1

Particle Swarm Optimization for

Voltage Stability Analysis

Dinesh Rangana Gurusinghe University of Manitoba, Canada

Weerakorn Ongsakul Asian Institute of Technolgy, Thailand

Electrical Power and Energy Conference 2012

Resilient Green Energy Systems for a Sustainable Society

October 12, 2012

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Outline

• Introduction

• Objectives

• Concept of Particle Swarm Optimization (PSO)

• Methodology

• Results and Discussion

• Conclusion and Recommendations

• Areas for Improvements

3

Introduction

• Voltage collapse point (VCP) : following a disturbance there is a

time where power system voltages become uncontrollable and it

is known as VCP

• An effective approach to determine VCP greatly assists planning

and operation of power system

• Already establish methods, such as Multiple Power Flow (MPF)

and Continuation Power Flow (CPF) methods provides the

accurate VCP but relatively more time consuming as they

engaged with several power flow computations

• But effective optimization approaches can furnish the Optimal

Operating Condition (OOC) with adequate accuracy but less

computation effort

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Objectives

The primary objective of the research is to introduce accurate,

but less time consuming PSO based novel approach to find

VCP in power system.

1. To develop an effective PSO based approach for determining

the VCP of power systems

2. To apply the proposed approach for analysing diverse

applications of VSA

3. To compare the effectiveness of the proposed approach

including different versions of PSO to CPF method and

eigenvalue analysis

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Concept of Particle Swarm Optimization (PSO)

II IV

I

III

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PSO Algorithm

Initialize Particles

Evaluate Particles’ Fitness

Update Particles

iter=iter+1

iter<iter_max

Stop

Yes

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Methodology – Outlined Flow Chart

Determine the VCP point using

different versions of PSO, namely,

Basic PSO, TVIW and TVAC

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Methodology – Problem Formulation

• Objective Function

• At the VCP point, active and reactive power at all load buses are

maximized

• In the study, active power at a random load bus is selected as the

objective function

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Methodology – Problem Formulation (Cont…)

• Constraints

• The constraint related to the power factor at PQ buses

• The constraint related to the definite direction of power increase at

PQ buses (It is assumed that bus 1 is selected as the objective bus)

• The constraint related to the constant active power generation at PV

buses

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Methodology – Problem Formulation (Cont…)

• Constraints – Cont…

• The constraint related to reactive power limit of the PV buses and

the slack bus

• The constraint related to active power limit of the PV buses and the

slack bus

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Methodology – PSO

• Number of particles is set as d and each particle should have attributes

of voltage magnitudes of PQ buses and phase angles of both PQ and

PV buses

• Phase angles are randomly initialized in such a way that initialized

values should be lied within ±100 and voltage magnitudes for PQ buses

are initialized according to the modified constraint equation,

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Methodology – PSO (Cont…)

• Active power adjustments (PV buses PQ buses except selected load

bus) to satisfy equality constraints,

• For PV buses if

• For PV buses if

• In PQ buses, phase angle should be adjusted in opposite way

• The phase angle adjustment process should be continued until the

residuals of active power differences within the specified accuracy limit.

i.e.

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Methodology – PSO (Cont…)

• Particles can be represented as,

or

• The velocity vectors corresponding to the particles are randomly

initiated as represented as

• Generator reactive power limits can be handled with a Penalty function

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Methodology – PSO Method (Cont…)

• Adjust voltage magnitudes of generation buses according to reactive

power injection,

• Adjust voltage magnitudes of voltage compensation buses according to

reactive power injection,

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Methodology – PSO Method (Cont…)

• The best previous position of a particle is recorded and represented as,

• The best among all particles in the group so far, it is represented as,

• The particle positions are updated according to the velocity equation as,

• The new position of the particle can be obtained as,

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Methodology – PSO Method (Cont…)

• In Basic PSO, all four parameters of the velocity equation are fixed

• In TVIW PSO,

• In TVAC PSO,

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Test Results

Values for Tuning Parameters of Proposed PSO Versions

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Test Results

There are four test cases, specifically,

• Determination the SNB point

• considering reactive power limits of generators

• optimal operating condition (OOC) considering both active and reactive power limits of generators

• Diverse applications of voltage stability analysis under optimal operating condition

• OOC under (N-1) contingency criterion

• OOC with a voltage compensation devices

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NEW ANURADHAPURA

MAHO

HORANA

AMBALANGODA

PANNALA

ATURUGIRIYA

SAPUGASKANDA

PANNIPITIYA

ORUWALA

BIYAGAMA

VEYANGODA

MATUGAMA

KELANITISSA

COL-F

COL-E

COL-C

KELANITISSA

RATMALANA

KOLONNAWA

PANADURA

DEHIWALA

SRI J'PURA

KERAWALAPITIYA

KATUNAYAKE

KOTUGODA

BOLAWATTA

ANIYAKANDA

LAKDANAWI

ATURUGIRIYA

ORUWALA

SRI J'PURA

DEHIWALA

RATMALANA

COL-A

PANNIPITIYA

KHD

COL-I

KOLONNAWA

MADAMPE

NOROCHCHOLAI

PUTTALAM

RATNAPURA

MATARA

KUKULE

DENIYAYA

HAMBANTOTA

SAMANALAWEWA

UPPER KOTMALE

WIMALASURENDRA

KOTMALE

SEETHAWAKA

POLPITIYA

KOSGAMA

LAXAPANA

CANYON

LAXAPANA

NEW

KIRIBATHKUMBURA

THULHIRIYA

N'ELIYA

BALANGODA

BADULLA

RANDENIGALA

VICTORIA

PALLEKELE

RANTEMBE

KURUNEGALA

HABARANA

BOWATENNA

UKUWELA

NAULA

POLONNARUWA

MONARAGALA

INGINIYAGALA

AMPARA

PADDIRIPPU

VALACHCHANAI

CHUNNAKAM

KERAWALAPITIYA

BIYAGAMAKELANIYAS'KANDA

ANIYAKANDA

KOTUGODA

220/132 kV Sub Station

Thermal Power Station

Hydro Power Station

132kV GS

KAPPALTURAI

ANURADHAPURA

VAVUNIA

KILINOCHCHI

220kV Line

132kV : Line

132kV : Underground Cable

BEDDEGAMA

GALLE

MAHIYANGANA

NEW HABARANA

TRINCOMALEE PS

TRINCOMALEE

NEW CHILAW

BELIATTA

WELIGAMA

MORATUWA

KEGALLE

PILIYANDALA

COL-B

COL-K

KIRINDIWELA

KADAWATHA

ARANGALA

Test Results : Power System of Sri Lanka (182 buses)

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• 1 : Considering Reactive Power Limit of Generators

Test Results : Power System of SL (Cont…)

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• 2 : Optimal Operating Condition with Generator Limits

Test Results : Power System of SL (Cont…)

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• 3 : OOC under (N-1) Contingency Criterion

Test Results : Power System of SL (Cont…)

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• 3 : OOC under (N-1) Contingency Criterion (Cont…)

Test Results : Power System of SL (Cont…)

0.54

0.56

0.58

0.60

0.62

0.64

0.66

0.68

Base 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52

Contingency

Loa

ding

Fac

tor,

λc

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• 4 : OOC with an installation of 100MVar SVC at bus 45 (JPURA_3)

Test Results : Power System of SL (Cont…)

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• Summary results of Test System

Test Results : Power System of SL (Cont…)

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• The study introduces a new optimization approach, which directly calculates the VCP without several power flow computations by PSO

• The effectiveness of the proposed approach has been tested on the power system of Sri Lanka. Test results are evaluated with the CPF method and the optimality is verified by eigenvalue analysis

• Results confirms that the proposed PSO based approach is very valuable as it produces accurate, technically feasible, optimal solution for the 182-bus power system of Sri Lanka

• It is recommended to install sufficient reactive power resources to most critical buses identified in (N-1) contingency criterion to enhance the VCP of the power system of Sri Lanka

Conclusion and Recommendations

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• It is important to study the behaviour of OLTC and the optimal

tap setting, which furnishes the OOC

• It is better to check the performance of the proposed PSO based

approach with different types of voltage compensators other than

capacitors and SVC

• The study is limited to Basic PSO, TVIW PSO, and TVAC PSO

and they do not show a significant difference. However, it is vital

to consider other types of PSO versions

Areas for Improvements

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Thank You and

Questions?

Acknowledgement

The Royal Thai Government

(HM Queen Scholarship Program)