- Email: [email protected]
A closed-loop reactive power controller for power system voltage stability
Electrical Power & Energy Systems, Vol. 19, No. 3, pp. 153-164, 1997 © 1997 Elsevier Science Ltd Printed in Great Britain. All fights reserved
ELSEVIER
PII: S0142-0615(96)00007-5
0142-0615/97/$17.00+0.00
A closed-loop reactive power controller for power system
voltage stability V Veera Raju CMC Limited, Old Bombay Highway Road, Hyderabad - 500 019, India
A Kuppurajulu Department of Electrical Engineering, I.I.T. Madras - 600 036, India
due to reactive power disturbance is demonstrated with examples. © 1997 Elsevier Science Ltd
Any imbalance between reactive power supply and demand disturbs the normal operation of a power system. Power system contingencies sometimes cause excessive reactive power imbalance, even leading to total system breakdown. The problem is usually aggravated when the system is heavily loaded. Generator overload due to excessive reactive power generation ;?s one of the most common and serious causes of voltage instability. Low voltage at load buses is another cause which is likely to result in voltage stability problems. By closely monitoring the reactive power generation and load voltages, it is possible to avoid such major disturbances. A closed-loop controller can steer the system to a safer state by rescheduling the reactive power generation from generators and SVCs through voltage set point controls in real time. A closed-loop controJler which dynamically steers the system to a safer state on violation of specified operating conditions of reactive power generation and load bus voltages is designed. During normal operation, the controller minimizes active power transmission losses due to reactive power transfers. The principle of the controller is based on a multi-variable control concept. A closed-loop controller is synthesized to steer the system dynamically to an acceptable state while satisfying Kuhn-Tucker conditions of optimality in sfeady state. The proposed closedloop reactive power controller which gives set point control signals to A VRs and SVCs in the secondary mode of control, can be viewed as a parallel to the AGC for active power/frequency control. The controller performs this task on a real-time basis using SCADA measurements. The controller also issues load shedding commands in case it is necessary. The controller is tested under normal as well as contingency operation. Broad details of the closed-loop controller and its efficacy in avoiding system breakdown
Keywords: on-line control, emergency control, closed loop control, reactive power control, voltage stability, multivariable control
I. Introduction It is important to operate a power system within specified limits of frequency and voltage to avoid risk of disturbances. The disturbance can be due to a series of contingencies leading to a system emergency state which might lead to a total system breakdown. To avoid the danger of system breakdown, it is necessary to maintain a balance between supply and demand of both real and reactive power and also sufficient reserves for contingency situations. The IEEE task force report on Var Management [1] highlighted the importance and complexity of maintaining reactive power balance in the power system. Lachs [2-5] proposed automatic counter measures to mitigate the problem associated with reactive power deficit and surplus. The measures are broadly categorized into:
• raising EHV voltages; • restricting system load; and • improving reactive power reserves. Brownell and Clark [6] have stressed the need for new analytical tools in control centres to steer the system away from the voltage instability state. Goossens [7] recommended specific measures to provide voltage support sources with automatic controls based on their practical experience. Taylor [8] investigated under voltage load shedding for voltage stability
Received 21 September 1994; accepted4 January 1996
153
154
Closed-loop reactive power controller." V. Veera Raju and A. Kuppurajulu
for the Puget Sound area of the Pacific Northwest utility. In summary, the work carried out so far with respect to voltage collapse/stability and control broadly falls into the following categories: (i)
provision of preventive controls so as to keep the power system away from the voltage instability region; (ii) on the occurrence of a disturbance, provision of automatic controls for immediate mitigation of the danger of voltage collapse so as to give enough time for the operator to steer the system to a safer power system state; and (iii) development of algorithms to help drive the immediate post disturbance state to a safer power system state. While investigations for better procedures and methods are being carried out to understand and solve reactive power-voltage related problems, efforts to control voltage in closed loops have also been reported. Paul et al. [9] have surveyed the voltage control of French power systems. They propose a coordinated secondary voltage control against the practice of a threelevel hierarchy, viz. local primary control, regional level secondary control and a national level tertiary control. Lagonotte et al. [10], Thorp et al. [11], Ilic and Stobart [12] and Stankovic et al. [13] have investigated automatic voltage/reactive power control methodologies in realtime. Ilic [14] surveyed the approaches to voltage monitoring and control and gave a methodical treatment of the primary and secondary control philosophy. Carpentier et al. [14] have proposed a new concept of secondary voltage control as part of OPF in closed-loop secure AGC. Brandwajn et al. [16] have discussed the evolutionary trends in generation control and proposed that new control algorithms, such as coordinated multivariable techniques, are the future framework for research. In this paper a multi-variable closed-loop controller is proposed to mitigate voltage related problems during system disturbances leading to reactive power problems. The controller under normal operation minimizes system transmission losses, whereas under contingency operation it dynamically steers the system to a safer state by giving incremental signals in each SCADA sampling period in terms of generator voltage set points and SVC voltage set points. In extreme situations where the controller is unable to bring the system back to normality, for reasons such as inadequate reactive power reserves, rapid deterioration of system conditions from the reactive power point of view, etc., load shedding is automatically invoked to save the power system from voltage stability problems. Investigation of multivariable control as a secondary control system based on the extension of Kuhn-Tucker conditions of optimality to dynamic systems have been attempted by a group from IIT, Madras [17-21]. The basic mathematical principle was first applied to power system security based on active power dispatch [19]. To gain further confidence, it was tested on a dynamic simulator and is reported in Reference [20]. Investigations on active power controls for voltage stability are reported in Reference [21]. Investigations in this paper are primarily focused on formulation of reactive power control problems for the improvement of voltage stability. The controller acts as a secondary voltage control by providing voltage set points to the primary control devices, viz. generator AVRs in power plants and SVCs in
sub-stations. The primary control devices provide the fast acting local control requirement whereas the proposed controller provides a slow acting secondary control satisfying the desired objective by providing incremental control signals. The efficacy of the controller is tested on a simulated 6 bus power system. As the main purpose of this paper is to illustrate the underlying principle of the voltage controller, it was felt that a smaller system can bring out more clearly the interaction between various variables much more clearly. In any case, reactive power transfer over long distances is not possible. We have to look at controlling the sources close to the disturbed point. Using a dynamic power system simulator to model the system, typical outages were created and the response of the system was studied with and without the controller. The role of SVCs as sources of reactive power, the possibility of reactive power and the possibility of their set point control have been illustrated. A few case studies of line/generator outages leading to system wide breakdown are simulated on a dynamic PSS. Effectiveness of the proposed reactive power controller in arresting the system breakdown is demonstrated. It is proposed that SVCs also be used as control devices during such emergencies, not only in primary control but also in secondary control through the proposed controller. In addition, the effectiveness of the controller during normal operation in minimizing transmission losses while meeting the voltage constraints at load buses and reactive power limits of generating units is also demonstrated. Formulation of the problem in terms of structure of the controller and broad details of the proposed reactive power-voltage control in closed loop are explained in Section II. Testing methodology and several case studies are described in Section III.
II. Description of proposed controller Problem formulation of reactive power control, including the dynamic equations of the proposed controller, is explained in this section. The real-time computations involved and the operation of the controller are also discussed in this section. The basic dynamic control scheme around which the problem formulation is carried out is explained in Reference [17], however, for quick reference it is enclosed in Appendix A. 1. With the feedback control structure described in Appendix A. l, the system can be driven to an optimal steady-state point. The control vector is evaluated from the measurements of the system. As and when the operating point deviates from the optimal point, the feedback controller gives incremental control signals to drive the system to a steady-state optimal point. The controller specifically tries to alleviate reactive power violations at generating buses and voltage violations at load buses under emergency conditions of power system operation. Under normal system operation, the controller minimizes active power transmission losses arising due to reactive power transfers in the network. I1.1 Problem formulation and control equations The controller is designed with the following objectives:
• to ensure generators do not get overloaded due to excessive reactive power generation;
Closed-loop reactive power controller." V. VeeraRaju and A. Kuppurajulu • to ensure load bus voltages are within a specified operating range; • to avoid voltage stability problems; • to respond quickly even during contingency situations such as line outage, generator outage, etc.; • to have reasonable cycle time, say about 5-10 s; and • to exploit possible savings during normal system operation Keeping the above objectives in view, the problem formulation is explained as follows. The objective function of reactive power control is chosen as minimization of total transmission losses p, i.e. min p
155
and
Qi - Qmax
ii :
i = 1,2,..., G
(7)
i=G+S+I,...,G+S+L
(8)
Ai~> 0
~i=v~n-vi '7i>~ 0
The expressions for partial derivatives Op/OX, OQi/OX and OVi/OX are derived in Appendix A.2. Expressions for OX/OUk are derived in Appendix A.3. Controller equations (5), (7) and (8) can be rewritten as
Ai = J(Qi - Qmax)dt
i = 1,...,G
")'i = I ( V ~ in - Vi)dt
i=G+S+I,...,G+S+L
(9)
where G+S+LG+S+L p--1/2 Z Z P/J i=l j=l
(1)
where P/j is the loss in tlhe line connecting buses i andj. G is number of generating buses, S is number of SVC buses and L is number of load buses. While the state vector X is the voltage magnitudes of all buses, the control vector U includes voltage magnitudes at G-type (P-V type) buses and voltage magnitudes at SVC buses, i.e.
xt = [V 1V2... VGVG+I... VG+SVG+s+I... VG+S+L] u t = [V 1V2... VGVG+I... VG+S] It is also necessary that reactive power limits at G-type buses and voltage magnitude limits at L-type (P-Q) buses are not violated, i.e.
Qi- Qmax~ <0
i:-- 1,2,... ,G
(2)
v~nin -- V < 0
i::G+S+I,...,G+S+L
(3)
(10) f
= j0kdt
k= 1,...,G+S
(11)
with Ai >--0 and % t> 0. 11.2 Operation of the controller Referring to Figure 2, power system data are acquired in real-time under the control of SCADA software in an Energy Management Centre (EMC). SCADA software acquires the data from the RTUs. The RTUs acquire data locally at the generating plants and sub-stations through necessary field interfaces. In addition to the data acquisition through these interfaces, the RTUs also carry out supervisory and closed-loop control commands issued from the Energy Management Centre computer system.
Similar constraints can be added for reactive power low limits at generating buses and voltage high limits at load buses. The constraints on the control vector are not specifically shown as they are taken care of while transmitting the control signals. The following closed-loop control algorithm, solved on the real-time computer, will evaluate the required control signal G G+S+L L = p ~- Z / ~ i ( Q i - gmax)_~_ Z ~[i( V~fin - Vi) i=l i=G+S+I
P(M~W)~ 1.0 H sSlE #
5'
I
""" t" Y /i
IC
D--0. 8
--
0.6
Qm/"
0.4
~ B minimum im . .P. O . _ _n~ . lwerlimit/
(4) It may be noted that the Lagrange coefficients ~ and 7 are used for constraints on gen bus reactive power violation and load bus voltage violation, respectively. There are no equality constraints as described in the general equation (A.4) in Appendix A. 1.
Ok = -OL/OUk
k = 1,2,..., G + S
iF 0.4
0.2
0
(Underexcited)
G -F Z Ai(OQi/Ox)t(ox/OUk) i=1 G+S+L (6)
,:A(
0.2
rm 0.4
I
,
0.6
(Overexcited) Q
AB BCH HIJK CDE EF
OL/OUk = (Op/OX)t(OX/dUk)
i=G+S+I
I
0.6
:
(5)
where
+ Z % ( O V , IOX)t(ox/ouk)
0.2
t, ~ ~. t, t,
i^
0.8
,
1.0
(MVAR) ,,
Rotorheatinglimit Statorwindingheatinglimit Statorend ironheatinglimit Turbineoutputlimit Practicalstabilitylimit withAVR
Figure 1. Capability curve of a typical 68 MVA turbo generator
156
Closed-loop reactive power controller." V. Veera Raju and A. Kuppurajulu
Under normal conditions of power system operation, the controller generates voltage set point signals to AVRs and SVCs to achieve minimum active power transmissions losses. On violation of the reactive power (Qg) high limit of the generating unit or load bus voltage (111) low limit, the controller generates signals to bring back the Qg and V1 values within the operating range by issuing voltage set point controls to AVRs and SVCs in every scan period of SCADA cycle, such that over a few cycles the system is steered to within the operating limits. It can be seen from equation (6), that if there are no violations of Qg or v1, the As and 7s are zero in steady state. Therefore, only the loss minimization signals are issued for control. Referring again to equation (6), on violation of the Qg high limit at a bus, the corresponding A at the bus would be non-zero [from equation (9)]. Control signals through the second component of the right-hand side of equation (6) are generated accordingly to counter the violation. On violation of the load bus voltage low limit, -~ at the bus would be non-zero [from equation (10)]. Control signals through the third component of the right-hand side of equation (6) are generated to bring back the voltage within the operating limits. It is likely that during contingency operation when violation of Qg or load bus voltage takes place, the control signals can conflict with loss minimization signals. In order to have a smooth control, equation (6) is modified as follows:
OL/OUk=
k, (Op/ox)t(ox/o~k)
G
+ k2 ~ Ai(OQi/Ox)t(ox/OUk) i=1 G+S+L q-k 3 ~ ")'i(OVillOX)t(o.,~/Oek) (12) i=G+S+I where constants kl, k2, k3 are heuristically chosen and can be tuned for each power system. The significance of kl, k2 and k3 is described with examples in Section III. In case of inadequate Q reserves, the Lagrangian multipliers keep increasing, thus indicating the necessity of more drastic action. Hence load shedding is automatically initiated. Effectiveness of the controller through several case studies is described in the following section. 11.3 Real-time computations The basic principle which drives the controller to achieve the desired objective is described in equation (6). The Lagrange multipliers A and 7 are obtained from equations (9) and (10), respectively. The main computations are to evaluate the partial derivatives and to carry out the matrix operations in equation (6). It can be seen that the partial derivatives (refer to Appendix A.2) can be picked-up directly from the B matrix of the network. The X matrix can be computed off-line, whereas the real-time computations include change in the B and X matrices for change in network topology, whose calculations are simple. Matrix operations do not include inverse computations in real-time. For large networks, standard sparsity techniques and the Inverse Matrix Multiplication Lemma (IMML) technique could be used to further reduce computational times. Hence large size network
calculations can also be handled with very little computational times. Therefore the computations involved to arrive at the control signals can very well be handled in real-time within the SCADA scan cycle. The measurements include topological changes, active and reactive power generation, reactive power flows, bus voltages and bus load measurements.
III. Case s t u d i e s The controller is tested for its efficacy during normal power system operation and during contingency operation. Studies are conducted with generator and line outages. Each of the case studies, viz. generator outage, line outage, normal operation, are studied separately. Without the controller it is shown that some outages could lead to total system breakdown due to reactive power problems. The controller is brought in to the system and the studies are repeated. It is demonstrated how the breakdowns could be averted. The role of SVCs during normal operation and contingency operation is demonstrated. Load shedding, which is a measure taken as a last resort, is also demonstrated. Outages leading to system breakdown are simulated on a power system dynamic simulator. The actions of the controller are tested with a static simulator starting from the immediate post disturbance state, as given by the dynamic simulator. It is adequate to test the system on a static simulator, since the active power is not expected to play any role and the dynamics of reactive power settle down within a SCADA update cycle time. The SCADA update cycle time is taken as the control cycle time of the proposed controller. The testing methodology with the dynamic simulator and static simulator and the case studies are described in the following sections. II1.1 Testingmethodology A dynamic power system simulator [22] (PSS) is used for simulating system breakdowns. The PSS was built on the lines of an advanced Dispatcher Training Simulator [23] using a multi-computer configuration. The power system was modelled on a mini-computer system in much greater detail and includes models of turbines, governors, AVRs, circuit breakers, relays, transmission lines, two winding and three winding transformers, SVCs, frequency/ voltage dependent loads, etc. The human interface is built on a separate personal computer (PC) with suitable communication interfaces and protocols.
~
SCADA
RTUs,
H PLCC,
Transducers,~ Microwave, relays, ] ] etc. etc. | Field interface system
data base
- ~
Q controller AGC etc.
Commn. system
Computer system Energy management centre
I
Figure 2. Components of the energy management system
Closed-loop reactive power controller: K Veera Raju and A. Kuppurajulu 122,34
BI
0.97
V
180,87 1.00 V
J~'; 49.98 Itz
V
Bi ~ MW, MVARvalues
are adjacent to each other
V
_d ~ I (0.95v)
I
121,73 (230)
6O,2O (98)
1.00 V
[
0.95 V 65,21 (0.92 V)
175,85
Limit is shown below the value in brackets
Figure 3. Gen outage study--pre-outage state
To demonstrate the proposed control scheme, a power system is simulated using a static simulator which is based on a power flow program. The simulator carries out power flow computations and sends the measurements related to reactive power such as bus voltages, reactive power from generating units, etc., to the controller. The controller computes control signals based on the proposed logic. The simulator receives the control signals from the controller, changes the system state accordingly and sends the measurements corresponding to the new state to the controller. The controller recalculates the new control signals based on these measurements. In a few cycles, the desired objective of the controller is achieved. The efficacy of the controller is demonstrated on a 6 bus example system with a few case studies. The example system has 9 transmission lines, 4 generator buses and 2 load buses with reactive power support from SVC at one load bus. Details of the test system are in Appendix A.4. The system load is about 600 MW. The following sections describe details of different studies which are broadly categorized under the headings of generator outage study, line outage study and normal system study. 111.2 Generator outage study In this study, experiments are conducted to demonstrate:
157
B4 had to be catered for by a single unit after outage of one unit. Due to this, the reactive power generation far exceeded the unit limit value. The SVC at bus B6 was not contributing any reactive power since the voltage set point was 0.91 p.u. Referring to Table 1, it can be seen that the voltage started falling, being unable to maintain the set voltage at bus B4. Reactive power from gen unit at bus B5 went on increasing and crossed the limit value of 60 MVAR by the 60th second. Due to armature overcurrent sustained over a long period, over current relays (OCR) of units at bus B4 and B5 tripped at the ll0th second, taking the gen units off-bars. This resulted in a greater shock leading to tripping of other units at buses B2 and B3, which led to total system collapse. It can be seen that for most of the time, the frequency does not look bad and neither are the voltages. However, due to the gen unit exceeding its reactive power limit, the whole system has ultimately deteriorated.
111.2.2 System stabilisation with controller In the preceding section, it was shown that the system had ultimately led to a total collapse, whereas if the controller were to be there, the scenario is described as follows. The overload on gen unit at bus B4 is reduced by reducing the voltage set point at the bus and by increasing the neighbouring bus voltages at buses B2 and B5 in an incremental fashion in each cycle. The violation of reactive power at bus B4 is totally corrected 150 s after outage. Variation of reactive power (Qg) from the unit at bus B4 is plotted with respect to time in Figure 5.
111.2.2.1 Significance of A From Figure 5, it may be seen that the A value started increasing from immediate post-outage state. With the corrective signals, A is driven to zero. Then the corrective signals are stopped. When A attains zero, the control signals for Qg violation are stopped. It may be noted that the corrective signals are sent even after Qg has come within the limits QgaX. This is because the A value is computed as a time integral of the amount of deviation from the limit value. Until this becomes zero, control signals are given. The greater the deviation, the larger the value of A and the stronger the corrective signals.
159,21
BI
0.97 V [ (0.95V)
I [
r,ttt~gx
146,65 (215)
t
• possibility of a total system breakdown due to reactive power problems arising out of generator outage; • effectiveness of the controller in averting the system breakdown; and • better tapping of reactive power from SVC during emergencies through 'voltage set point control
180,87 1.00 V
1.00 V I ~ /
60,20 (60)
f = 49.61 Hz
1.02 V
1.00 V
The details of the experiments are described below.
111,2.1 Generator outage leading to system breakdown The system state before outage of the generating unit is shown in Figure 3. The active and reactive power generations are very much within the limits. Figure 4 gives the system state immediately after outage of the unit. It can be seen that the lost active power generation is met with additional active power generation from all the other generating units. Due to the additional generation, the reactive power limit of each unit has come down (refer to Figure 1). Further to this, the reactive power generation which was shared by both units at bus
6• B
MW, MVARvalues
are adjacent to each other
Limit is shown below
the
[ 1
" 65,21 0.95 V (0.92 V)
T
175,85
value in brackets
~
Device outage simulation
Figure 4. Gen outage study--immediate post outage state
158
Closed-loop reactive power controller: V. Veera Raju and A. Kuppurajulu
Table 1. Gen outage study--operating values without controller Generation values Active power in MW (reactive power in MVAR) B2Ul B3U1 B 4 U 1 B4U2
BsU1
0.95
122 (34)
121 (73)
122 (58)
122 (58)
121 (21)
1.02
0.95
122 (34)
121 (73)
122 (58)
0 (0)
121 (21)
1.00
1.02
0.95
159 (21)
146 (65)
159 (141)
0 (0)
144 (15)
0.97
1.00
1.01
0.94
158 (34)
145 (65)
158 (102)
0 (0)
146 (41)
49.62
0.97
1.00
1.00
0.94
158 (46)
146 (65)
158 (63)
0 (0)
146 (67)
0100
49.62
0.97
1.00
1.00
0.94
158 (46)
146 (65)
158 (63)
0 (0)
146 (67)
0110
49.62
0.97
1.00
1.00
0.94
158 (46)
146 (65)
0 (0)
0 (0)
146 (67)
B4U1tripped due to armature overcurrent relay
0120
48.37
0.97
1.00
0.97
0.92
203 (70)
196 (48)
0 (0)
0 (0)
0 (0)
BsU 1 tripped due to armature O/C relay. U/F load shedding B2U1, B3U 1 tripped due to low frequency
0130
0.0
0.0
0.0
0.0
0.0
0 (0)
0 (0)
0 (0)
0 (0)
0 (0)
System collapsed at 130 s
P.U. bus voltages Time (s)
Frequency (Hz)
V1
V3
V4
V6
0000
49.98
0.97
1.00
1.02
0030
49.98
0.97
1.00
0040
49.61
0.97
0050
49.62
0060
Comments
B4U2 tripped
V2 = 1.00V p.u. V5 = 1.00V p.u. 111.2.2.2 Prioritization of controls Table 2 includes the system status over a longer period in large intervals. It can be seen from the table that the control signals are issued even after limit violations are corrected. These signals try to minimize the system losses. The requirements, viz. initial thrust on correction
x
150
~ 100 I V ~x
/ i /xL i
of violations and minimization of losses after the system has corrected the violations, can be achieved with appropriate selection of constant values k~, k2 and k 3 in equation (12) as explained in Section 11.3. Higher values of k2 and k 3 would correct the violations quicker, whereas a small value Ofkl enables the loss minimization to be attained slowly over a longer period of time. It
-- 10 BI
,97 (209)
amda4
1.01 V
B2
x. x I ;'tx I~ I ~-.-~--~7" ~\ ,_ t/
o
.=_,o
\/\
X-x.x.x-x-x
I 60,20
0.988 V
(56)
0.99 V
:"
- 4
,=='
-2
x
,57
(215)
1.00 V
I
o
QgS4
0.978 V l (0.95v)
,0
QgB4max -- 6 .~_
~1
l 180,87
--8
,33 50
]
(o) 60,20
65,21 0.925 V (0.92 V)
MW, MVAR values are adjacent to each other
-wo
0
50
I 100
I x\..... ;.. !.. 150 200
0 250
Time (seconds)
Figure 5. Gen outage study--variation of reactive power and lamda
Limit is shown below the value in brackets
~
Device outage simulation
Figure 6. Gen outage study--ultimate controller action
state with
Closed-loop reactive power controller." I/. Veera Raju and A. Kuppurajulu Table 2. Gen outage s t u d y - - o p e r a t i n g
159
values with controller
Reactive power gen in MVAR Bus voltages in p.u. Time (s)
PLOSS MW
V1
V2
V4
V5
V6
B2
B3
84
hi B4
B5
hi B5
LMD4
LMD5
0 200 800 1000 1800 2800 3000
7.79 9.05 8.26 8.13 7.88 7.92 7.92
0.974 0.987 0.983 0.982 0.979 0.978 0.978
1.000 1.032 1.022 1.020 1.013 1.010 1.010
1.020 0.990 0.993 0.993 0.993 0.989 0.988
1.000 0.991 0.991 0.991 0.993 0.990 0.990
0.947 0.926 0.928 0.928 0.929 0.926 0.925
22 183 140 131 106 99 97
65 -2 23 28 42 55 57
142 10 36 37 38 35 33
54 35 38 38 37 35 34
15 55 45 48 57 54 56
60 56 56 56 57 56 56
0.00 0.00 0.00 0.06 0.11 0.11 0.00
0.00 0.00 0.00 0.00 0.06 0.05 0.00
V3 = 1.000 V p.u. G A M A 6 = 0.0.
i can be noted from the table that the losses, when the violations are corrected, are brought down from 9.05 MW to an ultimate value of 7.92 over a very long period. The ultimate state of the system is shown in Figure 6. Since the active power generation and loads are not changed, they are not shown in the figure to reduce cluttering. It can be seen that all reactive power generations and load bus voltages are within their limits.
With this it can be summarized that, with changing the set point control of SVC, instead of the normal practice of a fixed SVC set point, it is possible to use the extra reserve during emergencies. This helps in bringing the system back to normality more quickly and also in containing the violations better.
111.2.3 Effective utilisation of reactive power from SVC In the same example of generator outage, post outage simulation is carried out with the voltage set point of SVC at bus B6 kept at 0.965 V p.u. Comparison is made with the fixed set point of SVC (with only local control active) versus SVC being controlled by changing the voltage set point by the controller along with the gen units voltage set points. Figure 7 gives a comparison of the Q output of SVC with fixed set point versus voltage set point control. It may be noted that Q from SVC is higher with changing voltage set point control. Due to this, the amount of violation is lesser when compared to the fixexiset point of SVC, which can be seen from A values at buses B4 and B5 in Figure 8. At bus Bs, A has reached zero earlier, with the set point control of SVC voltage when compared to the fixed set point at SVC.
• possibility of a total system breakdown due to reactive power problems arising out of line outage; • effectiveness of the controller in averting system breakdown; and • initiation of automatic load shedding by the controller when it becomes necessary as a last resort.
0.98
--
V6 . j~,...
X
...:P(
. . . . . .•4(. ,K'" X... R...)e..
" "-;-.-. x - -
"
x --
x --
~, 0 . 9 6 ," ~D
/
I ""
x ,,~B'~( --
~*
--
90
--
80
. X - _-_ . X --X. ~(
x --
x - -
V6
x --
x
Qsvc x
x
x
x
x
These are demonstrated below.
111.3.1 Line outage leading to system breakdown System loads are close to that in Figure 2. A line outage (one of the parallel lines between buses B4 and B6) is simulated. Reactive power generation at bus B 5 crosses the limit value after the line outage. It can be seen from Table 3 that the gen unit at bus B5 has ultimately tripped at the 150th second due to OCR operation. This resulted in increased reactive power generation from units at buses B3 and B4. The units at bus B4 are overloaded and 5 F
Qsvc x --
111.3 Line outage study In this study, experiments are conducted to demonstrate:
ixX~Lamda4
With fixed
~ /~
< >
set point control
4 --
70
--
60
..... I x /
>
~1
With v o l t a g e set p o i n t control
,,
,~ 0.94
_
/'
/
; / ff
× /
ff ×
0 0.92
0.90
=..'/
mm
With fixed setpoint With voltage setpoinl~ c o n t r o l
I 20
I 40
LamdaSx
0
x/
I 60
I 80
--
--
I 100
50
o
40
30 120
Time (seconds)
Figure 7. Gen outage study--comparison of SVC output
- 7/ l
V. i
V
~~
#e
0-- = J: 0
20
40
##
,
x~ :.\\i amda5 tt, xlt
~I _ J_ I
Time
60
80
lO0
120
(seconds)
Figure 8. Gen outage study-comparison violation correction
of Og
Closed-loop reactive power controller." V. Veera Raju and A. Kuppurajulu
160
Table 3. Line outage study--operating values without controller PgB2
PgB3 MW
PgB4 PgB~
PgB5
Bus voltages in p.u. Time (s)
Frequency (Hz)
V1
V3
V4
(QgB2) (QgB3) (MVAR)
(QgB4) (QgB5) (QgB~)
0
49.97
0.974
1.000
1.020 1.000 0.930
123 (34)
122 (73)
123 (51)
122 (42)
20
49.97
0.974
1.000
1.020
1.000 0.930
123 (34)
122 (73)
123 (51)
122 (42)
30
49.97
0.974
1.000
1.020 1.000 0.903
123 (34)
122 (73)
123 (39)
123 (76)
120
49.96
0.974
1.000
1.020 1.000 0.903
124 (34)
123 (73)
124 (39)
123 (76)
150
49.96
0.974
1.000
1.020 1.000 0.903
124 (34)
123 (73)
124 (39)
0 (0)
B5U 1 tripped due to
B4U1, B4U2 overload
V5
V6
Comments
Line B4-B 6 CKT2 tripped
armature OCR
160
49.60
0.974
1.000
1.020 0.969 0.876
159 (22)
146 (119)
162 (67)
0 (0)
370
49.60
0.966
0.988
1.020 0.964 0.871
160 (53)
147 (76)
160 (74)
0 (0)
380
49.60
0.966
0.988
1.020 0.964 0.871
160 (53)
147 (76)
0 (0)
0 (0)
B4U1, B4U2 tripped due to armature OCR, B2U1, B3UI tripped due to U/F relay
390
0.0
0.0
0.0
0.0
0 (0)
0 (0)
0 (0)
0 (0)
System collapsed in 383 s
0.0
0.0
V2 = 1.000V p.u.
ultimately tripped due to operation of OCRs at the 380th second. This has resulted in a larger difference between supply and load and the remaining units also tripped due to under frequency relay operation of gen units resulting in total system collapse. The experiment is demonstrated to draw attention to the fact that a line outage can sometimes cause total system breakdown due to reactive power problems. In order to demonstrate this, however, a value of 0.8 kA of maximum armature current limit is used as against 0.9 kA shown in Appendix A.4, thereby lowering the maximum MVAR limit of the unit, which means that the units which are close to their limit values run a greater risk of leading to total system breakdown even with small disturbances. 111.3.2 System stabilisation with controller In the preceding section it is shown that the line outage has ultimately resulted in system collapse. In the presence of the controller the system stabilises. The ultimate state is shown in Figure 9. However, load shedding of 22 MVAR is carried out since it is unable to maintain the voltage of even 0.91 V p.u. at bus B6. While simulating the controls, only the reactive power of the load is shed, to avoid representing real power dynamics. However, if both active power and reactive power are shed, which happens in practice, the relief obtained would be better, thus giving a better margin of security. The scheme of load shedding is described below. 111.3.2.1 Automatic load shedding Load shedding is carried out in four steps. In each step, a quarter of the load is shed with total load shedding in the
last step, at the chosen buses. Pre-set limiting values of/or g at any bus can initiate load shedding at that bus. A minimum time interval between successive load shed commands ensures the active power dynamics settle down and also gives sufficient time for the controller to reverse the trend of violations. With this scheme, the load shedding is carried out automatically to bring the voltage at bus B6 within operating limits. The load shedding scheme is usually quite specific to each utility, any other BI
,64
(230)
0.976 V
I ~
I (0.95v)
,63 (229)
180,87 B2
1.0005 V
.23
1.000 V
I
I
6O,2O (3)
0.997 V +
I
r 6.'.20 l
60,20 0.915 V (0.91 V)
MW, MVAR values are adjacent to each other
180,65
Limit is shown below the value in brackets
# ~
Line outage simulation
Figure 9. Line outage study--ultimate state with controller action
Closed-loop reactive power controller." V. Veera Raju and A. Kuppurajulu 1.045
%
1.1140
....
....
--
8.05
-
8.00
From the initial state, when the controller is introduced, it keeps giving incremental voltage signals to minimize the losses ultimately reducing to 7.84MW. Variation of losses and also the gen bus voltages with respect to time are shown in Figure 10.
v2 .-. 1.035
U
~/x-x-x-x-x-x-x-,x-x-x- -x-x-x-x =x~-x-x-x-x-x-x-x=,x-x-x-x-x-x-x-x-x \ ~x-x-x-x X, ..... /x ......
V3 V4 V5
7.95
1.o3o
7.90
0
1.025:
/
"~'X~x. x
,..1 Losses %x.,x--x-x-x-x-x-x-x--x
7.85
--
1.020
1.015
I
I
I
50
100
150
7.80
7.75 200
Time (seconds)
Figure 10. Normal system study--loss minimization with Vg controls scheme could as well be incorporated in the overall control logic.
111.4 Normal system study As indicated in earlier sections, minimization of active power losses arising due to reactive power transfers is chosen as the objective function. Experiments are conducted to demonstrate: • loss minimization by varying the generator voltage set points; and • minimization of losses with proper scheduling of voltages at SVC buses instead of keeping a constant set point voltage. These experiments are demonstrated below.
111.4.1 Loss minimization through Vg controls System loads are same as in Figure 2, except that at bus B5 the load is 80,40(MW,MVAR) instead of 65,21(MW,MVAR). Initial losses are equal to 8.01 MW. SVC is considered to be 'switched off' in the system.
~"
8.5
--
8.0
~X=x
With fixed
7.0
svc v o l t a g e
• ~x-x.x.x.~.~
.... x .....
x-~-~.x.~.~
6.5
With s v c v o l t a g e set point control
0
111.4.2 Comparison of loss minimization with different options In this experiment three studies are conducted with the controller in action, viz. (a) without SVC in the system; (b) with SVC in the system at bus B6 where SVC is in local control mode with fixed set point voltage; and (c) with SVC in the system with voltage set point control. In all the three cases, generator voltage set point control signals are also given. Referring to Figure 11, the variation of losses with respect to time can be seen for all the three cases identified separately. In summary, during normal operation, as many savings as possible can be achieved by exercising the voltage set point controls both at gen buses and SVC buses. 111.5 Discussion The method presented here, unlike conventional static optimization methods, is based on a closed-loop dynamic control approach, The operating state is driven over a period of time to the optimum solution with incremental controls in each time step, satisfying the Kuhn-Tucker conditions of optimality. It is important that the overall control loop time should be much slower than the fast acting local control loops of AVR and SVC. Unlike the normal practice of keeping the voltage set points fixed at SVC, better results can be obtained by changing the voltage set point. This helps both in emergency operation, by contributing to quicker mitigation of violations, and in normal operation, by contributing to further loss minimization. The scheme is an automatic secondary voltage control in closed loop (which can be viewed as parallel to AGC for active power) with an overall objective function of loss minimization while satisfying voltage and reactive power constraints. To maintain voltage stability, apart from gen unit voltage set point controls and SVC controls, transformer tap changes would also play a definite role. However, transformer tap changing is slow. Typically it may take more than 20 s for each step of tap change. A deeper investigation is needed to include transformer tap control for voltage stability.
Without s v c ~X'X-x.x.x.,x=x--x.x.X.X.x.X.X.X
7.5
6.0
161
I
I
I
I
50
100
150
200
Time (seconds)
Figure 11. Normal system study--losses with and without SVC set point control
IV. C o n c l u s i o n s A technique for synthesizing a closed-loop reactive power controller for voltage stability is presented in this paper. The controller is based on a multi-variable control approach. Unlike conventional static optimization techniques, the controller dynamically steers the system to an acceptable state in a closed loop satisfying the Kuhn-Tucker conditions of optimality. The controller issues set point control signals to generator AVRs and SVCs in real time. It is an Automatic Voltage Control scheme which can be viewed as a parallel to AGC for active power. The scheme is tested both in normal and contingency situations. It has also been demonstrated how the controller is able to effectively steer the system in case of serious reactive power violations on gen units and low load bus voltages when
162
Closed-loop reactive power controller: V. Veera Raju and A. Kuppurajulu
contingencies occur. The benefit of SVCs with changing set point control is demonstrated both in normal and emergency operation. Automatic load shedding is also demonstrated in the scheme. The controller can be implemented as part of the Energy Management System on a real-time basis. Computations required for the controller can easily be managed on the real-time computer even for fairly large practical power systems.
V. Acknowledgements The authors gratefully acknowledge the Indian Institute of Technology, Madras, and CMC Limited (R&D), Hyderabad for the facilities provided to carry out this work. The authors thank Mr Shirish S Kulkarni, an M. Tech student from liT, Madras, for his timely help in bringing the document to its present form.
VI. References 1 Snyder, WL, Raine, JG, Christie, RD, Ritter, F and Reed R. 'Var management-problem recognition and control, Var management task force report' IEEE Trans. Power Syst. (1984) 2108-2116 2 Lacks, W R 'Countering calamitous system disturbances' in International Conference in Reliability of Power Supply Systems, London. IEE publication No 225, 1983, pp 79-83 3 Lacks, W R 'Insecure system reactive power balanceanalysis and counter measures' IEEE Trans. Power Apparatus & Syst. Vol PAS-104 (1985) 2413-2419 4 Lacks, W R 'Automatic control of system voltage stability by an expert system' in Proceedings of Tenth Power Systems Computation Conference, Graz, Austria, 19-24 August 1990, pp 1057-1064 5 Lacks, W R and Sutanto, D 'Voltage instability in interconnected power systems--a simulation approach' IEEE Trans. Power Syst. Vol 7 No 2 (1992) 753-761 6 Brownell, G and Clark, H 'Analysis and solutions for bulk system voltage instability' IEEE Trans. Comput. Applicat. Power Vol 2 No 3 (1989) 31-35 7 Goossens, J 'Reactive power and system operationincipient risk of generator constraints and voltage collapse' in IFAC Proceedings of Conference on Power System and Power Plant Control, Seoul, South Korea, 22-25 August 1989, pp 1-10 8 Taylor, C W 'Concepts of under voltage load shedding for voltage stability' IEEE Trans. Power Delivery Vol 7 No 2 (1992) 480-488 9 Paul, J P, Leost, J Y and Tesseron, J M 'Survey of the secondary voltage control in France: present realisation and investigations' IEEE Trans. Power Syst. Vol PWRS-2 No 2 (1987) 505-511 10 Lagonotte, P, Sabonnadiere, J C, Leost, J Y and Paul, J P 'Structural analysis of the electrical system: Application to secondary voltage control in France' IEEE Trans. Power Syst. Vol 4 No 2 (1989) 479-486 11 Thorp, J S, llle-Spong, M and Varghese, M 'An optimal secondary voltage-VAR control technique' Automatica Vol 22 No 2 (1986) 217-221 12 Ilie, M and Stobart, W 'Development of smart algorithm for voltage monitoring and control' IEEE Trans. Power Syst. Vol 5 No 4 (1990) 1883-1993
13 Stankovie, A, llie, M and Maratukulam, D 'Recent results in secondary voltage control of power systems' IEEE Trans. Power Syst. Vol 6 No 1 (1990) 94-101 14 lllc, M 'New approaches to voltage monitoring and control' IEEE Control Syst. Vol 9 No 1 (1989) 5-10 15 Carpentier, J, Gillon, A, Jegonzo, Y, Caraman, F, Grimonpont, R, Pellen, F and Tounebise, P 'Real time optimal power flow for application to automatic control' in Proceedings of Tenth PSCC, 19-24 August 1990, pp 66-73 16 Brandwajn, V, Ipakchi, A and Sherkat, V 'Tracking evolutionary trends in generation control' IEEE Comput. Appficat. Power Vol 6 No 1 (1993) 22-26 17 Kuppurajulu, A 'A multivariable closed loop controller for real-time application' J. Inst. Engineers India-EL Vol 70 EL1 (1990) 203-205 18 Kuppurajulu, A 'Closed loop reactive power control for use in energy management systems' J. Inst. Engineers India-EL Vol 71 EIA (1990) 159-162 19 Kuppurajulu,A and Ossowski, P'An integrated real time closed loop controller for normal and emergency operation of power systems' IEEE Trans. Power Syst. Vol 1 No 1 (1986) 242-249 20 Vinod Kumar, D, Veera Raju, V and Kuppurajulu, A 'A real time closed loop controller for security dispatch' Int. J. Elec. Power & Energy Syst. Vol 15 No 5 (1993) 307-314 21 Veera Raju, V and Kuppurajulu, A 'A closed loop controller for voltage stability' Int. J. Elec. Power & Energy Syst. Vol 15 No 5 (1993) 283-292 22 Kuppurajulu, A and Ramar, R 'Workshop on power system simulator' Elect. India Vol XXX No 5 (1990) 11-13 23 Sato, K, Yamazaki, Z, Haba, T, Fukushima, N, Masegi, K and Hayashi, H 'Dynamic simulation of a power system network for dispatcher training' IEEE Trans. Power Apparatus & Syst. Vol PAS-101 (1982) 3742-3750
Appendix A.1 General concept of multivariable dynamic control A.1.1 Multivariable control Many practical multivariable systems are comprised of a number of subsystems each having their own fast response feedback loops. In addition, an overall control loop exists to operate the system so as to achieve a desired objective of minimum cost, optimum performance, etc. The main purpose o f this loop is to ensure that the system functions in a desired manner and none of the subsystems reach critical states under slowly varying operating conditions. A real-time dynamic controller can be designed to provide this overall control loop. Each of the subsystems can be described by a set of dynamic equations, namely
Xi : fi(Xi, Ui) Yi =
li(xi, Ui),
for i = 1 , 2 , . . . , N
where xi, yi, u i are the state, output and control vectors of the ith subsystem and Nis the total number of subsystems in the system. The feedback loops and protective devices of the subsystems are such that inequality constraints of the type gi(xi, Ui) ~<0 and equality constraints of the type hi(xi~ ui) = 0 are satisfied.
Closed-loop reactive power controller: V. Veera Raju and A. Kuppurajulu System
Thus the overall system can be modelled by the following equations:
I f (X,U) = 0 _
U = Input
= f ( X , U) "~
(A1)
min C(X, U).
Feedback control Feedback controller
(A3)
The dynamic controller should be designed to provide a real-time closed loop feedback of the type U = p(Y), which achieves the objective in equation (A3) under the constraints in equation (A2). Assuming the time response of the subsystems is sufficiently fast compared with the real-time closed-loop response, the system can be represented by its static equivalent f(X, U) = 0. The objective of the dynamic controller is similar to that of an optimization problem. The necessary and sufficient conditions to ensure optimality are required to satisfy the Kuhn-Tucker conditions. Thus the controller is designed such that it steers the system to an optimal state which satisfies the Kuhn-Tucker conditions of optimality. It may be noted that the objective of the proposed controller differs from the: classical optimal controller in that the speed of response is not very critical, whereas it primarily aims at satisfying the constraints. A.1.2 Structure of the multivariable dynamic controller The problem is to design a feedback controller for the system such that the objective function C(X, U) is minimized subject to the constraints
gk(X, U) ~<0,
k = l, 2 , . . . , m inequality constraints
hk(X, U) = 0,
k = 1 , 2 , . . . , n equality constraints.
A modified objective function is formed by choosing a 'Lagrange multiplier' for each of the constraints. L = modified objective function : C + )~tg +'Tth m
,;--h
j.gj +
]-
k=g,k~0
Figure A1. Block diagram of feedback controller
Appendix A.2 A.2.1 Derivation of Op/OX X is a state vector consisting of voltages at all buses. The expression for Op/OV i is derived below. The real power loss PU in a line having a conductance value of g~ connecting two buses i and j having voltages V i L Oi and Vj / Oj can be written as
PO = ( V2 + VJ2 - 2ViVjc°sOq)go where Oij = Oi - Oj. Real power flow F O.in the line from bus i to busj can be written as:
Fij = ( Vi Vj / xo. ) sin 0/j From the above expression, cos 0• can be written as COS 0/j = (V?Vj 2 --
F2x~ij)I/2/(ViVj)
By substituting cos 00- in the expression for losses in the line we get,
Pij = go.[V~ + Vf. -- 2(V?Vj 2 -- l"ijXij ) ' ' 22,1/2,] Total losses: P=
ZP0 all lines
Therefore,
2"1
(A4)
where Aj=Lagrange multiplier corresponding to inequality constraint g j, and 7j = Lagrange multiplier corresponding to equality constraint hi. The dynamic controller is designed by the following set of equations 0L OUk'
Y=Output
min C(X,U)
g(X, U)~
~k --
g (x,u) < o
-1 h (X,U) = 0
v = t(x, u)
= c +
163
01)/OVi= E { V g -
J
2 2 1/2]}g/j Vj[ViVj/(V?Vj2-F~xo')
A.2.2 Expressionfor OQ/OX
OQ,/Ox O(Q,/V,)lOX X is a state vector consisting of voltages at all buses,
for kth control variable
(A5)
J~k = gk ~, Ak >~0 J
for kth inequality constraint
(A6)
"~k = hk,
for kth equality constraint
(A7)
Representation of the controller in the form of a block diagram can be seen in Figure A 1.
O(Qi/Vi)/OVi = Big and
O(Qi/Vg)OVj = B o.
where Big and Bij are diagonal and off-diagonal elements of network B matrix (expressions are derived in Appendix B). A.2.3 Expression for OV/OX With X as a state vector consisting of the voltage at buses
Closed-loop reactive power controller: V. Veera Raju and A. Kuppurajulu
164
By comparing the above expression with equation (AS) D 1 = --BL 1 BLG and D2 = -BZ~ BLs. With these expressions, D can be evaluated. General expressions for the elements of BLt, Brc, BLs are O/OVi(Qi/Vi) = Bii and O/OVj(Qi/Vi) = Bij where Big and B/j are the diagonal and off-diagonal elements of network B bus matrix.
in the network,
OVi/OVj=O and OVi/OVi=l.O.
Appendix A.3 A.3.1 Derivation of partial derivative OX/OU In the expression
Appendix A.4 Important parameters of 6 bus power system
AX = D AU
Base MVA = 200, network voltage level = 100 KV X is a state vector consisting of voltages at all buses in the network, and U is a control vector consisting of voltages at generator buses and voltages at SVC buses. D needs to be evaluated. The incremental state vector can be expressed in terms of the incremental control vector as AV G AV s
I =
0
0
i I v°l AVs
AVL
D1
D2
From the above expression, AVL = [D1 D21
bvol
(A8)
[AVsJ
where D1 and D 2 are derived below. At any load bus we can write
A.4.1 Line data
S No.
Line
Resist (p.u.)
React (p.u.)
Line chrg admit. (p.u.)
1 2 3 4 5 6 7 8 9
Ba-BI Bs-B 6 B2-B4 B3-B 5 Ba-B5 B2-B1 B2-B3 B4-B6(1 ) Ba-B6(2)
0.0150 0.0562 0.0534 0.0384 0.0300 0.0200 0.0600 0.1500 0.0750
0.0730 0.1526 0.1640 0.1150 0.1000 0.1100 0.1300 0.5400 0.2700
0.0900 0.0350 0.0170 0.0528 0.0000 0.0000 0.0000 0.0000 0.0000
A.4.2 Gen units data
AQL = O/OVG(QL)AV6 + O/OVs(QL)AVs + O/0VL(QL)AVL We can write QL/VL in place of QL. Then, A(QL/VL) = O/OVG(QL/VL)AVc
+ O/OVs(QL/VL)AVs + O/OVL(QL/VL)AVL Since, at the load bus there is no reactive power support, A(QL/VL) = 0. In addition, by writing 0/OVo(Qt/VL)=BLG; O/OVs(QL/VL) = BLs; and 0/aVL(QL/Vt) = BLL, then AVL can be written as:
AVL =--[BZ 1
BZ '
r LAVsJ
Armature max current limit (kA/phase)
Bus
Capacity Unit (MW)
B2 B3 B4 B4 B5
B2U1 250 B3U 1 250 B4U 1 175 B4U2 1 7 5 , B s U 1 175
B6
SVC capacity (MVAR) 0 to 120
Trip setting f ( I - Imax)dt (kAs/ph)
1.50 1.50
9.00 9.00
1.90 0.90
11.40 4.05
ELSEVIER
PII: S0142-0615(96)00007-5
0142-0615/97/$17.00+0.00
A closed-loop reactive power controller for power system
voltage stability V Veera Raju CMC Limited, Old Bombay Highway Road, Hyderabad - 500 019, India
A Kuppurajulu Department of Electrical Engineering, I.I.T. Madras - 600 036, India
due to reactive power disturbance is demonstrated with examples. © 1997 Elsevier Science Ltd
Any imbalance between reactive power supply and demand disturbs the normal operation of a power system. Power system contingencies sometimes cause excessive reactive power imbalance, even leading to total system breakdown. The problem is usually aggravated when the system is heavily loaded. Generator overload due to excessive reactive power generation ;?s one of the most common and serious causes of voltage instability. Low voltage at load buses is another cause which is likely to result in voltage stability problems. By closely monitoring the reactive power generation and load voltages, it is possible to avoid such major disturbances. A closed-loop controller can steer the system to a safer state by rescheduling the reactive power generation from generators and SVCs through voltage set point controls in real time. A closed-loop controJler which dynamically steers the system to a safer state on violation of specified operating conditions of reactive power generation and load bus voltages is designed. During normal operation, the controller minimizes active power transmission losses due to reactive power transfers. The principle of the controller is based on a multi-variable control concept. A closed-loop controller is synthesized to steer the system dynamically to an acceptable state while satisfying Kuhn-Tucker conditions of optimality in sfeady state. The proposed closedloop reactive power controller which gives set point control signals to A VRs and SVCs in the secondary mode of control, can be viewed as a parallel to the AGC for active power/frequency control. The controller performs this task on a real-time basis using SCADA measurements. The controller also issues load shedding commands in case it is necessary. The controller is tested under normal as well as contingency operation. Broad details of the closed-loop controller and its efficacy in avoiding system breakdown
Keywords: on-line control, emergency control, closed loop control, reactive power control, voltage stability, multivariable control
I. Introduction It is important to operate a power system within specified limits of frequency and voltage to avoid risk of disturbances. The disturbance can be due to a series of contingencies leading to a system emergency state which might lead to a total system breakdown. To avoid the danger of system breakdown, it is necessary to maintain a balance between supply and demand of both real and reactive power and also sufficient reserves for contingency situations. The IEEE task force report on Var Management [1] highlighted the importance and complexity of maintaining reactive power balance in the power system. Lachs [2-5] proposed automatic counter measures to mitigate the problem associated with reactive power deficit and surplus. The measures are broadly categorized into:
• raising EHV voltages; • restricting system load; and • improving reactive power reserves. Brownell and Clark [6] have stressed the need for new analytical tools in control centres to steer the system away from the voltage instability state. Goossens [7] recommended specific measures to provide voltage support sources with automatic controls based on their practical experience. Taylor [8] investigated under voltage load shedding for voltage stability
Received 21 September 1994; accepted4 January 1996
153
154
Closed-loop reactive power controller." V. Veera Raju and A. Kuppurajulu
for the Puget Sound area of the Pacific Northwest utility. In summary, the work carried out so far with respect to voltage collapse/stability and control broadly falls into the following categories: (i)
provision of preventive controls so as to keep the power system away from the voltage instability region; (ii) on the occurrence of a disturbance, provision of automatic controls for immediate mitigation of the danger of voltage collapse so as to give enough time for the operator to steer the system to a safer power system state; and (iii) development of algorithms to help drive the immediate post disturbance state to a safer power system state. While investigations for better procedures and methods are being carried out to understand and solve reactive power-voltage related problems, efforts to control voltage in closed loops have also been reported. Paul et al. [9] have surveyed the voltage control of French power systems. They propose a coordinated secondary voltage control against the practice of a threelevel hierarchy, viz. local primary control, regional level secondary control and a national level tertiary control. Lagonotte et al. [10], Thorp et al. [11], Ilic and Stobart [12] and Stankovic et al. [13] have investigated automatic voltage/reactive power control methodologies in realtime. Ilic [14] surveyed the approaches to voltage monitoring and control and gave a methodical treatment of the primary and secondary control philosophy. Carpentier et al. [14] have proposed a new concept of secondary voltage control as part of OPF in closed-loop secure AGC. Brandwajn et al. [16] have discussed the evolutionary trends in generation control and proposed that new control algorithms, such as coordinated multivariable techniques, are the future framework for research. In this paper a multi-variable closed-loop controller is proposed to mitigate voltage related problems during system disturbances leading to reactive power problems. The controller under normal operation minimizes system transmission losses, whereas under contingency operation it dynamically steers the system to a safer state by giving incremental signals in each SCADA sampling period in terms of generator voltage set points and SVC voltage set points. In extreme situations where the controller is unable to bring the system back to normality, for reasons such as inadequate reactive power reserves, rapid deterioration of system conditions from the reactive power point of view, etc., load shedding is automatically invoked to save the power system from voltage stability problems. Investigation of multivariable control as a secondary control system based on the extension of Kuhn-Tucker conditions of optimality to dynamic systems have been attempted by a group from IIT, Madras [17-21]. The basic mathematical principle was first applied to power system security based on active power dispatch [19]. To gain further confidence, it was tested on a dynamic simulator and is reported in Reference [20]. Investigations on active power controls for voltage stability are reported in Reference [21]. Investigations in this paper are primarily focused on formulation of reactive power control problems for the improvement of voltage stability. The controller acts as a secondary voltage control by providing voltage set points to the primary control devices, viz. generator AVRs in power plants and SVCs in
sub-stations. The primary control devices provide the fast acting local control requirement whereas the proposed controller provides a slow acting secondary control satisfying the desired objective by providing incremental control signals. The efficacy of the controller is tested on a simulated 6 bus power system. As the main purpose of this paper is to illustrate the underlying principle of the voltage controller, it was felt that a smaller system can bring out more clearly the interaction between various variables much more clearly. In any case, reactive power transfer over long distances is not possible. We have to look at controlling the sources close to the disturbed point. Using a dynamic power system simulator to model the system, typical outages were created and the response of the system was studied with and without the controller. The role of SVCs as sources of reactive power, the possibility of reactive power and the possibility of their set point control have been illustrated. A few case studies of line/generator outages leading to system wide breakdown are simulated on a dynamic PSS. Effectiveness of the proposed reactive power controller in arresting the system breakdown is demonstrated. It is proposed that SVCs also be used as control devices during such emergencies, not only in primary control but also in secondary control through the proposed controller. In addition, the effectiveness of the controller during normal operation in minimizing transmission losses while meeting the voltage constraints at load buses and reactive power limits of generating units is also demonstrated. Formulation of the problem in terms of structure of the controller and broad details of the proposed reactive power-voltage control in closed loop are explained in Section II. Testing methodology and several case studies are described in Section III.
II. Description of proposed controller Problem formulation of reactive power control, including the dynamic equations of the proposed controller, is explained in this section. The real-time computations involved and the operation of the controller are also discussed in this section. The basic dynamic control scheme around which the problem formulation is carried out is explained in Reference [17], however, for quick reference it is enclosed in Appendix A. 1. With the feedback control structure described in Appendix A. l, the system can be driven to an optimal steady-state point. The control vector is evaluated from the measurements of the system. As and when the operating point deviates from the optimal point, the feedback controller gives incremental control signals to drive the system to a steady-state optimal point. The controller specifically tries to alleviate reactive power violations at generating buses and voltage violations at load buses under emergency conditions of power system operation. Under normal system operation, the controller minimizes active power transmission losses arising due to reactive power transfers in the network. I1.1 Problem formulation and control equations The controller is designed with the following objectives:
• to ensure generators do not get overloaded due to excessive reactive power generation;
Closed-loop reactive power controller." V. VeeraRaju and A. Kuppurajulu • to ensure load bus voltages are within a specified operating range; • to avoid voltage stability problems; • to respond quickly even during contingency situations such as line outage, generator outage, etc.; • to have reasonable cycle time, say about 5-10 s; and • to exploit possible savings during normal system operation Keeping the above objectives in view, the problem formulation is explained as follows. The objective function of reactive power control is chosen as minimization of total transmission losses p, i.e. min p
155
and
Qi - Qmax
ii :
i = 1,2,..., G
(7)
i=G+S+I,...,G+S+L
(8)
Ai~> 0
~i=v~n-vi '7i>~ 0
The expressions for partial derivatives Op/OX, OQi/OX and OVi/OX are derived in Appendix A.2. Expressions for OX/OUk are derived in Appendix A.3. Controller equations (5), (7) and (8) can be rewritten as
Ai = J(Qi - Qmax)dt
i = 1,...,G
")'i = I ( V ~ in - Vi)dt
i=G+S+I,...,G+S+L
(9)
where G+S+LG+S+L p--1/2 Z Z P/J i=l j=l
(1)
where P/j is the loss in tlhe line connecting buses i andj. G is number of generating buses, S is number of SVC buses and L is number of load buses. While the state vector X is the voltage magnitudes of all buses, the control vector U includes voltage magnitudes at G-type (P-V type) buses and voltage magnitudes at SVC buses, i.e.
xt = [V 1V2... VGVG+I... VG+SVG+s+I... VG+S+L] u t = [V 1V2... VGVG+I... VG+S] It is also necessary that reactive power limits at G-type buses and voltage magnitude limits at L-type (P-Q) buses are not violated, i.e.
Qi- Qmax~ <0
i:-- 1,2,... ,G
(2)
v~nin -- V < 0
i::G+S+I,...,G+S+L
(3)
(10) f
= j0kdt
k= 1,...,G+S
(11)
with Ai >--0 and % t> 0. 11.2 Operation of the controller Referring to Figure 2, power system data are acquired in real-time under the control of SCADA software in an Energy Management Centre (EMC). SCADA software acquires the data from the RTUs. The RTUs acquire data locally at the generating plants and sub-stations through necessary field interfaces. In addition to the data acquisition through these interfaces, the RTUs also carry out supervisory and closed-loop control commands issued from the Energy Management Centre computer system.
Similar constraints can be added for reactive power low limits at generating buses and voltage high limits at load buses. The constraints on the control vector are not specifically shown as they are taken care of while transmitting the control signals. The following closed-loop control algorithm, solved on the real-time computer, will evaluate the required control signal G G+S+L L = p ~- Z / ~ i ( Q i - gmax)_~_ Z ~[i( V~fin - Vi) i=l i=G+S+I
P(M~W)~ 1.0 H sSlE #
5'
I
""" t" Y /i
IC
D--0. 8
--
0.6
Qm/"
0.4
~ B minimum im . .P. O . _ _n~ . lwerlimit/
(4) It may be noted that the Lagrange coefficients ~ and 7 are used for constraints on gen bus reactive power violation and load bus voltage violation, respectively. There are no equality constraints as described in the general equation (A.4) in Appendix A. 1.
Ok = -OL/OUk
k = 1,2,..., G + S
iF 0.4
0.2
0
(Underexcited)
G -F Z Ai(OQi/Ox)t(ox/OUk) i=1 G+S+L (6)
,:A(
0.2
rm 0.4
I
,
0.6
(Overexcited) Q
AB BCH HIJK CDE EF
OL/OUk = (Op/OX)t(OX/dUk)
i=G+S+I
I
0.6
:
(5)
where
+ Z % ( O V , IOX)t(ox/ouk)
0.2
t, ~ ~. t, t,
i^
0.8
,
1.0
(MVAR) ,,
Rotorheatinglimit Statorwindingheatinglimit Statorend ironheatinglimit Turbineoutputlimit Practicalstabilitylimit withAVR
Figure 1. Capability curve of a typical 68 MVA turbo generator
156
Closed-loop reactive power controller." V. Veera Raju and A. Kuppurajulu
Under normal conditions of power system operation, the controller generates voltage set point signals to AVRs and SVCs to achieve minimum active power transmissions losses. On violation of the reactive power (Qg) high limit of the generating unit or load bus voltage (111) low limit, the controller generates signals to bring back the Qg and V1 values within the operating range by issuing voltage set point controls to AVRs and SVCs in every scan period of SCADA cycle, such that over a few cycles the system is steered to within the operating limits. It can be seen from equation (6), that if there are no violations of Qg or v1, the As and 7s are zero in steady state. Therefore, only the loss minimization signals are issued for control. Referring again to equation (6), on violation of the Qg high limit at a bus, the corresponding A at the bus would be non-zero [from equation (9)]. Control signals through the second component of the right-hand side of equation (6) are generated accordingly to counter the violation. On violation of the load bus voltage low limit, -~ at the bus would be non-zero [from equation (10)]. Control signals through the third component of the right-hand side of equation (6) are generated to bring back the voltage within the operating limits. It is likely that during contingency operation when violation of Qg or load bus voltage takes place, the control signals can conflict with loss minimization signals. In order to have a smooth control, equation (6) is modified as follows:
OL/OUk=
k, (Op/ox)t(ox/o~k)
G
+ k2 ~ Ai(OQi/Ox)t(ox/OUk) i=1 G+S+L q-k 3 ~ ")'i(OVillOX)t(o.,~/Oek) (12) i=G+S+I where constants kl, k2, k3 are heuristically chosen and can be tuned for each power system. The significance of kl, k2 and k3 is described with examples in Section III. In case of inadequate Q reserves, the Lagrangian multipliers keep increasing, thus indicating the necessity of more drastic action. Hence load shedding is automatically initiated. Effectiveness of the controller through several case studies is described in the following section. 11.3 Real-time computations The basic principle which drives the controller to achieve the desired objective is described in equation (6). The Lagrange multipliers A and 7 are obtained from equations (9) and (10), respectively. The main computations are to evaluate the partial derivatives and to carry out the matrix operations in equation (6). It can be seen that the partial derivatives (refer to Appendix A.2) can be picked-up directly from the B matrix of the network. The X matrix can be computed off-line, whereas the real-time computations include change in the B and X matrices for change in network topology, whose calculations are simple. Matrix operations do not include inverse computations in real-time. For large networks, standard sparsity techniques and the Inverse Matrix Multiplication Lemma (IMML) technique could be used to further reduce computational times. Hence large size network
calculations can also be handled with very little computational times. Therefore the computations involved to arrive at the control signals can very well be handled in real-time within the SCADA scan cycle. The measurements include topological changes, active and reactive power generation, reactive power flows, bus voltages and bus load measurements.
III. Case s t u d i e s The controller is tested for its efficacy during normal power system operation and during contingency operation. Studies are conducted with generator and line outages. Each of the case studies, viz. generator outage, line outage, normal operation, are studied separately. Without the controller it is shown that some outages could lead to total system breakdown due to reactive power problems. The controller is brought in to the system and the studies are repeated. It is demonstrated how the breakdowns could be averted. The role of SVCs during normal operation and contingency operation is demonstrated. Load shedding, which is a measure taken as a last resort, is also demonstrated. Outages leading to system breakdown are simulated on a power system dynamic simulator. The actions of the controller are tested with a static simulator starting from the immediate post disturbance state, as given by the dynamic simulator. It is adequate to test the system on a static simulator, since the active power is not expected to play any role and the dynamics of reactive power settle down within a SCADA update cycle time. The SCADA update cycle time is taken as the control cycle time of the proposed controller. The testing methodology with the dynamic simulator and static simulator and the case studies are described in the following sections. II1.1 Testingmethodology A dynamic power system simulator [22] (PSS) is used for simulating system breakdowns. The PSS was built on the lines of an advanced Dispatcher Training Simulator [23] using a multi-computer configuration. The power system was modelled on a mini-computer system in much greater detail and includes models of turbines, governors, AVRs, circuit breakers, relays, transmission lines, two winding and three winding transformers, SVCs, frequency/ voltage dependent loads, etc. The human interface is built on a separate personal computer (PC) with suitable communication interfaces and protocols.
~
SCADA
RTUs,
H PLCC,
Transducers,~ Microwave, relays, ] ] etc. etc. | Field interface system
data base
- ~
Q controller AGC etc.
Commn. system
Computer system Energy management centre
I
Figure 2. Components of the energy management system
Closed-loop reactive power controller: K Veera Raju and A. Kuppurajulu 122,34
BI
0.97
V
180,87 1.00 V
J~'; 49.98 Itz
V
Bi ~ MW, MVARvalues
are adjacent to each other
V
_d ~ I (0.95v)
I
121,73 (230)
6O,2O (98)
1.00 V
[
0.95 V 65,21 (0.92 V)
175,85
Limit is shown below the value in brackets
Figure 3. Gen outage study--pre-outage state
To demonstrate the proposed control scheme, a power system is simulated using a static simulator which is based on a power flow program. The simulator carries out power flow computations and sends the measurements related to reactive power such as bus voltages, reactive power from generating units, etc., to the controller. The controller computes control signals based on the proposed logic. The simulator receives the control signals from the controller, changes the system state accordingly and sends the measurements corresponding to the new state to the controller. The controller recalculates the new control signals based on these measurements. In a few cycles, the desired objective of the controller is achieved. The efficacy of the controller is demonstrated on a 6 bus example system with a few case studies. The example system has 9 transmission lines, 4 generator buses and 2 load buses with reactive power support from SVC at one load bus. Details of the test system are in Appendix A.4. The system load is about 600 MW. The following sections describe details of different studies which are broadly categorized under the headings of generator outage study, line outage study and normal system study. 111.2 Generator outage study In this study, experiments are conducted to demonstrate:
157
B4 had to be catered for by a single unit after outage of one unit. Due to this, the reactive power generation far exceeded the unit limit value. The SVC at bus B6 was not contributing any reactive power since the voltage set point was 0.91 p.u. Referring to Table 1, it can be seen that the voltage started falling, being unable to maintain the set voltage at bus B4. Reactive power from gen unit at bus B5 went on increasing and crossed the limit value of 60 MVAR by the 60th second. Due to armature overcurrent sustained over a long period, over current relays (OCR) of units at bus B4 and B5 tripped at the ll0th second, taking the gen units off-bars. This resulted in a greater shock leading to tripping of other units at buses B2 and B3, which led to total system collapse. It can be seen that for most of the time, the frequency does not look bad and neither are the voltages. However, due to the gen unit exceeding its reactive power limit, the whole system has ultimately deteriorated.
111.2.2 System stabilisation with controller In the preceding section, it was shown that the system had ultimately led to a total collapse, whereas if the controller were to be there, the scenario is described as follows. The overload on gen unit at bus B4 is reduced by reducing the voltage set point at the bus and by increasing the neighbouring bus voltages at buses B2 and B5 in an incremental fashion in each cycle. The violation of reactive power at bus B4 is totally corrected 150 s after outage. Variation of reactive power (Qg) from the unit at bus B4 is plotted with respect to time in Figure 5.
111.2.2.1 Significance of A From Figure 5, it may be seen that the A value started increasing from immediate post-outage state. With the corrective signals, A is driven to zero. Then the corrective signals are stopped. When A attains zero, the control signals for Qg violation are stopped. It may be noted that the corrective signals are sent even after Qg has come within the limits QgaX. This is because the A value is computed as a time integral of the amount of deviation from the limit value. Until this becomes zero, control signals are given. The greater the deviation, the larger the value of A and the stronger the corrective signals.
159,21
BI
0.97 V [ (0.95V)
I [
r,ttt~gx
146,65 (215)
t
• possibility of a total system breakdown due to reactive power problems arising out of generator outage; • effectiveness of the controller in averting the system breakdown; and • better tapping of reactive power from SVC during emergencies through 'voltage set point control
180,87 1.00 V
1.00 V I ~ /
60,20 (60)
f = 49.61 Hz
1.02 V
1.00 V
The details of the experiments are described below.
111,2.1 Generator outage leading to system breakdown The system state before outage of the generating unit is shown in Figure 3. The active and reactive power generations are very much within the limits. Figure 4 gives the system state immediately after outage of the unit. It can be seen that the lost active power generation is met with additional active power generation from all the other generating units. Due to the additional generation, the reactive power limit of each unit has come down (refer to Figure 1). Further to this, the reactive power generation which was shared by both units at bus
6• B
MW, MVARvalues
are adjacent to each other
Limit is shown below
the
[ 1
" 65,21 0.95 V (0.92 V)
T
175,85
value in brackets
~
Device outage simulation
Figure 4. Gen outage study--immediate post outage state
158
Closed-loop reactive power controller: V. Veera Raju and A. Kuppurajulu
Table 1. Gen outage study--operating values without controller Generation values Active power in MW (reactive power in MVAR) B2Ul B3U1 B 4 U 1 B4U2
BsU1
0.95
122 (34)
121 (73)
122 (58)
122 (58)
121 (21)
1.02
0.95
122 (34)
121 (73)
122 (58)
0 (0)
121 (21)
1.00
1.02
0.95
159 (21)
146 (65)
159 (141)
0 (0)
144 (15)
0.97
1.00
1.01
0.94
158 (34)
145 (65)
158 (102)
0 (0)
146 (41)
49.62
0.97
1.00
1.00
0.94
158 (46)
146 (65)
158 (63)
0 (0)
146 (67)
0100
49.62
0.97
1.00
1.00
0.94
158 (46)
146 (65)
158 (63)
0 (0)
146 (67)
0110
49.62
0.97
1.00
1.00
0.94
158 (46)
146 (65)
0 (0)
0 (0)
146 (67)
B4U1tripped due to armature overcurrent relay
0120
48.37
0.97
1.00
0.97
0.92
203 (70)
196 (48)
0 (0)
0 (0)
0 (0)
BsU 1 tripped due to armature O/C relay. U/F load shedding B2U1, B3U 1 tripped due to low frequency
0130
0.0
0.0
0.0
0.0
0.0
0 (0)
0 (0)
0 (0)
0 (0)
0 (0)
System collapsed at 130 s
P.U. bus voltages Time (s)
Frequency (Hz)
V1
V3
V4
V6
0000
49.98
0.97
1.00
1.02
0030
49.98
0.97
1.00
0040
49.61
0.97
0050
49.62
0060
Comments
B4U2 tripped
V2 = 1.00V p.u. V5 = 1.00V p.u. 111.2.2.2 Prioritization of controls Table 2 includes the system status over a longer period in large intervals. It can be seen from the table that the control signals are issued even after limit violations are corrected. These signals try to minimize the system losses. The requirements, viz. initial thrust on correction
x
150
~ 100 I V ~x
/ i /xL i
of violations and minimization of losses after the system has corrected the violations, can be achieved with appropriate selection of constant values k~, k2 and k 3 in equation (12) as explained in Section 11.3. Higher values of k2 and k 3 would correct the violations quicker, whereas a small value Ofkl enables the loss minimization to be attained slowly over a longer period of time. It
-- 10 BI
,97 (209)
amda4
1.01 V
B2
x. x I ;'tx I~ I ~-.-~--~7" ~\ ,_ t/
o
.=_,o
\/\
X-x.x.x-x-x
I 60,20
0.988 V
(56)
0.99 V
:"
- 4
,=='
-2
x
,57
(215)
1.00 V
I
o
QgS4
0.978 V l (0.95v)
,0
QgB4max -- 6 .~_
~1
l 180,87
--8
,33 50
]
(o) 60,20
65,21 0.925 V (0.92 V)
MW, MVAR values are adjacent to each other
-wo
0
50
I 100
I x\..... ;.. !.. 150 200
0 250
Time (seconds)
Figure 5. Gen outage study--variation of reactive power and lamda
Limit is shown below the value in brackets
~
Device outage simulation
Figure 6. Gen outage study--ultimate controller action
state with
Closed-loop reactive power controller." I/. Veera Raju and A. Kuppurajulu Table 2. Gen outage s t u d y - - o p e r a t i n g
159
values with controller
Reactive power gen in MVAR Bus voltages in p.u. Time (s)
PLOSS MW
V1
V2
V4
V5
V6
B2
B3
84
hi B4
B5
hi B5
LMD4
LMD5
0 200 800 1000 1800 2800 3000
7.79 9.05 8.26 8.13 7.88 7.92 7.92
0.974 0.987 0.983 0.982 0.979 0.978 0.978
1.000 1.032 1.022 1.020 1.013 1.010 1.010
1.020 0.990 0.993 0.993 0.993 0.989 0.988
1.000 0.991 0.991 0.991 0.993 0.990 0.990
0.947 0.926 0.928 0.928 0.929 0.926 0.925
22 183 140 131 106 99 97
65 -2 23 28 42 55 57
142 10 36 37 38 35 33
54 35 38 38 37 35 34
15 55 45 48 57 54 56
60 56 56 56 57 56 56
0.00 0.00 0.00 0.06 0.11 0.11 0.00
0.00 0.00 0.00 0.00 0.06 0.05 0.00
V3 = 1.000 V p.u. G A M A 6 = 0.0.
i can be noted from the table that the losses, when the violations are corrected, are brought down from 9.05 MW to an ultimate value of 7.92 over a very long period. The ultimate state of the system is shown in Figure 6. Since the active power generation and loads are not changed, they are not shown in the figure to reduce cluttering. It can be seen that all reactive power generations and load bus voltages are within their limits.
With this it can be summarized that, with changing the set point control of SVC, instead of the normal practice of a fixed SVC set point, it is possible to use the extra reserve during emergencies. This helps in bringing the system back to normality more quickly and also in containing the violations better.
111.2.3 Effective utilisation of reactive power from SVC In the same example of generator outage, post outage simulation is carried out with the voltage set point of SVC at bus B6 kept at 0.965 V p.u. Comparison is made with the fixed set point of SVC (with only local control active) versus SVC being controlled by changing the voltage set point by the controller along with the gen units voltage set points. Figure 7 gives a comparison of the Q output of SVC with fixed set point versus voltage set point control. It may be noted that Q from SVC is higher with changing voltage set point control. Due to this, the amount of violation is lesser when compared to the fixexiset point of SVC, which can be seen from A values at buses B4 and B5 in Figure 8. At bus Bs, A has reached zero earlier, with the set point control of SVC voltage when compared to the fixed set point at SVC.
• possibility of a total system breakdown due to reactive power problems arising out of line outage; • effectiveness of the controller in averting system breakdown; and • initiation of automatic load shedding by the controller when it becomes necessary as a last resort.
0.98
--
V6 . j~,...
X
...:P(
. . . . . .•4(. ,K'" X... R...)e..
" "-;-.-. x - -
"
x --
x --
~, 0 . 9 6 ," ~D
/
I ""
x ,,~B'~( --
~*
--
90
--
80
. X - _-_ . X --X. ~(
x --
x - -
V6
x --
x
Qsvc x
x
x
x
x
These are demonstrated below.
111.3.1 Line outage leading to system breakdown System loads are close to that in Figure 2. A line outage (one of the parallel lines between buses B4 and B6) is simulated. Reactive power generation at bus B 5 crosses the limit value after the line outage. It can be seen from Table 3 that the gen unit at bus B5 has ultimately tripped at the 150th second due to OCR operation. This resulted in increased reactive power generation from units at buses B3 and B4. The units at bus B4 are overloaded and 5 F
Qsvc x --
111.3 Line outage study In this study, experiments are conducted to demonstrate:
ixX~Lamda4
With fixed
~ /~
< >
set point control
4 --
70
--
60
..... I x /
>
~1
With v o l t a g e set p o i n t control
,,
,~ 0.94
_
/'
/
; / ff
× /
ff ×
0 0.92
0.90
=..'/
mm
With fixed setpoint With voltage setpoinl~ c o n t r o l
I 20
I 40
LamdaSx
0
x/
I 60
I 80
--
--
I 100
50
o
40
30 120
Time (seconds)
Figure 7. Gen outage study--comparison of SVC output
- 7/ l
V. i
V
~~
#e
0-- = J: 0
20
40
##
,
x~ :.\\i amda5 tt, xlt
~I _ J_ I
Time
60
80
lO0
120
(seconds)
Figure 8. Gen outage study-comparison violation correction
of Og
Closed-loop reactive power controller." V. Veera Raju and A. Kuppurajulu
160
Table 3. Line outage study--operating values without controller PgB2
PgB3 MW
PgB4 PgB~
PgB5
Bus voltages in p.u. Time (s)
Frequency (Hz)
V1
V3
V4
(QgB2) (QgB3) (MVAR)
(QgB4) (QgB5) (QgB~)
0
49.97
0.974
1.000
1.020 1.000 0.930
123 (34)
122 (73)
123 (51)
122 (42)
20
49.97
0.974
1.000
1.020
1.000 0.930
123 (34)
122 (73)
123 (51)
122 (42)
30
49.97
0.974
1.000
1.020 1.000 0.903
123 (34)
122 (73)
123 (39)
123 (76)
120
49.96
0.974
1.000
1.020 1.000 0.903
124 (34)
123 (73)
124 (39)
123 (76)
150
49.96
0.974
1.000
1.020 1.000 0.903
124 (34)
123 (73)
124 (39)
0 (0)
B5U 1 tripped due to
B4U1, B4U2 overload
V5
V6
Comments
Line B4-B 6 CKT2 tripped
armature OCR
160
49.60
0.974
1.000
1.020 0.969 0.876
159 (22)
146 (119)
162 (67)
0 (0)
370
49.60
0.966
0.988
1.020 0.964 0.871
160 (53)
147 (76)
160 (74)
0 (0)
380
49.60
0.966
0.988
1.020 0.964 0.871
160 (53)
147 (76)
0 (0)
0 (0)
B4U1, B4U2 tripped due to armature OCR, B2U1, B3UI tripped due to U/F relay
390
0.0
0.0
0.0
0.0
0 (0)
0 (0)
0 (0)
0 (0)
System collapsed in 383 s
0.0
0.0
V2 = 1.000V p.u.
ultimately tripped due to operation of OCRs at the 380th second. This has resulted in a larger difference between supply and load and the remaining units also tripped due to under frequency relay operation of gen units resulting in total system collapse. The experiment is demonstrated to draw attention to the fact that a line outage can sometimes cause total system breakdown due to reactive power problems. In order to demonstrate this, however, a value of 0.8 kA of maximum armature current limit is used as against 0.9 kA shown in Appendix A.4, thereby lowering the maximum MVAR limit of the unit, which means that the units which are close to their limit values run a greater risk of leading to total system breakdown even with small disturbances. 111.3.2 System stabilisation with controller In the preceding section it is shown that the line outage has ultimately resulted in system collapse. In the presence of the controller the system stabilises. The ultimate state is shown in Figure 9. However, load shedding of 22 MVAR is carried out since it is unable to maintain the voltage of even 0.91 V p.u. at bus B6. While simulating the controls, only the reactive power of the load is shed, to avoid representing real power dynamics. However, if both active power and reactive power are shed, which happens in practice, the relief obtained would be better, thus giving a better margin of security. The scheme of load shedding is described below. 111.3.2.1 Automatic load shedding Load shedding is carried out in four steps. In each step, a quarter of the load is shed with total load shedding in the
last step, at the chosen buses. Pre-set limiting values of/or g at any bus can initiate load shedding at that bus. A minimum time interval between successive load shed commands ensures the active power dynamics settle down and also gives sufficient time for the controller to reverse the trend of violations. With this scheme, the load shedding is carried out automatically to bring the voltage at bus B6 within operating limits. The load shedding scheme is usually quite specific to each utility, any other BI
,64
(230)
0.976 V
I ~
I (0.95v)
,63 (229)
180,87 B2
1.0005 V
.23
1.000 V
I
I
6O,2O (3)
0.997 V +
I
r 6.'.20 l
60,20 0.915 V (0.91 V)
MW, MVAR values are adjacent to each other
180,65
Limit is shown below the value in brackets
# ~
Line outage simulation
Figure 9. Line outage study--ultimate state with controller action
Closed-loop reactive power controller." V. Veera Raju and A. Kuppurajulu 1.045
%
1.1140
....
....
--
8.05
-
8.00
From the initial state, when the controller is introduced, it keeps giving incremental voltage signals to minimize the losses ultimately reducing to 7.84MW. Variation of losses and also the gen bus voltages with respect to time are shown in Figure 10.
v2 .-. 1.035
U
~/x-x-x-x-x-x-x-,x-x-x- -x-x-x-x =x~-x-x-x-x-x-x-x=,x-x-x-x-x-x-x-x-x \ ~x-x-x-x X, ..... /x ......
V3 V4 V5
7.95
1.o3o
7.90
0
1.025:
/
"~'X~x. x
,..1 Losses %x.,x--x-x-x-x-x-x-x--x
7.85
--
1.020
1.015
I
I
I
50
100
150
7.80
7.75 200
Time (seconds)
Figure 10. Normal system study--loss minimization with Vg controls scheme could as well be incorporated in the overall control logic.
111.4 Normal system study As indicated in earlier sections, minimization of active power losses arising due to reactive power transfers is chosen as the objective function. Experiments are conducted to demonstrate: • loss minimization by varying the generator voltage set points; and • minimization of losses with proper scheduling of voltages at SVC buses instead of keeping a constant set point voltage. These experiments are demonstrated below.
111.4.1 Loss minimization through Vg controls System loads are same as in Figure 2, except that at bus B5 the load is 80,40(MW,MVAR) instead of 65,21(MW,MVAR). Initial losses are equal to 8.01 MW. SVC is considered to be 'switched off' in the system.
~"
8.5
--
8.0
~X=x
With fixed
7.0
svc v o l t a g e
• ~x-x.x.x.~.~
.... x .....
x-~-~.x.~.~
6.5
With s v c v o l t a g e set point control
0
111.4.2 Comparison of loss minimization with different options In this experiment three studies are conducted with the controller in action, viz. (a) without SVC in the system; (b) with SVC in the system at bus B6 where SVC is in local control mode with fixed set point voltage; and (c) with SVC in the system with voltage set point control. In all the three cases, generator voltage set point control signals are also given. Referring to Figure 11, the variation of losses with respect to time can be seen for all the three cases identified separately. In summary, during normal operation, as many savings as possible can be achieved by exercising the voltage set point controls both at gen buses and SVC buses. 111.5 Discussion The method presented here, unlike conventional static optimization methods, is based on a closed-loop dynamic control approach, The operating state is driven over a period of time to the optimum solution with incremental controls in each time step, satisfying the Kuhn-Tucker conditions of optimality. It is important that the overall control loop time should be much slower than the fast acting local control loops of AVR and SVC. Unlike the normal practice of keeping the voltage set points fixed at SVC, better results can be obtained by changing the voltage set point. This helps both in emergency operation, by contributing to quicker mitigation of violations, and in normal operation, by contributing to further loss minimization. The scheme is an automatic secondary voltage control in closed loop (which can be viewed as parallel to AGC for active power) with an overall objective function of loss minimization while satisfying voltage and reactive power constraints. To maintain voltage stability, apart from gen unit voltage set point controls and SVC controls, transformer tap changes would also play a definite role. However, transformer tap changing is slow. Typically it may take more than 20 s for each step of tap change. A deeper investigation is needed to include transformer tap control for voltage stability.
Without s v c ~X'X-x.x.x.,x=x--x.x.X.X.x.X.X.X
7.5
6.0
161
I
I
I
I
50
100
150
200
Time (seconds)
Figure 11. Normal system study--losses with and without SVC set point control
IV. C o n c l u s i o n s A technique for synthesizing a closed-loop reactive power controller for voltage stability is presented in this paper. The controller is based on a multi-variable control approach. Unlike conventional static optimization techniques, the controller dynamically steers the system to an acceptable state in a closed loop satisfying the Kuhn-Tucker conditions of optimality. The controller issues set point control signals to generator AVRs and SVCs in real time. It is an Automatic Voltage Control scheme which can be viewed as a parallel to AGC for active power. The scheme is tested both in normal and contingency situations. It has also been demonstrated how the controller is able to effectively steer the system in case of serious reactive power violations on gen units and low load bus voltages when
162
Closed-loop reactive power controller: V. Veera Raju and A. Kuppurajulu
contingencies occur. The benefit of SVCs with changing set point control is demonstrated both in normal and emergency operation. Automatic load shedding is also demonstrated in the scheme. The controller can be implemented as part of the Energy Management System on a real-time basis. Computations required for the controller can easily be managed on the real-time computer even for fairly large practical power systems.
V. Acknowledgements The authors gratefully acknowledge the Indian Institute of Technology, Madras, and CMC Limited (R&D), Hyderabad for the facilities provided to carry out this work. The authors thank Mr Shirish S Kulkarni, an M. Tech student from liT, Madras, for his timely help in bringing the document to its present form.
VI. References 1 Snyder, WL, Raine, JG, Christie, RD, Ritter, F and Reed R. 'Var management-problem recognition and control, Var management task force report' IEEE Trans. Power Syst. (1984) 2108-2116 2 Lacks, W R 'Countering calamitous system disturbances' in International Conference in Reliability of Power Supply Systems, London. IEE publication No 225, 1983, pp 79-83 3 Lacks, W R 'Insecure system reactive power balanceanalysis and counter measures' IEEE Trans. Power Apparatus & Syst. Vol PAS-104 (1985) 2413-2419 4 Lacks, W R 'Automatic control of system voltage stability by an expert system' in Proceedings of Tenth Power Systems Computation Conference, Graz, Austria, 19-24 August 1990, pp 1057-1064 5 Lacks, W R and Sutanto, D 'Voltage instability in interconnected power systems--a simulation approach' IEEE Trans. Power Syst. Vol 7 No 2 (1992) 753-761 6 Brownell, G and Clark, H 'Analysis and solutions for bulk system voltage instability' IEEE Trans. Comput. Applicat. Power Vol 2 No 3 (1989) 31-35 7 Goossens, J 'Reactive power and system operationincipient risk of generator constraints and voltage collapse' in IFAC Proceedings of Conference on Power System and Power Plant Control, Seoul, South Korea, 22-25 August 1989, pp 1-10 8 Taylor, C W 'Concepts of under voltage load shedding for voltage stability' IEEE Trans. Power Delivery Vol 7 No 2 (1992) 480-488 9 Paul, J P, Leost, J Y and Tesseron, J M 'Survey of the secondary voltage control in France: present realisation and investigations' IEEE Trans. Power Syst. Vol PWRS-2 No 2 (1987) 505-511 10 Lagonotte, P, Sabonnadiere, J C, Leost, J Y and Paul, J P 'Structural analysis of the electrical system: Application to secondary voltage control in France' IEEE Trans. Power Syst. Vol 4 No 2 (1989) 479-486 11 Thorp, J S, llle-Spong, M and Varghese, M 'An optimal secondary voltage-VAR control technique' Automatica Vol 22 No 2 (1986) 217-221 12 Ilie, M and Stobart, W 'Development of smart algorithm for voltage monitoring and control' IEEE Trans. Power Syst. Vol 5 No 4 (1990) 1883-1993
13 Stankovie, A, llie, M and Maratukulam, D 'Recent results in secondary voltage control of power systems' IEEE Trans. Power Syst. Vol 6 No 1 (1990) 94-101 14 lllc, M 'New approaches to voltage monitoring and control' IEEE Control Syst. Vol 9 No 1 (1989) 5-10 15 Carpentier, J, Gillon, A, Jegonzo, Y, Caraman, F, Grimonpont, R, Pellen, F and Tounebise, P 'Real time optimal power flow for application to automatic control' in Proceedings of Tenth PSCC, 19-24 August 1990, pp 66-73 16 Brandwajn, V, Ipakchi, A and Sherkat, V 'Tracking evolutionary trends in generation control' IEEE Comput. Appficat. Power Vol 6 No 1 (1993) 22-26 17 Kuppurajulu, A 'A multivariable closed loop controller for real-time application' J. Inst. Engineers India-EL Vol 70 EL1 (1990) 203-205 18 Kuppurajulu, A 'Closed loop reactive power control for use in energy management systems' J. Inst. Engineers India-EL Vol 71 EIA (1990) 159-162 19 Kuppurajulu,A and Ossowski, P'An integrated real time closed loop controller for normal and emergency operation of power systems' IEEE Trans. Power Syst. Vol 1 No 1 (1986) 242-249 20 Vinod Kumar, D, Veera Raju, V and Kuppurajulu, A 'A real time closed loop controller for security dispatch' Int. J. Elec. Power & Energy Syst. Vol 15 No 5 (1993) 307-314 21 Veera Raju, V and Kuppurajulu, A 'A closed loop controller for voltage stability' Int. J. Elec. Power & Energy Syst. Vol 15 No 5 (1993) 283-292 22 Kuppurajulu, A and Ramar, R 'Workshop on power system simulator' Elect. India Vol XXX No 5 (1990) 11-13 23 Sato, K, Yamazaki, Z, Haba, T, Fukushima, N, Masegi, K and Hayashi, H 'Dynamic simulation of a power system network for dispatcher training' IEEE Trans. Power Apparatus & Syst. Vol PAS-101 (1982) 3742-3750
Appendix A.1 General concept of multivariable dynamic control A.1.1 Multivariable control Many practical multivariable systems are comprised of a number of subsystems each having their own fast response feedback loops. In addition, an overall control loop exists to operate the system so as to achieve a desired objective of minimum cost, optimum performance, etc. The main purpose o f this loop is to ensure that the system functions in a desired manner and none of the subsystems reach critical states under slowly varying operating conditions. A real-time dynamic controller can be designed to provide this overall control loop. Each of the subsystems can be described by a set of dynamic equations, namely
Xi : fi(Xi, Ui) Yi =
li(xi, Ui),
for i = 1 , 2 , . . . , N
where xi, yi, u i are the state, output and control vectors of the ith subsystem and Nis the total number of subsystems in the system. The feedback loops and protective devices of the subsystems are such that inequality constraints of the type gi(xi, Ui) ~<0 and equality constraints of the type hi(xi~ ui) = 0 are satisfied.
Closed-loop reactive power controller: V. Veera Raju and A. Kuppurajulu System
Thus the overall system can be modelled by the following equations:
I f (X,U) = 0 _
U = Input
= f ( X , U) "~
(A1)
min C(X, U).
Feedback control Feedback controller
(A3)
The dynamic controller should be designed to provide a real-time closed loop feedback of the type U = p(Y), which achieves the objective in equation (A3) under the constraints in equation (A2). Assuming the time response of the subsystems is sufficiently fast compared with the real-time closed-loop response, the system can be represented by its static equivalent f(X, U) = 0. The objective of the dynamic controller is similar to that of an optimization problem. The necessary and sufficient conditions to ensure optimality are required to satisfy the Kuhn-Tucker conditions. Thus the controller is designed such that it steers the system to an optimal state which satisfies the Kuhn-Tucker conditions of optimality. It may be noted that the objective of the proposed controller differs from the: classical optimal controller in that the speed of response is not very critical, whereas it primarily aims at satisfying the constraints. A.1.2 Structure of the multivariable dynamic controller The problem is to design a feedback controller for the system such that the objective function C(X, U) is minimized subject to the constraints
gk(X, U) ~<0,
k = l, 2 , . . . , m inequality constraints
hk(X, U) = 0,
k = 1 , 2 , . . . , n equality constraints.
A modified objective function is formed by choosing a 'Lagrange multiplier' for each of the constraints. L = modified objective function : C + )~tg +'Tth m
,;--h
j.gj +
]-
k=g,k~0
Figure A1. Block diagram of feedback controller
Appendix A.2 A.2.1 Derivation of Op/OX X is a state vector consisting of voltages at all buses. The expression for Op/OV i is derived below. The real power loss PU in a line having a conductance value of g~ connecting two buses i and j having voltages V i L Oi and Vj / Oj can be written as
PO = ( V2 + VJ2 - 2ViVjc°sOq)go where Oij = Oi - Oj. Real power flow F O.in the line from bus i to busj can be written as:
Fij = ( Vi Vj / xo. ) sin 0/j From the above expression, cos 0• can be written as COS 0/j = (V?Vj 2 --
F2x~ij)I/2/(ViVj)
By substituting cos 00- in the expression for losses in the line we get,
Pij = go.[V~ + Vf. -- 2(V?Vj 2 -- l"ijXij ) ' ' 22,1/2,] Total losses: P=
ZP0 all lines
Therefore,
2"1
(A4)
where Aj=Lagrange multiplier corresponding to inequality constraint g j, and 7j = Lagrange multiplier corresponding to equality constraint hi. The dynamic controller is designed by the following set of equations 0L OUk'
Y=Output
min C(X,U)
g(X, U)~
~k --
g (x,u) < o
-1 h (X,U) = 0
v = t(x, u)
= c +
163
01)/OVi= E { V g -
J
2 2 1/2]}g/j Vj[ViVj/(V?Vj2-F~xo')
A.2.2 Expressionfor OQ/OX
OQ,/Ox O(Q,/V,)lOX X is a state vector consisting of voltages at all buses,
for kth control variable
(A5)
J~k = gk ~, Ak >~0 J
for kth inequality constraint
(A6)
"~k = hk,
for kth equality constraint
(A7)
Representation of the controller in the form of a block diagram can be seen in Figure A 1.
O(Qi/Vi)/OVi = Big and
O(Qi/Vg)OVj = B o.
where Big and Bij are diagonal and off-diagonal elements of network B matrix (expressions are derived in Appendix B). A.2.3 Expression for OV/OX With X as a state vector consisting of the voltage at buses
Closed-loop reactive power controller: V. Veera Raju and A. Kuppurajulu
164
By comparing the above expression with equation (AS) D 1 = --BL 1 BLG and D2 = -BZ~ BLs. With these expressions, D can be evaluated. General expressions for the elements of BLt, Brc, BLs are O/OVi(Qi/Vi) = Bii and O/OVj(Qi/Vi) = Bij where Big and B/j are the diagonal and off-diagonal elements of network B bus matrix.
in the network,
OVi/OVj=O and OVi/OVi=l.O.
Appendix A.3 A.3.1 Derivation of partial derivative OX/OU In the expression
Appendix A.4 Important parameters of 6 bus power system
AX = D AU
Base MVA = 200, network voltage level = 100 KV X is a state vector consisting of voltages at all buses in the network, and U is a control vector consisting of voltages at generator buses and voltages at SVC buses. D needs to be evaluated. The incremental state vector can be expressed in terms of the incremental control vector as AV G AV s
I =
0
0
i I v°l AVs
AVL
D1
D2
From the above expression, AVL = [D1 D21
bvol
(A8)
[AVsJ
where D1 and D 2 are derived below. At any load bus we can write
A.4.1 Line data
S No.
Line
Resist (p.u.)
React (p.u.)
Line chrg admit. (p.u.)
1 2 3 4 5 6 7 8 9
Ba-BI Bs-B 6 B2-B4 B3-B 5 Ba-B5 B2-B1 B2-B3 B4-B6(1 ) Ba-B6(2)
0.0150 0.0562 0.0534 0.0384 0.0300 0.0200 0.0600 0.1500 0.0750
0.0730 0.1526 0.1640 0.1150 0.1000 0.1100 0.1300 0.5400 0.2700
0.0900 0.0350 0.0170 0.0528 0.0000 0.0000 0.0000 0.0000 0.0000
A.4.2 Gen units data
AQL = O/OVG(QL)AV6 + O/OVs(QL)AVs + O/0VL(QL)AVL We can write QL/VL in place of QL. Then, A(QL/VL) = O/OVG(QL/VL)AVc
+ O/OVs(QL/VL)AVs + O/OVL(QL/VL)AVL Since, at the load bus there is no reactive power support, A(QL/VL) = 0. In addition, by writing 0/OVo(Qt/VL)=BLG; O/OVs(QL/VL) = BLs; and 0/aVL(QL/Vt) = BLL, then AVL can be written as:
AVL =--[BZ 1
BZ '
r LAVsJ
Armature max current limit (kA/phase)
Bus
Capacity Unit (MW)
B2 B3 B4 B4 B5
B2U1 250 B3U 1 250 B4U 1 175 B4U2 1 7 5 , B s U 1 175
B6
SVC capacity (MVAR) 0 to 120
Trip setting f ( I - Imax)dt (kAs/ph)
1.50 1.50
9.00 9.00
1.90 0.90
11.40 4.05