Load Flow Calculation

This calculation determines the voltage drop of a secondary circuit. The following algorithm is used to compute the voltage at each bus (e.g., service point) and the power flow through each conductor in the circuit. All quantities are modeled by double precision complex numbers.

Load Initialization for Points Imported From ArcFM: Designer allows the user to select a feature on the map, right-click it and select Secondary Circuit Analysis. In this case, the analysis calculator determines the initial load estimate for all service points connected to the selected feature by multiplying the following values:

  • ServiceCurrentRating: value obtained from the service point feature in Designer.

  • SecondaryCircuitBaseVolts: value obtained from the Registry: HKEY_CURRENT_USER\Software\Miner and Miner\Designer8\Secondary Circuit Analysis\SecondaryCircuitBaseVolts. This value specifies the nominal consumer voltage of the secondary circuit, and is used to convert the service's load current to units of kVA as reported in the Properties dialog.

  • ServiceLoadDemandFactor: value obtained from the Registry: HKEY_CURRENT_USER\Software\Miner and Miner\Designer8\Secondary Circuit Analysis\ServiceLoadDemandFactor. This value corresponds to the Scale Multiplier field in the Service Point Properties dialog. This Registry value may NOT be changed by modifying the Properties dialog. It must be changed in the registry.

Inputs:

Total apparent load Li at each service bus i. Value input on the Service Point Properties dialog (see image below).

Power factor PFi of the load at each service bus i. Value input on the Service Point Properties dialog (see image below).

Impedance Zj for each conductor segment j. This value is determined by the type of conductor selected on the Conductor Properties dialog.

TIP: This is the sum of the impedances for the neutral and the phase conductor.

Transformer impedance ZXFR. This value is input on the Transformer Properties dialog.

Per unit voltage Vo at the transformer primary bus (e.g., normalized to the nominal secondary circuit voltage). This value is input on the Transformer Properties dialog.

Outputs:

Voltage Vi at each bus i in the secondary circuit. This value may be found in the Voltage field on the Service Point Properties dialog (see image below).

Magnitude of power |Sj| and current |Ij| flowing through each conductor j. This value may be found in the Load Power Factor field on the Conductor Properties dialog.

Magnitude of total power |S| delivered to all loads on the circuit. This value may be found in the Load Power Factor field on the Transformer Properties dialog.

The figure below illustrates the Load Flow calculation utilizes the values highlighted in the red. The Voltage output is displayed in the Voltage field (highlighted in blue)

Algorithm:

  1. Compute the complex load Si at each service bus i as   

    where Li is the total apparent load and PFi the power factor reported for the service, and 

  2. Initialize each bus voltage Vi to the infinite bus voltage value Vo.

  3. Compute load current flow ILOADi into each service bus as   

    where * is the complex conjugate operator.

  4. Compute the complex current flow ICNDj through each conductor j as the sum of all load currents into service buses that are downstream of the conductor. Compute the current flow IXFR through the transformer as the sum of all load currents in the circuit.

  5. Compute the end-to-end voltage drop ?Vj in each conductor j as  

     ?Vj= ICNDj Zj Where Zj is the sum of the impedances of the neutral and phase conductors for the given segment j.

  6. Compute the voltage drop in the transformer as the product of the total circuit load current and the transformer impedance.

  7. Revise each bus voltage Vi in the circuit by subtracting from it: (a) the sum of the end-to-end voltage drops ?Vj for all conductors on the path connecting bus i to the transformer primary bus, and (b) the voltage drop in the transformer itself.

  8. Repeat from step 3, until the maximum change made to any bus voltage in step 7 is less than 1%. (If the change to any bus voltage is ever more than 20% then halt the iterations and issue a warning that the model may be unstable.)

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