IBR power-factor, Volt-var and Volt-watt controls

Page status: self-checked control equations and examples for a local development candidate; physical controller validation remains open.

An inverter-based resource (IBR) may have both a control law and capability limits. Can a supplied point satisfy them together? Work from the declared equations and check each obligation. A solver label or reported power cannot settle that intersection.

For a first calculation, work through Check a converter operating point by hand. Its P–Q diagram and voltage phasors show the distinctions used below without requiring a package checkout.

The code examples require the local candidate identified in experiments/integration/linear-audit-candidate.json. The published integration does not provide these audit APIs. The workbook environment table gives the separate execution routes. The evaluator checks equations under the PSK-000013 boundary; it does not validate physical controller behavior or the selected objective. Its calculations do not use the native model builder or reported powers as their oracle.

Two declarations, two mathematical objects

Constant PF fixes a signed relationship between injected P and Q. Minimum PF bounds a generation-only operating envelope. Neither replaces authored P/Q/I/S capability limits.

Predict: an IBR injects P = 4 W under constant PF 0.8, with minimum PF 0.8 and q_min=-2 var. Can its controller satisfy the case simply by clipping Q to −2 var?

Use RMS phasors. Positive P and Q denote injection into the network. For each admitted ordered voltage/current pair, the audit recomputes

\[S_k=U_k\overline{I_k}=P_k+\mathrm jQ_k.\]

It does not recover current by dividing reported power by voltage. The PF audit covers two-endpoint SINGLE_PHASE, explicit-neutral FOUR_LEG, and exactly three cyclic-coil THREE_LEG connections. Constant and minimum PF are checked per branch. Volt-var and Volt-watt, separately or together, apply only to the single-pair and explicit-neutral four-leg models. In a cyclic model, coil current differs from reconstructed terminal current; the physical adequacy of the THREE_LEG convention remains unresolved.

The following JSON blocks are network-field excerpts; the runnable fixture supplies the complete bus and device data. A pure constant-PF declaration is:

"control_profile": {
  "pf": {"power_factor": {"pf": 0.8}}
}

The IBR refers to it with "control_profile":"pf". For a finite signed target $f$ satisfying $0<|f|\le1$, define

\[a=|f|,\qquad b=\sqrt{(1-a)(1+a)}.\]

The native equality and independent weighted residual are

\[\operatorname{sign}(f)aQ_k+bP_k=0,\qquad r_k^{\mathrm{constant}}= \left|\operatorname{sign}(f)aQ_k+bP_k\right|.\]

This signed target convention belongs to the declared controller, not to every data format. At positive P, positive f absorbs reactive power (negative Q), while negative f reverses that sign. Both signed unity targets require Q = 0. The equality alone also admits the signed absorption extension with negative P; it does not impose generation direction. No tangent or acos evaluation is needed, including near zero targets.

For $0<m\le1$ and $c=\sqrt{(1-m)(1+m)}$, the native constraints are

\[P_k\ge0,\qquad mQ_k\le cP_k,\qquad -mQ_k\le cP_k.\]

The corresponding independent residuals are

\[r_k^{\mathrm{generation}}=\max(0,-P_k),\quad r_k^{+}=\max(0,mQ_k-cP_k),\quad r_k^{-}=\max(0,-mQ_k-cP_k).\]

Generation residuals use W; constant and weighted reactive residuals use VA. All use the absolute SI power_tol setting. The checks use the actual injected power computed from supplied V/I, not p_max, nameplate power, available PV power or optional reported pg/qg.

Capability is an intersection

For P = 4 W and f = 0.8, the constant-PF equality gives Q = −3 var. That point also lies on the m = 0.8 minimum-PF boundary. It violates q_min=-2 by 1 var. Clipping Q to −2 at P = 4 would violate the constant-PF equality instead.

Because f = m here, the whole constant-PF ray is that boundary. In floating point, the minimum-PF verdict at any point on the ray therefore rests on power_tol, not on a margin. The converter tutorial uses f = 12/13 > m so that the ray lies strictly inside the envelope.

Native supplied-point inspection confirms the Q-cap violation at the first point. A separate fixed-P conflict attempt retains its termination, primal and raw statuses, returned point and independent audit. It is not a global infeasibility certificate. The maximum-P comparison is a bounded native recipe, not a general selected-objective or optimality check.

These are per-branch constraints. In a four-leg minimum-only fixture, ordered powers P = [1,10,10] W and Q = [3,0,0] var have aggregate PF $21/\sqrt{21^2+3^2}>0.8$. The first phase still violates its own upper envelope by 1.8 VA. Reordering the map moves that violation with its physical phase; neutral position does not create or remove a PF slot. Signed single-pair reversal preserves its power and control obligations when its current is negated.

Zero power and small coefficients

At P = Q = 0, both the equality and envelope are satisfied. A PF quotient there is undefined; the audit assigns none. At unity minimum PF, Q must be zero, and the separate P ≥ 0 row still matters: negative P with zero Q can satisfy both reactive rows while failing generation direction.

A fixed absolute weighted tolerance does not certify a PF ratio. For example, at m = $10^{-20}$, P = 0 W and Q = 1 var, the upper weighted excess is only $10^{-20}$ VA. It passes the default $10^{-6}$ VA tolerance but fails at $10^{-22}$ VA. Exact envelope membership would require Q = 0 at P = 0, yet finite-tolerance weighted checks alone do not establish that exact property. Tiny constant-PF targets have the same distinction: bounded coefficients avoid tangent overflow but do not make a fixed residual tolerance scale-free.

The independent audit evaluates the stated native constraints without division by P or apparent power. It does not substitute the existing reported-P/Q profiler's special zero-P rule or relative tolerance. These are different numerical checks with explicit obligations, not interchangeable PF certificates.

Applicability and missing evidence

Minimum PF is a separate package-owned policy in the schema's extras namespace:

"extras": {
  "bmopftools": {
    "minimum_power_factor": {
      "schema": "bmopftools.minimum_power_factor/v1",
      "ibr": {
        "i": {"pf_min": 0.8, "direction": "generation", "scope": "per_coil"}
      }
    }
  }
}

The admitted profile contains only power_factor, whose object contains only pf. The minimum-policy wrapper and per-IBR requests have exactly the fields shown above. Targets must be finite, nonzero and representable in Float64; constant targets may have either sign and minimum targets are positive. Minimum-policy applicability additionally requires full finite nonnegative p_min, and p_max if present, plus a compatible constant target $|f|\ge m$. A constant target below the requested minimum is rejected by native construction; its bounded audit reports unknown policy applicability rather than inventing a constructed constraint or a numerical feasibility failure. The point P = Q = 0 still satisfies both weighted laws even for such targets. The construction policy is therefore stricter than algebraic intersection; additional bounds would be needed to exclude that point.

Unresolved/null references, empty/extra profiles, PF/droop mixtures, malformed policies, unknown targets and unused invalid profiles remain visible as unassessed control declarations. Known V/I powers, capability checks and current incidence survive those control-only unknowns. A valid constant equality can still be evaluated when a separate minimum request is malformed. Unrelated extras namespaces or package fields remain unsupported and suppress complete network KCL/power; they are not accepted through the new policy path.

Missing required branch current or voltage leaves its control residual unknown, while known failures on other branches survive. Complete network KCL/power is suppressed when current/state contributions cannot be established. Optional P/Q reports are separate consistency checks: forging Q cannot repair a control failure computed from the supplied voltage and current.

The package-owned examples/ibr_pf_audit.jl and fixture test/data/linear_audit/ibr-pf.json supply the source-bound computational route. In the locked run, the six controlled SI/per-unit cases solve and pass their scoped audits. The fixed-P/Q-cap conflict reports LOCALLY_INFEASIBLE and its returned-point audit fails one check with zero unknowns. These are local recipe observations, without a global infeasibility or initialization guarantee. The examples include analytic points, native SI/per-unit attempts, signed/unity/zero boundaries, hard-Q capability intersection, per-coil and partial-observation witnesses, and native primal inspection. Adding constant PF plus minimum PF adds four native constraints per branch and no variables. Native helpers, role/index resolvers, control decoders and reported-power profilers are not used as the independent audit's oracle.

Filters, internal/grid-forming voltages and DC dynamics need other models. The running network contains no IBR, so its audit does not exercise these controllers; use the dedicated fixtures above.

Transfer exercise. Distinguish a constant-PF equality, a generation-only minimum envelope and an authored Q cap. Construct a per-phase violation hidden by an aggregate check, then explain what a weighted residual pass at tiny m can and cannot establish about an actual PF ratio.

Volt-var: requested graph and assumed smooth model

A Volt-var law links reactive injection to a measured voltage. Here it uses a pure volt_var profile on SINGLE_PHASE or explicit-neutral FOUR_LEG. Check the voltage monitor, static curve, Q capability and minimum-PF envelope separately. The supplied result does not reveal the solver's smoothing recipe.

State the graph and normalization first

A bounded profile has four positive, finite, strictly increasing breakpoints $x_1<x_2<x_3<x_4$ in SI volts, and q_limits=[q_absorb,q_inject] with $q_{\mathrm{absorb}}\le0\le q_{\mathrm{inject}}$. Only q_unit=VA_FRACTION and q_ref=VAR_MAX are admitted. Despite that reference label, native normalization uses each branch's s_max, not q_max, total three-phase power, available P or a measured reactive capability. Fractions alone do not establish a rating guarantee; P/Q/I/S caps remain separate.

The requested graph is constant at $q_{\mathrm{inject}}$ below $x_1$, falls linearly to zero at $x_2$, stays zero through $x_3$, falls linearly to $q_{\mathrm{absorb}}$ at $x_4$ and stays there above $x_4$. Multiplication by the branch's $S_{\max,k}$ produces its requested PWL target in var.

Predict: at U = 9 V, breakpoints [8,9,11,12] V, fractions [−0.6,0.44] and S_max=20 VA, the requested target is Q = 0. Does that establish the reactive equality imposed by a smoothed native model?

The first supported model assumption is the native user_defined softplus encoding with an explicit positive relative width $\rho$. In physical volts,

\[\epsilon=\rho\frac{x_1+x_2+x_3+x_4}{4},\qquad s_\epsilon(z)=\epsilon\log(1+\exp(z/\epsilon)).\]

The declared static smooth target is

\[\begin{aligned} Q_k^{\mathrm{model}}&=S_{\max,k}q_{\mathrm{inject}}\\ &\quad-\frac{S_{\max,k}q_{\mathrm{inject}}}{x_2-x_1} [s_\epsilon(U-x_1)-s_\epsilon(U-x_2)]\\ &\quad+\frac{S_{\max,k}q_{\mathrm{absorb}}}{x_4-x_3} [s_\epsilon(U-x_3)-s_\epsilon(U-x_4)]. \end{aligned}\]

For the prediction's point and $\rho=0.02$, $\epsilon=0.2$ V and the smoothed target is approximately 1.208 var. A supplied point on the requested Q = 0 graph fails that smooth equality, despite valid voltage/current balance. The requested graph and the smooth model are different obligations. Smoothing can change the response on either side of the zero band; no conservative-Q-cap or one-sided target guarantee is inferred.

Make the model assumption explicit

The network and supplied result do not establish the native build's global volt_var_watt_eps, softplus mode or later coefficient updates. The Julia audit therefore requires a separate declaration before assessing smooth equality:

audit_solution(net, result; volt_var_model=Dict(
    "schema" => "bmopftools.audit.volt_var_model/v1",
    "softplus" => "user_defined",
    "volt_var_watt_eps" => 0.02))

This is an unauthenticated assumption, not a recovered build certificate. A profile alone does not silently select the default native width. Omitting or malforming the declaration leaves the smooth equality unassessed while retaining known capability checks, current incidence and the requested PWL diagnostic. A recipe placed in the supplied result or a successful solver label is not used as authority. The fixed-linear API does not certify these controller assumptions.

Each numerical row exposes monitored V, the requested PWL target, assumed smooth target, smoothing width in V, target difference, base VA, VI-derived Q and an absolute var residual under power_tol. build_recipe_authenticated and live_coefficient_updates_checked remain false. Selected/reported objective and optimality flags retain the earlier boundary.

The independent evaluator derives these equations without the native curve, smoothing, role/index or profiler helpers. High-precision scalar arithmetic reduces cancellation in the declared static formula; finite coefficient and operator-argument checks refuse unsupported representation ranges. This is not a general floating-point/backend, derivative-range or convergence certificate. Builtin and Swish modes, exact-PWL build recipes and live coefficient providers remain outside this first slice. A native mode name is not interchangeable with another mathematical surrogate.

Voltage references and averaging have their own incidence

The six admitted reference values combine PN/PG/PP with PER_PHASE or AVERAGED. An omitted profile reference has the documented PN_PER_PHASE default, recorded as a default. Invalid references stay unassessed; native warning-and-fallback paths are not accepted as the authored control.

For averaged control, the monitor is the mean of the magnitudes, not the magnitude of the mean phasor. Each branch still uses its own s_max; the ratings are not averaged. An explicit IBR voltage_aggregation=AVERAGE or PER_PHASE overrides the profile's aggregation. A single pair has only one magnitude, so averaging does not create a new voltage reference. The four-leg one-phase PP fallback to PG is refused, and native THREE_LEG droop skipping is not a checked Volt-var law. The physical adequacy of the cyclic THREE_LEG model remains unresolved.

The floating-neutral witness makes the distinction visible: a single pair has PN magnitude 9 V but first-endpoint PG magnitude $\sqrt{12^2+4^2}$ V. They legitimately demand different Q. Four-leg cases test all six references, non-last neutral position, arithmetic magnitude averaging and both legacy overrides. Native supplied-primal inspections agree for those constructed floating-neutral cases. Missing one monitored phase leaves an averaged monitor unknown; no partial mean is substituted. In per-phase mode, known other phase observations and failures survive.

Hard limits and minimum PF remain intersected

The healthy single-pair point has P = 4 W and Q approximately 1.208 var under the declared smooth law. Setting q_max=0.2 var rejects the point even though its droop equality passes. Lowering actual P to 0.2 W also makes that Q violate the generation-only minimum-PF 0.8 envelope. Available power, p_max or nominal rating cannot replace that curtailed P in the minimum-PF check.

The model does not clip Q to either bound. The source-bound recipe retains native fixed-voltage Q-cap and minimum-PF conflict attempts, with termination, primal/raw status, returned points and independent audits. In the locked run, both conflict attempts report LOCALLY_INFEASIBLE; their returned audits fail two and one checks respectively with zero unknowns. Those local outcomes are not global infeasibility or unrestricted controller-feasibility certificates.

Changing a reported qg does not repair or break a control equality computed from supplied V/I; the report gets its separate consistency check. Missing current can leave the monitor and requested graph known while the Q residual stays unknown. Missing voltage/current contributions still suppress complete network KCL/power. Malformed control declarations preserve known hard-limit violations rather than dropping fields or returning zero residuals.

At zero voltage, a finite nonzero supplied current gives Q = 0. This low-voltage curve still requests approximately 8.8 var, so its equality fails. No current is recovered by dividing that target by zero voltage, and no clipping or zero-Q fallback is invented.

Computational scope

examples/ibr_volt_var_audit.jl and test/data/linear_audit/ibr-volt-var.json provide the package-owned route included by the book's source-bound companion. It compares analytic points, native SI/per-unit solves under the declared smoothing recipe, requested-PWL versus smooth points, floating-reference primal inspections, aggregation overrides and retained capability/minimum-PF conflicts. Scaling voltage and breakpoints together also checks the physical smoothing width transformation; it is not an all-asset network-equivalence claim.

The combined audit adds Volt-watt without replacing these obligations. PF/droop mixtures, unsupported references, units and topologies, filters and DC dynamics remain outside this model. A native warning that skips a declaration does not establish compliance with it.

Transfer exercise. Distinguish requested PWL response, assumed smoothed response, reported Q and actual VI-derived Q. Then change averaging or curtail P without relaxing a Q cap or minimum-PF policy, and identify which observations, model assumptions and failure evidence must be retained.

Volt-watt: a cap with a declared normalization base

Volt-var fixes Q under an assumed model; Volt-watt limits P from above. A point below the cap may comply. It need not sit on the curve, and curtailment is not an equality to available power.

Predict: a single-pair converter has Smax = 20 VA, authored p_max=10 W, scalar p_avail=1 W and actual P = 4 W. With no availability-based controller, does that scalar alone reject P = 4 W?

The candidate admits pure volt_watt profiles on the same SINGLE_PHASE and explicit-neutral FOUR_LEG domains as Volt-var. The declaration is:

"control_profile": {
  "vw": {"volt_watt": {
    "breakpoints": [9.0, 11.0], "p_limits": [0.2, 1.0],
    "p_unit": "VA_FRACTION", "p_ref": "S_MAX",
    "voltage_reference": "PN_PER_PHASE"
  }}
}

The IBR references "control_profile":"vw". Two finite positive strictly increasing knots are SI volts. Fractions are finite, nonnegative and ordered [low,high]; the audit does not invent an upper limit of one. The requested clamped graph is

\[C_{\mathrm{PWL},k}(U)=B_k\begin{cases} p_{\mathrm{high}},&U\le u_1,\\ p_{\mathrm{high}}+(p_{\mathrm{low}}-p_{\mathrm{high}}) \dfrac{U-u_1}{u_2-u_1},&u_1<U<u_2,\\ p_{\mathrm{low}},&U\ge u_2. \end{cases}\]

The default p_unit="VA_FRACTION" is the admitted unit convention. The base must be explicit and complete for its selected reference:

Missing, prefix, extra, negative or nonfinite bases remain unassessed. Native zero fallbacks for missing normalization data do not establish compliance with the intended declaration. Empty or absent p_max still means no authored P box in the injection audit; it cannot supply a P_MAX normalization base.

Requested graph, assumed smooth cap and hard box

The six PN/PG/PP per-phase/averaged monitors and legacy aggregation precedence are the same as in Volt-var. There is no partial average on missing observations and no inferred one-phase PP fallback or THREE_LEG droop. An independent static softplus cap requires:

audit_solution(net, result; volt_watt_model=Dict(
    "schema" => "bmopftools.audit.volt_watt_model/v1",
    "softplus" => "user_defined",
    "volt_var_watt_eps" => 0.02))

Let the relative width be rho, epsilon = rho times the mean of the two SI knots, and let s be the softplus hinge defined above. The assumed cap and residual are

\[\begin{aligned} C_{\epsilon,k}(U)&=B_kp_{\mathrm{high}}\\ &\quad+\frac{B_k(p_{\mathrm{low}}-p_{\mathrm{high}})}{u_2-u_1} \bigl[s_\epsilon(U-u_1)-s_\epsilon(U-u_2)\bigr],\\ r_k&=\max(0,P_k-C_{\epsilon,k}(U_k)). \end{aligned}\]

The residual has units W under absolute power_tol. The independent P comes from supplied ordered V/I. Each row retains the requested PWL cap, assumed smooth cap, physical smoothing width, selected base, observed P and effective upper cap. With a known authored p_max, that last cap is the minimum of the box and smooth curve. A malformed box leaves the intersection unknown while the independently known curve can still pass or fail. Hard lower P, Q/I/S and actual-P minimum-PF checks remain separate.

For the declaration above with base 20 VA and epsilon = 0.2 V:

At U = 9 V, P = 4 W passes below the cap. Tightening p_max to 3 W rejects that point despite a passing curve row. A separate native maximum-P comparison returns approximately 3 W under that hard box. With P_MAX and the original 10 W box, the corresponding native comparison reaches approximately 9.446 W. The comparison fixes P through an added constraint on the public power expression, preserving the original p_max; changing the box to fix dispatch would change a P_MAX-normalized model.

The recipe is an unauthenticated assumption. A result's modeled_volt_watt coefficient rows and reported cap are comparison data, not the independent oracle. Omitting or rejecting the recipe leaves smooth-cap compliance unknown while preserving requested PWL diagnostics, known boxes and current incidence. Mathematical high-precision hinge evaluation and finite-range guards do not certify backend arithmetic, derivatives or convergence. The native constructor has one global smoothing width; differing declared widths for separately used Volt-var and Volt-watt families create an unknown compatibility obligation, while preserving their individually assessed assumed equations.

Availability is an input declaration with provenance

Resolve the prediction: scalar p_avail=1 W alone does not enforce P <= 1 W. The metadata-only P = 4 W case passes both the independent audit and a controlled native solve with the 10 W box. The audit records the scalar but does not authenticate a resource fact, PV model or energy guarantee over time. Its presence also does not establish a particular augmentation recipe.

The native P_AVAILABLE divisor counts non-neutral mapped terminals. One phase-neutral pair has divisor one; one phase-to-phase SINGLE_PHASE coil has divisor two. The same scalar 12 W therefore produces bases 12 W and 6 W in those cases. At U = 9 V with the example fractions and width, P = 8 W passes the phase-neutral cap and fails the phase-to-phase cap. This is an indexing applicability observation about the candidate implementation, not a physical allocation rule inferred from coil count.

Three-phase FOUR_LEG uses divisor three even with its neutral first in the map. The scalar 12 W produces [4,4,4] W bases. An explicit augmentation can instead derive a missing p_max proportionally to s_max: ratings [20,12,10] VA give approximately [5.714,3.429,2.857] W. Scenario operations can scale availability and write new boxes subject to equipment/authored ceilings. Those are distinct transformations; this audit does not call them or invent missing P limits. Audit the resulting network and retain its transformation provenance separately. Native SI/per-unit comparisons preserve the scalar in W and divide by the local power base once.

examples/ibr_volt_watt_audit.jl and test/data/linear_audit/ibr-volt-watt.json are included by the source-bound companion. They compare all three bases in SI/per-unit, floating-reference primal points, both smooth corners, hard-box intersection, metadata-only availability and the phase-pair divisor. Malformed curves/bases, forged coefficient rows and partial observations preserve known failure evidence. PF/droop mixtures, THREE_LEG droop, unsupported native warning/fallback paths, builtin/Swish/live updates, filters/internal voltages and physical availability/DC dynamics remain outside this model.

Transfer exercise. Change a scalar availability declaration without changing an authored P box, then change the curve from S_MAX to P_AVAILABLE. Explain which cap changes. Repeat with a phase-to-phase pair and with an explicitly augmented network, retaining the distinct base, divisor and provenance.

Combined droop: intersected obligations and monitor applicability

A profile containing exactly both volt_var and volt_watt now composes the bounded single-pair and explicit-neutral four-leg audits. The two subobjects retain their own knots, fractions, reference and normalization. Volt-var imposes its assumed Q equality; Volt-watt adds its assumed P upper cap. Neither law replaces a hard capability limit or applicable minimum-PF envelope.

Predict: at fixed U = 9 V, the earlier Volt-var law requests approximately Q = 1.208 var. A P_AVAILABLE-based Volt-watt cap permits approximately 0.970 W. Can a generation-only minimum PF of 0.8 be met by curtailing P further?

For a fixed monitored state, write the assumed family responses as Q = q(U) and P <= c(U). With minimum PF m strictly between zero and one, its weighted inequalities require

\[P\ge\frac{m|q(U)|}{\sqrt{1-m^2}},\qquad P\ge0.\]

If an apparent-power cap is present and $|q(U)|\le S_{\max}$, it additionally requires

\[P\le\sqrt{S_{\max}^2-q(U)^2}.\]

The available P interval must also intersect the authored P box and c(U). If $|q(U)|>S_{\max}$, that circle cannot admit the requested Q. At m = 1, minimum PF instead requires Q = 0 and P >= 0; the divided expression above is inapplicable. These are fixed-state branch implications, not a sufficient network-feasibility test. Individual and shared-return current caps, other branches, KCL and the rest of the network still apply. The implementation checks the original weighted residuals and supplied V/I; it does not use this divided formula as its oracle or assign a PF quotient at zero power.

Resolve the prediction: Q approximately 1.208 var requires P at least approximately 1.611 W under that minimum PF. A 0.970 W upper cap cannot meet it at this voltage under the declared models. A supplied P = 0.5 W point passes both droop rows and fails the minimum-PF upper inequality. Further curtailment does not fix the reactive demand. The native fixed-P conflict attempt retains its local solver status and returned-point audit; it is not a global solver infeasibility certificate.

The companion also retains a Q-box conflict and an apparent-power-circle conflict. In the latter, s_max=4 VA reduces the Volt-var normalization target to approximately 0.242 var, while a P_MAX-normalized Volt-watt cap still admits P = 4 W. The apparent power exceeds 4 VA even though both control rows pass. The controller is not clipped to the circle. Actual P, Q and ordered current observations remain separate from reported pg/qg fields.

Separate model assumptions and partial evidence

Both earlier Julia keywords are required independently for their respective smooth-law residuals. The native build has one relative volt_var_watt_eps, so those declared relative widths must agree. The physical widths need not agree: Volt-var knots [8,9,11,12] V have mean 10 V, while Volt-watt knots [9,13] V have mean 11 V. A shared relative width 0.02 gives epsilon values 0.2 V and 0.22 V. Using one physical epsilon for both would describe a different pair of laws.

A missing or unsupported family recipe leaves that law unknown while retaining the other known law, requested-graph diagnostic, hard limits and current incidence. An unequal pair of declared relative widths adds an unknown global compatibility obligation; it does not erase the individually evaluated assumed responses. The declarations still do not authenticate an actual build or live coefficient updates.

The combined profile decoder likewise retains a known family when the other family's curve or selected normalization base is malformed. The incomplete combination and its minimum-PF applicability stay unknown; known other-family failures and electrical contributions survive. A mixture containing power_factor or extra profile fields remains unassessed. Native PF priority or a warning that skips a requested curve is not a compliance argument.

Native monitor sharing retains controller-specific inputs

Each family independently selects PN, PG or PP, and per-phase or averaged monitoring. Equal references can share native magnitude variables; different quantities need distinct observations. Sharing a static profile ID does not make two devices share voltage state, rating, availability, terminal order or local coordinate bases.

The earlier candidate's duplicate-key failure came from caching physical magnitudes by aggregation (review R2). The repaired candidate shares magnitude definitions while registering each controller's input: Volt-var PN_PER_PHASE can use individual magnitudes while Volt-watt PN_AVERAGED uses their mean. Sharing an observation does not identify the laws.

The package route examples/ibr_droop_composition_audit.jl with fixture test/data/linear_audit/ibr-droop-composition.json builds all 36 reference pairs per bounded topology. It also compares all three P bases in SI/per-unit, legacy overrides, missing recipes, capability/PF conflicts and device-specific bases. Unbalanced floating-neutral tests check individual and mean inputs and unique magnitude definitions in both coordinate systems. These repair the recorded constructor boundary; residuals still do not authenticate a build or recipe. Native objects are comparison evidence, never the independent evaluator's oracle.

Parameterized/live providers and profile caches, physical controller/filter/DC adequacy, THREE_LEG droop, selected objectives and optimality remain outside this audit.

Transfer exercise. Change one curve's voltage reference, then override averaging. Identify the changed observation, residual and build applicability. Explain why passing controls alone certify neither capability, network feasibility nor an authenticated build.