Correcting Endogeneity Bias in Field-Measured Conservation Voltage Reduction Factors: A Common-Bus Instrumental Variable Approach for Industrial Facilities

Conservation voltage reduction (CVR) factors are usually estimated from field measurements by regressing load power on voltage. At the level of an individual industrial branch circuit, this regression is confounded, because a branch’s own current draw lowers its own bus voltage through simple Ohm’s-law feeder impedance. The naive coefficient then reflects reverse causation rather than the demand response to voltage that CVR programs are meant to quantify. This paper demonstrates the problem and tests a partial remedy using minute-resolution voltage (PT) and current/power (CT) data from 24 branch–hub pairings (23 analyzable) at three industrial facilities: a textile mill (SHIC), a metal heat-treatment plant (YC2), and a metal fabrication job shop (DSPM). All three sites are metered hierarchically, so every branch shares a common upstream (hub) bus, and the data span 63–90 days each across two non-overlapping calendar years. Naive ordinary least squares (OLS) regressions of log power on log branch voltage, with hour-of-day and day-of-week fixed effects and standard errors clustered by calendar day (residual autocorrelation remains above 0.68 at a 3 h lag, so conventional heteroskedasticity-robust errors are not adequate), produce CVR factors as extreme as −67, far outside the physically expected 0–2 range. Instrumenting each branch’s voltage with the site’s hub-bus voltage in a two-stage least squares (2SLS) design brings 5 of 13 severely biased branches within a credible magnitude bound (|β_IV| ≤ 2) across the three sites; all five, however, retain a negative sign that is physically anomalous for a passive load, so none become plausible by the strict 0-to-2 definition used throughout this paper. Properly clustered inference shows this magnitude-bound result is also precisely estimated, i.e., reliably distinguishable from zero, for only two of the five. The branches that reach the magnitude bound track each site’s hub-bus exogeneity rather than any branch-level property. At the one site with a near-exogenous hub (YC2, r = −0.07 between hub voltage and total site power), three of three severely biased branches have their magnitude brought within bound, though none precisely and all remain negative-signed. At the two sites with a substantially endogenous hub (SHIC, r = −0.57; DSPM, r = −0.71, using a same-facility proxy bus after its designated main proved unusable because its logged period did not overlap the rest of the site’s instrumentation), only 1 of 5 branches at each site has its magnitude brought within bounds, precisely (t < −6 in both cases) but still negative-signed. The same low magnitude-bounding rate recurs at a third site in a different calendar year; with only three site-level observations, we treat this as an exploratory extension of the pattern rather than an independent statistical replication. A further robustness check instruments YC2 with a second, more upstream measurement point. It fails outright: the cluster-robust first-stage F falls to 0.005–0.89 for every branch, against 3.5 × 103–2.1 × 106 for the hub used in the main design. The reason is that this alternative point sits on the far more tightly regulated side of the site’s service transformer (voltage SD ≈ 0.5% of mean) and shares little variation with the internally generated fluctuations (SD ≈ 3%) it would need to instrument. A valid instrument must share the endogenous variable’s own variation; sitting further upstream is not enough. The method requires no logged transformer tap-change event, unlike existing measurement-based CVR practice, and uses only the hierarchical metering structure already present in many industrial submetering deployments. Its contribution, however, is to bound the magnitude of a severe bias, not to restore full physical plausibility: without a ground-truth benchmark, we cannot claim the shifted estimates are closer to the true CVR factor, only that their magnitude changed and, in five of 13 cases, moved within a credible bound. The result is partial, site-conditional, persistently wrong-signed, and in most cases imprecise.