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 L_i at each service bus i. Value input on the Service Point Properties dialog (see image below).

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

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

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

Per unit voltage V_o 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 V_i 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 |S_j| and current |I_j| 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 S_i at each service bus i as   

   where L_i is the total apparent load and PF_i the power factor reported for the service, and 

2. Initialize each bus voltage V_i to the infinite bus voltage value V_o.

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

   where * is the complex conjugate operator.

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

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

    ?V_j= I_CNDj Z_j Where Z_j 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 V_i in the circuit by subtracting from it: (a) the sum of the end-to-end voltage drops ?V_j 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.)