More on area interconnection and on models

20 março 2018, 11:00 • Luis Marcelino Ferreira

Review of previous class

Two or more areas interconnected

Modelling and what to do with models

Example of a change in DPd1 and its effect on frequency deviation -- steady-state response

Suppose KI1=0 and KI2=0 and input is a step

Beta=1/R+D as generating unit characteristic

Load as a trend and noise

Df=-Sum(DPdi)/Sum(Betai)

Advantages of interconnections

Electric network is the biggest machine ever

Trend modeled by DPref

What do we know about load -- what we assume

Convention assumes a step perturbation -- not what actually happens

Aside: Descartes and cogito ergo sum

Special cases: one is not interested in observing delta1 and delta2; one is not interested in observing Df1 and Df2; the two areas have exactly the same parameters

In addition, if all Tau’s are neglected, then one gets a second-order system -- that’s the simplest interconnected system one can get

Fig9.3 hydro turbine response to opening gate

Fig9.4a response to reduction of gate opening: immediate increase in head and power before decaying, continuous decrease in velocity

Fig9.4b response to gradual, ramp reduction of gate opening: a composition of curves

Fig9.5 Electrical analog -- the role of L in making voltage across the load to make a sudden jump

Fig9.7 Block diagram for hydro turbine with nonlinear operations (multiplication and division) -- model for analysis and simulation

FigE9.3 Block diagram for control -- linearized model

Fig9.16 Steam turbine configurations, HP, IP, LP

Effect of reheat (in Rankine cycle to gain enthalpy for the IP or LP turbine)

Eq(9.89) A simplified TF

FigE9.6 A simple linearized power system with a simple model for a steam turbine

Fig9.23 A generic model (for analysis and simulation)

Practical class #4 group of Thursday

15 março 2018, 09:30 • Célia Maria Santos Cardoso de Jesus

Resolution of problem 2 (conclusion).

One generator, one plant - two generators, one area, two areas interconnected

15 março 2018, 08:00 • Luis Marcelino Ferreira

Review of previous class

Complete block diagram for frequency regulation of a single generator

Primary control and secondary control

Gains for primary and secondary

No secondary -- what happens (with no interconnection)

High KI and instability

Low R and instability

Stability role for H

Two generators in parallel

What parallel means for our model

How many nodes?

Two R’s and two KI’s -- can take on different values

One plant or one system control area

Two areas interconnected by a transmission line

Line dynamics: what are they, can be neglected?

Algebraic model

Approximation to a linear constant model

We need angles: two integrators

We need angle difference: one integrator

An extra node

Block for line yields P12

Where does P12 go?

Overall vision of an interconnected two-area system

Extension to general multi-area system

Start discussion on how to model a network including load substations

Practical class #4 group of Wednesday

14 março 2018, 09:00 • Célia Maria Santos Cardoso de Jesus

Resolution of problem 2 (conclusion).

Frequency control: primary and secondary

13 março 2018, 11:00 • Luis Marcelino Ferreira

Review of last class, as per Summary

Minimum phase, non-minimum phase, maximum phase systems

Hydro turbine is a maximum phase system (pi at low frequencies)

Modelling: powers node, in pu

1/(2Hs) is an integrator of power

Sometimes shown model of spinning masses as K/(1+ST)

Role of sensitivity, or elasticity, of demand wrt f

Typical elasticity D, 100%

Elasticity D is a natural negative feedback of frequency

TF for turbines: hydro, steam, gas, wind

Often wind power output not controlled, non-participating

Hydro best for secondary control (ahead)

Input to turbine: valve position (for hydro and steam)

Valve opening system or governor

Hydraulics and servomotor, time constants

Models for governor

Power reference and/or speed reference

1/R, primary control

Meaning of R: view in steady-state

f=-R*Pd  negative slope

The lower the R, the lower the change in f caused by a change in PD

Df=-R*DPd

The lower the R, the higher the proportional feedback gain

Danger of instability

Role of Pref in shifting the (f,Pd) line

DPref-1/R*Df=DPd

Steady-state error or deviation

How to make error small?

An engineering solution based on PID

Secondary control or integral control, KI/s

High gain for integrator (high KI) jeopardizes stability

Fig 9.1 - functional block diagram for generation-frequency control

Fig 9.9 - schematic of a governor

How it works