Voltage Sag and Network Disturbances in High-Power DOL Motor Starting

Electrodynamic and Transient Fundamentals of Direct-On-Line (DOL) Starting

Direct-On-Line (DOL) starting of high-power induction motors represents one of the most severe electromagnetic and electromechanical transients in industrial electrical power systems. By instantaneously applying nominal voltage to the stator terminals, the machine transitions from a standstill state to a highly demanding dynamic regime, where electrical and magnetic variables undergo extreme variations before reaching steady-state equilibrium.

Physics of Magnetic Coupling and Inrush Current

At the initial instant of starting ($t = 0^+$), the machine's slip is unity ($s = 1$). From an electromagnetic perspective, the induction motor behaves like a three-phase transformer with its secondary winding (the rotor) short-circuited and a significant air gap. The impedance seen from the stator terminals is minimal, limited solely by the stator and rotor resistances and leakage reactances.

The initial transient current consists of two primary components: the steady-state symmetrical short-circuit current (due to the subtransient reactance of the machine) and a decaying exponential unidirectional direct current (DC offset) component. This transient DC component is necessary to satisfy the law of conservation of magnetic flux at the instant of circuit breaker contact closure. The mathematical expression of the instantaneous current in one of the phases is described by the following equation:

Where:

• $Icc$ is the root-mean-square (RMS) value of the symmetrical short-circuit current of the motor under locked-rotor conditions.
• $\alpha$ is the voltage phase angle at the instant of energization.
• $\phi$ is the short-circuit impedance angle of the motor, where $\phi = \arctan(Xeq/Req)$.
• $T_a$ is the damping time constant of the DC component, defined by the ratio between the equivalent inductance and resistance of the fault loop:

The absolute peak value of the inrush current, which occurs approximately half a cycle after the start of the transient ($t \approx 8.33 ms$ for a 60 Hz frequency), can reach values between 1.8 and 2.8 times the RMS value of the locked-rotor current ($ILRC$), causing colossal electrodynamic stresses on the stator windings.

Temporal Evolution of Rotor Impedance and Slip

During the acceleration process, the slip ($s$) decreases from 1.0 to its nominal value (typically between 0.005 and 0.03). The equivalent impedance of the induction motor varies dynamically as a function of this parameter, according to the Steinmetz equivalent circuit model:

As the rotor accelerates and the slip decreases, the apparent rotor resistance term $\frac{R_r'}{s}$ increases drastically. This causes a progressive reduction in the stator current and an increase in the motor power factor.

Additionally, in high-power motors, the design of the rotor bars (deep bars or double squirrel cage) introduces the skin effect. At the start of the starting sequence, the frequency of the rotor currents is equal to the grid frequency ($f_r = s \cdot f = 50 Hz o 60 Hz$). This high frequency forces the current toward the top of the rotor bars, reducing the effective conduction area, which artificially increases the rotor resistance ($R_r'$) and decreases the rotor leakage inductance ($X_r'$). As the speed increases, the rotor frequency decreases to values below 3 Hz, restoring the nominal direct-current values for both rotor resistance and inductance.

Electromagnetic Torque Equations and Acceleration Dynamics

The instantaneous electromagnetic torque induced on the motor shaft is directly coupled to the behavior of the current and the air-gap magnetic flux. The fundamental equation governing electromagnetic torque as a function of slip is given by the simplified Kloss formula or, rigorously, derived from the equivalent circuit:

Where $Vth$ and $Zth = Rth + jX_{th}$ are the Thévenin equivalent voltage and impedance seen from the rotor. The electromechanical acceleration dynamics are governed by the rotational motion differential equation:

Where:

• $T_L(\omega_m)$ is the load torque curve (quadratic for centrifugal pumps and fans, constant for positive displacement compressors).
• $J$ is the total combined moment of inertia of the motor rotor and the coupled load, referred to the rotational axis ($J = J_m + J_L$).
• $B$ is the viscous friction coefficient.
• $\omega_m$ is the mechanical angular velocity of the rotor.

If the motor terminal voltage drops due to grid impedance during starting, the electromagnetic torque decays proportionally to the square of the supply voltage:

A 20% reduction in terminal voltage ($0.8 pu$) translates to a 36% loss of available torque, which critically prolongs the starting time ($tstart$) or may even prevent the motor from overcoming the breakdown torque point, resulting in thermal locking of the rotor.

Analysis of Transient Voltage Dip/Sag

The magnitude of the voltage drop at the Point of Common Coupling (PCC) during the starting of a high-power motor is a direct function of the upstream grid stiffness and the magnitude of the motor starting current.

Modeling of Grid Impedance and the Point of Common Coupling (PCC)

To analyze the impact of starting, the upstream electrical grid is modeled using its Thévenin equivalent at the PCC, characterized by an open-circuit voltage $V_0$ and a system short-circuit impedance $Zsys = Rsys + jX_{sys}$.

The system impedance is determined from the three-phase short-circuit capacity ($Scc$) at the PCC and the grid $X/R$ ratio:

Analytical Calculation of Static and Dynamic Voltage Drop

During starting, the motor is represented as a time-varying impedance $Z_m(t)$. The voltage drop at the PCC can be evaluated using the complex voltage divider:

For a rapid engineering calculation, the approximate percentage voltage drop can be estimated using the longitudinal component of the voltage drop:

Where $\cos \phi_{\text{start}}$ represents the extremely low power factor during starting (typically between 0.15 and 0.30 inductive). Due to this low power factor, the voltage drop is dominated almost entirely by the inductive reactance of the grid ($Xsys$) and intermediate power transformers.

Effect of the Short Circuit Ratio (SCR)

The Short Circuit Ratio (SCR) at the PCC defines the sensitivity of the grid to heavy load disturbances. It is defined as:

Where $Pmotor$ is the nominal active power of the induction motor.

• Strong Grids (SCR > 20): The voltage drop at the PCC is typically below 5%. The impact on other loads is minimal.
• Weak Grids (SCR < 10): The voltage drop can exceed 15% or 20%. A detailed dynamic analysis and the implementation of assisted starting methods or dynamic reactive power compensation are strictly required.

Related Grid Disturbances and Power Quality

Direct-On-Line starting of large motors not only generates localized voltage drops but also globally degrades the power quality indices of the entire associated industrial distribution network.

Voltage Fluctuations and Flicker (IEC 61000-3-7 / IEEE 1453 Standards)

The phenomenon of flicker is the subjective visual impression of luminance fluctuation in lamps caused by rapid variations in grid voltage. Repetitive starting of large motors (for instance, in pumping systems with frequent cycles or refinery compressors) introduces severe disturbances evaluated by the short-term flicker severity indicator ($Pst$, measured over 10-minute intervals) and long-term flicker severity indicator ($Plt$, measured over 2-hour intervals).

The IEC 61000-3-7 standard establishes strict limits for voltage fluctuation emissions based on the grid voltage level. For medium-voltage grids, the typical planning limit for $Pst$ is 0.9 and for $Plt$ is 0.7. A single DOL start of a 10 MW motor can instantaneously raise the $Pst$ above 1.5 at the common node if the short-circuit capacity is insufficient.

Phase Unbalance and Transient Harmonics

During the switching and acceleration phase, any constructive asymmetry in the motor, the power cables, or the non-simultaneous closure of the power circuit breaker poles (pole discrepancy) introduces negative-sequence ($I_2$) and zero-sequence ($I_0$) components.

The resulting transient voltage unbalance causes pulsating torques at twice the grid frequency ($2f = 100 Hz / 120 Hz$), generating severe torsional stresses on the motor's mechanical coupling. Likewise, the transient magnetic saturation of the supply transformer core, caused by the high inrush current and its DC component, introduces low-frequency harmonics (especially the 2nd and 3rd harmonics), temporarily distorting the voltage waveform at the PCC.

Effects on Sensitive Loads and Contactor Dropout

A severe voltage drop on industrial distribution buses (typically below 85% of nominal voltage) has immediate operational consequences:

• Control and Automation Systems: Auxiliary relays, control contactors, and PLCs can drop out or reset if the voltage falls below their holding threshold (typically 70% to 80% of nominal voltage for more than one grid cycle).
• Variable Frequency Drives (VFDs) and Drivers: Variable speed drives of other collateral critical processes typically trip on DC link under-voltage protection, halting entire production lines.
• Operating Induction Motors: Motors already operating at full load will experience an increase in their operating current to compensate for the voltage drop and maintain the torque demanded by their loads, accelerating their thermal aging.

Forensic Failure Analysis of Electrical System Components

The cumulative and instantaneous impact of Direct-On-Line starting subjects the power infrastructure to physical stress levels close to their short-circuit design limits.

Thermal and Mechanical Fatigue in Transformer Windings

The power transformer feeding the motor substation experiences electrodynamic forces that vary with the square of the starting current ($F \propto Istart^2$). These forces are divided into:

• Radial Forces: These tend to compress the inner winding (generally low voltage) and expand the outer winding (high voltage), which can cause buckling collapse of the copper conductors.
• Axial Forces: Caused by the physical misalignment between the magnetic centers of the high and low-voltage windings, pushing the windings in opposite directions toward the core yokes, destroying insulation support blocks and clamping wedges.

From a thermal perspective, Joule heating dissipation in the transformer windings during the prolonged starting of a large motor is massive. The heat generated in the copper is not immediately transferred to the insulating oil due to the system's thermal time constant, causing localized hot spots that exponentially degrade the cellulose insulating paper according to the Arrhenius equation for insulation aging:

Where $\theta_{hs}$ is the hot-spot temperature. Each 6 °C increase above the design temperature doubles the rate of the transformer's loss of life.

Electrodynamic Stresses in Power Cables and Raceways

Medium-voltage cables interconnecting the substation with the high-power motor experience extreme magnetic attraction and repulsion forces during the peak inrush current. The force per unit length between two parallel conductors in a flat three-phase system is calculated by:

Where $d$ is the distance between conductor centers. For starting currents on the order of 15 kA, these forces can exceed 500 kg/m of cable. If cable cleats or cable trays are not correctly calculated and spaced, physical deformation of the metallic cable shields, tearing of the PVC/LSZH sheaths, and eventual phase-to-phase short circuits due to mechanical fatigue of the XLPE/EPR insulation will occur.

Circuit Breaker Contact Wear and Insulation Fatigue

The power circuit breaker (vacuum or SF6 gas) performing the direct-on-line switching operation suffers accelerated wear due to:

• Electric Arc Erosion: Upon closing the breaker, the mechanical contact bounce, although lasting only milliseconds, establishes electric micro-arcs under extremely high currents. This vaporizes the contact alloy material (typically Copper-Tungsteno or Silver-Nickel), degrading contact resistance and causing permanent hot spots.
• Transient Recovery Voltage (TRV): If the motor is switched off during starting or under normal conditions, the interruption of highly inductive currents generates a TRV with a very high rate of rise ($dV/dt$), subjecting the breaker insulation and the motor windings to overvoltages due to arc re-strikes.

Nuisance Tripping of Protection Relays (ANSI 50/51, 49, 46)

The parameterization of protection functions in numerical relays for high-power motors requires a critical balance between selectivity and effective asset protection:

• ANSI 50 (Instantaneous Overcurrent): Must be set above the peak value of the inrush current, considering a safety margin (typically $1.3 \times I_{LRC,peak}$) to prevent tripping at the instant of energization. A common error is parameterizing the instantaneous unit based solely on the symmetrical RMS value.
• ANSI 51 (Inverse-Time Overcurrent): The motor starting curve ($I^2t$) must lie below the thermal damage curve of the stator and rotor (cold and hot locked-rotor limits), but above the actual motor acceleration current curve under the worst-case voltage drop condition. If the voltage drop prolongs starting, the ANSI 51 protection may experience nuisance tripping by mistaking the slow start for a locked-rotor fault.
• ANSI 49 (Thermal Overload based on Thermal Image Model): Utilizes the motor's thermal time constant to estimate heating. During repetitive starts, the relay accumulates thermal history; if the cooling times prescribed by the manufacturer (e.g., two cold starts or one hot start) are not respected, the relay will block motor starting to prevent melting of the rotor bars.

Component	Critical Parameter / Standard	Operating / Design Limit	Transient Fault Condition	Direct Physical Consequence
Power Transformer	IEC 60076-5 (Short-Circuit Stresses)	Radial compression force < Copper buckling limit	Repetitive starting current $I_s > 6 \cdot I_n$	Winding deformation, loss of dielectric strength, internal short circuit.
Medium-Voltage Cables	IEC 60287 / ICEA S-93-639	Maximum short-circuit temperature in XLPE: 250 °C	Prolonged starting ($tstart > 15 s$) with voltage drop	Melting of XLPE insulation, degradation of copper shield, ground fault.
Power Circuit Breaker	IEEE C37.06 / IEC 62271-100	Number of operations at nominal starting current < 500 operations	Opening operation under locked-rotor current	Severe erosion of vacuum/SF6 contacts, arc re-strike due to high TRV.
Induction Motor	IEEE 112 / IEC 60034-1	Hot locked-rotor limit (Safe Stall Time): 10 to 15 s	Grid voltage drop reducing torque to 50%	Cracking of rotor bars at the short-circuit ring joint due to differential thermal expansion.
Electrical Grid (PCC)	IEEE 519 / IEC 61000-3-7	Voltage drop at PCC < 10% (transient)	Grid SCR < 8 at the connection node	Tripping of collateral variable frequency drives, dropout of control contactors.

Mitigation Strategies and Detailed Engineering Design

The selection of the optimal mitigation strategy requires evaluating the technical-economic trade-off between the starting torque required by the load and the maximum voltage drop permitted by the grid.

Technological Comparison of Starting Methods

Various technologies exist to limit the starting current, each with specific operating characteristics that directly impact system behavior.

• Direct-On-Line (DOL) Starting: Provides the maximum possible starting torque ($1.5 - 2.5 pu \mu_{lti}$), but demands the maximum current ($6.0 - 8.0 pu$). Its implementation cost is the lowest, but it requires an extremely robust grid.
• Star-Delta ($Y-\Delta$) Starting: Reduces the starting current and torque to one-third ($1/3$) of their DOL values. It presents the severe drawback of extremely high transient currents (re-energization peaks) during the transition from star to delta, which can be more detrimental to the grid than the DOL start itself if the transition is not properly synchronized.
• Autotransformer Starter: Allows adjusting the starting voltage using taps (typically 50%, 65%, and 80%). The current on the line side is reduced by the square of the transformation ratio ($a^2$):

This makes it a robust and efficient option for high-inertia loads that do not require high starting torque.

• Soft Starter: Uses anti-parallel thyristors (SCRs) to control the firing angle and gradually increase the voltage applied to the stator from an initial value to the nominal voltage. This provides a smooth acceleration ramp and limits the current to a pre-established constant value (typically $3.0 - 4.5 pu$). However, it introduces harmonics into the grid during the starting ramp and does not allow for precise speed control.
• Variable Frequency Drive (VFD): This is the ultimate technical solution. By simultaneously controlling voltage and frequency while keeping the $V/f$ ratio constant, the VFD allows starting the motor with full nominal torque while drawing a starting current that does not exceed the motor's nominal current ($Istart \le 1.0 - 1.1 pu$). It completely eliminates the transient voltage drop on the grid, but represents the highest capital expenditure (CAPEX) and requires a dedicated cooling system, in addition to introducing permanent harmonics during normal operation that require filtering.

Starting Method	Starting Current ($I/I_n$)	Starting Torque ($T/T_n$)	Relative Cost (CAPEX)	Grid Impact (Flicker/Sag)	Maintenance Complexity
Direct-On-Line (DOL)	6.0 - 8.0	1.5 - 2.5	1.0 (Base)	Very High (Critical for weak grids)	Minimal
Star-Delta ($Y-\Delta$)	2.0 - 2.5	0.5 - 0.8	1.5	Medium (High transients during transition)	Low
Autotransformer (65% Tap)	2.5 - 3.5	0.6 - 1.0	2.5	Low-Medium	Medium (Contactor wear)
Soft Starter	3.0 - 4.5	0.5 - 1.2	3.5	Low (Controlled ramp)	Medium (Power electronics)
Variable Frequency Drive (VFD)	1.0 - 1.1	1.5 - 2.0	8.0 - 12.0	Negligible (Optimal start)	High (Requires qualified personnel)

Sizing Criteria for Starting Transformers and Autotransformers

When a dedicated transformer is selected for starting a large motor (or a distribution transformer sharing loads), its kVA capacity ($Stx$) must be sized to limit the voltage drop on the secondary side to the specified value (e.g., $\le 15\%$). The minimum required short-circuit apparent power on the transformer secondary to meet this limit is expressed as:

Where $S_{start\_motor} = Vnom \cdot ILRC \cdot \sqrt{3}$.

For the thermal sizing of an intermittent-duty starting autotransformer, duty factors based on the IEEE C57.132 standard are employed. Since the autotransformer only operates during the acceleration time ($tstart$ of 10 to 30 seconds), it does not require a continuous-duty design (S1), but rather a limited-time duty design (S2 or S3). This allows under-sizing the continuous nominal rating of the autotransformer to as low as 20% or 30% of the motor power, significantly reducing cost and physical footprint in the electrical room, provided it is verified that the design Joule integral of the winding withstands the temperature transient:

Where $A$ is the cross-sectional area of the copper conductor and $K$ is a material constant.

Dynamic Reactive Power Compensation (STATCOM, SVC, Detuned Capacitor Banks)

Because the starting current of an induction motor is predominantly inductive, the rapid injection of capacitive reactive power at the PCC is a highly effective method for supporting the voltage profile.

• Fixed or Automatic Capacitor Banks: These are not recommended for mitigating the initial transient voltage drop due to their slow response time (switching contactors or thyristors operate in cycles, and the pre-discharge of the capacitor takes seconds). Furthermore, connecting capacitors at the moment of starting can amplify transient inrush currents and generate harmonic resonances with the motor's leakage inductance.
• Static Var Compensator (SVC): Uses thyristor-controlled reactors (TCR) in parallel with fixed capacitor banks. Its response time is 1 to 2 grid cycles (20-40 ms), allowing it to dynamically compensate for the reactive power demanded during motor starting, thereby stabilizing the voltage at the PCC very efficiently.
• Static Synchronous Compensator (STATCOM): This is the state-of-the-art technology based on voltage-source inverters (VSI) with IGBT transistors. The STATCOM can inject reactive current instantaneously (response time under 5 ms) and, unlike capacitors or the SVC, the maximum current it can inject does not depend on the grid voltage. Even if the voltage drops to 0.7 pu, the STATCOM maintains its nominal reactive current injection capability, providing excellent dynamic voltage support:

Case Study and Integrated Simulation with Vexten Suite

To consolidate the theoretical concepts presented, a detailed engineering analysis is provided for the integration of a high-power induction motor in a petrochemical plant, utilizing the Vexten Suite electrical engineering software.

Study System Parameters:

• Utility Grid: $Vlinea = 115 kV$, $Scc = 1500 MVA$, $X/R$ ratio = 15.
• Main Transformer (Substation): $15 MVA$, $115 kV / 6.6 kV$, short-circuit impedance $Zcc = 8.5\%$, $X/R$ ratio = 18.
• Power Cable (Substation to Motor): A three-phase circuit of single-core copper cables of $3 \times 240 mm ^2$ with XLPE insulation, length $L = 350 m$, installed in a perforated cable tray.
• High-Power Induction Motor (Gas Compressor):
  • Nominal Power ($P_n$): $4500 kW$ ($4.5 MW$)
  • Nominal Voltage ($V_n$): $6.6 kV$
  • Locked-Rotor Current ($ILRC$): $6.5 \cdot I_n$
  • Starting Power Factor ($\cos \phi_{\text{start}}$): $0.20 inductive$
  • Nominal Efficiency ($\eta$): $96.2\%$
  • Nominal Power Factor ($\cos \phi_n$): $0.88$
  • Combined Moment of Inertia ($Jtotal$): $450 kg \cdot m ^2$

Short-Circuit Calculation according to IEC 60909 / IEEE 141

Using the Vexten Short-Circuit module, the equivalent system impedances referred to the medium-voltage side ($6.6 kV$) are calculated to determine the grid stiffness at the industrial substation buses.

Upstream grid impedance (Utility) referred to $6.6 kV$:

Power transformer impedance referred to $6.6 kV$:

Total equivalent power system impedance at the $6.6 kV$ buses (excluding the cable):

The actual short-circuit capacity at the $6.6 kV$ buses calculated by Vexten Short-Circuit according to IEC 60909 is:

Cable Sizing according to IEC 60287 / NEC 310

The Vexten Cable-Sizer module evaluates the conductor cross-section considering three fundamental criteria: steady-state ampacity, steady-state and transient voltage drop, and short-circuit thermal limit.

For the $4.5 MW$ motor:

The Direct-On-Line (DOL) starting current is:

For a copper cable with XLPE insulation of $3 \times 240 mm ^2$, the manufacturer specifies the following impedance parameters at the maximum operating temperature of 90 °C:

• $Rcable = 0.0984 \ \Omega/ km$
• $Xcable = 0.112 \ \Omega/ km$

For a length of $350 m$ ($0.35 km$):

Vexten Cable-Sizer verifies the cable ampacity according to IEC 60287 (installation in a perforated tray at an ambient temperature of 40 °C with grouping factors applied), determining that the continuous current capacity of the $240 mm ^2$ cable is $510 A$, which is sufficient for the nominal current of $464.8 A$.

However, during starting, the voltage drop in the cable must be rigorously evaluated using the starting current and power factor values:

(Note: $\sin\phi_{\text{start}} = \sqrt{1 - 0.20^2} \approx 0.9798$)

The percentage voltage drop in the cable with respect to the nominal voltage of $6.6 kV$ is:

Dynamic Motor Starting Analysis and Resonance Mitigation

The Vexten Dynamic-Sim module executes a time-domain simulation to evaluate the voltage profile at the substation buses ($Vbarras$) and at the motor terminals ($Vmotor$) during direct-on-line starting.

The total impedance seen from the ideal grid source to the motor terminals during starting is:

The total cumulative voltage drop at the motor terminals at the initial starting instant ($t = 0^+$) is calculated through the interaction of the starting current with the total impedance:

The percentage voltage drop at the motor terminals is:

The remaining voltage at the motor terminals during starting is only $74.77\%$ ($0.748 pu$). This value is well below the limit recommended by the IEEE 399 (Brown Book) standard, which states that the motor terminal voltage should not fall below $80\%$ to ensure safe acceleration and prevent slip stalling.

The voltage drop at the $6.6 kV$ substation buses (PCC) is calculated considering only the grid and transformer impedance:

A voltage drop of $21.64\%$ at the substation buses will cause nuisance tripping of all variable frequency drives in the plant and the dropout of control contactors for essential auxiliary pumps, which is unacceptable for the continuous operation of the petrochemical facility.

Study of Mitigation Alternatives in Vexten Dynamic-Sim:

To resolve this critical issue, three mitigation scenarios are simulated in the suite:

• Scenario A: Implementation of a Soft Starter. A current limit of $3.5 \cdot I_n$ ($1626.8 A$) is parameterized.
  • The voltage drop at the PCC decreases to:
  $$\Delta V_{PCC\_Soft} = 21.64\% \times \left( \frac{3.5}{6.5} \right) = 11.65\%$$
  • The remaining voltage at the PCC rises to $88.35\%$, which is acceptable to prevent contactor dropout (typical limit of $85\%$). The motor starting torque is reduced to $29\%$ of its nominal DOL value. Dynamic analysis confirms that the motor successfully accelerates the load in 14.2 seconds without exceeding the rotor's thermal limit.
• Scenario B: Installation of a 5 MVAR Static Synchronous Compensator (STATCOM).
  • The STATCOM detects the instantaneous voltage drop and injects $437 A$ of pure quadrature reactive current at the PCC in less than 4 ms.
  • The dynamic simulation in Vexten Dynamic-Sim demonstrates that the voltage drop at the substation buses stabilizes at only $7.8\%$, maintaining the operability of the entire plant without needing to alter the motor's DOL starting method, thereby preserving the machine's maximum acceleration torque.
• Scenario C: Verification of Transient Harmonic Resonance.
  • While simulating Scenario B, the potential resonant interaction between the STATCOM output capacitance and the leakage reactances of the transformer and motor is evaluated. The frequency response module of Vexten Suite plots the system impedance curve as seen from the PCC. It is verified that the parallel resonance frequency is located at 410 Hz (8.2nd harmonic for 50 Hz), remaining well outside the characteristic harmonic frequencies of the grid (especially the 5th and 7th harmonics), thereby ensuring absolute stability of the STATCOM control loop during the starting transient.

This comprehensive analysis demonstrates the necessity of performing rigorous dynamic simulations using advanced tools such as Vexten Suite to guarantee the safety, stability, and operational reliability of complex, high-power industrial electrical installations.