How Design Optimization Works: Methodology and Algorithms

Transformer Selection

Design Optimization selects the transformer layout (number of transformers and their geographic location) and the transformer type (size and kVA rating) that meet URD load demands in the most cost-effective manner. Design Optimization uses the following input data to select the optimal transformer type and layout:

  • Diversified peak kVA load

  • Maximum allowable transformer overload factor

  • Cost considerations

Diversified Peak kVA Load

Diversified peak kVA load considers the probability that all customers' maximum demand will not occur at the same time. The following formula is used to calculate diversified peak kVA load:

  • where:
  • kVAdiv is the total diversified peak load downstream of a point in the circuit,
  • N is the number of customers downstream of the point being considered,
  • C is the Coincidence function, which maps N onto a number in the interval (0-1], and
  • kVAi is the expected peak load for the ith customer.

kVAi can in turn be estimated for a given customer as the product of the floor area of a building and a load factor that typifies a category of customer.

Design Optimization uses the customer load profile to obtain the building floor area and peak kVA per area values. The coincidence function is used to account for the non-simultaneous maximum demand. The coincidence function is configurable; its definition is stored in the customer load profile as an array of values indexed by the number of customers (e.g. the nth value in the array gives the value of the coincidence function for n customers).

Maximum Allowable Transformer Overload Factor

After calculating the diversified peak kVA load for the design, Design Optimization selects a transformer that meets the peak kVA load demand within the established maximum allowable transformer overload factor. The maximum allowable transformer overload factor is determined by the service policy. Design Optimization chooses a transformer that satisfies the demand and the overload factor from all available transformers listed in a transformer catalog.

Refer to Transformer Selection Example to see an example of how Design Optimization selects an optimized transformer for a URD.

Conductor Selection

Design Optimization selects the optimal conductor type and layout that meet URD load demands in the most cost-effective manner using three main parameters:

  • Maximum voltage flicker

  • Maximum voltage drop

  • Cost considerations

Maximum Voltage Flicker

Design Optimization uses a voltage flicker model to calculate maximum voltage flicker. The voltage flicker circuit model is a radial model that considers single customer circuits to each service point using straight line distances to the centroid of every parcel.

The known quantities used by the circuit model to determine maximum voltage flicker include:

  1. Transformer impedance (provided by the transformer type catalog entry)

  2. Conductor length to each service point (derived from geographic data)

  3. Conductor impedance per unit length (provided in the conductor type catalog entry)

  4. Motor start load for each service point (derived from kVA plus a motor starting power factor)

  5. Maximum allowable voltage flicker (provided in the electrical policy)

Design Optimization uses these five values to calculate the impedance-per-unit-length for each service point. Using the impedance-per-unit-length values, Design Optimization then chooses a subset of conductors that satisfy the voltage flicker requirements from a master catalog of all conductor types.

The following diagram illustrates the voltage flicker circuit model:

The following algorithms are used to compute the voltage flicker:

IInrush = kVAInrush/V0

  • where V0 is the nominal secondary circuit voltage

VFlicker = IInrush [(RXFR + RPath) cos? + (XXFR + XPath) sin?]

  • where RXFR and XXFR are the transformer resistance and reactance, respectively, and RPATH and XPATH are the total resistance and reactance, respectively, of theconductor path joining bus i to the transformer secondary bus, and ? is the power angle for the motor starting current (i.e. cos? is the motor starting power factor).

Maximum Voltage Drop

The voltage drop circuit model is a radial model that considers all service point peak loads simultaneously using straight line distances to the centroid of every parcel. This model accounts for the fact that current flow to any one service point can affect the other service point voltages.

The known quantities in determining maximum voltage drop include:

  • Impedance-per-unit-length (derived from voltage flicker model)

  • Conductor length to each service point (derived from geographic data)

  • Conductor impedance (derived from conductor material catalogs)

  • Peak load of each service point (derived from?)

  • Maximum allowable voltage drop (determined by electrical policy)

The following example portrays the voltage drop circuit model:

The following algorithm is used to compute the voltage drop:

V = IRcosµ+ IXsinµ

where

  • V — is the voltage drop in a circuit
  • I — is the current flowing in a conductor
  • R — is the line resistance for one conductor, in ohms
  • X — is the line reactance for one conductor, in ohms
  • µ — is the angle whose cosine is the load power factor
  • cosµ — is the load power factor, in decimals
  • sinµ — is the load reactive factor, in decimals

Maximum Voltage Drop Percentage Calculation

This calculation determines the maximum allowable 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.

  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.)

Cost Considerations in Transformer and Conductor Selection

Design Optimization runs the previously described algorithms to select the best subset of transformers and conductors. Design Optimization also calculates transformer and conductor costs from catalog entries and will choose the least costly transformer and conductor combination from this subset.

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