Conservation Voltage Reduction Factor (CVRf)

CVRf is a dimensionless ratio defined as the percentage change in active power (P) consumption divided by the percentage change in service voltage (V).

• Formula: CVRf = (ΔP/P) / (ΔV/V)
• A CVRf of 0.8 means a 1% voltage reduction yields a 0.8% demand reduction.
• Values typically range from 0.5 to 1.5 depending on load composition.

The CVRf value is not a universal constant; it is highly dependent on the composition of the load being served.

• Constant Impedance Loads (Z): Incandescent lights, resistive heaters. Exhibit a CVRf near 2.0 (P ∝ V²).
• Constant Current Loads (I): Certain motor-driven applications. Exhibit a CVRf near 1.0 (P ∝ V).
• Constant Power Loads (P): Regulated power supplies, modern electronics. Exhibit a CVRf near 0.0 (no change).
• Mixed Loads: The aggregate CVRf is the weighted average of these components.

Accurate CVRf calculation requires isolating the voltage-demand relationship from other variables like weather and spontaneous load changes.

• Regression Analysis: Uses historical SCADA and AMI data to fit a statistical model, separating the voltage effect from temperature and time-of-day influences.
• Controlled Experiments (CVR ON/OFF): Alternating periods of normal voltage and reduced voltage on a feeder to directly measure the difference in demand.
• Comparison Groups: Using a similar, non-regulated feeder as a baseline to subtract background load variations from the test feeder.

CVRf is the critical parameter for validating Conservation Voltage Reduction (CVR) as a cost-effective demand-side management resource.

• Demand Forecasting: A known CVRf allows grid operators to predict the exact MW reduction from a planned voltage decrease.
• VVO Optimization: Advanced VVO engines use real-time CVRf estimates to decide if lowering voltage is more efficient than switching capacitors to reduce losses.
• Regulatory Credit: Utilities must prove a stable, verifiable CVRf to receive energy efficiency credits from public utility commissions.

High penetration of Distributed Energy Resources (DERs) like rooftop solar and smart inverters significantly complicates CVRf measurement.

• Behind-the-Meter Generation: Net load measured at the meter is reduced by local solar production, masking the true voltage response of the gross load.
• Smart Inverter Modes: Inverters operating in Volt-VAR or Volt-Watt modes autonomously inject or absorb reactive power, altering the feeder's voltage profile independently of the substation LTC.
• Dynamic CVRf: The effective CVRf becomes a time-varying function, requiring continuous, high-resolution estimation rather than a static annual value.

While often used interchangeably, a distinction exists between the theoretical load model and the measured CVRf.

• Load Sensitivity (n): The theoretical exponent in the exponential load model P = P₀(V/V₀)^n. It describes the physical response of a device.
• CVRf: The empirically measured factor, which includes the effects of voltage regulators, line drop compensation, and feeder impedance.
• A measured CVRf may differ from the pure load sensitivity because a voltage reduction at the substation does not translate to an equal percentage reduction at every customer meter due to distribution line voltage drop.

The foundational demand-side management strategy that CVRf quantifies. CVR intentionally lowers service voltage to the lower bound of the ANSI C84.1 allowable range (e.g., from 120V to 114V on a 120V base) to reduce energy consumption without requiring customer action.

• Mechanism: Exploits the voltage-dependent nature of loads
• Constant Impedance Loads: Power demand reduces quadratically with voltage (P ∝ V²)
• Constant Power Loads: Electronic loads with regulated power supplies show near-zero reduction
• CVRf directly measures the aggregate mix of these load types on a feeder

The mathematical foundation for predicting CVRf. Load models decompose total demand into three components using ZIP coefficients:

• Z (Constant Impedance): P ∝ V² — resistive loads like incandescent lighting
• I (Constant Current): P ∝ V¹ — certain motors and fluorescent ballasts
• P (Constant Power): P ∝ V⁰ — switch-mode power supplies, modern electronics

CVRf ≈ 2 × Z% + 1 × I% + 0 × P%

A feeder with 60% constant impedance, 20% constant current, and 20% constant power yields a theoretical CVRf of approximately 1.4.

The algorithmic engine that provides the voltage visibility required to calculate CVRf accurately. A DSE processes redundant, noisy, and asynchronous sensor data to compute the most probable steady-state voltage phasors for every node in a distribution feeder.

• Without DSE: CVRf relies on sparse AMI endpoint measurements, introducing estimation error
• With DSE: Full feeder observability enables precise calculation of voltage reduction magnitude at every load point
• Enables time-series CVRf calculation that tracks how the factor evolves with changing load composition throughout the day

The primary data source for empirical CVRf measurement. AMI provides granular voltage and energy consumption data from customer endpoints at intervals of 15, 30, or 60 minutes.

• CVRf calculation methods:
  • Regression-based: Fit a linear model of ΔP% vs. ΔV% over multiple time periods
  • Day-on/Day-off: Compare consumption on days with CVR enabled vs. disabled
  • Pre/Post comparison: Analyze baseline vs. post-deployment consumption
• AMI data quality directly impacts CVRf accuracy — voltage measurement errors propagate to factor estimates

A distributed resource that complicates CVRf measurement. Per IEEE 1547-2018, smart inverters autonomously inject or absorb reactive power based on terminal voltage using a piecewise linear Volt-VAR curve.

• Interaction with CVR: Inverter reactive power injection locally boosts voltage, potentially counteracting CVR voltage reduction
• CVRf must be calculated net of inverter compensation effects
• Volt-Watt mode (curtailing active power at high voltage) further alters the apparent CVRf by changing the load composition seen at the substation
• Modern CVRf analysis requires coordinating inverter settings with regulator controls to isolate the true load response