Appendix E: Electrical Transient & Demand Charge Modeling
This appendix details the mathematical modeling and equations used by R-THYM to simulate electric power draw, motor startup transients (inrush peak power), and the resulting utility peak demand charges.
1. Pump Electrical Power Baseline
Before estimating transient surges or start methods, R-THYM establishes the steady-state electrical power baseline (running load) at the pump's active operating point.
The hydraulic power output $P_{\text{hydraulic}}$ (in horsepower, HP) is calculated as:
$$P_{\text{hydraulic}} = \frac{Q \times H}{3960}$$Where: * $Q$ = Operating flow rate (GPM). * $H$ = Total Dynamic Head (ft). * $3960$ = Hydraulic constant conversion factor.
To find the steady-state electrical power input $P_{\text{running}}$ (in Kilowatts, kW), the hydraulic horsepower is adjusted by the pump's nameplate design efficiency and converted to electrical power:
$$P_{\text{running}} = \left( \frac{P_{\text{hydraulic}}}{\eta / 100} \right) \times 0.7457 = \left( \frac{Q \times H}{3960 \times (\eta / 100)} \right) \times 0.7457$$Where: * $\eta$ = Nameplate pump efficiency (%). * $0.7457$ = Conversion factor from HP to kW.
2. Startup Inrush & Peak Power Estimation
When a constant-speed pump transitions from a dead stop (OFF to ON), the electric motor draws a massive inrush current (locked-rotor amps) before reaching operating speed. R-THYM models this transient peak power draw ($P_{\text{startup}}$) by applying an inrush multiplier based on the motor's starting method configuration:
The inrush multipliers ($M_{\text{inrush}}$) utilized in R-THYM calculations are:
| Starting Method | Multiplier ($M_{\text{inrush}}$) | Description |
|---|---|---|
| Direct On Line (DOL) | 6.0 | Across-the-line starting. Draws full locked-rotor current. |
| Soft Starter | 3.0 | Reduced-voltage starting. Restricts voltage/current dynamically. |
| Variable Frequency Drive (VFD) | 1.2 | Variable speed acceleration. Limits start-up surge near running current. |
[!NOTE] For pumps configured as Variable Speed (under Pump Type), R-THYM automatically defaults the starting method to VFD and enforces the 1.2x multiplier.
3. Transient Speed Ramp Interpolation
During Extended Period Simulations (EPS), the time steps are coarse (typically 5 to 15 minutes). If a pump turns ON, the actual physical motor acceleration (which happens over 5–10 seconds) occurs entirely within a single simulation tick.
To prevent this short inrush peak from being completely flattened out by the coarse time step, R-THYM runs a sub-second analytical transient speed ramp calculator:
- Ramp Transition Duration ($t_{\text{transition}}$): The time required to accelerate from the starting speed ($S_{\text{start}}$) to the ending speed ($S_{\text{end}}$) is calculated using the motor's Ramp Time parameter:
Where the Ramp Rate is defined as $100\% / \text{Ramp Time (sec)}$.
- Substep Evaluation: The transition window is divided into $0.25$-second steps. The engine calculates the motor's instantaneous speed and uses the pump's head/flow curves to evaluate the electrical power at each interval. The absolute maximum power resolved during these sub-steps is stored as the pump's Peak Power ($P_{\text{peak\_power\_kW}}$):
This peak power is captured and displayed in the live telemetry panel under the Peak Power parameter and is logged as a transient spike on telemetry charts.
4. Utility Billing & Peak Demand Charges
Most commercial water utilities bill electricity costs using a two-part tariff structure: 1. Energy Consumption Charge: Billed per kilowatt-hour (kWh) of total electricity consumed. 2. Demand Charge: Billed per kilowatt (kW) of the Peak Demand recorded during the billing period.
Peak Demand Tracking
The Utility Grid component tracks the total load of all connected electrical devices (pumps, switches, batteries, generators) at each simulation step:
$$\text{Grid Load (kW)} = \sum P_{\text{pumps}} + \sum P_{\text{battery\_charging}} - \sum P_{\text{generation}} - \sum P_{\text{battery\_discharging}}$$At each step, the Utility Grid updates its peak demand record:
$$\text{Peak Demand (kW)} = \max\left(\text{Peak Demand}, \text{Grid Load}\right)$$Because motor startups draw massive inrush current, the timing of pump start events directly drives the recorded Peak Demand. By utilizing soft starters or variable frequency drives, operators can lower the inrush multiplier $M_{\text{inrush}}$, reducing the overall peak demand and significantly lowering utility demand charges.