Medium Voltage Motor Stator Protection: Embedded PT100 RTDs and PTC Thermistors

Thermodynamics and Thermal Dynamics of the Stator in Medium-Voltage Motors

The thermal behavior of medium-voltage asynchronous and synchronous machines (typically from $2.3 kV$ to $13.8 kV$) is governed by the internal generation of ohmic losses ($I^2 R$), magnetic core losses in the ferromagnetic laminations (hysteresis and eddy current losses), mechanical friction and windage losses, and stray load losses. The fundamental, transient, spatially distributed heat conduction differential equation across the three-dimensional stator domain is expressed according to the Fourier-Poisson formulation:

where $\rho(\mathbf{r})$ represents the mass density of the constituent materials ($kg/m ^3$), $c_p(\mathbf{r})$ is the specific heat capacity ($J /( kg \cdot K )$), $k(\mathbf{r})$ is the orthotropic thermal conductivity tensor ($W /( m \cdot K )$), $T(\mathbf{r}, t)$ is the scalar temperature field ($K$), and $q'''(\mathbf{r}, t)$ is the volumetric heat generation rate density ($W/m ^3$).

Material Heterogeneity and Thermal Conduction Anisotropy

The medium-voltage stator exhibits a highly anisotropic composite structure. The windings consist of preformed copper bars (form-wound coils), insulated with mica paper tapes agglomerated with epoxy resins under vacuum pressure impregnation (VPI) processes. The thermal conductivity of pure copper ($k_{ Cu } \approx 380 to 400 W /( m \cdot K )$) contrasts sharply with the orthotropic conductivity of the mica-epoxy insulation package:

• Longitudinal thermal conductivity (parallel to tape layers): $k_{\parallel} \approx 0.8 to 1.2 W /( m \cdot K )$.
• Transverse thermal conductivity (perpendicular to slot groundwall insulation thickness): $k_{\perp} \approx 0.2 to 0.35 W /( m \cdot K )$.
• Silicon steel lamination stack conductivity: $k_{ lam, axial } \approx 1.5 to 4.0 W /( m \cdot K )$ across the interlaminar insulation varnish layer (C-5), versus $k_{ lam, radial/azimuthal } \approx 25 to 40 W /( m \cdot K )$ within the lamination grain plane.

This pronounced divergence in thermal conductivities establishes a steep temperature gradient across the groundwall insulation thickness. The steady-state temperature drop $\Delta T_{ aisl }$ across an insulation layer of thickness $\delta_{ aisl }$ with a surface heat flux $q''$ is quantified by the one-dimensional Fourier law:

In $6.6 kV$ or $13.8 kV$ motors, where $\delta_{ aisl }$ ranges between $1.8 mm$ and $4.5 mm$, the full-load thermal drop $\Delta T_{ aisl }$ can reach values between $15 K$ and $35 K$. Consequently, superficial temperature measurements of the magnetic core stack or the cooling air critically underestimate the internal copper conductor temperature, establishing the mandatory requirement for temperature sensors embedded directly inside the stator slot.

Stator Hotspot Location and Thermal Profiling

The winding hotspot does not develop uniformly along the stator length. Its specific spatial location depends on the ventilation circuit topology (radial, axial, symmetrical or asymmetrical axial-radial according to IEC 60034-6 and IEEE Std 620 standards). In a symmetrical cooling system with dual-end air intake and central radial discharge (IC01, IC611, or IC81W), the longitudinal conductor temperature profile $T_{ Cu }(z)$ exhibits a parabolic distribution with its absolute maximum situated at the stator axial midpoint ($z = L/2$):

where $\dot{m}$ is the coolant mass flow rate, $h_{ conv }$ is the surface convective heat transfer coefficient ($W /( m ^2\cdot K )$), and $P_{\text{ perím }}$ is the wetted perimeter exposed to the coolant flow.

Solid-State Physics and Transducer Principles: PT100 versus PTC

Stator thermal protection in medium-voltage machinery relies on two primary technologies rooted in semiconductor and transition-metal physics: platinum resistance temperature detectors (RTD PT100) and positive temperature coefficient (PTC) thermistors.

Platinum Resistance Temperature Detectors (PT100)

The PT100 transducer operates on the physical principle of conduction electron scattering caused by lattice vibrations (phonons) within high-purity platinum ($99.99\%$), microscopically characterized by Matthiessen's rule. The electrical resistivity $\rho(T)$ increases linearly across a broad temperature spectrum.

Pursuant to international standard IEC 60751 (and its counterpart ASTM E1137), the resistance-temperature relationship for platinum with a temperature coefficient $\alpha = 0.00385055 ^\circ C ^{-1}$ (DIN/IEC standard) is analytically defined by the Callendar-Van Dusen equation:

where $R_0 = 100.00 \Omega$ at $0^\circ C$, with standardized polynomial coefficients:

• A = 3.9083 \times 10^{-3} ^\circ C ^{-1}
• B = -5.7750 \times 10^{-7} ^\circ C ^{-2}
• C = -4.1830 \times 10^{-12} ^\circ C ^{-4}

The sensitivity or differential thermal variation coefficient $S_{ PT100 }(T)$ is obtained by differentiating the quadratic relationship:

At $T = 100^\circ C$, $S_{ PT100 } \approx 0.379 \Omega/^\circ C$, yielding a highly linear transfer function with a typical measurement uncertainty below $\pm 0.3 K$ for Class A elements (per IEC 60751: $\Delta T_{ tol } = \pm (0.15 + 0.002 |T|) ^\circ C$).

Positive Temperature Coefficient Thermistors (PTC)

PTC thermistors are polycrystalline doped semiconductor ceramics based on barium titanate ($BaTiO _3$). Below the Curie temperature ($T_C$), the material resides in a tetragonal ferroelectric phase exhibiting high spontaneous polarization at grain boundaries, which neutralizes interface potential traps and maintains low baseline resistivity.

When the critical temperature $T_C$ is exceeded (metallurgically engineered between $110^\circ C$ and $180^\circ C$ for Class B, Class F, or Class H electrical insulation systems), the crystal lattice undergoes a phase transition to a cubic paraelectric state. The relative permittivity $\varepsilon_r$ collapses in accordance with the Curie-Weiss law:

This dielectric collapse eliminates space-charge compensation at the grain boundaries, triggering an exponential increase in the electrostatic Schottky potential barrier height ($\Phi_b$). The macroscopic bulk resistivity $\rho(T)$ displays a steep step increase modeled by Heywang’s equation:

where $N_s$ is the grain boundary interface trap density, $N_d$ is the bulk donor concentration, $e$ is the elementary electron charge, and $k_B$ is Boltzmann's constant.

For temperatures $T < T_{ TNF } - 20 K$ (rated response temperature per DIN 44081/44082), the typical resistance of a PTC probe remains within $20 \Omega$ to $250 \Omega$. In the immediate vicinity of $T_{ TNF }$, resistance surpasses $1\,000 \Omega$ (standard alarm threshold) and exceeds $4\,000 \Omega$ at $T = T_{ TNF } + 15 K$ (mandatory trip threshold), functioning as a binary solid-state thermal switch.

Technical / Operational Parameter	RTD PT100 Sensor (IEC 60751)	PTC Thermistor Sensor (DIN 44081 / 44082)
Physical Principle	Linear resistive variation via phonon scattering in noble metal (Platinum)	Ferroelectric-to-paraelectric structural phase transition in $BaTiO _3$
Linearity Range	Excellent ($-50^\circ C$ to $+250^\circ C$, $\alpha = 0.00385$)	Extremely non-linear; step-function high-pass switching behavior
Primary Protective Relay Function	Continuous monitoring, trending, $dT/dt$ gradient calculation, ANSI 49	Catastrophic point-overtemperature fast-trip protection
Thermal Time Constant ($\tau_{63.2\%}$)	Moderate ($1.5 s$ to $5.0 s$ embedded in stator slot)	Fast ($0.5 s$ to $2.0 s$ due to reduced thermal mass)
EMI / Transient Noise Immunity	Medium-Low (requires active analog filtering and 3/4-wire topology)	High (order-of-magnitude resistance change minimizes noise sensitivity)
Typical Failure Mode	Positive resistance drift under mechanical stress, open circuit from vibration	Open circuit via ceramic substrate fracture or overvoltage degradation

Mechanical and Dielectric Integration Design of Embedded Sensors

The mechanical insertion of sensors within medium-voltage stator windings introduces physical discontinuities and localized electrostatic field concentrators inside the Class F ($155^\circ C$) or Class H ($180^\circ C$) insulation systems.

Stator Slot Installation Architecture

In compliance with IEEE Std 620, IEC 60034-11, and IEEE Std 1434 standards, three thermal sensor installation methodologies are implemented within stator cores:

1. Slot Embedded Sensor (Slot RTD - Between Coils): Standardized mandatory location for medium-voltage machines. The sensor, manufactured as a flat, rigid fiberglass-epoxy encapsulated strip (NEMA Grade G-10 or G-11) with typical dimensions of $2 mm \times 10 mm \times 150 -- 500 mm$, is inserted along the radial centerline of the slot, sandwiched between the top coil side and bottom coil side. In this interface, the sensor measures a thermally weighted temperature:
   $$T_{ sensor } \approx \frac{k_{\perp, sup } T_{ Cu,sup } + k_{\perp, inf } T_{ Cu,inf }}{k_{\perp, sup } + k_{\perp, inf }}$$
2. End-Winding Sensors (End-Winding RTD/PTC): Mechanically secured and laced with glass-fiber/Nomex cords directly onto the external groundwall insulation of the end-windings prior to the VPI process. They monitor localized thermal buildup resulting from ventilation dead-zones or negative-sequence harmonic currents ($I_2$).
3. Core Tooth Sensors (Stator Core RTDs): Embedded within precision-machined cavities in the core laminations to supervise interlaminar eddy current losses caused by degradation of the surface lamination insulation.

Galvanic Isolation, Electric Field Concentration, and Partial Discharges

The rated phase-to-ground operating voltage at the terminals of a motor with line voltage $U_n$ is defined by $V_{ ph-g } = U_n / \sqrt{3}$. For a $13.8 kV$ motor, the nominal crest voltage stress applied across the groundwall insulation is:

Sensor instrumentation signal leads operate at the ground reference potential of the protection cubicle or control room (PE, $0 V$). When a sensor is placed between coils belonging to different phases within the same slot (phase-inversion zone, where the inter-coil potential difference can reach $U_n$), the sensor dielectric barrier must simultaneously withstand full electrical potential stress and thermomechanical shear forces.

The dielectric sheath integrated into the flat slot RTD body ($t_{ sonda }$) exhibits a relative permittivity $\varepsilon_{r, sonda } \approx 4.5$, whereas the impregnated epoxy resin presents $\varepsilon_{r, epoxi } \approx 3.8$. In the event of unimpregnated microvoids ($\varepsilon_{r, aire } = 1.0$) along the coil-to-sensor interface, the normal component of the electrostatic field within the air void $E_{ aire }$ is intensified inversely proportional to permittivity:

If $E_{ aire }$ exceeds the critical breakdown strength of air ($E_{ Paschen } \approx 3.0 kV/mm$ at atmospheric pressure), high-energy Partial Discharge (PD) activity ignites. Sustained PD activity causes ionic bombardment of the sensor epoxy substrate, initiating electrical treeing degradation, dielectric puncture of the sensor sheath, and subsequent catastrophic flashover of full line voltage ($13.8 kV$) directly into the low-voltage analog input modules of numerical protection relays.

Per IEEE Std 43, IEC 60034-1, and IEC 60255-27, medium-voltage embedded sensors must incorporate integral reinforced insulation and undergo 100% factory dielectric withstand proof testing at a power-frequency voltage of not less than:

Furthermore, signal exit leads must feature a continuous tinned-copper braided shield, grounded strictly at the protective relay chassis end to safely bypass stray capacitive displacement currents.

Mathematical Modeling of the Measurement Chain and Error Compensation

High-precision RTD PT100 temperature acquisition requires complete mitigation of two metrological error mechanisms: lead-wire parasitic series resistance ($R_L$) and excitation-induced self-heating ($I_{ exc }$).

Connection Circuit Analysis: Wheatstone Bridge and Analog Signal Conditioning

The total cable run from inside the stator to the motor auxiliary junction box and onward to the central control panel often exceeds $100 m$. Utilizing standard $0.75 mm ^2$ instrumentation cable ($\rho_{ Cu,20 } \approx 0.024 \Omega/ m$), the round-trip loop resistance $2 R_L$ reaches $6.4 \Omega$, introducing an intolerable systematic offset of:

To cancel this line resistance error, multiconductor bridge and ratiometric conditioning configurations are implemented:

Three-Wire Compensation Topology

In a balanced 3-wire topology connected to a differential Analog-to-Digital Converter (ADC) using dual matched constant current sources $I_1 = I_2 = I_{ exc }$:

Assuming strict thermal and geometric symmetry between conductors ($RL1 = RL2 = R_L$):

The measured differential voltage becomes completely independent of cable length. However, if asymmetric terminal resistance develops or a differential thermal gradient occurs between cores ($\Delta R_L = |RL1 - RL2| \ne 0$), a residual error manifests:

Four-Wire Kelvin Absolute Measurement Topology

The 4-wire Kelvin configuration routes a dedicated constant excitation current $I_{ exc }$ through outer force leads (1 and 4), while potential drop is measured across inner sense leads (2 and 3) utilizing a high-impedance instrumentation stage ($Z_{ in } \ge 10 G \Omega$):

This eliminates lead resistance errors entirely, independent of lead-length imbalances or thermal gradients.

Self-Heating Error Analysis

Ohmic power dissipation within the platinum sensing element due to the continuous flow of excitation current generates internal heat that elevates the sensor temperature above the surrounding medium:

The steady-state self-heating error $\theta_{ self }$ is governed by the sensor package thermal dissipation constant $\delta_{ th }$ ($mW /^\circ C$):

For an RTD embedded in solid epoxy insulation ($\delta_{ th } \approx 2.0 mW /^\circ C$) operating at $150^\circ C$ ($R_{ PT100 } \approx 157.3 \Omega$):

• With $I_{ exc } = 5.0 mA$: $P = (5 \times 10^{-3})^2 \times 157.3 = 3.93 mW \implies \theta_{ self } = 3.93 / 2.0 \approx +1.97 K$ (unacceptable measurement bias).
• With $I_{ exc } = 1.0 mA$: $P = (1 \times 10^{-3})^2 \times 157.3 = 0.157 mW \implies \theta_{ self } = 0.157 / 2.0 \approx +0.08 K$ (negligible).

Consequently, high-accuracy protective IED RTD cards restrict continuous excitation to $I_{ exc } \le 1.0 mA$ (often applying synchronized microsecond current pulses to minimize time-integrated energy dissipation).

Digital Protection Strategies and Parameter Settings (ANSI 49, 49S, 49R)

Stator thermal protection within numerical Intelligent Electronic Devices (IEDs) integrates the current-based dynamic thermal replica model (ANSI 49 / 49S) with direct real-time feedback acquired from embedded RTD/PTC sensors (ANSI 49R).

Digital Thermal Image Dynamic Coupling with RTD Biasing

The standardized first-order thermal replica model implemented in digital relays per IEC 60255-149 recursively solves the differential thermal energy balance equation:

where $\theta(t)$ is the used thermal capacity ($0 \le \theta \le 1.0$ or $100\%$), $\tau_{ th }$ is the global stator thermal time constant, and $I_{ eq }$ is the equivalent thermal current incorporating unbalance and harmonic heating terms ($I_2$):

The RTD Biasing algorithm uses the maximum instantaneous temperature reading from the hottest stator sensor ($T_{ max,RTD }$) to continuously recalibrate the internal state of the thermal replica integrator. The thermal capacity derived from RTD biasing ($\theta_{ RTD }$) is defined using a piecewise linear transfer function bounded by three operating temperatures:

The relay dynamically selects the dominant thermal state for protection decisions: $\theta_{ final } = \max\left( \theta_{ corriente }, \theta_{ RTD } \right)$. This dynamic biasing compensates for environmental and physical variables unobservable via line current alone, including cooling air filter blockages, extreme ambient temperatures, or cooling water loss in heat exchangers (CACW / CACA systems).

Insulation Class (IEC 60085)	Maximum Thermal Limit ($T_{ max }$)	Allowable Rise ($\Delta T$ by Resistance)	Recommended Alarm Level (Slot RTD)	Recommended Trip Level (Slot RTD)
Class B	$130^\circ C$	$80 K$ (at $T_{ amb } = 40^\circ C$)	$115^\circ C$	$125^\circ C to 130^\circ C$
Class F (Operated at Class B Rise)	$155^\circ C$	$80 K$ (conservative design providing $2\times$ life margin)	$120^\circ C$	$130^\circ C to 135^\circ C$
Class F	$155^\circ C$	$105 K$	$140^\circ C$	$150^\circ C to 155^\circ C$
Class H	$180^\circ C$	$125 K$	$160^\circ C$	$170^\circ C to 175^\circ C$

Voting Logic and Measurement Artifact Filtering

Sensor line faults (open circuits or low-resistance short circuits) produce extreme spurious data readings ($-50^\circ C$ or $+300^\circ C$), which could induce nuisance tripping of critical power assets. Protective IED firmware executes real-time validity screening matrices prior to committing trip commands:

• Open / Broken Sensor Detection: If $R_{ medida } > 390 \Omega$ ($T > 850^\circ C$), the input is immediately blocked and tagged with a Sensor Fault diagnostic status.
• Shorted Sensor Detection: If $R_{ medida } < 18 \Omega$ ($T < -200^\circ C$), the input channel is marked invalid.
• Rate-of-Change Plausibility Check ($dT/dt$): Stator core and coil thermal inertia physically restricts temperature gradients to $< 2 K/s$. If $\left| \frac{dT}{dt} \right| > 5 K/s$, the reading is rejected as an induced electromagnetic interference artifact.
• Cross-Voting Logic (2ooN Architecture): To assert an irreversible master lockout trip (ANSI 86), the scheme requires that at least two independent sensors confirm overtemperature beyond $T_{ disparo }$ within the same slot or adjacent phases ($2 oo 3$ or $2 oo 6$ logic), or the simultaneous coincidence between the current-based thermal replica alarm (ANSI 49) and a single RTD exceeding $T_{ disparo }$.

Forensic Failure Analysis and Dielectric-Thermal Degradation Mechanisms

Root cause analyses of catastrophic stator failures in medium-voltage motors indicate that embedded sensors can act as either victims of severe operational stress or active initiators of winding insulation breakdown.

Electrodynamic Vibration and Fretting Wear Degradation

At line frequency ($50 Hz$ or $60 Hz$), current-carrying conductors inside stator slots experience double-frequency ($100 Hz$ or $120 Hz$) oscillating radial electrodynamic forces proportional to the square of total slot current:

During direct-on-line (DOL) motor starting where $I_{ arr } \approx 6.0 to 7.5 I_n$, these radial forces intensify by a factor of $36 to 56$. If slot wedge tensioning relaxes over time due to thermal cycling:

1. Top and bottom coil sides experience relative axial and radial micro-motion.
2. The RTD body is subjected to persistent abrasive fretting wear.
3. The glass-epoxy body of the sensor gradually abrades, exposing inner platinum sensing elements or internal connection tracks.
4. Subsequent direct contact between the exposed metallic elements and the damaged coil groundwall initiates a major phase-to-ground flashover ($I_{ sc,ph-g }$) channeled directly through the low-voltage instrumentation cabling.

Fast-Transient Coupling ($dv/dt$) from VFD / PWM Switching Inverters

When medium-voltage motors are fed by variable frequency drives utilizing high-speed IGBT or IGCT switching stages (two-level or multilevel PWM topologies), high-voltage steep-front pulses are applied to the motor terminals ($dv/dt > 5 to 10 kV /\mu s$).

Due to the distributed parasitic coupling capacitance ($C_{ acopl }$) between the high-voltage conductor and the embedded sensor core (typically $15 to 40 pF$ per slot sensor), high-frequency common-mode current pulses ($i_{ mc }$) are injected directly into the analog measurement circuits:

For a wavefront of $dv/dt = 10 kV /\mu s = 10^{10} V/s$ and $C_{ acopl } = 30 pF$:

As this high-frequency common-mode current returns to station earth through the finite input impedance of the RTD card, transient overvoltages develop ($V_{ GND } = i_{ mc } \cdot Z_{ chasis }$). These surges frequently exceed the breakdown ratings of Transient Voltage Suppression (TVS) diodes, puncturing monolithic analog multiplexers and causing permanent failure of the thermal monitoring IED.

Applied Engineering and Multi-Physics Validation with Vexten Suite

Comprehensive thermal sizing, starting transient validation, and protective coordination across all machine states are executed through the advanced engineering modules of Vexten Suite.

Analytical Workflow in Vexten Suite

1. Short-Circuit and Dielectric Stress Analysis (IEC 60909 / IEEE 141 Module):
   • Models the complete medium-voltage network to calculate prospective symmetrical ($I_k''$) and peak asymmetrical ($i_p$) short-circuit fault levels.
   • Evaluates line-to-ground Temporary Overvoltages (TOV) generated during asymmetrical ground faults, verifying that the embedded sensor dielectric insulation system maintains safe operating margins below the partial discharge inception voltage (PDIV).
2. Dynamic Motor Acceleration and Thermal Limit Simulation (Motor Acceleration Module):
   • Calculates rotor and stator thermal damage curves under locked-rotor conditions and severe high-inertia load starts ($J_{ carga } \gg J_{ motor }$).
   • Interactively overlays ANSI 49 dynamic thermal replica operating curves with the simulated time-temperature response of embedded RTD/PTC sensors.
   • Optimizes transient thermal gradient trip inhibit delays during acceleration, ensuring coordinated asset protection before copper conductors exceed maximum allowable insulation limits ($T_{ limit,F } = 155^\circ C$).
3. Cable Ampacity Sizing and Thermal Correction (IEC 60287 / NEC 310 Module):
   • Integrates harmonic current heating penalties produced by non-linear VFD inverters to calculate the derating of power feeds and low-voltage signal cables.
   • Models inductive and capacitive crosstalk between medium-voltage motor power feeders and shielded PT100 signal lines, validating that induced series-mode noise levels remain below $10 mV$ RMS to maintain measurement errors within $\pm 0.25 K$.

This multi-physics modeling approach within Vexten Suite establishes full engineering coordination between machine electromagnetic design, embedded sensor dielectric integrity, and substation numerical protection settings.