Power Systems Fundamentals

Common connection point where circuit elements meet, characterized by voltage phasor.

In power systems, each node has:

• Voltage magnitude $|V|$
• Voltage angle $\theta$

Circuit element connecting two nodes with impedance:

$$Z = R + jX$$

Examples: transmission lines, transformers, cables.

Non-impedant conductive bar serving as central power distribution point in substations.

Image: Wikimedia Commons, Public Domain

KCL (Current Law): Sum of currents entering a node equals sum leaving.

KVL (Voltage Law): Sum of voltages around any closed loop equals zero.

Tree-shaped network with single path from source to consumer.

Pros: Simple, lowest cost, easy protection Cons: No redundancy - single fault causes outage Use: Rural areas, residential distribution

Closed loop providing two alternative paths.

Can be operated as:

• Open ring: One point normally open (like two radials)
• Closed ring: Full loop energized (better reliability)

Use: Urban distribution, commercial areas

Multiple interconnections creating redundant paths.

Pros: Highest reliability, load sharing Cons: Complex protection, highest cost Use: Transmission networks, critical industrial loads

Simplified representation showing three-phase system as single line.

Why simplify? Three phases are balanced in normal operation, so one line represents all three.

Image: Wikimedia Commons, CC BY-SA 3.0

Standard approach:

1. Start at top (highest voltage)
2. Work down to lowest voltage
3. Left-to-right for same voltage level

Real power doing useful work (motors, heating, lighting).

Units: Watts (W, kW, MW)

$$P = V \cdot I \cdot \cos(\phi)$$

For three-phase:

$$P_{3\phi} = \sqrt{3} \cdot V_{LL} \cdot I \cdot \cos(\phi)$$

Power that oscillates between source and load, maintaining magnetic/electric fields.

Units: Volt-Amperes Reactive (VAR, kVAR, MVAR)

$$Q = V \cdot I \cdot \sin(\phi)$$

• Inductors (motors, transformers): Consume Q (lagging)
• Capacitors: Supply Q (leading)

Vector sum of P and Q - total power the system must deliver.

Units: Volt-Amperes (VA, kVA, MVA)

$$S = P + jQ$$

$$|S| = \sqrt{P^2 + Q^2}$$

Graphical representation relating P, Q, and S:

Image: Wikimedia Commons, CC BY-SA 3.0

• Horizontal: Active power P
• Vertical: Reactive power Q
• Hypotenuse: Apparent power S
• Angle φ: Power factor angle

Ratio of real power to apparent power:

$$PF=\frac{P}{S}=\cos (\varphi )$$PF = \frac{P}{S} = \cos(\phi)

• PF = 1.0 (unity): Pure resistive, V and I in phase
• PF = 0: Pure reactive, no real power transferred
• Typical industrial: 0.7 - 0.9 lagging

Describes current relative to voltage:

• Lagging PF: Current lags voltage (inductive loads - motors)
• Leading PF: Current leads voltage (capacitive loads)

Memory aid: ELI the ICE man

• ELI: Voltage (E) leads Current (I) in Inductors (L)
• ICE: Current (I) leads Voltage (E) in Capacitors (C)

Adding capacitors to cancel inductive reactive power:

$$Q_C = P \cdot (\tan\phi_1 - \tan\phi_2)$$

Where:

• $\phi_1$ = original PF angle
• $\phi_2$ = target PF angle

Target: PF > 0.95 to avoid utility penalties

Power loss in transmission:

$$P_{loss} = I^2 R$$

For fixed power $P = V \cdot I$, doubling voltage halves current, reducing losses to one quarter.

Example: 100 MW at 400 kV vs 11 kV

• At 400 kV: I = 144 A
• At 11 kV: I = 5,249 A (36× higher losses!)

Typical power flow path:

1. Generation (11-25 kV)
2. Step-up to transmission (275-400 kV)
3. Transmission (bulk power transfer)
4. Step-down to sub-transmission (132 kV)
5. Distribution (33 kV → 11 kV → 400 V)
6. Consumer (400 V three-phase / 230 V single-phase)

Quantities expressed as dimensionless fractions of base values:

$$X_{pu} = \frac{X_{actual}}{X_{base}}$$

Advantages:

• Transformer impedances same on both sides
• Equipment values fall in narrow range (0.05-0.15 pu)
• Simplifies hand calculations

Choose two independent bases (typically):

• $S_{base}$ = 100 MVA (industry standard)
• $V_{base}$ = Nominal system voltage at each level

Derived bases:

$$I_{base} = \frac{S_{base}}{\sqrt{3} \cdot V_{base}}$$

$$Z_{base} = \frac{V_{base}^2}{S_{base}}$$

Converting actual impedance to per-unit:

$$Z_{pu} = Z_{actual} \cdot \frac{S_{base}}{V_{base}^2}$$

Example: 10 Ω line at 11 kV on 100 MVA base

$$Z_{base} = \frac{11^2}{100} = 1.21 \text{ Ω}$$

$$Z_{pu} = \frac{10}{1.21} = 8.26 \text{ pu}$$

Converting between different bases:

$$Z_{pu,new} = Z_{pu,old} \cdot \frac{S_{base,new}}{S_{base,old}} \cdot \left(\frac{V_{base,old}}{V_{base,new}}\right)^2$$

Used when combining equipment with different nameplate bases.

Answers the question: "Given generation and load, what are the voltages and power flows?"

Calculates:

• Voltage magnitude and angle at each bus
• Real and reactive power flow in each branch
• System losses
• Equipment loading (% of rating)

Each bus must be classified for the solver:

Typically: 1 slack, few PV, many PQ buses.

• Planning: Assess new generation/transmission options
• Operations: Real-time monitoring and control
• Contingency (N-1): What if a line/generator trips?
• Voltage assessment: Find weak points needing reactive support
• Loss calculation: Optimize power flow paths

Load flow equations are nonlinear (power = V × I, but I depends on V).

No closed-form solution exists for networks with more than a few buses.

Must iterate: guess → calculate → refine → repeat until converged.

Sequential update of each bus voltage:

$$V_i^{(k+1)} = \frac{1}{Y_{ii}} \left[ \frac{P_i - jQ_i}{V_i^{(k)*}} - \sum_{j \neq i} Y_{ij} V_j^{(k)} \right]$$

Pros: Simple to understand and code

Cons: Slow (100+ iterations), poor convergence for large/meshed networks

Use: Small systems, educational purposes

Solves power mismatch equations using Jacobian matrix:

$$\begin{bmatrix} \Delta P \\ \Delta Q \end{bmatrix} = \mathbf{J} \begin{bmatrix} \Delta \theta \\ \Delta V \end{bmatrix}$$

Jacobian structure:

$$\mathbf{J} = \begin{bmatrix} \frac{\partial P}{\partial \theta} & \frac{\partial P}{\partial V} \\ \frac{\partial Q}{\partial \theta} & \frac{\partial Q}{\partial V} \end{bmatrix}$$

Pros: Fast (3-5 iterations), robust, industry standard

Cons: More complex, requires Jacobian calculation

Simplification of N-R exploiting natural decoupling:

• P-θ: Real power strongly coupled to angles
• Q-V: Reactive power strongly coupled to voltages

Solves two smaller systems instead of one large one. Even faster for transmission networks.

Converged: Mismatches below tolerance (typically 0.001 pu)

Divergence causes:

• Poor initial guess (use flat start: V=1.0, θ=0)
• Excessive reactive demand
• Islanded sections
• Negative impedance (modelling error)

Plot of voltage magnitude across buses, typically ordered by electrical distance from source.

Acceptable range: Usually 0.95 - 1.05 pu (±5%)

Violations indicate:

• Heavy loading (voltage drop)
• Insufficient reactive support
• Need for tap changer adjustment or capacitor banks

Power flow as percentage of thermal rating:

$$\text{Loading} = \frac{|S_{flow}|}{S_{rating}} \times 100\%$$

Watch for:

• >80% - approaching limit, monitor closely
• >100% - overloaded, requires action

Heavily loaded lines are bottlenecks limiting power transfer.

Total real power losses:

$$P_{loss} = \sum P_{generation} - \sum P_{load}$$

Typical values: 2-8% of total generation

Loss breakdown:

• Transmission: ~2-3%
• Distribution: ~4-6%

High losses indicate inefficient power flow paths.

Shows where Q is generated and consumed.

Key observations:

• Generators at Q limits? May need more reactive support
• Long lines consuming Q? Consider series compensation
• Transformers with high Q flow? Check tap positions

Typical load flow output:

Negative P/Q = load consuming power

All three phases short-circuited together (with or without ground).

Image: Wikimedia Commons, CC BY-SA 3.0

• Severity: Most severe (highest current)
• Frequency: Rarest (~5% of faults)
• Analysis: Simplest - system remains balanced, only positive sequence needed

One phase contacts ground.

• Severity: Depends on grounding (can exceed 3-phase in solidly grounded systems)
• Frequency: Most common (~70-80% of faults)
• Analysis: Requires all three sequence networks in series

Common causes: Lightning, tree contact, insulator flashover

Two phases short-circuited together (not involving ground).

• Severity: ~87% of three-phase fault current
• Frequency: ~15-20% of faults
• Analysis: Positive and negative sequence networks in parallel

Two phases short-circuited together and to ground.

• Severity: Can exceed three-phase in some cases
• Frequency: ~5-10% of faults
• Analysis: Most complex - all sequences in parallel

For solidly grounded systems (typical UK distribution):

$$I_{3\phi} > I_{SLG} > I_{LLG} > I_{LL}$$

For impedance grounded systems:

$$I_{3\phi} > I_{LLG} > I_{LL} > I_{SLG}$$

Three-phase fault is usually used for equipment rating as it's the worst case.

Unbalanced three-phase systems are difficult to analyze directly.

Solution: Decompose into three balanced systems that can be analyzed independently, then recombine.

Invented by Charles Fortescue (1918).

Image: Wikimedia Commons, CC BY-SA 4.0

Positive sequence (1): ABC rotation (normal operating condition)

• Generators produce only positive sequence EMF

Negative sequence (2): ACB rotation (reverse)

• Created by unbalanced conditions
• Causes heating in machines

Zero sequence (0): All three phasors in phase

• Represents ground return current
• Only flows if there's a ground path

Complex operator that rotates by 120°:

$$a = 1 \angle 120° = -0.5 + j0.866$$

$$a^2 = 1 \angle 240° = -0.5 - j0.866$$

$$a^3 = 1$$

$$1 + a + a^2 = 0$$

Phase to sequence:

$$\begin{bmatrix} V_0 \\ V_1 \\ V_2 \end{bmatrix} = \frac{1}{3} \begin{bmatrix} 1 & 1 & 1 \\ 1 & a & a^2 \\ 1 & a^2 & a \end{bmatrix} \begin{bmatrix} V_a \\ V_b \\ V_c \end{bmatrix}$$

Sequence to phase:

$$\begin{bmatrix} V_a \\ V_b \\ V_c \end{bmatrix} = \begin{bmatrix} 1 & 1 & 1 \\ 1 & a^2 & a \\ 1 & a & a^2 \end{bmatrix} \begin{bmatrix} V_0 \\ V_1 \\ V_2 \end{bmatrix}$$

For each fault type, connect sequence networks differently:

Maximum power (MVA) or current (kA) that flows during a fault at a given point.

Two expressions:

$$\text{Fault MVA} = \frac{S_{base}}{Z_{pu}}$$

$$\text{Fault kA} = \frac{\text{Fault MVA}}{\sqrt{3} \times kV}$$

For three-phase fault at a bus:

$$I_f (pu) = \frac{V_{pre-fault}}{Z_{total}}$$

Usually assume $V_{pre-fault} = 1.0$ pu.

Example: If total impedance to fault = 0.1 pu:

$$I_f = \frac{1.0}{0.1} = 10 \text{ pu}$$

Quick calculation without per-unit conversion:

Series impedances: $\frac{1}{MVA_{total}} = \frac{1}{MVA_1} + \frac{1}{MVA_2}$

Parallel sources: $MVA_{total} = MVA_1 + MVA_2$

Example:

• Grid infeed: 500 MVA
• Transformer: 10% on 20 MVA base → $\frac{20}{0.1} = 200$ MVA

$$\frac{1}{MVA_f} = \frac{1}{500} + \frac{1}{200}$$

$$MVA_f = 143 \text{ MVA}$$

Ratio of reactance to resistance in fault path.

Importance:

• Determines DC offset decay rate
• Affects peak asymmetrical current
• Higher X/R → slower decay → higher peak

Typical values:

• Transmission: X/R = 15-30
• Distribution: X/R = 5-15
• LV systems: X/R = 2-5

Making current: Peak asymmetrical (first half-cycle)

$$I_{peak} = I_{sym} \times \sqrt{2} \times (1 + e^{-\frac{R}{X}\$$pi})

Breaking current: RMS symmetrical (after few cycles)

Circuit breakers rated for both values.

All equipment must withstand fault conditions:

Under-rated equipment can fail catastrophically during faults.

Relay settings require accurate fault currents:

• Pick-up settings: Must detect minimum fault current
• Time grading: Based on fault magnitude variation
• Reach settings: Distance relays need accurate impedances

Wrong fault data = wrong protection = nuisance trips or failure to operate.

Arc flash energy proportional to fault current and duration:

$$E = I^{1.081} \times t \times k$$

Higher fault level → higher incident energy → more PPE required.

IEEE 1584 standard requires fault study for arc flash assessment.

Adding DG increases fault levels:

• Synchronous generators: Contribute 4-6× rated current
• Inverter-based (solar/wind): Limited to 1.1-1.5× rated

Existing equipment may become under-rated when DG added.

Re-assessment required for any new generation connection.

Key fault calculation standards:

• IEC 60909: International standard, uses voltage factors
• IEEE C37 series: North American practice
• ENA G74: UK-specific for DG connections

IPSA supports IEC 60909 and multiple other methods.

Detect abnormal conditions and isolate faulted equipment to:

• Protect people from electric shock and arc flash
• Limit equipment damage by clearing faults quickly
• Maintain system stability by preventing cascade failures
• Minimize outage extent by isolating only faulted section

Speed: Clear faults quickly (typically <100ms for transmission)

• Limits equipment damage
• Reduces arc flash energy
• Maintains stability

Selectivity: Only trip the minimum necessary equipment

• Also called "discrimination"
• Faulted section isolated, rest remains energized

Sensitivity: Detect all faults, even low-magnitude ones

• Must see minimum fault current
• Balance with security (avoid nuisance trips)

Security/Reliability: Operate when required, not otherwise

• Dependability: Will operate for genuine faults
• Security: Won't operate for external faults or load

Image: Wtshymanski, Wikimedia Commons, CC BY-SA 3.0

CT (Current Transformer): Measures current, isolates relay from HV

VT (Voltage Transformer): Measures voltage, provides isolation

Relay: Processes CT/VT signals, makes trip decision

Circuit Breaker: Interrupts fault current

DC Supply: Battery-backed power for relays and trip coils

Fault → CT/VT detect → Relay processes → Trip signal → Breaker opens

Typical times:

• Relay operation: 20-40 ms
• Breaker operation: 40-80 ms
• Total clearance: 60-120 ms (transmission)
• Distribution: up to 500 ms+ (for coordination)

Trips when current exceeds a threshold.

50 - Instantaneous: Fixed time, high pickup

• Typically set to see close-in faults only
• Operates in 20-50 ms

51 - Time Overcurrent: Inverse time characteristic

• Higher current = faster operation
• Allows coordination with downstream devices

Application: Distribution networks, motor protection, backup protection

Inverse Definite Minimum Time curves:

Image: Wikimedia Commons, CC BY-SA 4.0

$$t = \frac{TMS \times k}{(I/I_s)^\alpha - 1}$$

Where:

• TMS = Time Multiplier Setting
• $I_s$ = Pick-up current setting
• k, α = curve constants

VI/EI used where fault current varies significantly with location.

Measures impedance (Z = V/I) to determine fault location.

Zones:

• Zone 1: 80-85% of line, instantaneous
• Zone 2: 100-120% of line, ~0.3s delay
• Zone 3: 150-200%, backup, ~1s delay

Application: Transmission line protection

Compares current entering vs leaving protected zone.

$$I_{operate} = |I_{in} - I_{out}|$$

If difference exceeds threshold → internal fault → trip.

Key property: 100% selective - only operates for internal faults

Applications:

• Transformer (87T)
• Generator (87G)
• Busbar (87B)
• Motor (87M)

Standard numbering for protection functions:

Suffix letters: N=neutral, G=ground, T=transformer

Goal: Only the device closest to the fault should operate.

If fault at point F:

Source ──[A]──[B]──[C]── F ──[Load]

Relay C should trip first. If C fails, B backs up. If B fails, A backs up.

Achieved through time grading and/or current grading.

Upstream devices have progressively longer delays.

Coordination Time Interval (CTI): 0.3 - 0.5 seconds

Accounts for:

• Breaker operating time (~50-80 ms)
• Relay overshoot (~50 ms)
• Safety margin (~100 ms)

Example:

• Relay C: 0.1s at max fault
• Relay B: 0.1 + 0.4 = 0.5s
• Relay A: 0.5 + 0.4 = 0.9s

Use fault current magnitude differences to discriminate.

Fault current decreases with distance from source due to line impedance.

Set instantaneous elements (50) to see only close-in faults:

$$I_{pickup} > I_{fault,downstream}$$

Limitation: Doesn't work well on short feeders or where fault current doesn't vary much.

For IDMT relays, check coordination at maximum fault current through both devices:

1. Calculate downstream relay time at max fault
2. Add CTI (0.3-0.5s)
3. Calculate upstream TMS to achieve this time

$$TMS_{upstream} = \frac{(t_{downstream} + CTI) \times ((I/I_s)^\alpha - 1)}{k}$$

Parallel feeders: Both see same fault current - need directional elements (67)

Ring networks: Fault current from both directions - need directional or differential

DG infeed: Changes fault current magnitude and direction

Motor contribution: Adds to fault current, decays quickly

Log-log plot showing operating time vs current.

Axes:

• X-axis: Current (log scale), usually in Amps
• Y-axis: Time (log scale), in seconds

Why log-log? Covers wide ranges (0.01s to 1000s, 10A to 100kA)

Fuses: Show as bands (two lines)

• Left line: Minimum melting time
• Right line: Total clearing time

Relays: Show as single lines (adjustable)

• Family of curves for different TMS settings

Breakers: Vertical lines at:

• Continuous rating
• Instantaneous trip (if equipped)

Rules for proper coordination:

1. Downstream curve must be below and left of upstream
2. Maintain CTI gap at all fault current levels
3. Check at both minimum and maximum fault points

Crossover: Where curves intersect = loss of coordination

Equipment withstand limits plotted on same TCC:

Cable damage curve: $$I^2 t = k$$ Where k depends on conductor material and insulation

Transformer: Inrush point and thermal damage

Motor: Starting current and locked rotor time

Rule: Protective device curve must be left of damage curve (faster operation).

Reading a coordination study:

Time (s)
1000 |
 100 |          [Upstream Relay]
  10 |     [Downstream Relay]
   1 |  
 0.1 | [Fuse]
0.01 |_________________________
     10   100   1k   10k   Current (A)

Check gaps between curves at fault current levels.

A zone is an area of the network protected by a specific relay or set of relays.

Zone boundaries defined by CT locations.

Principle: Every element must be within at least one zone.

Zones should overlap at circuit breakers to avoid blind spots.

Zone A              Zone B
|<────────────>|<────────────>|
CT            CB            CT

Fault at CB location seen by both zones - both may trip (acceptable for reliability).

First line of defense for a zone.

Characteristics:

• Fast operation (instantaneous or Zone 1)
• Highly selective (only for internal faults)
• Examples: Differential (87), Distance Zone 1 (21)

Should clear ~90% of faults.

Local backup: Duplicate protection within same zone

• Same speed and selectivity as primary
• Protects against relay/CT failure
• Example: Dual main protections

Remote backup: Protection from adjacent zones

• Slower (time-delayed)
• Less selective (trips more than necessary)
• Example: Distance Zone 2/3, time-graded overcurrent

What if the breaker doesn't open?

Breaker Failure (50BF):

1. Trip signal sent to breaker
2. Timer starts (typically 150-200ms)
3. If fault current still flowing → trip all adjacent breakers

Last resort backup - isolates larger area but prevents catastrophic failure.

Image: Wikimedia Commons, CC BY-SA 3.0

Voltage transformation by turns ratio:

$$\frac{V_1}{V_2} = \frac{N_1}{N_2}$$

Ratings specified:

• MVA (apparent power)
• Primary/secondary voltage (kV)
• Impedance (%Z on rating)
• Vector group

Impedance limits fault current and causes voltage drop.

Typical values:

• Distribution (11/0.4kV): 4-6%
• Primary (33/11kV): 7-10%
• Transmission (132/33kV): 10-15%

Fault current through transformer:

$$I_{fault} = \frac{100}{Z\%} \times I_{rated}$$

Example: 10% impedance → fault current = 10× rated

Adjust turns ratio to regulate voltage.

OLTC (On-Load Tap Changer):

• Changes taps without interrupting load
• Typical range: ±10% in 1.25% or 1.67% steps
• Located on HV winding (lower current)
• Automatic voltage regulation (AVR) control

Off-circuit tap changer:

• Must de-energize to change
• Used for fixed adjustment only

Image: Wikimedia Commons

Notation describes winding connections and phase shift.

Letters:

• D/d = Delta
• Y/y = Star (Wye)
• N/n = Neutral brought out
• Capital = HV, lowercase = LV

Number: Phase shift in clock hours (× 30°)

Common groups:

Transformers in parallel must have:

1. Same vector group (or compatible: Dy1 with Dy1)
2. Same voltage ratio (within tap range)
3. Similar impedance (within 10% for load sharing)

Mismatched vector groups → circulating currents → overheating

Image: Wikimedia Commons, CC BY-SA 3.0

Layers (inside out):

1. Conductor (copper or aluminium)
2. Conductor screen
3. Insulation (XLPE, EPR, or PVC)
4. Insulation screen
5. Metallic sheath/screen
6. Outer sheath (PE or PVC)

Insulation temperature limits:

• XLPE: 90°C continuous, 250°C short-circuit
• PVC: 70°C continuous

Cables have higher R/X ratio than overhead lines.

Typical values at 50Hz:

High R/X ratio means voltage drop dominated by real power at LV.

Maximum continuous current limited by:

• Conductor temperature
• Insulation thermal limits
• Heat dissipation (installation method)

Base rating from manufacturer tables, then apply derating:

$$I_{rated} = I_{base} \times K_1 \times K_2 \times K_3 \times K_4$$

Example: 400A base × 0.9 × 0.7 × 0.95 × 0.98 = 235A

Three-phase voltage drop:

$$\Delta V = \frac{\sqrt{3} \times I \times L \times (R \cos\phi + X \sin\phi)}{1000}$$

Where:

• I = current (A)
• L = length (m)
• R, X = resistance, reactance (Ω/km)

UK limits (BS 7671):

• Lighting: 3%
• Other: 5%
• Total from origin: 5%

Image: Wikimedia Commons, CC BY-SA 4.0

Conductor types:

• ACSR: Aluminium Conductor Steel Reinforced
• AAAC: All Aluminium Alloy Conductor
• HTLS: High Temperature Low Sag (for uprating)

Typical spans:

• Distribution: 50-150m
• Transmission: 300-500m

Overhead lines have lower R/X ratio than cables.

Typical values (per km):

Higher X due to wider conductor spacing (air insulation).

Current limited by conductor temperature (sag limit or annealing).

Static rating: Conservative fixed value

• Assumes: high ambient, full sun, low wind
• Typically 50-75% of actual capacity

Dynamic Line Rating (DLR): Real-time calculation

• Uses weather data (wind, ambient, solar)
• Can increase capacity 10-30%
• Requires monitoring equipment

Conductor sag increases with:

• Temperature (thermal expansion)
• Current (resistive heating)
• Ice loading (weight)

Sag formula (parabolic approximation):

$$S = \frac{wL^2}{8T}$$

Where:

• w = weight per unit length
• L = span length
• T = conductor tension

Clearance requirements (to ground, buildings, other lines) set maximum allowable sag.

Image: Wikimedia Commons, Public Domain

Speed-frequency relationship:

$$f = \frac{P \times N}{120}$$

Where:

• f = frequency (Hz)
• P = number of poles
• N = speed (rpm)

For 50Hz: 2-pole = 3000rpm, 4-pole = 1500rpm

Multiple reactances for different timescales:

Fault studies use $X''_d$ for maximum (initial) fault current.

Image: Wikimedia Commons, CC BY-SA 4.0

P-Q diagram showing operating limits:

Limits:

• Right arc: Armature current (MVA rating)
• Top arc: Field current (over-excitation)
• Bottom curve: Stator end heating (under-excitation)
• Vertical line: Prime mover (MW limit)

Generator can operate anywhere inside the curve.

Field current controls reactive power output:

Over-excited: High field current → exports Q → supports voltage

Under-excited: Low field current → absorbs Q → may depress voltage

AVR (Automatic Voltage Regulator):

• Maintains terminal voltage setpoint
• Adjusts field current automatically
• Droop setting for load sharing

In load flow analysis:

PV mode (voltage control):

• P and V specified
• Q calculated (within limits)
• Normal operation

PQ mode (fixed output):

• P and Q both specified
• V calculated
• Used when at reactive limit

Slack bus:

• V and θ specified (reference)
• P and Q calculated
• Balances system losses

Generator fault current decays over time:

$$I''_f = \frac{E''}{X''_d}$$ (sub-transient, first few cycles)

$$I'_f = \frac{E'}{X'_d}$$ (transient, up to ~2 seconds)

$$I_f = \frac{E}{X_d}$$ (steady-state, if fault sustained)

Typical contribution: 4-6× rated current initially

Image: Wikimedia Commons, CC BY-SA 3.0

Connection chain:

PV Panels (DC) → Inverter (DC/AC) → Transformer → Grid

Inverter functions:

• DC to AC conversion
• Maximum Power Point Tracking (MPPT)
• Grid synchronisation
• Power factor control
• Anti-islanding protection

Image: Arne Nordmann, Wikimedia Commons, CC BY-SA 2.5

Two main types:

DFIG (Doubly-Fed Induction Generator):

• Partial converter (30% rating)
• Limited fault ride-through
• Older technology

Full Converter:

• 100% power through converter
• Better fault ride-through
• Decoupled from grid frequency
• Modern standard

Voltage level based on capacity:

DNO specifies minimum connection voltage in offer.

Key differences from synchronous machines:

Grid-forming vs Grid-following:

• Grid-following: Needs grid voltage reference
• Grid-forming: Can establish voltage/frequency (emerging)

Typical DG connection includes:

• Inverter(s) with protection settings
• LV switchboard with metering
• Transformer (if HV connection)
• HV switchgear (ring main unit or circuit breaker)
• G99 protection relay (interface protection)
• Metering (import/export, half-hourly)

Engineering Recommendation G99 (replaced G59 in 2019)

Aligns UK with EU Requirements for Generators (RfG).

Applies to all new generation connecting to distribution networks (up to 132kV).

Key document: ENA Engineering Recommendation G99

Based on capacity and connection voltage:

Higher types have more onerous requirements.

Frequency response:

• LFSM-O: Reduce output above 50.4Hz
• LFSM-U: Maintain output down to 47.5Hz
• FSM: Optional fast frequency response

Voltage ride-through:

• Must stay connected during voltage dips
• Type-dependent duration and depth

Reactive capability:

• Power factor range (typically 0.95 lag to 0.95 lead)
• Voltage control modes

Protection settings:

• Over/under frequency and voltage
• Rate of Change of Frequency (RoCoF)
• Vector shift (Loss of Mains)

G100 allows connection where network capacity is limited.

Active Network Management (ANM):

• Real-time curtailment signals
• Generator reduces output when network constrained
• Enables more DG without reinforcement

Principle of Access:

• Last-in, first-off (LIFO)
• Or pro-rata sharing

Steps to connect:

1. Application: Submit G99 form A to DNO
2. Assessment: DNO studies impact (4-12 weeks)
3. Offer: Connection offer with costs and timescales
4. Acceptance: Sign agreement, pay charges
5. Design: Detailed design and approval
6. Construction: Install equipment
7. Commissioning: Witness tests, settings verification
8. Energisation: Final Operating Notification (FON)

Typical timescales: 3-18 months depending on complexity

Traditional networks designed for one-way power flow:

Substation → Feeder → Loads
(Voltage drops along feeder)

With DG, power can flow backwards:

Substation ← DG export
(Voltage rises at DG location)

Voltage may exceed statutory limits (+10% / -6% in UK).

Approximate voltage change from injected power:

$$\Delta V \approx \frac{P \cdot R + Q \cdot X}{V}$$

Where:

• P, Q = active/reactive power injection
• R, X = resistance/reactance to source
• V = nominal voltage

In per-unit:

$$\Delta V_{pu} \approx P_{pu} \cdot R_{pu} + Q_{pu} \cdot X_{pu}$$

Key insight: At LV, voltage rise mainly from real power export.

Reactive power absorption has limited effect on LV voltage.

Statutory limits (ESQCR):

• LV: 230V +10% / -6% (216V to 253V)
• HV: ±6% of nominal

DNO planning limits (more conservative):

• Typically allow +3% rise from DG at minimum load
• Ensures headroom for voltage regulation

Network solutions:

• Conductor upgrades (reduce R)
• New transformer (reduce impedance)
• Voltage regulators / boosters

DG solutions:

• Reactive power absorption (Q negative)
• Power factor control (limited at LV)
• Active power curtailment
• Export limiting (G100)

Smart solutions:

• OLTC coordinated control
• Active Network Management (ANM)
• Battery storage for peak shaving

Image: Wikimedia Commons, CC BY-SA 4.0

Islanding: DG continues to energise a section of network that has been disconnected from the main grid.

Can occur when:

• Upstream breaker opens (fault, maintenance)
• DG output matches local load (balanced island)

Safety:

• Network assumed dead may be live
• Risk to personnel working on "isolated" network
• Public contact with downed conductors

Equipment:

• Poor power quality (voltage/frequency drift)
• Out-of-phase reclosing (severe damage)
• Fault clearance failure (no grid fault current)

Requirement: Disconnect within 2 seconds of island forming.

Detect abnormal conditions caused by islanding:

Limitation: May not detect balanced island (generation = load).

Inverter deliberately perturbs output to detect island:

Frequency shift: Slight bias causes runaway if islanded

Reactive power variation: Inject Q pulses, monitor V response

Impedance measurement: Inject signal, measure grid impedance

More reliable than passive methods but can interact between multiple inverters.

Loss of Mains (LoM) protection settings:

Note: RoCoF settings relaxed from 0.125 Hz/s to 1.0 Hz/s to improve stability with low inertia.

Vector shift generally not used in UK (nuisance tripping).

G99-compliant protection relay provides:

• Voltage and frequency protection (27, 59, 81)
• RoCoF protection (df/dt)
• Intertrip receive (from DNO)
• Status monitoring and event logging

Must be type-tested to G99 requirements.

Common manufacturers: Woodward, Schneider, ABB, Siemens

Image: Wikimedia Commons, CC BY-SA 3.0

Great Britain has a unified synchronous grid covering England, Wales, and Scotland.

Northern Ireland is part of the all-island Irish system (connected via HVDC).

Key principle: Separation of system operation from asset ownership.

NESO (formerly National Grid ESO, separated October 2024)

Role: Balances supply and demand in real-time

Responsibilities:

• Frequency control (maintain 50Hz ± 0.5Hz)
• Voltage management
• Constraint management
• Balancing mechanism operation
• Future Energy Scenarios (FES)
• Network planning and connections

Not an asset owner - operates the system impartially.

Own and maintain the high-voltage transmission network:

Note: 132kV is transmission in Scotland, distribution in England & Wales.

Regulated by Ofgem under RIIO-T2 price control.

Own and operate local distribution networks:

14 licensed DNO areas across GB.

Regulated under RIIO-ED2 price control.

Ofgem: Independent regulator

• Sets price controls (allowed revenues)
• Enforces licence conditions
• Protects consumer interests

ELEXON: Settlement body

• Balancing and Settlement Code (BSC)
• Calculates imbalance charges

Energy Networks Association (ENA):

• Industry body for network operators
• Publishes Engineering Recommendations (G99, P28, etc.)

Supergrid (England & Wales):

• 400kV - Main bulk transmission
• 275kV - Older transmission, some areas

Scotland:

• 400kV, 275kV - Main transmission
• 132kV - Transmission (not distribution)

Interconnectors:

• HVDC links to France, Netherlands, Belgium, Norway, Ireland
• Typically ±320kV to ±525kV DC

Note: Some areas have 20kV or 22kV instead of 11kV.

Grid Supply Point (GSP):

• Transmission to distribution interface
• 400kV/275kV → 132kV (or 33kV in some areas)
• Metering point for settlement

Bulk Supply Point (BSP):

• 132kV → 33kV transformation
• Feeds multiple primary substations

Primary Substation:

• 33kV → 11kV transformation
• Feeds HV distribution network

Secondary Substation (Distribution):

• 11kV → 400V transformation
• Pole-mounted or ground-mounted
• Feeds LV network to consumers

Typical voltage hierarchy:

400kV ──┬── GSP
        │
132kV ──┼── BSP
        │
 33kV ──┼── Primary
        │
 11kV ──┼── Secondary
        │
400V ───┴── Consumer

Each step typically has 2-3 transformers for redundancy.

Nominal voltage: System design voltage (e.g., 11kV, 400V)

Declared voltage: What supplier declares to customers

• LV: 230V (was 240V until 1995 harmonisation)
• Tolerance: +10% / -6% (216V to 253V)

Historical note: UK moved from 240V ±6% to 230V +10%/-6%, effectively the same range but aligned with European standard.

Engineering Recommendations (ERECs) published by ENA:

Industry-agreed technical standards for:

• Generator connections (G-series)
• Power quality (P-series)
• Design and planning (various)

Not legally binding but effectively mandatory via DNO connection agreements.

G99: Requirements for connection of generation equipment

Replaced G59 (large) and G83 (small) in April 2019.

Scope: All generation 0.8kW to 50MW connecting at <110kV

Key requirements:

• Frequency and voltage ride-through
• Reactive capability
• Protection settings (LoM, over/under V & f)
• Compliance process and testing

See earlier topic on G99 for details.

G100: Technical requirements for export limiting schemes

Allows connection where network capacity limited:

• ANM (Active Network Management): Real-time curtailment
• Export limiting: Fixed maximum export
• Timed connections: Export only at certain times

Enables more DG without costly reinforcement.

P28: Planning limits for voltage fluctuations

Flicker: Rapid voltage variations causing visible light flicker

Limits:

• Short-term severity $P_{st} \leq 1.0$
• Long-term severity $P_{lt} \leq 0.8$
• Step changes $\leq 3\%$ (frequent) or 6% (infrequent)

Causes: Motor starting, arc furnaces, wind turbines

Assessment: Required for large loads or generation connections

P29: Planning limits for voltage unbalance

Unbalance: Difference between phase voltages

$$\text{VUF} = \frac{V_2}{V_1} \times 100\%$$

Where $V_2$ = negative sequence, $V_1$ = positive sequence

Limits:

• Planning level: 1.3%
• Compatibility level: 2.0%

Causes: Single-phase loads, unbalanced three-phase loads

G5/4-1: Planning levels for harmonic voltage distortion

THD (Total Harmonic Distortion):

$$THD = \frac{\sqrt{\sum_{h=2}^{40} V_h^2}}{V_1} \times 100\%$$

Planning limits (% of fundamental):

Causes: Power electronics, VFDs, rectifiers, LED lighting

Security standards:

• SQSS: Security and Quality of Supply Standard (transmission)
• P2/6: Security of supply (distribution) - being replaced by P2/8

Design standards:

• BS 7671: Wiring Regulations (LV installations)
• ENA TS 41-24: Guidelines for LV connections

Grid codes:

• Grid Code: Transmission-connected parties
• Distribution Code: Distribution-connected parties
• CUSC: Connection and Use of System Code

Target: 50.00 Hz ± 0.2 Hz (normal operating range)

Frequency rises when generation > demand Frequency falls when demand > generation

Response services:

NESO procures these services from generators and batteries.

BM: Real-time market for balancing

How it works:

1. Generators/suppliers submit bids and offers
2. Bid: Price to reduce output (or increase demand)
3. Offer: Price to increase output (or reduce demand)
4. NESO accepts bids/offers to balance system
5. Settled at bid/offer price (pay-as-bid)

Gate closure: 1 hour before delivery

Imbalance price: Cash-out for parties not in balance

Constraint: When power flow exceeds line/transformer rating

Causes:

• High renewable output in weak areas
• Outages reducing network capacity
• Demand patterns

Actions:

• Re-dispatch generation (BM actions)
• Curtail wind/solar
• Intertrips (automatic post-fault)

Constraint costs: £500M+ annually (growing with renewables)

NESO forecasts demand to plan generation:

Timescales:

• Week ahead: Unit commitment
• Day ahead: Final schedules
• Intraday: Adjustments
• Real-time: Balancing actions

Factors:

• Weather (temperature, wind, solar)
• Time of day/week/year
• TV pickups (kettles at half-time!)
• Bank holidays
• COVID showed how much patterns can change

System operation becoming more complex:

Low inertia:

• Less synchronous generation
• Faster frequency changes
• Need for synthetic inertia from batteries/IBRs

Variable renewables:

• High instantaneous penetration (>70% at times)
• Need for flexibility (storage, DSR, interconnectors)

Distributed resources:

• Millions of small generators/batteries
• Visibility challenge for NESO
• Local vs national balancing