on-line transient stability and voltage collapse ... · on-line transient stability and voltage...

On-Line Transient Stability and Voltage Collapse Prediction

Using Multi-Agent Technique

George G. Karady Ahmed A. Daoud Mansour A. Mohamed

Fellow IEEE Visiting Scholar Electrical Engineering Dept., Electrical Engineering Dept.,

Arizona State University, Tempe, AZ, USA Suez Canal University, Port Said, Egypt

©2002 Arizona State University

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ACKNOWLEDGEMENT

Authors acknowledge the support of the EPRI-DoD project.

IntroductionThe modern electric power systems is vulnerable for faults, which can produce cascading outage.The most frequent fault scenario is a short circuit initiated transient stability problem.

The transient instability can cause wide spread outages

Problem FormulationIn this study we assumed that a three-phase fault, occurs in a power system.The fault is cleared by the protection.

After fault clearance, the system may oscillate and that results in the loss of synchronism of some generator or voltage collapse.This can initiate cascading failure

The system stability can be maintained by switching off generators, but this may require load reduction in a latter state.

A feasible remedial action is the fast valving of selected generators.

This reduces the acceleration and oscillation of the generators without reduction of generation capacity.

Problem Formulation

Problem Formulation

This paper propose a method for the prediction of:

Transient instability Voltage instability

Investigate the effectiveness the fast valving as a remedial action

Multi-Agent TechniquePrediction Agent

Predict system status after fault occurrence using measured dataIf generator instability is predicted the control agent is activated.

Control AgentSelect generators for fast valvingInitiate fast valving

Generators’ rotorAngle measurements

ETMSP

Fault Occurred

Fault cleared at 0.12 sec.

Measurement of generators rotorangles & velocities

Prediction Agent(output )

System stable Control Agent(Fast Valving)

Normal Operation

NO

NO

YES

YES

Fig (1) Multi-agent technique

Prediction Agent Using Robotic Ball Catching

In recent years, fast learning algorithms were developed in the robotics area.The robot measures the coordinate and speed of a moving object and predicts its future position within milliseconds.The moving object parameters are not needed for the prediction.This algorithm is adapted to predict generator instability

Adapted Prediction Agent

The moving object in ball catching algorithm is replaced by generator rotor angle.

The vision system in robotic ball catching algorithm is replaced by measurements of rotor angle directly from generators in the power system.

Prediction Agent OperationThe generator rotor angle, after a fault is measured for a predetermined time (0.5sec)

Using this data a Coarse Tuning Algorithmpredicts the approximate rotor angle.

Using the predicted angle and measured data a Fine Tuning Algorithm improves the prediction.

Mathematical Analysis1- Coarse Tuning “Rotor angle trajectory building”

Tracker angular position is represented by angle λ and the rotor angle is represented by δ. Objective function is given by:

−+−+•− 22

f,T

)()() (T f

νωνωσνωρν

yyxxMin (1)

( ) 0T f =−+−−−−−ωνδλ

ρ and σ are weighting functions. ω, ν are the rotor and predictor velocities respectively.λ = cos (λ ), δ = cos (δ)

λ = sin (λ ), δ = sin (δ)x x

y y

Where, T is a rough estimate of the final prediction time obtained from the following equation:f

Coarse Tuning “Rotor angle trajectory building”

The minimum of the objective function is held by differentiating and put the equation equals to zero.

A third order differential equation will result in and solved forν y

0432

23

1 =+++ φνφνφνφ yyy (2)

The x- component of is given by:ν

)()()(

ωνδλδλων yy

yy

xxxx −

−−

+= (3)

If , Switch to the fine tuningTOL≤− λδ

2. Fine Tuning “Rotor angle prediction”

The fine tuning use a Taylor Series Expansion of the angular velocity

The angular velocity extrapolation is given by:

( ) ( ) ( ) ( )( )tTtTtTtT ffffpred 212212. −−+−+= ααωω

Fine tuning of the Prediction

210 tand , t,t are the last three measurements’ time

= prediction periodT f

Fine tuning of the Prediction

( ) ( ))(

)(11

010

tttt

−−

=ωωα

)()(

02

012

tt −−

=ααα

Integrating equation (4) the rotor angle is expressed by:

( )))t(tt)/2t)(t(t)/3t((α

)t(tα)/2t(α)t)((t)δ(t

02120

221

30

32

02120

21020.

−+−+−−+

−+−+−+=

TTT

TTTT

fff

ffffpred ωδ

(5)

( ) ( ))(

)(12

121

tttt

−−

=ωωα

Rotor Angle PredictionIn our investigation we used the 179-bus WSCC test system.

The rotor angle is sampled at a rate of 600 times per second. This new fast learning algorithm predicts the rotor angle 500 millisecond into the future.

The increase of the generator angle beyond a predetermined threshold is a prediction that loss of synchronism will occur.

RESULTS of the PREDICTION

Fig. (2) 29 Generators, WSCC system, rotor angles after 3-phase fault at EMERY 20 cleared at 0.12 sec.

RESULTS of the PREDICTION

Fig. (3) Actual and predicted rotor angles for generators 8, 11, 13, and 15 for duration of 2 sec.

Fig (6) Active power of generators 8, 11, 13, and 15 after 3-phase fault cleared at 0.12 second.

•The difference between electric power before and after short circuit (power mismatch) is measured (calculated) for each unstable generator.

•The fast valving is applied to the generator with maximum mismatch

Selection of Generator for FastValving

Turbine Fast Valving Control

Fig. (5) Valve stroke characteristic curve

•Upon the recognition of a potentially unstable generator fast valving is initiated •The turbine steam valve is closed to the minimal position µmin as rapidly as possible. •The valve remain in this position for a dead time of tf•The valve will reopen to an appropriate final position µinf. •The positions are calculated using the load data

CONTROL AGENTTurbine Fast Valving Control

Fast Valving Input VariablesThe pre-fault output power of generator unit in

steady state denoted by Po

The post-fault output power of each generator denoted by P

The predicted relative rotor angle of each generator unit .

CONTROL AGENTTurbine Fast Valving Control

Identification of the generators for fast valvingusing the prediction results.

Selection a generator for fast valving

Calculation of the required valve closing/opening data.

Initiation of fast valving

Study System DescriptionEach generator in the WSCC system is simulated

with detailed six-state variable representation.

The excitation system for each generator is represented by one of the WSCC excitation systems model.

The governor systems and turbines are simulated. The turbines used in the simulation are tandem compound or cross compound. The model includes fast valving.

Verification of Control Agent Operation


Fast Valving Process

• Run ETMSP pre, on, and post fault.• Obtain the generator’s power, and rotor angle• Predict the stability of generators• Identify the unstable generators.• Calculate the power mismatch of each unstable

unit.


Fast Valving ProcessCalculate the minimal valve position.Set a delay time = 0.1 secondSet the closing time of the valve = 0.25 secondsSet the dead time of the valve =0.1 secondSet the opening time = 0.95 secondsUse fast valving to stabilize the system.

RESULTS

Fig. (7) Relative rotor angle of four predicted unstable units after applying fast valving control agent.

RESULTS

Fig. (8) Mechanical and electrical power change vs. time during and after application of control agent to unit EMERY 20

RESULTS

Fig. (9) ) Speed of the four units vs. time before, during and after control agent application.

ConclusionsThe main advantage of the proposed

method are:On line prediction of instability and initiation of remedial fast valvingwithin 0.6 second after the fault.

The use of measured data.

The knowledge of detailed system parameters and status is not necessary

ConclusionsThe presented simulation results proved that the proposed multi agent method can be used online to eliminate transient stability caused outages if the generators are capable fast valving.The effectiveness of the proposed method suggests the investigation of the feasibility to install fast valving on key generators in a power system

Voltage Instability Prediction Agent

Voltage instability problem has received increased attention over the last decade because several occurrences have shown that the problem have serious consequences.Major cause of voltage instability are:

Major system breakups. Overloading of existing generation and transmission Increased use of shunt capacitor banks for reactive power compensation

Transient voltage stability is often inter-linked with transient rotor angle stability even the mechanisms are difficult to separate.


The time required for the development of voltage instability ranging from seconds to hours. The time scale of depends on the cause of the voltage instability The time scales are

Transient time scale: Electromechanical transients (e.g. generators, regulators, induction machine) and power electronics(e.g. SVC, HVDC) in the time range of seconds.Medium term time scale Discrete switching devices, such as load tap changers and excitation limiters acting at intervals of tens of seconds.Long term time scale Load recovery processes spanning several minutes.


This paper proposes a development of an on-line transient voltage instability prediction agent.A proven robotic ball catching algorithm has been modified to predict voltage instabilityThis algorithm has been used before to predict power system transient instability according to rotor angle measurements.This agent does not require any prior knowledge of network topology or configuration except for continual measurements of bus voltages.


The prediction agent monitors the variation of the voltage magnitude of each bus in the system and predicts magnitude of voltage for 500 msec in advance. This period of time is sufficient, in the transient period, to activate remedial control scheme to avoid voltage instability and/or collapse. Typical remedial actions are load shedding, reactive power compensation.

PREDICTION AGENT MATHEMATICS

The algorithm is divided into two parts: The first part is building a voltage trajectory that gives the approximate value of the expected variation of the bus voltage (increase, decrease, oscillate).When the difference between the magnitude of voltage trajectory and the actual measured value is less than a set tolerance, the algorithm converts to a pure prediction process. This prediction process uses the values obtained from the tracking process and a feedback of voltage magnitude measurements every 200 msec. The feedback period can be adjusted according to the accuracy desired.


Trajectory building algorithm

(1)

−+−+•−••••••

•

−

])()[()( 22

,tymytxmxtmt

VTVVVVVVTMIN

tt

ξλ

where, is the tracking time in sec, λ and ξ are

weighting functions,

are measured voltage derivative components in x-y plan

are tracked voltage derivative components in x-y plan

tT

mxV•

myV•

txV•

tyV•


The second equation is:

Differentiating equation (1) and after minimization the two equation is combined together, which results in:

0)( =−+−••

mtftm VVTVV

)()()(

mytymyty

mxtxmxtx VV

VVVV

VV••••

−−−

+=


The values calculated with the previous equation is compared with the measure values.

When the difference is less than the tolerance we switch to the prediction mode

The starting point of the prediction is the last obtained voltage values and the trajectory equation

TolVV tm ≤−

PREDICTION MODE

• Third order Taylor series expansion is used for the prediction equation

33

221)( predpredpredopredpred TbTbTbbTV +++=

+

+−−

+−−=

)2

)(3

(

)2

()()(

2121

223

22

12

2

tttttt

tVd

ttt

VdttVdtVb

oo

ot

tot

oot

ttotomo

PREDICTION MODE

• Third order Taylor series expansion coefficients are:

2123

22

12

21 **)( ttVdtVdtVdbt

tott

ttt ++=

)(22 21

2

032

12

2 ttVdVd

b

t

ttt

tt+

−

=3

2

03

3

t

ttVdb =

APPLICATION OF PREDICTION AGENT

Voltage instability prediction agent is a computer programThis agent is linked to network measurement agent, control agent, communication agent, etc. to form a multi-agent network that will detect and control any instability problem.The proposed algorithm was coded using MATLAB and applied on a voltage instable bus of IEEE 50 generator test systemExtended Transient Mid-Term Stability Program (ETMSP) simulated the network


A three-phase fault was applied on the line connecting between buses 58 and 87. At 335 msec after fault initiation, the fault was cleared by opening the faulted line. After clearing the fault, measurement of bus voltages indicated that bus 90 AGU1752T has an oscillating decrease of voltage. The prediction agent was applied to bus 90 AGU1752T

and voltage magnitude was predicted.Table (1) gives the constraint and measured time for the prediction time


Actual and predicted voltage magnitude for bus 90 AGU1752T


Percentage Error as a function of time

CONCLUSIONS

The results indicates that the voltage instability can be predicted with less than 10% accuracyThe advantage of the method is that knowledge of network topology or configurations is not neededThe prediction is based on the voltage magnitude measurement The voltage instability agent communicates with other agents (measurement agent) to improve its prediction.Similar prediction agent can be used to predict other parameters than voltage.

on-line transient stability and voltage collapse ... · on-line transient stability and voltage...

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