power stem dynamics

8/2/2019 Power Stem Dynamics

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K.R.Padiyar I.I.Sc.1

POWER SYSTEM DYNAMICS

K.R.Padiyar, I.I.Sc.


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OBJECTIVES

To discuss importance of System Dynamicsin Power System Operation and Control

To present historical development of PSD

To present new results in-

Transient (Structure Preserving) Energy

Functions and its applications for on-linedetection of LOS and discrete control

Phenomenon of Strong Resonance


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Why Study Power System Dynamics

In steady state, for a specified networkconfiguration, a system supplies power (P)and reactive power (Q) at load nodes byadjusting generations. We say the system isin equilibrium.

As load/generation change and/or networkchange, the equilibrium point changes.

Can we assume that the transition is smoothor reasonably fast?


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Why Study Power System Dynamics

It is possible that the system loses stability (unable

to reach the desired equilibrium)

The system controls are complex and diverse (e.g.voltage and frequency control)

Some controls are fast , some are slow. It isnecessary to ensure coordination for improved

system performance.

System stability can be improved by special controlssuch as PSS, HVDC and FACTS controllers


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Complexities in System Operation

1. In steady state, all generators have tooperate synchronously.

2. Fast and efficient energy storage devicesare not yet available for practical use.

3. The electrical power flows at speeds

approaching that of light.NOTE: 2 and 3 imply that at any time the

generated power equals load plus losses


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Complexities

4. Most transmission lines are AC and have no

control options unless introduced usingFACTS Controllers. HVDC links are

controllable, but are limited in number.

5. The system is very large, complex and

spread over a wide geographic areaNOTE: The above implies need for

decentralized or hierarchical control


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Complexities

6. The load variations with time are notprecisely known and require forecasting.

7. There are limits on the rate of change ofgenerator output depending on the primemover characteristics.

8. Power flows in AC transmission lines arealso determined by KVL in addition toinjections. Deregulation has increaseduncertainties in power injections


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Complexities

9. The AC lines generate or consume reactive

power depending on the power flow.Reactive power control is necessary to

regulate voltages and ensure stability.

10. Loss of synchronous operation caused by

small or large disturbances leads to systembreak up and power blackouts. It is essential

to stabilize the system for robust operation


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System States


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Control Objectives

In Normal Secure State: Power/Frequency

(P/F) and Reactive Power/Voltage (Q/V)control

Insecure State: Preventive control (Infeasiblein systems with power shortages)

Emergency State: Emergency control toremove limit violations and stabilize the

system


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Control Objectives

In Extremis State: Control to cut losses and

protect the system (Note: the system hasalready separated into islands that have to

be protected to prevent further collapse)

In Restorative State: Resynchronization to

restore loads and system integrity


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Historical Development

Loss of Synchronism (LOS) due to majordisturbances (faults followed by clearing)was a major problem till fast acting circuitbreakers and AVR were introduced. This wastermed as TRANSIENT (Angle) STABILITY

The study of transient stability was performedby AC network analyzers

The classic texts by Crary and Kimbark werepublished in the fifties


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In the sixties, the systems started experiencingspontaneous, low frequency (0.2-2 Hz) oscillations

which can grow and result in LOS. The problem wastraced to fast acting excitation systems with highgain AVR. The oscillations are observed at highloading condition with long lines.

The solution was to introduce Power SystemStabilizers (PSS) with inputs from speed, frequencyor power (or a combination of speed and power).The design of PSS to damp inter-area modes can becomplex.


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In early seventies, the problem of Sub-SynchronousResonance (SSR) involving Torsional Interaction (TI)

was experienced. The torsional modes (10-50 Hz)can be negatively damped due to interactionbetween the electrical and mechanical systems.

The series capacitors can cause maximumundamping when the electrical resonance mode hasa frequency (f

e) = f

o f

m, f

mis freq. of torsional

mode. HVDC converters and FACTS controllers can also

result in SSR. However, TCSC can damp SSR.


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In late seventies, the systems ,due to

stressed transmission network and reactivepower constraints, experienced voltage

instability and collapse (although no LOS

occurs). The operation of OLTC can cause

voltage collapse. Transient voltage instability can be caused

by induction motor loads and HVDC inverters


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Transient Voltage Instability due to

Induction Motor Load


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Voltage Stability

It can be difficult to distinguish betweenvoltage stability and angle stability

Loss of synchronism can also beaccompanied by voltage collapse

Hence care needs to be taken in identifying

the nature of instability Analysis of Voltage Instability decoupled from

Angle Instability is important


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SMIB System- Swing curves


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SMIB System- Terminal voltage


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Some Facts on Voltage Stability

The simplest system that exhibits voltage

instability is Single Machine Load Bus(SMLB) system.


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Dynamics of Load Restoration


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Some Facts on Voltage Stability


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Some facts about Voltage stability


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An Interesting Example


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Region of Stability in K-T plane


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Eigenvalue Loci (SM and EM)


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Simulation Results


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Simulation Results


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Study Tools

Time domain simulation

Transient stability simulation (< 20 s)

Midterm simulation (< 5 mts)

Long term simulation

Electro-Magnetic Transient simulation

(when network transients are considered inSSR simulation)

Small signal stability analysis


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Study Tools

Frequency domain analysis (damping torque

analysis for SSR studies)

Transient Energy Function analysis for direct

stability evaluation

Bifurcation analysis (AUTO 97 software by

Doedel et al)


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Transient Energy Functions on

Structure Preserving Models


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Recent Developments in SPEF

By applying network analogy, where power is

analogous to current, frequency variation

analogous to voltage, it is possible to

represent a lossless system by a network

consisting of nonlinear inductors

(representing transmission lines) andcapacitors representing rotor inertias, excited

by current sources.


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Structure Preserving Energy Functions


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On-line Detection of LOS


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Single line diagram of 10 generator

New England system


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Angle across Series Elements for the

Critically Unstable Case


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Power Flow and rate of change of

angle for the stable and unstable cases


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A New Discrete Control Algorithm

based on Energy Function


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Control Strategy for a Two Machine

System


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Control Strategy for a Two Machine

System


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Control Strategy


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Extension to Multi-machine Systems


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Potential Energy in Multi-machine

Systems


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A Case Study of Ten Machine System


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Swing Curves and Energy Variation


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A UPFC Connected in a Line


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Optimization of Power Flow Using

UPFC


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Expressions for Max and Min Power

Flows in a Line with UPFC


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Strong Resonance Phenomenon


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Analysis of Strong Resonance


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Strong Resonance between Swing and

Exciter Modes


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Implications of Strong Resonance

The eigenvalue sensitivities are very high

near strong resonance. Methods of controller

tuning based on sensitivity information may

be unreliable.

Optimal choice of controller parameters may

result in operation near strong resonance. Detection of strong resonance is possible

using reduced order models.


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POWER SYSTEM DYNAMICS

THANK YOU

power stem dynamics

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