AC System Losses

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Summary

AC System Losses account for power dissipation in the AC electrical infrastructure between the inverter output and the point of interconnection. After AC degradation is applied (if Linear AC or Stepped AC selected), PlantPredict calculates losses in the following sequence: (1) Auxiliary Loads (DAS, cooling, tracker motors), (2) MV Transformer, (3) AC Collection System, (4) HV Equipment (transformers and transmission lines), (5) Availability Loss, and (6) Grid Limit. Both MV and HV transformers use the same quadratic loss model. AC Collection uses a quadratic (Version 12+) or flat percentage (Versions 3-11) loss model.

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Inputs

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Outputs

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Detailed Description

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Array-Level Losses

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Auxiliary Load Losses

Auxiliary loads are deducted from the degraded AC power output before transformer losses: $$P_{aux,out} = P_{AC,in} - L_{DAS} - L_{cooling} - L_{tracker}$$ where:

• $L_{DAS}$ is the data acquisition system load (constant when energized)
• $L_{cooling}$ is the inverter/equipment cooling load (applied when power output is positive)
• $L_{tracker}$ is the tracker motor load (applied when power output is positive)

When nighttime disconnect is triggered, auxiliary loads are set to zero.

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MV Transformer Losses

The MV transformer uses a quadratic loss model (see Transformer Loss Model): $$P_{MV,out} = P_{aux,out} - L_{MV,trans}$$

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AC Collection System Losses

AC Collection System losses are calculated after the MV transformer. Version 12+ (Quadratic Loss Model): $$L_{coll} = \left| \frac{P_{MV,out}^2}{P_{AC,rated}} \times f_{coll} \right|$$ $$P_{coll,out} = P_{MV,out} - L_{coll}$$ Loss scales quadratically with power flow, representing I²R characteristic of conductor losses. Versions 3-11 (Flat Percentage Model): Daytime operation ($P_{MV,out} > 0$): $$L_{coll} = P_{MV,out} \times f_{coll}$$ $$P_{coll,out} = P_{MV,out} - L_{coll}$$ Nighttime operation ($P_{MV,out} \leq 0$): $$L_{coll} = |P_{MV,out} \times f_{coll}|$$ $$P_{coll,out} = (P_{MV,out} - L_{coll}) \times (1 + f_{coll})$$ Nighttime formula accounts for power drawn from grid to energize transformers, with losses applied both to incoming power and additional draw from grid. Array Output Aggregation: Array outputs are aggregated to block level: $$P_{block} = \sum_{arrays} P_{coll,out} \times N_{repeater}$$ Rated capacity $P_{AC,rated}$ is sum of all inverter kVA ratings in the array: $$P_{AC,rated} = \sum_{inverters} kVA_{rated} \times N_{repeater} \times 1000$$

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Plant-Level Losses

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HV Equipment Losses

Sum power from all blocks (after AC collection): $$P_{HV,in} = \sum_{blocks} P_{block} \times N_{repeater}$$ HV transformers and transmission lines are applied in user-defined ordinal sequence. HV Transformer: $$P_{out} = P_{in} - L_{HV,trans}$$ Transmission Line: $$P_{out} = P_{in} - L_{line}$$ Final HV equipment output: $$P_{HV,out} = P_{HV,in} - \sum L_{equipment}$$

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Availability Loss

$$P_{avail} = P_{HV,out} \times \frac{100 - L_{avail}}{100}$$

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Grid Limit (Capacity Limit)

If LGIA limitation enabled: $$P_{grid} = \min(P_{avail}, P_{POI})$$ $$L_{grid} = \max(0, P_{avail} - P_{POI})$$ If LGIA time series enabled, $P_{POI}$ varies by timestep.

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Transformer Loss Model

Used for both MV and HV transformers. Loss components: $$L_{NL,abs} = L_{NL} \times S_{rated}$$ $$L_{FL,abs} = (L_{NL} + L_{FL}) \times S_{rated}$$ $$L_{load} = L_{FL,abs} - L_{NL,abs}$$ Quadratic loss equation: Version 3: $$L_{trans} = \frac{1}{2 L_{load}} \left( S_{rated}^2 + 2 L_{load} P_{in} - S_{rated} \sqrt{S_{rated}^2 + 4 L_{load} (P_{in} - L_{NL,abs})} \right)$$ Requires: $L_{NL} > 0$ and $L_{FL} > 0$ Version 4+: Same formula but requires: $L_{FL} \geq 0.0001$ Nighttime disconnect: If nighttime disconnect triggered, $L_{NL,abs} = 0$ for MV transformer. Output power: $$P_{out} = P_{in} - L_{trans}$$

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Transmission Line Loss Model

Total line resistance (SI units): $$\ell_m = \frac{\ell}{0.3048}$$ $$R_{total} = \ell_m \times \frac{R_{unit}}{1000}$$ Phase current: $$I_{phase} = \frac{1}{\sqrt{3}} \times \frac{P_{in}}{V_{line} \times pf}$$ Three-phase power loss: $$L_{line} = I_{phase}^2 \times R_{total} \times \frac{3}{N_{cond}}$$ Output power: $$P_{out} = P_{in} - L_{line}$$

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HV Equipment Sequence

HV transformers and transmission lines are applied in an ordinal sequence defined by the user. Each piece of equipment is assigned a sequence number, and losses are calculated in ascending order. Voltage Selection for Transmission Lines: The voltage used for transmission line loss calculations depends on the equipment sequence:

• If the transmission line is the first piece of HV equipment (no prior HV transformer), the voltage is set to the highest secondary voltage among all MV transformers in the plant.
• If an HV transformer precedes the transmission line in the sequence, the voltage is set to the high-side (secondary) voltage of that transformer.

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References

• King, D. L., Boyson, W. E., & Kratochvil, J. A. (2004). Photovoltaic array performance model. SAND2004-3535, Sandia National Laboratories.