Simplified energy flow model

This document outlines the Simplified Energy Flow Model, a comprehensive framework designed to predict and analyze the dynamics of energy production, storage, and consumption in solar energy systems. It captures the essence of energy movement within these systems, optimizing the balance between solar energy production, energy storage, and consumption demands. The model considers efficiencies, losses, and operational parameters to ensure accurate energy management and planning.

Note on modeling at Size.Solar

Important: Size.Solar adopts a quasi-dynamic (or semi-dynamic) modeling approach, providing a nuanced representation of energy flows over time. This enhances prediction accuracy for production, storage, and consumption patterns compared to the static Simplified Energy Flow Model, which offers foundational insights for advanced, real-world system analysis.

Overview

The Simplified Energy Flow Model is a foundational tool for engineers, designers, and energy managers to:

• Estimate net energy production under real-world conditions.
• Strategize on energy storage and utilization to improve system efficiency and reliability.
• Perform detailed cost and savings analysis for economic implications.

Incorporating elements like the Derating Factor (DF) refines adjustments for inefficiencies, offering a realistic representation of energy flows.

Net energy production

NE (Net Energy): Determines the net balance of energy production versus consumption, adjusted for system losses and inefficiencies.

$NE = (SP \times DF) - C$

Where:

• SP = Solar Production (kWh)
• DF = Derating Factor (unitless, typically < 1)
• C = Consumption (kWh)

Energy storage update

If net energy > 0 (surplus energy):

Chargeable energy (CE)

$CE = \min(\text{Storage Capacity} - \text{Current Storage}, NE \times \text{Charge Efficiency} \times DF)$

• Storage Capacity = Total system storage capacity (kWh)
• Current Storage = Present energy amount stored (kWh)
• Charge Efficiency = Charging efficiency of storage (unitless, typically < 1)

Exportable energy (EE)

$EE = NE - (CE / (\text{Charge Efficiency} \times DF))$

If net energy < 0 (energy deficit):

Drawable energy (DE)

$DE = \min(\text{Current Storage} / (\text{Discharge Efficiency} \times DF), |NE|)$

• Discharge Efficiency = Efficiency of discharging from storage (unitless, typically < 1)

Grid draw (GD)

$GD = |NE| - (DE \times \text{Discharge Efficiency} \times DF)$

Cost/savings calculation with electricity cost

Consumption cost (CC)

$CC = GD \times \text{Electricity Cost Rate} (ECR)$

• ECR = Electricity Cost Rate ($/kWh)

Export revenue (ER)

$ER = EE \times \text{Export Compensation Rate} (ECR)$

• Export Compensation Rate (ECR) = Rate at which exported energy is compensated ($/kWh)