RATING (PQR)
CURRENT
FAILURE RISK
SYSTEM LOSSES
Understanding Power Quality Metrics
Power Quality Rating (PQR)
One score for the whole system
PQR combines three factors: true power factor, harmonic distortion and phase balance. The model follows the IEEE 1459-2010 definition of power factor, active power over apparent power. It estimates it from the terms below.
- TPF (True Power Factor)
- = cos(φ) / [√(1+THDI²) × √(1+THDV²)]
- cos(φ)
- Displacement power factor: the ratio of real power (P) to apparent power (S) at the fundamental frequency
- THDI, THDV
- Total harmonic distortion of current and voltage, as IEEE 519-2022 defines it
- BF (Balance Factor)
- = max(0, 1 − Imbalance%/100). It lowers the score when the phases carry unequal current.
| PQR score (model bands) | Rating | Meaning |
|---|---|---|
| ≥80% | Excellent | Close to the ideal load |
| 50% to 79% | Moderate | Some extra current and heat; watch the trend |
| <50% | Poor | High losses and equipment stress |
Neutral Current
Current in the return conductor
The model combines three sources of neutral current. It adds them as a root sum of squares. Triplen currents are in phase on the three phase conductors, so on the neutral they add. A balanced load with 15% third harmonic on each phase puts 45% of the fundamental phase current on the neutral.
- Iimbalance
- Vector sum of phase currents at 120° separation
- Itriplen
- Triplen current (3rd and 9th) of the three phases, added arithmetically. Triplens are zero sequence in Fortescue’s symmetrical components.
- Ivoltage
- Additional current from voltage unbalance
Rasmussen, N., “Harmonic Currents in the Data Center: A Case Study,” a leading maker’s White Paper 38
| Neutral (% of phase), model bands | Status | Action |
|---|---|---|
| <10% | Minimal | Normal operation |
| 10% to 30% | Elevated | Watch conductor temperature |
| 30% to 100% | Critical | Check neutral sizing |
| Above 100% | Critical | The neutral carries more than a phase |
Critical Failure Risk
A thermal stress score
The model adds four stress terms. It does not compute temperature. It scores stress from K-factor, power factor, THD and load. IEEE C57.91-2011 gives the aging equation for oil-filled transformers.
- K-Risk
- Harmonic heating in transformers (IEEE C57.110-2018)
- PF-Risk
- Excess current from low power factor
- THD-Risk
- Eddy current and skin effect losses
- Load-Risk
- Thermal stress from operation above rating
| Risk score | Model label | Meaning |
|---|---|---|
| <10% | Minimal | Near design conditions |
| 10% to 30% | Elevated | Extra heat; watch the trend |
| 30% to 50% | High | Equipment runs hot |
| Above 50% | High | Sustained thermal stress |
Electric System Losses
Power wasted as heat
Conductor losses scale with the square of current. Current rises as true power factor falls, so a small drop in power factor raises losses by more. The table shows the arithmetic at constant power and voltage.
- TPF
- True Power Factor (includes harmonic distortion)
- Equipment_Losses
- Operating losses of correction equipment (if present)
| True PF | Current Increase | I²R Loss Increase |
|---|---|---|
| 1.00 | Baseline | Baseline |
| 0.95 | +5% | +11% |
| 0.85 | +18% | +38% |
| 0.75 | +33% | +78% |
Annual Downstream Cost Impact
The model’s yearly estimate of what poor power quality costs
The cost has four parts. Energy waste is the easiest to see. In the model it is often not the largest part. The equipment part leads in the data center, HVAC and shipboard scenarios.
| Category | What It Measures | Primary Drivers |
|---|---|---|
| Energy | Additional electricity from losses | Low TPF, harmonic current |
| Equipment | Accelerated replacement costs | K-Factor, imbalance, neutral heating |
| Downtime | Yearly outage cost in the model | Outage cost set per scenario, plus loss and K-factor terms |
| Infrastructure | Extra capital cost of PQ-rated equipment | K-rated transformers, oversized neutral |
Outage cost per incident, as set in the model:
Data center: $740,000 · Shipboard: $500,000 · Manufacturing: $260,000 · HVAC: $85,000
These are settings in the model. The Downtime Risk card below shows how it uses them.
System Strength
How stiff the supply is
Short-Circuit Ratio (SCR) measures source stiffness:
- THDV and THDI
- Each scenario sets its own voltage THD. A weak source turns the same current distortion into more voltage distortion.
Resiliency Score is a weighted sum set by the model:
| SCR (model bands) | Strength | Resiliency | Rating |
|---|---|---|---|
| 50 (Ideal Baseline) | Strong | ≥70% | Strong |
| 20 to 50 | Strong | 40% to 69% | Moderate |
| 10 to 20 | Moderate | <40% | Vulnerable |
| <10 | Weak | n/a | High risk |
Compliance Summary
Four checks against published limits
Current THD IEEE 519-2022 Table 2
Total demand distortion (TDD) limits the harmonic current a site sends back to the utility at the point of common coupling. The limit rises with the short-circuit ratio. It is 5% under 20, 8% from 20 to 50, 12% from 50 to 100, 15% from 100 to 1,000 and 20% above 1,000. The model applies the 5% row in every scenario, against the load’s current THD.
Neutral Current NEC 2023, 310.15(E)(3)
Neutral current must stay within the conductor’s ampacity. Where most of the load on a 4-wire wye circuit is nonlinear, the NEC counts the neutral as a current-carrying conductor when the cable is derated.
Power factor IEEE 1459-2010
IEEE 1459-2010 defines power factor. It sets no minimum. The model checks displacement power factor. Its limit is 0.90 for the ideal, HVAC and manufacturing scenarios, 0.85 for the data center and microgrid, and 0.80 for shipboard. Each utility tariff sets its own limit. Below it, losses rise and less capacity is left for useful load.
Phase imbalance NEMA MG 1, 14.36
The model flags current imbalance between phases above 2% for the ideal, HVAC and manufacturing scenarios, above 3% for the microgrid and shipboard, and above 10% for the data center. NEMA MG 1, clause 14.36 gives the motor derating curve for unbalanced voltage. A few percent matters, because motor heating rises faster than the unbalance.
Data Center / IT
High-density computing loads
- IEEE 519-2022, Table 2: TDD of 8% or less where the short-circuit ratio is 20 to 50. The model applies 5%.
- IEEE C57.110-2018: derating transformers that carry harmonic current
- ASHRAE TC 9.9: thermal guidelines for data processing environments
- Uptime Institute: Tier Standard for data center topology
In the model, switch-mode power supplies put current THD at 35% to 42% per phase. Single-phase supplies put triplen harmonics on the neutral. One outage costs $740,000 in the model. The source has a short-circuit ratio of 20.
HVAC / VFD Systems
Variable frequency drives
- IEEE 519-2022, Table 2: TDD of 8% or less where the short-circuit ratio is 20 to 50. The model applies 5%.
- NEMA MG 1, 14.36: motor derating for voltage unbalance
- NEMA MG 1, Part 31: motors fed from drives, including shaft voltage
- Model settings: a short-circuit ratio of 25 and an outage cost of $85,000
Six-pulse drives draw 5th and 7th harmonic current. In the model, current THD is 35% to 45% per phase. Fast voltage edges from a drive can push current through motor bearings and pit them.
Microgrid / DER
Distributed energy resources
- IEEE 1547-2018, 7.3: total rated-current distortion (TRD) of 5% or less
- IEEE 1547-2018, 6.4: voltage ride-through
- IEEE 1547-2018, 5.3: voltage and reactive power control, including volt-var
- Utility interconnection: site-specific requirements
The model sets a short-circuit ratio of 15. It fixes THDV below 1% and does not derive it from THDI. The three phases carry unequal load. Output that keeps changing cycles the inverter capacitors.
Shipboard Power
Isolated generator systems
- MIL-STD-1399 Section 300, Part 1 (2018), Table II: voltage harmonic distortion of 5% or less
- MIL-STD-1399: average line-to-line voltage within 5% and frequency within 3% of 60 Hz
- MIL-STD-461G: conducted emission limits
- IEEE 45.1-2023: electrical installations on shipboard, design
In the model, current THD is 38% to 42% per phase on an isolated generator with a short-circuit ratio of 10. A source that weak lets current distortion raise THDV. Power factor is about 0.84, so the generator carries current that does no work. One outage costs $500,000 in the model.
Manufacturing
Industrial production loads
- IEEE 519-2022, Table 2: TDD of 5% or less where the short-circuit ratio is under 20
- IEEE 141 (Red Book): power distribution for industrial plants
- NEMA MG 1: motor derating curves
- Utility tariffs: each sets its own power factor penalty; the model uses 0.90
In the model, welders and thyristor drives put current THD at 35% to 45% per phase. Power factor is about 0.84, below the 0.90 the model uses for a tariff penalty. One outage costs $260,000 in the model.
Ideal Baseline
Reference for comparison
- PQR of 100: the top of the scale
- THD = 0%: pure sine waves
- PF = 1.0: unity power factor
- Imbalance = 0%: equal current on all three phases
The Ideal Baseline is a reference, not a real site. It models linear resistive loads with equal current on each phase. Comparing a scenario with it shows what each problem costs in the model.
Energy Waste
Additional electricity from losses
Poor power quality makes more current flow for the same useful work. Conductor losses scale with I², so a small drop in power factor costs more than it looks.
Energy_Cost = Base_kW × Hours × Rate × (Loss%/100) × 0.5 × Multiplier + Correction_Equipment_Losses
- Base load: 1 MW at $0.12/kWh
- 8,760 hours a year (continuous operation)
- Diversity factor of 0.5 for load variation
- Does not include demand charges
The model uses one energy rate. Local tariffs differ.
Equipment Degradation
Accelerated aging and replacement
Heat from harmonics, imbalance and neutral overload shortens equipment life. The model charges a fixed cost per unit of K-factor, imbalance and neutral current. It does not compute temperature. IEEE C57.91-2011 gives the aging equation for oil-filled transformers.
Equipment_Cost = K_Stress + Imbalance_Stress + Neutral_Stress
K_Stress = max(0, K-1) × $40,000/yr
Imbalance = max(0, Imb%-2) × $600/yr
Neutral = max(0, N%-20) × $300/yr
- K-factor above 1: $40,000 a year per unit of K
- Phase imbalance above 2%: $600 a year per percentage point
- Neutral current above 20% of phase current: $300 a year per percentage point
These coefficients are model settings. A site’s own repair and replacement records give a better estimate.
Downtime Risk
Outage cost set per scenario
The model starts from an outage cost set for each scenario. It adds terms for losses above 3% and for K-factor, then applies the scenario multiplier. It does not use the risk score.
Downtime_Cost = [(Outage_Cost / $50,000) × $6,000 + max(0, Loss%-3) × $400 + max(0, K-1) × $1,500] × Multiplier
- Data center: $740,000
- Shipboard: $500,000
- Manufacturing: $260,000
- HVAC: $85,000; Ideal Baseline: $50,000; Microgrid: $1,477
These are settings in the model, not survey results. A site’s own outage history gives a better figure.
Infrastructure
Capital equipment premiums
Poor power quality calls for costlier equipment: K-rated transformers, larger neutrals and extra filters.
Infrastructure = K_Transformer + Neutral_Upgrade + Base
K_Transformer = max(0, K-1) × $5,000/yr (amortized)
Neutral_Upgrade = max(0, N%-25) × $150/yr
Base = $6,000/yr (maintenance overhead)
- K-factor above 1: $5,000 a year per unit of K, amortized
- Neutral current above 25% of phase current: $150 a year per percentage point
- A fixed $6,000 a year for maintenance
- NEC 2023, 310.15(E)(3): on a 4-wire, 3-phase wye circuit where most of the load is nonlinear, the neutral counts as a current-carrying conductor
The shipboard scenario doubles this part through its multiplier.
Data Center: Energy 1.5×, Equipment 2.0×, Downtime 3.0×, Infrastructure 1.8× · Shipboard: Energy 1.2×, Equipment 2.0×, Downtime 4.0×, Infrastructure 2.0× · Manufacturing: Energy 1.3×, Equipment 1.4×, Downtime 1.5×, Infrastructure 1.2× · Microgrid: Energy 0.6×, Equipment 0.8×, Downtime 0.5×, Infrastructure 1.4× The multipliers are model settings, not measured results.
Active Correction (VectorQ SDE)
Our VectorQ applies Software-Defined Electricity. It measures the electricity at the panel and corrects reactive power, harmonics and phase imbalance every cycle. Its capacity is finite, as the note below shows.
Capacity check: The model assumes one unit rated 150 kVA. The figures above hold while the correction demand stays under 85% of that rating. Above it, the model drops to partial correction and scales it down further as demand grows.
Passive Harmonic Filters
Tuned inductor and capacitor circuits absorb set harmonic frequencies. They work well on the 5th and 7th harmonics and do little for the triplens (3rd, 9th). Their tuning is fixed, so they cannot follow a changing load.
Capacitor Banks
Switched capacitor banks are the traditional fix for power factor. They correct displacement power factor but not harmonics. They can also form a resonance with the source. The 9% loss is a model setting, not a measured rate.
This simulator estimates a rating from the figures entered above. To have a real instrument recording analyzed, see Power Quality Risk Analysis.