coordinated stablity control

8/6/2019 Coordinated Stablity Control

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ABSTRACT:

An adaptive coordination scheme is proposed to improve the transient stability,

voltage security and frequency damping of a power system network by optimally scheduling

the parameters of the available controllers. A set of real-time stability indicators, including a

transient stability index, transient voltage stability index and damping factor are used to

reflect the stabilities of power systems. Then, the relative significances of a group of

controllers to the power system are used as references for the optimiser to schedule new

controller parameters. This coordinated control scheme effectively allocates power system

resources to handle different stability issues in different time frames. The results suggest that

power system security can be further enhanced by means of coordinated control.

1. Introduction:Power systems are becoming more complex with the increasingly stressed stability

margins resulting from the electricity market. Traditional vertically integrated power systems

are being replaced by market-based operation after deregulation. Consequently, it becomes

more difficult to predict the behavior of power systems. Furthermore, the introduction of

independent power producers and power electronic loads, which are nonlinear in nature, have

also complicated the operation of the grid. Although the operation and the interconnection of

power systems are evolving, two classes of approaches appear in the mainstream control of

power systems. The first approach is a decentralised controller design where classical linear

controllers as well as modern nonlinear controllers are designed for handling predictable local

problems [1,2]. Although remote interactions can be considered in terms of local control

variables, decentralised controllers rarely coordinate together to resolve any particular

problems from the viewpoints of the network, not to mention problems of an unusual nature.

The other approach is a hierarchical control design based on a wide-area measurement [35].


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Accelerated by fast communication facilities, the upper level controllers can obtain remote

information from different local controllers, and if local controllers have conflicting effects

with upper level control objectives, they will tune these local control systems in a coordinated

way according to various global optimisation procedures. These hierarchical optimal

controllers usually can achieve good performance for a single control objective or two, such

as transient stability, voltage regulation or oscillation damping, but may neglect the other

potential stability issues in power systems.

Power system stability issues are not mutually exclusive. There have been qualitative studies

[1, 6] showing that some controller interactions could degrade the power system stability

under certain circumstances for which they are not designed. The concept of coordinated

different control evolved from previous works [713]. A novel global control strategy was

introduced for coordinated transient stability and voltage regulation by excitation in [7, 8],

developing a framework for more general schemes involving the coordination of many

controls with diverse control goals. The framework was further refined in [9, 10], applied to a

benchmark test system and covered more different network scenarios. In addition, preventive

and emergency control actions were coordinated to enhance transient stability in [11, 12], and

an adaptive optimal control scheme has been applied against cascading blackouts in China

[13].

This paper extends the framework [8] to investigate coordinated security control. First,

various system trajectories are utilised to analyse the instability symptoms of transient

stability, voltage security assessment and small signal stability. The formulation of remedial

actions has to be based on the due consideration of thesesymptoms. Then, therelative

effectiveness of local controllers is evaluated for the capabilities to resolve transient

instability, voltage instability and small signal oscillatory problems.


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Power system signals such as rotor angles of the generators, bus voltage profiles and

oscillating frequencies are sensed and used to calculate the transient voltage and small signal

stability costs. Later, a sensitivity function is formed, which is used by the optimizer

later as a reference for control parameter scheduling. The severities of the stability issues are

compared based on their weighted costs, and a new set of controller parameters are optimally

calculated with the aim of reducing the total cost of system stability. It is to be emphasised

that it is not a centralised controller design but rather the maximal exploitation of available

control resources. The simulation results for a benchmark system show that this coordinated

control scheme is effective, robust and provides significant stability improvement for many

kinds of system disturbances.

The paper is structured as follows. The coordinated control scheme is described in Section 2.

Section 3 presents the power system models and the formulation of the coordinate control

system. The example power system, its coordinated control system and simulation results are

provided in Section 4, followed by discussions in Section 5 and conclusions in Section 6.

2. Coordinated control schemeThe goal of the proposed adaptive coordinated control is to maintain system stability

under all operating conditions, especially unforeseeable ones. It is a framework within

which a variety of methods and different controllers can be coordinated to handle

complex system problems to the extent allowed by the available information and

communication technology. Hill et al. and Guo et al. [7, 8] offered the possibility of

coordinating control actions across the whole system geographically and for all operating

situations in an adaptive way. Hill et al. [7]

referred to the collection of available control elements swarming onto the problems as

they arise.


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The coordinated control framework as shown in Fig. 1 has a two-tier structure, which is

local control and some degree of central coordinated control. The local controllers

perform their normal operations with the original local settings until an abnormal

situation occurs where the coordination control takes over. Based on the global control

objectives for the power system, a set of high-level coordination controllers (CCs) is built

as the supervisory controllers for the existing local controllers. This system-wide

coordinated control has four main tasks, namely: (1) indicator processing, (2) scheduling,

(3) optimisation and (4) actuation. The function

of each task is described as follows:

2.1. Indicator processing : The signal-processing layer of the CC collects and processes

raw network information from local controllers in real-time such as power flow, system

frequency, bus voltages and alarm signals. The signal is then transformed into

meaningful signals such as stability indicators. The CC will then determine the severity

of each kind of instability, that is to decide whether the system is in the proximity of

transient, voltage or frequency instability.

2.2. Scheduling : Depending on the severity of the particular type of instability, a group of

control actions will be scheduled (typically of the switching type) which have the

capacity, with further tuning, to overcome the instability.

2.3.Optimisation : The optimisation layer measures the degree of instability of the power

system and determines the necessary amount of control action to be provided from each

selected local controller. The stabilising effects of each local controller towards different

types of instabilities are calculated beforehand. The results can be recorded in the CC

either in the form of a lookup table or a set of linear/nonlinear equations.


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The information enables the optimisation algorithms to fine tune the action plan established

by the scheduler in step 2 for optimal performance.

Fig.1 Adaptive coordination control framework

Remark 1: The upper level CCs can handle either one single issue (such as voltage

regulation, oscillation damping and so on.) across a wide area or regional tasks,

spanning multiple stability issues from a small regional area to a wider interconnected

power grid. The designs of these upper level controllers are based on the global control

objective of the power system.


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These coordinated controllers can be installed in different areas of the power system and

linked together via a communication network, which will necessarily be limited in structure

and speed. Note that if a communication link to the controller is broken down, local

controllers can still provide adequate performance although it may not maximise their

contributions to the optimisation of the whole power system.

Remark 2: In real-time utilisation, the availability of Phase Measurement Units (PMUs) and

the locations of local controllers have to be considered such that the optimization procedure

can be simplified and the global control objective(s) guaranteed. In addition, the two-tier

structure of the coordinated control framework enables information processing and decision

making to be made at the local control systems by the use of distributed computation

technology. This can significantly reduce the computational burden on the CC and, thus,

reaction to the event in real time is possible. The proposed control scheme should be able to

reduce the overall processing time in comparison with the centralised control scheme.

3. Power system models and controller design3.1 Power system models :

The dynamics of interconnected power systems can be represented by a set of high-

order nonlinear differentialalgebraic formulas as follows

x = f (x, y, u, m)

0 = g(x, y, u, m) (1)

where the differential equation describes the dynamics of the power system components

including generators, dynamic load and control devices; the algebraic equation expresses the

voltage, current and network power flow equations in the system; x Rn

is the dynamic state

vector of the power system; y Rl

is the algebraic constraint vector ; u Rp

is disturbances,


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which make the power system move from one equilibrium point to another; and m Rq

is the

control vector, which consists of adjustable system parameters.

The operating point (x, y) of the power system (1) varies according to the disturbance and

the control vector m. When the specific disturbance 0 occurs, control vector =0++

where

0 is the control vector of the original steady state and +

is the adjusted control vector. The

aim of the proposed control scheme in Section 2 is to obtain the optimised adjustable control

vector . At the equilibrium point (x0, y0), power system dynamic state vector xand

disturbances u 0are equal to zero.

3.2. Stability assessment and cost

Three categories of stability analysis [6] are mainly involved in the systematical

controller design of power system, includingtransient stability, voltage stability and smallsignal stability analysis. In order to effectively allocate power system resources to handle

different stability issues in different time frames and situations, stability assessments and

indices are evaluated through various system trajectories in real time.

Despite different methods to study transient stability, the responses of power angle of the

generators are always regarded as the key trajectories to analyze the synchronization of

power system. Thus, it is obviously proper to employ power angle excursions to calculate

transient stability cost Cts , which is an important transient stability indicator for the

optimisation of the CCs.

For voltage stability assessment, a cost Ctvs which is based on the trajectories of bus voltages,

is used to measure how voltage unstable the system is.


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In the case of small signal oscillation, it is common that many different modes of oscillation

are presented in a multimachine power system. Each mode is characterised by its natural

frequency and damping factor. The normalized deviation of the damping factor of the

targeted mode is used to evaluate the small signal stability cost Css .

The costs Cts, Ctvs and Css can be estimated in real-time and are dependent on the existing

power system state variable x0, algebraic variables y0, disturbances u0 , controller parameters

0 and adjusted control variables +

. Thus, the estimated costs can be written as

WhereCts , Ctvsand Css represent the changes of transient stability cost Cts, voltage

stability cost Ctvs

and small signal stability cost Css

when control variables are adjusted.

The changes of stability cost Cts , Ctvsand Css are the indications of the capabilities of

the power system local controllers for different stabilities. In this paper, the sensitivity

matrix is proposed to measure the changes of stability cost at a nominal operating point. As a

first-order approximation, the relationship between cost changes and controller parameters

can be represented as follows

(3)

Where C is the sum of changes of different stability costs, A is the gradient between the

change of stability costs and the adjusted controller parameters K, that is the sensitivity

matrix.


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(Note that K can be any controller parameters, such as for load shed. Generally, K is the

parameters of the controllers and affects the output of the controllers .) The details of

calculating different stability costs will be provided later.Certainly, higher order nonlinearcontroller function can be designed, but it is not the focus and is therefore not covered in this

paper.

3.3. Optimisation

The determination of the local controller parameter actuation is formulated as a

constrained optimisation program. A quadratic objective function is proposed

minJ =tsC2

ts+ tvsC2

tvs+ ssC2

ss (4)

and

ts +tvs +ss = 1 (5)

Where the coefficients ts, ssand tvs are the weights for the corresponding stability indices.

They are determined with the aim to balance the contribution of each kind of stability in

different time intervals.

ThereforeJ is a function of current power system conditions and predicted optimal control

parameters,

J = J (x0, y0, u0, ) (6)

This objective function is subject to two inequality constraints

(a)Upper and lower boundslb ub (7)


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(b)Limited rate of change in controller parameters

(8)

The inequalities can be converted into the following general form

Gi () 0 (9)

3.4 Coordinated control design

The proposed coordinated controller design provides a supervisory feedback for the

adjustments of local controller parameters according to different network structures, distinct

operating conditions and various control objectives. The CC design involves the following

procedure:

1. design the scopes of upper level CCs based on the global control objectives and local

controllers in the existing state of the power system prior to any contingencies;

2. Choose the corresponding methods for upper level CCs to assess transient, voltage and

small signal stability;

3. Calculate different stability costs of local controllers and create a set of local controller

schedules for overcoming potential instabilities of power systems;

4. Analyse the relationship between cost changes and controller parameters and form the A-

matrix in (3);

5. solve the objective optimisation (4) and set up the relative significances of a group of

control actions according to the sensitivity matrix A and

6. schedule the actuation of the local controller parameters.


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4. Case study :To illustrate the proposed control framework, control of a typical two-area power

system will be investigated.

4.1 Two-area power system

Fig. 2 shows the diagram of a modified version of the two area system described in

[14]. The modifications are as follows:

Line 67 and line 910 are split into double circuits

Fig. 2 A modified 2-area system

Line 78 and line 89 are turned into four-line circuits Two static VAr compensators (SVC) are installed at Bus 7 and Bus 9

The 0.50.6 Hz inter-area mode of oscillation, which has the lowest damping factor

compared with other local modes of oscillation, is chosen as the target for damping in this

paper [1, 14]. Other modes are not adversely affected to an extent that they need special

attention in this system. All the dynamic data of the generators and static data of the system

remain unchanged from that given in [14].


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Throughout this paper, a number of contingencies are referred to. The descriptions of them

are as follows:

C1: Three-phase fault at Bus 7. Fault is cleared by tripping line 78 at 0.1 s later;

C2: Three-phase fault at Bus 8. Fault is cleared by tripping line 78 and line 89 at

0.1 s later;

C3: Three-phase fault at Bus 9. Fault is cleared by tripping line 89 at 0.1 s later;

C4: 10% load increase at Bus 9.

Fig. 3. Block diagrams of simple exciter system, PSS and SVC


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In the two-area power system, each of the four generators is equipped with a simple exciter

and power system stabilizer (PSS). The control blocks of the simple exciter, PSS and the

SVC are shown in Fig. 3. The parameters are listed in the Appendix.

4.2. Controller sensitivity tests

Power system controllers are mostly designed for some kind of primary

objectives. For example, PSS is designed for damping and SVC is for voltage support.

However, their contributions to other types of stability controls are also valuable. Information

like the relative strength of each controller is required for the coordinated control system to

formulate suitable switching actions.

In this paper, the stability assessments were calculated by using Powertechs Dynamic

Security Assessment Software Tools (DSA ToolsTM

).

4.2.1 Transient stability assessment:

The transient stability

index of a multi-machine system

can be computed by using the

extended equal area criteria

(EEAC) [15]. This method

separates the system generators

into two groups, that is the critical

cluster and the rest. The cluster of

critical machines is identified as

the group of candidate critical

machines which give the smallest

critical clearing time (CCT). Fig. 4. Power angle diagram


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The stability index is obtained by calculating the difference between the acceleration area

and deceleration area in the corresponding EEAC assessment. Fig. 4 identifies the quantities

referred to. Then the index

Where Ainc is equal to kinetic energy increasing area (during fault) and Adec is equal to kinetic

energy decreasing area (post fault).

The initial gain values of the exciter, PSS and SVC are set to be 200, 30 and 200,

respectively. By varying the gain of one kind of controller at a time, the transient stability

indices are found (see Fig. 5).

The following points are observed:

Small load change (in this case, 10%) does not affect transient stabilitysee Case C4;There are discontinuities in the stability indices. This is because the EEAC algorithm

separates different machines into different clusters according to the degrees they are

affected. Different combinations of critical generators will change the inertia base of the

calculation, resulting in the discontinuity of the plots;

It shows that increased gain in the excitation system does not always increase thestability index, and increase in PSS gain does not necessarily worsen the transient

stability. These two figures show that the actions of the excitation system and PSS in

transient stability tend to be oppositional; Increase in SVC gain does not improve the transient stability


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Fig. 5. Transient stability index with adjustable excitation, PSS and SVC gains


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4.2.2 Transient voltage stability assessment:

Voltage stability refers to the ability of a power system to maintain steady voltages at

all buses in the system after being subjected to a disturbance from a given initial operating

condition [6]. By estimating the distance to the proximity of voltage collapse, many

stability indices have been proposed [16]. In this paper, voltage security (or transient voltage

Stability), which describes the deviation of transmission system voltage from its nominal

value is used [17]. Based on signal energy analysis [18], a transient voltage instability index,

which measures the normalised distance of the transient voltage from the steady-state value,

is chosen.

The equation is stated below

where tvs is the transient voltage instability index, ncl is the time step at the clearing time;

and the subscript i denotes buses and i denotes the time step. Note that unlike the transient

stability index, ts (that the larger the index value, the more stable is the system), bigger tv

implies that the system is more voltage unstable.

Inspection on Fig. 6 reveals that:

the transient voltage instability index increases monotonically in a close-to-linearfashion as the excitation gains change from 100 to 300;

change in PSS gains has relatively much less effect on transient voltage stability; the SVC is the most effective device for transient voltage stability improvement; load variation has minimal effect on transient voltage stability.

It is therefore concluded that a reduction in excitation gain and an increase in SVC gain can

improve transient voltage stability.


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Fig. 6. Transient voltage stability index with adjustable excitation, PSS and SVC gains

4.2.3 Small signal stability assessment:

Different modes of oscillation are present in a multi-machine power system. Each

mode is characterised by its natural frequency and damping factor.


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Pronys method [19] is a common way to extract the frequency information in real-time. It

considers the sampled data as a linear combination of exponentials.

for 1 n N, where T is the sample interval,Ak is the amplitude, kis the damping factor,

fkis the sinusoidal frequency, k is the sinusoidal initial phase.

The p-exponent discrete-time function of (12) can be expressed in the form

(13)

The damping factor (), corresponding frequency (f) and damping index (ss) can be

calculated by

(14)

(15)

ss =

(16)

The diagrams in Fig. 7 show the damping variations with different controller gains. It is noted

that the damping ratio of the inter-area mode increases almost linearly with the increase of

PSS gains. On the other hand, although the damping factor increases in the excitation gain

ranges from 0 to about 60, it begins to decrease monotonically after the peak. The increase of

SVC gains also decreases the damping ratio in this case.


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Fig.7 Small signal stability index with adjustable excitation, PSS and SVC gains

(Frequency = 0.55 Hz)


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In general, the procedure of sensitivity measurements demonstrated above can be adopted for

any kinds of dynamic problems, indices and control actions. Those chosen here are for

illustration.

4.2.4 Stability costs:

Although the transient stability index from EEAC is a well-accepted indicator

for transient stability, it cannot provide a continuous assessment of the overall status of the

generator angles. A modified method to measure the overall rotor angle deviation is, thus,

proposed

(17)

where Mi is the moment of inertia of the ith machine in the S-cluster, Mj the moment of inertia

of the jth machine in the A-cluster, i the rotor angle of the ith machine in the S-cluster, j the

rotor angle of the jth machine in the A-cluster

To represent the angle excursion as a cost to the power system transient stability, the

following function is used

(18)

Where dc is the critical angle of the system. The value of C ts is between 0 and 1. The

transient stability limit is defined by Cts = 1.

Transient voltage instability index can be directly used as the cost to be minimised for

transient voltage stability, that is

(19


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Note that the value of the transient voltage stability cost is kept below l. During

phase-to-earth faults, voltage would momentarily drop to zero. The voltage deviation (thus

voltage stability cost) from the nominal value would be large when compared with other

stability costs. However, transient stability cost is considered to be the most important during

the fault period. For illustration here l is taken as 0.3, which covered the voltage fluctuations

encountered.

The small signal stability cost is the normalised deviation of the damping factor of the

frequency from the targeted one

where ss0 is the target damping factor. The maximum value of Css is 1 and the minimum

value is limited to 0, even ifssss0.

4.2.5 Sensitivity matrix:

From the analysis of above three sections, the relative effectiveness of three

controllers, namely an excitation controller, PSS and SVC have been evaluated for the

capabilities to resolve transient instability, voltage instability and small signal oscillatory

problems. Thus, the sensitivity matrix A in (3) can be summarised at a nominal operating

point. Due to the relatively simple relationship between cost changes and controller

parameters actuation, a linearised sensitivity matrix is formed as follows

The value of this A-matrix is provided in the Appendix.

(20)


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4.2.6 Optimisation function:

In order to realise the coordinated control and actuate various local controller

parameters, the quadratic objective function (4) must be chosen in advance. Since the two-

area power system is a comparatively small system and system response after disturbances

with limited time interval, the coefficients ts, ssand tvs are considered as constants. The

values are taken to be [0.6, 0.3, 0.1], respectively, in the simulation.

4.3. Simulation results

In this section, a network contingency scenario is demonstrated. The effects of the

global coordinated control scheme are compared with a conventional method where no global

control is used, that is parameters are fixed at values determined in the Appendix. The control

scheme is tested by simulations in MATLAB Power System Toolbox [20].

The load at Bus 9 is increased by 10% at t = 2.0 s. Then at t = 6.0 s, a fault occurs at Bus 8.

The fault is cleared by tripping one line 89. The results are shown in Figs. 8a8d. Fig. 8a

shows that the bus voltage under global control settles at a new equilibrium much faster than

the conventional scheme. The cost comparisons in Figs. 8b and 8c confirm that transient

stability, transient voltage stability and damping are improved by the proposed control

scheme. The controller gains in Fig. 8d highlight the point that the controllers can

automatically reschedule their parameters for successive events.


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Fig. 8 Figure 8 Responses of the global coordinated control with successive events

a Voltage magnitude at Bus 8

b Stability cost of the power system with global control

c Stability cost of the power system without global control

d Actual controller gain scheduling


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5. DiscussionsThe simulations have shown some significant improvements over a wide range of

power system stability problems by the proposed coordination scheme. There are some

points worth noting:

1. The coordinated control scheme used in Section 4 only coordinates controllers of

similar types. In general, the global control will be capable of handling a mixture (hybrid)

of continuous and discrete, dynamic and static control actions. Furthermore, advanced

controllers like FACTS devices are also suitable for this scheme [9].

2. This coordinated control scheme utilises a basic feedback control algorithm to improve

power system stability. Other advanced control algorithms such as model predictive

control [21] can also be adopted to predict the power system behaviour and to evaluate

parameters in advance.

3. The voltage cost in the objective function only considerstransient voltage stability

Long-term voltage stability can also be taken into account as an additional cost to the

objective function. Indicators like loading margin can be used and remedial actions

such as load shedding and capacitor switching can also be coordinated for voltage

regulation.


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6. ConclusionsThis paper presented a generic adaptive coordinated control scheme for

power systems as a further step towards universal type controllers which flexibly

respond to all stability problems. The controller uses measurable network

information to determine the locality and type of the stability nproblems. By

formulating and coordinating the necessary control actions from all available local

control actions, we can overcome system-wide power system problems. This

framework is flexible to adopt new elements such as stability indicators and

optimisation algorithms. The development of tests and models is further needed for

evaluating the capabilities of different controllers under different instabilities.


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7. References

[1] KUNDUR P.: Power system stability and control (McGraw-Hill, 1994)

[2] CHAPMAN J.W., ILIC M.D., KING C.A., ENG L., KAUFMAN H.:

Stabilizing a multimachine power system via decentralized feedback linearizing

excitation control, IEEE Trans. Power Syst., 1993, 8, (3), pp. 830839

[3] TAYLOR C.W., ERICKSON D.C., MARTIN K.E., WILSON R.E.,

VENKATASUBRAMANIAN V.: WACS-Wide-Area stability and voltage

control system: R&D and online demonstration, Proc. IEEE Energy Infrastruct.

Defense Syst., 2005, 93, (5), pp. 892906

[4] OKOU F., DESSAINT L.A., AKHRIF O.: Power systems stability

enhancement using a wide-area signals based hierarchical controller, IEEE Trans.

Power Syst., 2005, 20, (3), pp. 14651477

[5] MARQUES A.B., TARANTO G.N., FALCAO D.M.: A knowledge-based

system for supervision and control of regional voltage profile and security, IEEE

Trans. Power Syst., 2005, 20, (1), pp. 400407

[6] KUNDUR P., PASERBA J., AJJARAPU V., ANDERSSON G., BOSE A.,

CANIZARES C., ET AL.: Definition and classification of power system

stability, IEEE Trans. Power Syst., 2004, 19, (3), pp. 13871401 [IEEE/CIGRE

Joint Task Force on Stability Terms & Definitions]

[7] HILL D.J., GUO Y., LARSSON M., WANG Y.: Global hybrid control of

power systems. Preprints of Bulk Power System Dynamics and Control V, 2631

August 2001


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[15] XUE Y., CUTSEM T.V., RIBBENS-PAVELLA M.: Extended equal area

criterion justifications, generalizations, applications, IEEETrans. Power Syst.,

1989, 4, (1), pp. 4452

[16] Voltage Stability Assessment: Concepts, Practices and Tools: IEEE PES,

Power System Stability Subcommittee Special Publication, August 2002

[17] HISKENS I.A., HILL D.J.: Energy functions, transient stability and voltage

behaviour in power systems with nonlinear loads, IEEE Trans. Power Syst., 1989,

4, (4), pp. 15251533

[18] TUGLIE E.D., DICORATO M., SCALA M.L., SCARPELLINI P.: A

corrective control for angle and voltage stability enhancement on the transient

time-scale, IEEE Trans. Power Syst., 2000, 15, (4), pp. 13451353

[19] MARPLE S.L. JR., CAREY W.W.: Digital spectral analysis with

applications (Prentice-Hall, 1987)

[20] CHOW J.H.: Power system toolbox, a set of coordinated M-files for use with

MATLAB (Cherry Tree Scientific Software, 1996)

[21] LARSSON M., HILL D.J., OLSSON G.: Emergency voltage control using

search and predictive control, Int. J. Electr. Power Energy Syst., 2002, 24, pp.

121130


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8. Appendix The simple exciters have the following parameters:TR = 0.01,TA = 0.2, KEXC = 200.0,VRMAX = 7.0,VRMIN = 27.0, KEXC(MAX) = 300.0,

KEXC(MIN) = 0.0

The time constants (s) of the power system stabiliser are:T1 = .05, T2 = 0.02, T3 = 3.0, T4 = 5.4, Tw = 10, KPSS = 30.

The SVC parameters are specified as follows:TR = 0.05, KSVC = 200.0, BMAX = 3.0, BMIN = 23.0, KSVC(MAX) = 300.0,

KSVC(MIN) = 0.0

The upper and lower bounds of PSS are 150 and 0. The sensitivity matrix used is:

[ -0.2, 0.01, 0.05; 0.2, - 0.02, - 25 10-6

; 0.01, 0.005, -1.5]

coordinated stablity control

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