Transient Stability: Load Distribution Equivalent and TSDistEquivMVABase

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Each load can use a distribution equivalent in the transient stability simulation. This means that all load characteristics and load distributed generation models will be modeled at the end of a distribution transformer and feeder. The Distribution Equivalent is an independent assignment from the load characteristics and load distributed generation models.

In addition to the choice of a distribution equivalent, a specification of the MVA Base used for per unit parameters of the equivalent can be given in a few different ways. The distribution equivalent model itself has a parameter MBase which may specify this, but in addition each Load, Load Model Group, Owner, Zone, and Area has 2 fields associated with the distribution equivalent: TSDistEquiv and TSDistEquivMVABase. It is expected that the per unit distribution equivalent may be specified at an aggregate level such as a Load Model Group, owner, zone, or area. However, the MVABase assumed for those parameters for a particular load might then be specified with the load object itself.

Special Load Characteristics that have built-in Distribution Equivalents

There are also a few load models (CMPLDW, CMLD, and CLOD) that have a built-in distribution equivalent . If any of these load characteristic models end up being used by a particular load, then distributed equivalent model will be ignored.

Special Rules for when to Ignore Distribution Equivalent Models

For any load smaller than 0.001 per unit (0.1 MW when using System Base of 100 MVA), any distribution equivalent model will be ignored. Added in Version 18, build on Sept. 27, 2014.

There are options in Transient Stability Analysis Options: Power System Model which provide filters on the load record's MW, P/Q ratio, and initial per unit voltage which may cause a distribution equivalent model to be ignored. Added in Version 19, build on Sept. 14, 2016

Also in Transient Stability Analysis Options: Power System Model, there is a minimum nominal kV for transformer that can be specified. For any loads connected to a bus with a nominal voltage below this, the input term Xxf will be ignored and the transformer will be skipped in the modeling of the distribution equivalent. The other terms such as the feeder impedance (Rfdr, Xfdr) will still be used. Added in Version 20

Determining which Distribution Equivalent Models to Use

Distribution Equivalent Models may be applied to either a load, Load Model Group, owner, zone, or area. During the dynamic simulation, a particular load record will use the following priority when determining what to use as the distribution equivalent in the stability simulation.

Exception: if the Load object's TSDistEquivMVABase <> 0, that value will always be used directly even if the distribution equivalent model is obtained from one of the aggregation objects of a Load Model Group, owner, zone or area.

Note: This is different than for load characteristics which could also be applied to a Bus or the entire system).

Parameters of the distribution equivalent model

The input parameters for the distribution equivalent are as follows.

Mbase: this indicates the MVABase on which the input parameters Bss, Rfdr, Xfdr, Xxf, Rcmp, and Xcmp are specified. The value may be zero or negative and has specifal meaning in that situation. See the initializing the distribution equivalent models section below for more details on this.

Bss: Substation shunt capacitor susceptance in per unit

Rfdr: Feeder equivalent resistance in per unit

Xfdr: Feeder equivalent reactance in per unit

Fb: Fraction of feeder shunt capacitance at substation bus end

Xxf: Substation transformer reactance in per unit

Tfixhs: Transformer high side fixed tap in per unit

Tfixls: Transformer low side fixed tap in per unit

LTC: 1 for automatic tap adjustment (low side variable tap)

Tmin, Tmax, step: Minimum and maximum variable tap and step size (all in per unit)

Vmin, Vmax: Minimum and maximum low-side bus voltage

Tdel: Time delay to initiate tap adjustment, seconds

Tdelstep: Time delay between tap steps, seconds

Rcmp, Xcmp : Transformer LTC compensating resistance and reactance in per unit.

Initializing the Distribution Equivalent Models

The method used for initializing a distribution equivalent model is shown in the following image using the CMPLDW as an example. The original load is moved to the end of the distribution equivalent inside the transient stability run:

 

When calculating the parameters of the distribution equivalent the following calculations are done

  1. Determine the tempMVABase from TSDistEquivMVABase input parameters
    • If the load object has ( TSDistEquivMVABase <> 0) then tempMVABase = Load's TSDistEquivMVABase
    • Else if the aggregate level object from which the distribution equivalent model is chosen has ( TSDistEquivMVABase <> 0) then tempMVABase = Aggregate Object's TSDistEquivMVABase
    • If the tempMVABase = 0, then instead the distribution equivalent model's MBase value will be used instead.
  2. The actually Used Distribution Equivalent MVA Base is then determined based tempMVABase .
    • If (tempMVABase > 0) then UseDistEquivMVABase = tempMVABase
    • If (tempMVABase < 0) then UseDistEquivMVABase = Pinit/tempMVABase
    • If (tempMVABase = 0) then UseDistEquivMVABase = Pinit/0.8;
  3. The six impedance parameters (Bss, Rfdr, Xfdr, Xxf, Rcmp, Xcmp) of the Distribution Equivalent Type are assumed to be on this UseDistEquivMVABase and are converted the to the System MVA Base. For example, Xxf = Xxf * SystemMVABase/DistEquivMVABase.
  4. Transformer Taps and impedances are converted to the System MVA Base based on the fixed taps. (Note that the variable tab is assumed to be at the Low Side Bus).
    • Xxf = Xxf * (Tfixhs)2
    • Step = Step/Tfixhs
    • Tmin = (Tmin + Tfixls - 1)/Tfixhs
    • Tmax = (Tmax + Tfixls - 1)/Tfixhs
  5. The transformer tap ratio is assumed to be set such that the voltage at the Low Side Bus is equal to the average of Vmin and Vmax. The tap ratio is then rounded to the nearest discrete step and brought back within the Tmin - Tmax range if necessary.
  6. Using the impedances and taps now available, the Low Side Bus voltage is calculated exactly and the resulting flow on the Low Side Bus of the feeder is calculated exactly (PLS + jQLS).
  7. We now initially assume that Bf1 and Bf2 are both zero, and from this an estimate of the resulting flow reaching the Load Bus of the feeder is calculated as Pnew + jQnew and the resulting Load Bus Voltage as well.
  8. If the Load Bus voltage falls below 0.95 per unit, then the feeder impedances Rfdr and Xfdr are reduced by a factor that results in a Load Bus Voltage of 0.95 per unit. (Note: if the Low Side Bus Voltage is less than or equal to 0.95, then Rfdr and Xfdr are set to the minimum impedance values of 0.0000001 + j0.00001 and the load bus voltage is not enforced.)

The perfectly initialized voltage at the Load Bus and the values of Pnew + jQnew cannot be immediately calculated. This is because they will depend on the initialization of the transient load model that is assigned to this load record. During the initialization of the load model the resulting extra Mvar values calculated due to motor initialization will be assigned to the feeder shunt values Bf1 and Bf2 according to the parameter Fb. In the simplest case when Fb = 0, all the extra Mvars are assigned at the Load Bus (Bf2) and thus the estimate of the voltage at the Load Bus will not change. When Fb > 0 however, this means that some of the Mvars are assign to the Low Side Bus (Bf1) and this will slightly impact the calculation of the Load Bus voltage and the values of Pnew + jQnew. To accommodate the splitting of this admittance the initialization routine must iteratively perform load initialization and the allocation of the split of Bf1 and Bf2 until it converges to a consistent solution. Throughout this iteration the restriction that the Load Bus voltage not fall below 0.95 per unit must also be maintained. This is all done internally by Simulator.

 

Error Checking on Distribution Equivalent

The impedance parameters of the distribution equivalent are often given using either an MVABase <= 0 indicating that the MVABase for these impedances is a multiple of the initial power (MW) of the load. This can cause problems if the initial load has a very bad power factor. For example, a load which is 1.2 MW and 30 Mvars is going to cause trouble because the impedances will be based on an MVABase proportional to 1.2, but the 30 Mvars may then exceed the maximum steady state power transformer across the distribution equivalent. This will make it impossible to initialize the model. To detect this situation, PowerWorld Simulator does a simple validation check and will not permit the simulation to run if this validation check fails.

Validation Check: (Pinitpu^2 + Qinitpu^2)/(Vpu^2) *Rpu > Pinitpu

If this validation check is true, then the simulation is aborted and an appropriate error message is presented asking that the load Q/P ratio be fixed.