VD 0
B

denotes
the regulation condition when voltage is larger than the
set value; 1
22
()
t
VD 0
B


  denotes the regula-
tion condition when voltage is lower than the set value.
3() trtd
tT 0



(()
tT
ki
denotes OLTC delay of tap regula-
tion; 4ma
)0
T
kx


 
,5min
(() )0
tTT
ki k

 
,
6() trrt
tT 0



.
4.3. The Automata Model of Capacitor Switch-
ing Controller
Switching capacitors can produce or reduce system reac-
tive power. The term in Equation (11) is the
reactive power produced by the capacitor banks switched.
The switching conditions are as follows: when power
factor is lower than the setting value and at the same time
the voltage increase slowly, we switch on the capacitor;
when power factor is larger than the set value and the bus
voltage is higher than the setting value requested, the
capacitor is switched off.
2
0c
KBV
The condition of switching capacitor is described as
follows,
13 5
s
wc cc



 (17)
24rmccc5



 (18)
6rc c



(19)
The atomic propositions of the switching condition are


1mi
cos 0
cf

n


, 2max (cos) 0
cf

,
3c




0
csw
VV



, ,

40 ccrm
VV   



50 crc
tT 

 6 
,

0
rc
tT
cr


.
The control behavior is similar to the OLTC controller,
its automata model is as shown in Figure 4.
0
q
1
q
2
q
rm

s
w

rc

rc

Figure 4. The automata model of capacitor banks switching.

H. S. ZHAO ET AL.
122
4.4. The Automata Model of Load Shedding
Controller
Load shedding is the final measure used to avoid a wide
area voltage instability and voltage collapse when all
other effective measures are exhausted. The condition of
load shedding is: (i) The system active power safety
margin is less the setting, that is
s
et ; (ii) The volt-
age fall to 85～95％ of normal for a minimum of 5 sec-
onds. The automatic recovery of load isn’t considered in
this paper. The conditions mentioned above can be writ-
ten as follow,
SS
123
s
hs ss

  (20)
4rhs

  (21)
The atomic propositions are1() sset
SS 0

 ,
2(0.90) 0 sV

 , 3(
sr
)0
s
tT

 4(
, )
s
rr
tT
s


.
0
The automata model of load shedding is shown in
Figure 5.
4.5. The Coordinated Controller on Substation
In order to avoid the voltage instability or collapse, the
OLTC regulation, capacitor banks switching and load
shedding in substation have to coordinate with their ac-
tion each other, otherwise, would lead to control disorder
and even aggravate the deterioration of the voltage.
a) The coordinated control LTL specification formula
The action principle of coordinated controller: if
power system is lack of reactive power or in heavy load
or power safety margin close to its settings, the capacitor
should be switched on; if all capacitor banks are
switched on, and the safety margin of power is still out-
side its settings, some load should be shed. At the same
time, in order to avoid system voltage instability or col-
lapse, lock the OLTC controller.
For the OLTC controller, its LTL formula of the coor-
dinated adjustment is as follows
12
(
Tt
)
t

  (22)
For capacitor banks switching, the coordinated action
LTL formula is
12
(
Cc
)
c

  (23)
0
q
1
q
s
h

rs

Figure 5. Automata model of load shedding.
For load shedding, the coordinated action LTL for-
mula is
12
(
SsscT
())




 (2 4)
where, max
()
cCC
kk 0



T

denotes that all capacitor
banks are switched on,


denotes to lock the OLTC
operation during the load shedding.
The final LTL formula of coordinated controller
is
C

12
()
t

H
tTCS

   (25)
where


12tt



 denotes that the system is in the
steady-state and has not any control action.
b) Transform the LTL formula into the Hybrid Auto-
mata
In order to implement the LTL specification formula
of coordinated controller, the formula
H
 will be con-
verted to hybrid automata by those algorithms introduced
above. The hybrid automata model of LTL formula is
shown in Figure 6.
In Figure 6, 01tt2



 , and the symbol 0


denotes that the system is in the steady-state and has not
any control. 112tt



, and 1


denotes that the
coordinated controller allow the OLTC controller to
regulate. 212cc



, and 2


denotes allowing
the capacitor banks switching. 312
s
s

  , 3


denotes allowing load shedding. 4


denotes allowing
the OLTC to be regulated after capacitor banks switching.
5


denotes allowing the OLTC to be regulated after
load shedding.
5. Numerical Simulation
In order to verify the validity of power system voltage
hierarchical coordinated control based on LTL formula,
the operating process of the coordinated controller
and the dynamic behavior of power system under
several disturbances are simulated on the platform of
Dymola.
()C


0



1



2



3



5



4

Figure 6. The hybrid automata of the LTL formula
H

.

H. S. ZHAO ET AL.
123
0100 200 300 400 50
0
0.76
0.8
0.84
0.88
0.92
0.96
1
1.04 Bus 2 .V
(a)
0100 200 300 400 50
0
0.98
1
1.02
1.04
OLTC.y
(b)
0100 200 300 40050
0
-0.2
-0.1
0
0.1
0.2 CAP.y
(c)
Figure 7. The voltage curve without coordination on bus 2
and the actions of discrete controllers.
5.1. Fault Occurred under Normal State
A permanent short-circuit fault occurred under normal
state at 20 seconds and it was cleared after 0.1 second.
1) Without any coordination
The voltage simulating curve without any coordination
on the low voltage side bus2 is shown as Figure 7(a) and
the actions of the discrete controllers are shown as Figure
7(b) and Figure 7(c). We can know that one bank of ca-
pacitor is switched on, at the same time, the OLTC con-
troller has been up-regulated 3 times, then down-regu-
lated 3 times. But in practice the operation of OLTC
controller repeatedly is not desired since it reduces the
lifetime of contact of executer.
2) The operating process with coordinated controller
The voltage simulating curve and the actions of discrete
controllers with coordination are shown as Fig.8. We can
know that the results of action of controller under the
coordination: the capacitors needn’t to be put, only the
OLTC controller has been up-regulated 7 times, and the
voltage finally stabilized at its allowed level.
It can thus be seen that in such circumstances, only by
regulating OLTC, can make the voltage to satisfy system
requirements. This shows that the reactive power is ade-
quate under normal conditions, so don’t need input ca-
pacitors and only depending on LOTC regulation would
be able to meet the requirements of voltage. As can be
seen from Figure 7 without any coordination, the input
capacitor led to the OLTC regulation up-regulated and
down-regulated repeatedly.
5.2. Fault Occurred under Reactive Power
Deficiency
A permanent short-circuit fault occurred under reactive
power deficiency state at 20 seconds and it was cleared
after 0.1 second. Some cases involved in discrete con-
trollers are discussed in the following.
1) Only the OLTC regulated
For the system under the reactive power deficient in
Figure 2, if only OLTC regulated, the voltage collapsed
finally. Shown as Figure 9, the system voltage collapsed
near 710 seconds. This is because the reactive power is
deficiency, so the adjustment of OLTC not only can’t
make voltage satisfy system requirements, but will made
system further deteriorating.
2) The OLTC locked
If locked OLTC, the system collapse could be avoid
and the voltage eventually be stable at low value 0.78
p.u., shown as Figure 10. However, the level of voltage
is far from the system requirements.
0100 200 300 400 50
0
0.76
0.8
0.84
0.88
0.92
0.96
1
Bus2. V
(a)
0100 200300 400 50
0
0.98
1
1.02
1.04
1.06
1.08
1.1OLTC.y
(b)
Figure 8. The voltage curve with coordination on bus 2 and
the actions of discrete controllers.

H. S. ZHAO ET AL.
124
0100 200 300 400500 600 700 80
0
0.5
0.6
0.7
0.8
0.9
1
Bus2.V
(a)
0100 200 300 400500 600 700 80
0
1
1.04
1.08
1.12
OLTC.y
(b)
Figure 9. The voltage curve on bus 2 and the actions of dis-
crete controllers.
0100 200 300 400 500 600 700 80
0
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05 Bus2.V
(a)
Figure 10. The voltage curve on bus 2 and the actions of
discrete controllers.
3) Without any coordination
The voltage simulating curve without any coordination
on the low voltage side bus 2 is shown as Figure 11(a)
and the actions of the discrete controllers are shown as
Figure 11(b) and Figure 11(c). We can know that three
banks of capacitor are switched on and the OLTC con-
troller has been up-regulated four times, then
down-regulated three times. Although the final voltage
satisfied the system requirements, but all banks of ca-
pacitors are switched on and OLTC has been
up-regulated and down-regulated repeatedly.
4) The operating process with coordinated controller
The voltage simulating curve and the actions of the
discrete controllers with coordination are shown as Fig-
ure 12. Two banks of capacitors were switched on and
the OLTC is only up-regulated 6 times, then the power
0100 200 300 400 500 600 700 80
0
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05 Bus 2 .V
(a)
0100 200 300 400 500 600 700 80
0
0.99
1
1.01
1.02
1.03
1.04
1.05 OL TC.y
(b)
0100 200300400 500 600 70080
0
-0.1
0
0.1
0.2
0.3
0.4 CA P.y
(c)
Figure 11. The voltage curve without any coordination on
bus 2 and the actions of discrete controllers.
system finally stabilized at the allowed level of voltage.
From the simulating results, the coordinated controller
can significantly avoid the adjustment of OLTC repeat-
edly, at the same time, reduce one bank of capacitor
switching on.
5.3. Fault Occurred under the Heavy Load
When system is under the heavy load, a permanent
short-circuit fault is assumed at 20s and the fault was
cleared after 0.1s.
1) Without coordination
Due to power system operating under the condition of
heavy load, the system power margin is deficient when
the disturbance occurred, and the controllers of OLTC
and capacitor banks would operate respectively. The
Figure 13 shows the operating result of multi-controller
without coordination. The system voltage collapsed near
380 seconds. This shows that under the heavy load, the
operation only depended on capacitor banks and OLTC
is not enough.

H. S. ZHAO ET AL.
125
0100 200 300400500 600 700 80
0
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05 Bus 2. V
(a)
0100 200 300 400500600 700 80
0
0.98
1
1.02
1.04
1.06
1.08 OL TC. y
(b)
010020030040050060070080
0
-0.1
0
0.1
0.2
0.3
0.4 CA P.y
(c)
Figure 12. The voltage curve with coordination on bus 2
and the actions of discrete controllers.
0100200 300 400 50
0
0.4
0.5
0.6
0.7
0.8
0.9
1Bus 2 .V
(a)
0100200 300 400 50
0
1
1.04
1.08
1.12
OLTC.y
(b)
0.4 CA P.y
0100200 300 400 50
0
-0.1
0
0.1
0.2
0.3
(c)
Figure 13. The voltage curve without coordination on bus 2
and the actions of discrete controllers.
0100 200 300400 500 600700 80
0
0.72
0.76
0.8
0.84
0.88
0.92
0.96
1Bus 2. V
(a)
0100 200 300 400 500 600 70080
0
0.98
1
1.02
1.04
OLTC.y
(b)
0100 200300400500 600 700 80
0
-
0.05
0
0.05
0.1
0.15 LOAD.y
(c)
Figure 14. The voltage curve with coordination on bus 2
and the actions of discrete controllers.
2) The operating process with coordinated controller
The Figure 14 is shown the action result under the co-
ordination of the LTL specification formula, and the sys-
tem voltage is finally stabled at the level of system re-
quirements. Two groups of load are shed, and finally
make the voltage satisfy the system requirements by
OLTC adjustment. Through the analysis can be aware
that when fault occurred under heavy load, due to over-
loading, the input of capacitor banks will not achieve all
well. Therefore, the final measures to shed loads should
be made to avoid the system collapse.

H. S. ZHAO ET AL.
126
6. Conclusions
According to the hybrid characteristics of power system
voltage control, a hierarchical method is adopted for the
power system voltage control. The upper layer mainly
completes the coordination function, and the low layer is
system or equipment and the corresponding physical
system controller.
The coordinated controller synthesize problem in-
cludes two parts: the global specification formula and
design of the coordinated controller. We use the LTL
formula to describe the global stable specification of
voltage control. The LTL is a math language that can be
able to flexibly describe the real-time and logic functions,
and can be able to succinctly describe the coordination
and logic. For the design of the coordinated controller,
the proposed approach was to transform the LTL formula
into the hybrid automata model, and the hybrid automata
coordinated the all the low layer distributed controllers,
and implement the global voltage control with them to-
gether.
Finally, a simple example of the power system is
given, some cases using the proposed hierarchy coordi-
nated control method were simulated, and the results
show that the proposed method is feasible. The further
work is that we continue to study the wide-area power
system voltage coordinated control using the method
proposed in this paper.
7. References
[1] S. Fan, C. X. Mao, and L. N. Chen, “Optimal coordinated
PET and generator excitation control for power systems
[J],” Electrical Power and Energy Systems, Vol. 28,
Vol.5, pp. 158-165, 2006.
[2] Y. J. Li, D. Hill, and T. J. Wu, “Optimal coordinated
voltage control of power systems [J],” Journal of Zheji-
ang University SCIENCE A, Vol. 7, No. 2, pp. 257-262,
2006.
[3] Y. Q. Yuan and J. Wang, “Coordinated control for SVC
and generator excitation based on passivity and backstep-
ping technique [J],” Transaction of China Electro-technical
Society, Vol. 22, No. 6, pp. 135-140, 2007.
[4] H. J. Yan, “Some problems on integrated control for
voltage and reactive power in substation [J],” Power Sys-
tem Technology, Vol. 24, No. 7, pp. 41-43, 2000.
[5] M. E. Baran and M. Y. Hsu, “Vlot/Var control at distri-
bution substation [J],” IEEE Transaction on Power Sys-
tems, Vol. 14, No. 1, pp. 312-318, 1999.
[6] D. P. Buse, P. Sun, Q. H. Wu, et al., “Agent-based sub-
station automation [J],” IEEE Power and Energy Maga-
zine, Vol. 1, No. 2, pp. 50-55, 2008.
[7] T. Nagata and H. Sasak, “A multi-agent approach to
power system restoration [J],” IEEE Transaction on
Power Systems, Vol. 17, No. 2, pp. 457-462, 2002.
[8] N. Yorino, Y. Mori, H. Sasaki, et al., “A control problem
for decentralized autonomous voltage controllers [C],”
the 14th PSCC, pp. 24-28, 2002.
[9] M. S. Kwang, S. M Kyeong, and K. L Song, et al., “Co-
ordination of an SVC with a ULTC reserving compensa-
tion margin for emergency control [J],” IEEE Transaction
on Power Delivery, Vol. 15, No. 4, pp. 1193-1198, 2000.
[10] M. Kloetzer and C. Belta, “A fully automated framework
for control of linear systems from temporal logic specifi-
cations,” IEEE Transaction on Automatic Control [J],”
Vol. 53, No. 1, pp. 287-297, 2008.
[11] T. Moor and J. M. Davoren, “Robust controller synthsis
for hybrid systems using modal logic [M],” Spring-
er-Verlag, New York, pp. 433-446, 2001.
[12] P. Tabuada and G. J. Papas, “Linear time logic control of
discrete-time linear systems [J],” IEEE Transactions on
Automatic Control, Vol. 51, No. 1, pp. 1862-1877, 2006.
[13] E. A. Emerson, “Temporal and modal logic [M],” Hand-
book of Theoretical Computer Science: Formal Models
and Semantics, MIT press, pp. 995-1072, 1990.
[14] P. Gastin and D. Oddoux, “Fast LTL to Buchi automata
translation [M],” Springer-Verlag: In G. Berry, H. Comon, A.
Finkel, eds., Computer Aided Verification, pp. 37-43, 2001.
[15] G. Fainekos, A. Girard, and G. J. Pappas, “Hierarchical
synthesis of hybrid controllers from temporal logic speci-
fications [M],” Spring-Verlag: HSCC, LNCS 4416, pp.
203-216, 2007.
[16] A. Nerode and W. Kohn, “Models for hybrid systems:
Automata, topologies, stability [M],” Spring- er-Verlag,
New York, pp. 317-356, 1993.