progressive tripping and reconnecting block · else if frecon > 1.0 then frecon = 1.0 // order...

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2001 South First StreetChampaign, Illinois 61820+1 (217) 384.6330

2001 South First StreetChampaign, Illinois 61820+1 (217) 384.6330

Progressive Tripping and Reconnecting Block

Jamie Weber, [email protected]

217 384 6330 ext 13

mailto:[email protected]

2© 2017 PowerWorld Corporation

• The components inside the composite load model (CMPLDW, CMLD, CMPLDWNF) include “block tripping”– Voltage and Timer thresholds at which fractions of the load

are tripped (and reconnected)• Example: Drop below 0.8 pu voltage for 0.5 seconds and

trip 60% of a load– If it drops to 0.80001 pu for a few seconds nothing trips– If it drops to 0.79999 pur of 0.505 seconds 60% of load trips

• User Experience: Don’t trust results because very small changes in the output cause huge changes in results

Present Load Models


• For a single motor, then it either trips or doesn’t– It make sense to a have a relay like behavior where it either trips

or does not trip– In this situation, you will get big changes in output for small

changes in input– Acceptable and expected by engineer

• The composite load model is meant for 100s even 1000s of loads aggregated into a single model– Big changes in output for small changes in input is not acceptable

nor expected by engineer• We need to change our models

– Also must accept that we aren’t modeling an actual physical device like an under voltage relay, thermal relay, etc. anymore

Small Change in Input Big changes in Output


• Amount of load that is still connected becomes a continuous variable instead of experience discrete changes

• Use the work “reconnecting” purposefully– None of these models (CMPLDW, CMLD, etc) have

ever been modeling the “restarting” of induction motors

• Not modeling deceleration of loads after they trip• Not modeling starting torques and larger MW and Mvar

demand during start-up• Repeat: never been done for these composite models

Progressing Tripping and Reconnecting


• There are 1000s (infinitely many really) small induction motors

• Assume they are all sitting there experiencing the same terminal voltage and frequency the entire simulation– Thus we simulate only one set of differential equations even

though there are many motors– Even when the fraction goes to 0.0, our imaginary infinite

set of motors keeps running!• Power system only sees a fraction of the motors• This Fraction is what varies with tripping and

reconnecting– Presently it is block tripping and reconnecting– Proposal is to apply a continuous variation to this fraction

What does our model do?


1𝑠𝑠𝑇𝑇𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈

𝑇𝑇𝑈𝑈𝑈𝑈𝑑𝑑𝑑𝑑𝑑𝑑

𝑉𝑉𝑇𝑇𝑈𝑈

0

0

𝑇𝑇𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡

𝑉𝑉𝑡𝑡𝑖𝑖𝑡𝑡𝑖𝑖𝑡𝑡

𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹


Progressive Tripping and Reconnecting

8 input parameters• 𝑉𝑉1𝑜𝑜𝑖𝑖• 𝑉𝑉1𝑜𝑜𝑜𝑜𝑜𝑜• 𝑉𝑉2𝑜𝑜𝑖𝑖• 𝑉𝑉2𝑜𝑜𝑜𝑜𝑜𝑜• 𝐹𝐹𝑡𝑡𝑈𝑈𝑒𝑒𝑜𝑜𝑖𝑖• 𝑇𝑇𝑈𝑈𝑈𝑈𝑑𝑑𝑑𝑑𝑑𝑑• 𝑉𝑉𝑇𝑇𝑈𝑈• 𝑇𝑇𝑡𝑡𝑈𝑈𝑒𝑒𝑜𝑜𝑖𝑖

00 𝑉𝑉𝑡𝑡𝑖𝑖𝑡𝑡𝑖𝑖𝑡𝑡

1.0

𝐹𝐹𝑡𝑡𝑈𝑈𝑒𝑒𝑜𝑜𝑖𝑖 = 𝐵𝐵𝐴𝐴+𝐵𝐵

𝑉𝑉1𝑜𝑜𝑖𝑖𝑉𝑉2𝑜𝑜𝑖𝑖

𝑉𝑉1𝑜𝑜𝑜𝑜𝑜𝑜


A

B

Minimum Fraction Experienced during simulation

Feedback needed to keep track of minimum fraction during simulation 𝑉𝑉2𝑜𝑜𝑜𝑜𝑜𝑜 ≤ 𝑉𝑉1𝑜𝑜𝑜𝑜𝑜𝑜

𝑉𝑉1𝑜𝑜𝑖𝑖 ≥ 𝑉𝑉1𝑜𝑜𝑜𝑜𝑜𝑜𝑉𝑉2𝑜𝑜𝑜𝑜𝑜𝑜 ≤ 𝑉𝑉2𝑜𝑜𝑖𝑖 ≤ 𝑉𝑉1𝑜𝑜𝑖𝑖

∑

−

+

𝑑𝑑𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹

𝑑𝑑𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 < 0 𝑑𝑑𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 ≥ 0

𝑇𝑇𝑡𝑡𝑈𝑈𝑒𝑒𝑜𝑜𝑖𝑖

𝑇𝑇𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡

𝑇𝑇𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝑟𝑟𝑟𝑟𝑟𝑟


00 𝑉𝑉𝑡𝑡𝑈𝑈𝑡𝑡𝑡𝑡

1.0





A

B

Frst = Fraction of load that has tripped will restart


Tripping Characteristic

Restarting Characteristic

𝑉𝑉2𝑜𝑜𝑜𝑜𝑜𝑜 ≥ 𝑉𝑉1𝑜𝑜𝑜𝑜𝑜𝑜𝑉𝑉1𝑜𝑜𝑖𝑖 ≥ 𝑉𝑉1𝑜𝑜𝑜𝑜𝑜𝑜𝑉𝑉2𝑜𝑜𝑜𝑜𝑜𝑜 ≤ 𝑉𝑉2𝑜𝑜𝑖𝑖 ≤ 𝑉𝑉1𝑜𝑜𝑖𝑖


• 𝑉𝑉2𝑜𝑜𝑜𝑜𝑜𝑜 ≤ 𝑉𝑉1𝑜𝑜𝑜𝑜𝑜𝑜: obviously• 𝑉𝑉2𝑜𝑜𝑜𝑜𝑜𝑜 ≤ 𝑉𝑉2𝑜𝑜𝑖𝑖 ≤ 𝑉𝑉1𝑜𝑜𝑖𝑖: also obviously• 𝑉𝑉1𝑜𝑜𝑖𝑖 ≥ 𝑉𝑉1𝑜𝑜𝑜𝑜𝑜𝑜

– The picture below is possible not restricted to this

Restrictions on voltage thresholds

0.0

𝑉𝑉𝑡𝑡𝑈𝑈𝑡𝑡𝑡𝑡

1.0




A

B

Not Allowed



1.0




Simplified if𝑉𝑉2𝑜𝑜𝑜𝑜𝑜𝑜 = 𝑉𝑉2𝑜𝑜𝑖𝑖

A

B

𝐹𝐹𝐹𝐹𝑒𝑒𝐹𝐹𝑒𝑒𝑟𝑟 = 𝐵𝐵𝐴𝐴+𝐵𝐵




1.0




Simplified if𝑉𝑉2𝑜𝑜𝑜𝑜𝑜𝑜 = 𝑉𝑉2𝑜𝑜𝑖𝑖 𝐹𝐹𝑟𝑟𝑑𝑑 (𝑉𝑉1𝑜𝑜𝑜𝑜𝑜𝑜 = 𝑉𝑉1𝑜𝑜𝑖𝑖)

A

B

𝐹𝐹𝐹𝐹𝑒𝑒𝐹𝐹𝑒𝑒𝑟𝑟 = 𝐵𝐵𝐴𝐴+𝐵𝐵


Note: This is what PVD1, LDELEC and DER_A models use


User ParametersV1off, V2off, V1on, V2on, Vrst

Rules:V2off <= V1offV1on >= V1offV2off <= V2on <= V1on

Inputs to Block

DelayBlockOutput = output of Time Delay block

PresentV = measured voltage to block

Initialization section does the followingif Vrst < 0.0 then Vrst = 0.0

else if Vrst > 1.0 then Vrst = 1.0

// Order of precedence for trustworthiness of input is

// V1off, V2off, V2on, then V1on.

if V2off > V1off then V2off = V1off // decrease V2off to at least V1offif V1on < V1off then V1on = V1off // increase V1on to at least V1offif V2on < V2off then V2on = V2off // increase V2on to at least V2offif V1on < V2on then V1on = V2on // increase V1on to at least V2onVmin = V1offFracMin = 1.0

Following updated at the beginning of each Time Step// FracMin is the minimum fraction during the simulationif FracMin > DelayBlockOutput < then FracMin = DelayBlockOutputif FracMin >= 1.0 then Vmin = V1offelse if FracMin <= 0.0 then Vmin = V2offelse Vmin = V2off + FracMin *(V1off – V2off)

Following Function for calculating a new DelayBlockInputif PresentV <= Vmin then begin

if PresentV <= V2off then result = 0.0 // aaaaelse result = (PresentV – V2off)/(V1off – V2off) // bbbb red curve

endelse if (Vmin >= V1off) then result = 1.0 // cccc purple curveelse if (PresentV <= V2on) then result = FracMin // dddd light blue curveelse if (PresentV < V1on) then begin

if Vmin > V2on then tempV = Vmin else tempV = V2onresult = FracMin + Frecon*(1.0 - FracMin)*(PresentV - tempV)/(V1on – tempV) // eeee orange curve

endelse result = FracMin + Frecon*(1.0 - FracMin) // ffff green curve

Pseudo-Code to Implement

0.0PresentV

1.0

V1onV2on

V1off

V2offVmin

(Frecon)

aaaa

cccc

dddd

ffff

FracMin

0.0PresentV

1.0

V1onV2on

V1off

V2off

Vminaaaa

cccc

ffff

FracMin

Vmin > V2on


• V1off=V1on=0.8; V2off=V2on=0.2; Frecon = 0.5; Vtd=0• Trecon = Tdelay

What would these look like for Different Time Delays


• V1off=V1on=0.8; V2off=V2on=0.2; Frecon = 0.5 ; Vtd=0• Trecon = Tdelay

Different Voltage Signal

Don’t like orange and yellow reconnecting faster than blue and greenThis is because Trecon = Tdelay


• V1off=V1on=0.8; V2off=V2on=0.2; Frecon = 0.5 ; Vtd=0• Trecon = 2.0

Make Trecon its own value


• Call in CIM5_PTR– PTR = Progressive Tripping and Reconnecting

Proposed New Aggregate Induction Motor Model

MOTOR_CMP 19 Parameters

CIM5 Parameters 19 parameters

CIM5_PTR16 Parameters

Induction Motor

Ra, Ls, Lp, Lpp, Tpo, Tppo Ra, Xa, Xm, R1, X1, R2, X2 Ra, Xa, Xm, R1, X1, R2, X2Use the circuit parameters for the induction motor.

Saturation Saturation not modeled E1, SE1, E2, SE2 Saturation not modeled

Other Lfm, H, Etrq Mbase, Pmult, H, D Mbase, H, DVoltage Tripping

Vtr1, Ttr1, Ftr1, Vrc1, Trc1, Vtr2, Ttr2, Ftr2, Vrc2, Trc2

Vi, Ti, Tb V1, V2, Frecon, Tdelay, Vtd, Trecon

Starting Torque

Tnom = 1.0 hard-coded Tnom Tnom = 1.0 hard-coded


• Three ways to trip fractions of load– 2 stages of under voltage relays (tripping)– Contactor curve (tripping and reconnecting)– Thermal relay protection (tripping)

• Stalling and Restarting– Similar concern as tripping and reconnecting– We have discrete fractions that switch in and out of

the stall mode

Single Phase Air-Conditioner (LD1PAC)


Different Ways to Trip in LD1PACMotor B “unstalls”

Motor A doesnot “unstall”


• Merge the contactor and under-voltage relays using our Progressive Tripping and Reconnecting Block– No more block tripping

• Model the fraction of the load that is not stalled as a continuous variable – No more block stalling/reconnecting

Simplify Contactor and Under-Voltage Relays


• Input– Voltage signal again

• Output– Fnorm = Fraction of the LD1PAC model which is

operating in the normal mode– (1 – Fnorm) = Fraction of the LD1PAC model

which is operating in the stall mode– Continous variable transition instead of discrete

jumps

Transition of Stalling to Restarting


Progressive Stalling and Restarting Characteristic

1𝑠𝑠𝑇𝑇𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈


𝐹𝐹𝑟𝑟𝑒𝑒𝐹𝐹𝐹𝐹

00 𝑉𝑉𝑡𝑡𝑖𝑖𝑡𝑡𝑖𝑖𝑡𝑡

1.0

𝐹𝐹𝑡𝑡𝑈𝑈𝑡𝑡 = 𝐵𝐵𝐴𝐴+𝐵𝐵

𝑉𝑉𝑡𝑡𝑈𝑈𝑡𝑡1

Feedback needed to keep track of 𝐹𝐹𝑟𝑟𝑒𝑒𝐹𝐹𝐹𝐹𝑟𝑟𝑟𝑟𝑟𝑟 during simulation

∑

−

+ 𝑑𝑑𝐹𝐹𝑟𝑟𝑒𝑒𝐹𝐹𝐹𝐹

𝑑𝑑𝐹𝐹𝑟𝑟𝑒𝑒𝐹𝐹𝐹𝐹 < 0 𝑑𝑑𝐹𝐹𝑟𝑟𝑒𝑒𝐹𝐹𝐹𝐹 ≥ 0

𝑇𝑇𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈

𝐹𝐹𝑟𝑟𝑒𝑒𝐹𝐹𝐹𝐹𝑟𝑟𝑟𝑟𝑟𝑟

A

B


𝑇𝑇𝑈𝑈𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑1

𝑇𝑇𝑈𝑈𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑𝑠

𝑇𝑇𝑈𝑈𝑈𝑈𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑

𝑉𝑉𝑈𝑈𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑2

𝑇𝑇𝑈𝑈𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑2 𝑇𝑇𝑡𝑡𝑈𝑈𝑡𝑡

𝑉𝑉𝑡𝑡𝑈𝑈𝑡𝑡2𝑉𝑉𝑈𝑈𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑𝑠 𝑉𝑉𝑈𝑈𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑1

𝑇𝑇𝑈𝑈𝑡𝑡𝑈𝑈𝑡𝑡 𝑇𝑇𝑈𝑈𝑈𝑈𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑

𝑇𝑇𝑈𝑈𝑡𝑡𝑈𝑈𝑡𝑡


• LD1PAC has a simulation of 2 separate motors inside it– 1 fraction that may restart after stalling– 1 fraction that will not restart after stalling

• Why is this necessary: Thermal Protection– Current is calculated and 𝐼𝐼2𝑅𝑅 losses are assumed to contribute to

heating. Power loss is integrated to calculate heat– Fraction of motors that do not restart will see the same per unit

current throughout the simulation because they will operate on the same portion of the P/Q curve during simulation

• Problem: We want to model a gradual change of the fraction of motors stalling and restarting– Similar problem to model the restarting of AC induction motors– Changing to a continuous fraction means we are modeling an

infinite number of motors

Existing Thermal Relay in LD1PAC


• Voltage drops significantly causing 𝐹𝐹𝑟𝑟𝑒𝑒𝐹𝐹𝐹𝐹 to decrease (motors enter the stall curve)

• Voltage recovers back up, but 𝐹𝐹𝑡𝑡𝑈𝑈𝑡𝑡 is not 1.0, so a portion of the model remains in the stall mode (drawing huge currents)

• These stalled motors will remain that way even after voltage recovers

• Previously we had the thermal relay to trip those, but we don’t have that now

Can’t ignore thermal relay behavior


• Keep track of a single state indicating what percentage of all motors have not been tripped by thermal relays

• This is approximate

Approximate Solution for Thermal Relay

1.0

𝑇𝑇𝑡𝑡𝑡𝑡 𝑇𝑇𝑡𝑡𝑡𝑡

1.0

𝑇𝑇𝑡𝑡𝑡𝑡 𝑇𝑇𝑡𝑡𝑡𝑡

𝑃𝑃𝑖𝑖𝑜𝑜𝑡𝑡𝑡𝑡2 + 𝑄𝑄𝑖𝑖𝑜𝑜𝑡𝑡𝑡𝑡2

𝑉𝑉2𝑅𝑅𝑈𝑈𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑

𝑃𝑃𝑈𝑈𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑2 + 𝑄𝑄𝑈𝑈𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑2

𝑉𝑉2𝑅𝑅𝑈𝑈𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑

𝐹𝐹𝑟𝑟𝑒𝑒𝐹𝐹𝐹𝐹

1 − 𝐹𝐹𝑟𝑟𝑒𝑒𝐹𝐹𝐹𝐹

∑

+

+1

𝑠𝑠𝑇𝑇𝑡𝑡𝑡𝐾𝐾𝑡𝑡𝑡∑

0.0

Derivative <= 0Thermal relays don’t reconnect

+_


• Define– 𝑃𝑃𝑖𝑖𝑜𝑜𝑡𝑡𝑡𝑡 = yellow curve– 𝑃𝑃𝑈𝑈𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑 = green line – 𝑄𝑄𝑖𝑖𝑜𝑜𝑡𝑡𝑡𝑡 and 𝑄𝑄𝑈𝑈𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑 (similar)– 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 = output of progressive tripping and reconnecting – 𝐹𝐹𝑟𝑟𝑒𝑒𝐹𝐹𝐹𝐹 = output of fractional stalling characteristic– 𝐾𝐾𝑡𝑡𝑡 = output of thermal tripping characteristic

• Total P and Q of new model– 𝑃𝑃𝑡𝑡𝑜𝑜𝑡𝑡𝑑𝑑𝑑𝑑 = 𝐾𝐾𝑡𝑡𝑡 ∗ 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 ∗ 𝐹𝐹𝑟𝑟𝑒𝑒𝐹𝐹𝐹𝐹 ∗ 𝑃𝑃𝑖𝑖𝑜𝑜𝑡𝑡𝑡𝑡 + 1 − 𝐹𝐹𝑟𝑟𝑒𝑒𝐹𝐹𝐹𝐹 ∗ 𝑃𝑃𝑈𝑈𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑– 𝑄𝑄𝑡𝑡𝑜𝑜𝑡𝑡𝑑𝑑𝑑𝑑 = 𝐾𝐾𝑡𝑡𝑡 ∗ 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 ∗ 𝐹𝐹𝑟𝑟𝑒𝑒𝐹𝐹𝐹𝐹 ∗ 𝑄𝑄𝑖𝑖𝑜𝑜𝑡𝑡𝑡𝑡 + 1 − 𝐹𝐹𝑟𝑟𝑒𝑒𝐹𝐹𝐹𝐹 ∗ 𝑄𝑄𝑈𝑈𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑

New P/Q of LD1PAC_PTR


• Call in LD1PAC_PTR– PTR = Progressive Tripping and Reconnecting

Proposed New Aggregate Single Phase Airconditioner Model

LD1PAC_CMP 22 Parameters

LD1PAC_PTR Parameters24 Parameters

Induction Motor Lfm, CompPF, Rstall, Xstall, Tv Lfm, CompPF, Rstall, Xstall, Tv Voltage, Contactor Fuvr, uvtr1, ttr1, uvtr2, ttr2,

Vc1off, Vc2off, Vc1on, Vc2on, V1, V2, Frecon, Tdelay, Vtd, Trecon

Thermal Tripping Tth, Th1t, Th2t Tth, Th1t, Th2t

Stalling and Restarting

Vstall, Tstall, Frst, Vrst, Trst Vstall1, Tstall1, Vstall2, Tstall2, Vstall3, Tstall3, Frst, Vrst1, Vrst2, Trst


• There are two possible ways of combining low and high voltage tripping together– Fraction of devices that reconnect after low voltage

tripping is completely independent of the fraction of devices that reconnect after high voltage tripping

• Just model similar curve for high voltage tripping• FracTotal = FracLow * FracHigh

– The same devices that would reconnect after low voltage tripping are the ones that will reconnect after high voltage tripping.

• Instead implement them together into one function as follows

Integration of High and Low Voltage tripping into the same model


High and Low Voltage areIndependent


𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐿𝐿𝑒𝑒𝐿𝐿

𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐻𝐻𝑟𝑟𝐻𝐻𝑡

X 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝑇𝑇𝑒𝑒𝑡𝑡𝐹𝐹𝑟𝑟

Suspect this isn’t typical.Same devices that reconnect after a low voltage will also reconnect after high voltage


00


1.0


𝑉𝑉𝑟𝑟1𝑜𝑜𝑖𝑖𝑉𝑉𝑟𝑟2𝑜𝑜𝑖𝑖

𝑉𝑉𝑟𝑟1𝑜𝑜𝑜𝑜𝑜𝑜

𝑉𝑉𝑟𝑟2𝑜𝑜𝑜𝑜𝑜𝑜

A

B

The same devices reconnect for both High and Low Voltages

Tripping Characteristic

Restarting Characteristic𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝑟𝑟𝑟𝑟𝑟𝑟

𝑉𝑉𝑡2𝑜𝑜𝑜𝑜𝑜𝑜𝑉𝑉𝑡1𝑜𝑜𝑖𝑖

𝑉𝑉𝑡1𝑜𝑜𝑜𝑜𝑜𝑜

𝑉𝑉𝑡2𝑜𝑜𝑖𝑖


• 𝑉𝑉𝑟𝑟2𝑜𝑜𝑜𝑜𝑜𝑜 ≤ 𝑉𝑉𝑟𝑟1𝑜𝑜𝑜𝑜𝑜𝑜• 𝑉𝑉𝑟𝑟2𝑜𝑜𝑜𝑜𝑜𝑜 ≤ 𝑉𝑉𝑟𝑟2𝑜𝑜𝑖𝑖 ≤ 𝑉𝑉𝑟𝑟1𝑜𝑜𝑖𝑖• 𝑉𝑉𝑟𝑟1𝑜𝑜𝑖𝑖 ≥ 𝑉𝑉𝑟𝑟1𝑜𝑜𝑜𝑜𝑜𝑜• 𝑉𝑉h2𝑜𝑜𝑜𝑜𝑜𝑜 ≥ 𝑉𝑉h1𝑜𝑜𝑜𝑜𝑜𝑜• 𝑉𝑉h2𝑜𝑜𝑜𝑜𝑜𝑜 ≥ 𝑉𝑉h2𝑜𝑜𝑖𝑖 ≥ 𝑉𝑉h1𝑜𝑜𝑖𝑖• 𝑉𝑉h1𝑜𝑜𝑖𝑖 ≤ 𝑉𝑉h1𝑜𝑜𝑜𝑜𝑜𝑜• 𝑉𝑉𝑉1off ≥ 𝑉𝑉𝑟𝑟1𝑜𝑜𝑜𝑜𝑜𝑜• 𝑉𝑉𝑉1o𝑖𝑖 ≥ 𝑉𝑉𝑟𝑟1𝑜𝑜n

Restrictions on voltage thresholds

Same constraints as previous

Mirror of Low constraints

Prevent Low and High from intersecting


Pseudo-Code to Implement High and Low Together

User ParametersVl1off, Vl2off, Vl1on, Vl2on, FreconVh1off, Vh2off, Vh1on, Vh2on,

Rules that if violated would be consider a modeling errorVh1off >= Vl1offVh1on >= Vl1on

Rules: Vl2off <= Vl1offVl1on >= Vl1offVl2off <= Vl2on <= Vl1onVh2off >= Vh1offVh1on <= Vh1offVh2off >= Vh2on >= Vh1on

Inputs to BlockDelayBlockOutput = output of Time Delay blockPresentV = measured voltage to block

Initialization section does the followingif Frecon < 0.0 then Frecon = 0.0else if Frecon > 1.0 then Frecon = 1.0// Order of precedence for trustworthiness of input is Vl1off, Vl2off, Vl2on, then Vl1on. if Vl2off > Vl1off then Vl2off = Vl1off // decrease Vl2off to at least Vl1offif Vl1on < Vl1off then Vl1on = Vl1off // increase Vl1on to at least Vl1offif Vl2on < Vl2off then Vl2on = Vl2off // increase Vl2on to at least Vl2offif Vl1on < Vl2on then Vl1on = Vl2on // increase Vl1on to at least Vl2on// Order of precedence for trustworthiness of input is Vh1off, Vh2off, Vh2on, then Vh1on. if Vh2off < Vh1off then Vh2off = Vh1off // increase Vh2off to at least Vh1offif Vh1on > Vh1off then Vh1on = Vh1off // decrease Vh1on to at least Vh1offif Vh2on > Vh2off then Vh2on = Vh2off // decrease Vh2on to at least Vh2offif Vh1on > Vh2on then Vh1on = Vh2on // decrease Vh1on to at least Vh2on

Vmin = Vl1offVmax = Vh1offFracMin = 1.0


Pseudo-Code to Implement High and Low Together

Following Function for calculating a new DelayBlockInput

// Track the Max Portion of Curveif PresentV <= Vmin then begin

if PresentV <= Vl2off then result = 0.0 // aaaaelse result = (PresentV – Vl2off)/(Vl1off – Vl2off) // bbbb red curve

endelse if (Vmin >= Vl1off) then result = 1.0 // cccc purple curveelse if (PresentV <= Vl2on) then result = FracMin // dddd light blue curveelse if (PresentV < Vl1on) then begin

if Vmin > Vl2on then tempV = Vmin else tempV = Vl2onresult = FracMin + Frecon*(1.0 - FracMin)*(PresentV - tempV)/(Vl1on – tempV) // eeee orange

end// Track the Max Portion of CurveElse if PresentV >= Vmax then begin

if PresentV >= Vh2off then result = 0.0 // AAAAelse result = (PresentV – Vh2off)/(Vh1off – Vh2off) // BBBB red curve

endelse if (Vmax <= Vh1off) then result = 1.0 // CCCC purple curveelse if (PresentV >= Vh2on) then result = FracMin // DDDD light blue curveelse if (PresentV > Vh1on) then begin

if Vmax < Vh2on then tempV = Vmax else tempV = Vh2onresult = FracMin + Frecon*(1.0 - FracMin)*(PresentV - tempV)/(Vh1on – tempV) // EEEE orange

end// Otherwise we end up in the middleelse result = FracMin + Frecon*(1.0 - FracMin) // FFFF green curve

0.0PresentV

1.0

Vl1onVl2on

Vl1off

Vl2offVmin

FracMin+*Frecon(1-FracMin)

aaaa

cccc

dddd

ffff

FracMin

Vh1on Vh2on

Vh1off

Vh2offVmax

AAAA

CCCC

DDDD

FFFF

FracMin

progressive tripping and reconnecting block · else if frecon > 1.0 then frecon = 1.0 // order...

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