Distributed Generation

Photovoltaic Effect Fundamentals

Solar photovoltaic (PV) systems convert sunlight directly into electricity using semiconductor materials. When photons strike a PV cell, they excite electrons in the semiconductor material, creating electron-hole pairs. The built-in electric field of the p-n junction separates these charge carriers, producing direct current.

Cell Types and Characteristics

Series and Parallel Configurations

Modules in series increase voltage while maintaining current: $$V_{string} = n \times V_{module}$$ $$I_{string} = I_{module}$$

Modules in parallel increase current while maintaining voltage: $$V_{array} = V_{module}$$ $$I_{array} = n \times I_{module}$$

I-V Curve and Key Parameters

The current-voltage relationship follows the diode equation. Key points:

• Short-circuit current ($I_{SC}$): Maximum current when V = 0
• Open-circuit voltage ($V_{OC}$): Maximum voltage when I = 0
• Maximum Power Point (MPP): Where $P = V \times I$ is maximized

Fill Factor

Fill factor quantifies how "square" the I-V curve is: $$FF = \frac{V_{MPP} \times I_{MPP}}{V_{OC} \times I_{SC}} = \frac{P_{max}}{V_{OC} \times I_{SC}}$$

Typical values: 0.7-0.85 for crystalline silicon cells.

Module Efficiency

$$\eta = \frac{P_{max}}{G \times A} \times 100\%$$

Where $G$ = irradiance (W/m²) and $A$ = module area (m²).

Battery Types for Energy Storage

Capacity Calculations

Amp-hour capacity (Ah): $$C_{Ah} = I_{discharge} \times t_{hours}$$

Energy capacity (kWh): $$E_{kWh} = \frac{V_{nominal} \times C_{Ah}}{1000}$$

C-Rate

C-rate defines charge/discharge rate relative to capacity: $$\text{C-rate} = \frac{I_{charge/discharge}}{C_{rated}}$$

A 100Ah battery at 1C discharges at 100A (fully discharged in 1 hour). At 0.5C: 50A (2 hours). At 2C: 200A (30 minutes).

Depth of Discharge (DoD) and State of Charge (SoC)

$$DoD = \frac{C_{used}}{C_{rated}} \times 100\%$$

$$SoC = 100\% - DoD = \frac{C_{remaining}}{C_{rated}} \times 100\%$$

Usable Capacity

$$C_{usable} = C_{rated} \times (DoD_{max} - DoD_{min})$$

For LFP batteries with 90% usable DoD: $C_{usable} = 0.9 \times C_{rated}$

Round-trip Efficiency

$$\eta_{RT} = \frac{E_{discharged}}{E_{charged}} \times 100\%$$

Typical values: Li-ion 86-88%, Lead-acid 79-85%.

Grid-tied (On-Grid) Systems

Grid-tied systems operate in parallel with the utility network.

Architecture: PV array → Grid-tie inverter → AC panel → Utility meter → Grid

Advantages:

• Lower initial cost (no batteries)
• Higher overall efficiency
• Net metering benefits
• Grid acts as infinite "storage"

Limitations:

• No backup during outages (anti-islanding protection)
• Subject to grid regulations and export limits

Off-grid (Stand-alone) Systems

Off-grid systems operate independently without utility connection.

Architecture: PV array → Charge controller → Battery bank → Off-grid inverter → AC loads

Battery sizing requirement: $$C_{battery} = \frac{E_{daily} \times \text{Days of autonomy}}{V_{system} \times DoD_{max} \times \eta_{inverter}}$$

Hybrid Systems

Combine grid connection with battery backup:

• AC-coupled or DC-coupled configurations
• Seamless transfer during outages
• Can operate in grid-tied or island mode

Self-consumption vs Export

Self-consumption ratio: $$SCR = \frac{E_{consumed\text{ }directly}}{E_{generated}} \times 100\%$$

Higher self-consumption = better economics when export rates are low.

Feed-in Tariff (FIT) Fundamentals

A feed-in tariff is a policy mechanism offering long-term contracts to renewable energy producers, typically based on cost of generation.

Three key provisions:

1. Guaranteed grid access
2. Stable, long-term purchase contracts (10-25 years)
3. Cost-based payment rates

Payment Structures

Net Metering vs Net Billing

Net Energy Metering:

• Bill credits at full retail rate
• Grid acts as "financial storage"
• Meter runs backward during export

Net Billing:

• Export credited at predetermined sell rate
• Usually lower than retail rate
• Separate import/export accounting

UK Smart Export Guarantee (SEG)

Replaced FIT for new installations from January 2020:

• Suppliers with 150,000+ customers must offer SEG
• Rate must be greater than zero
• Requires MCS certification and DNO notification

Economic Analysis

Simple payback period: $$Payback = \frac{System\text{ }Cost}{Annual\text{ }Savings + Annual\text{ }Export}$$

Levelized Cost of Energy (LCOE): $$LCOE = \frac{\sum_{t=1}^{n}\frac{I_t + M_t}{(1+r)^t}}{\sum_{t=1}^{n}\frac{E_t}{(1+r)^t}}$$

IEC 60038 Voltage Classifications

Extra-Low Voltage Categories

• SELV: Separated Extra-Low Voltage (no earth connection, double insulation)
• PELV: Protective Extra-Low Voltage (earth connection permitted)
• FELV: Functional Extra-Low Voltage (requires additional protection measures)

Regional Voltage Differences

Supply Voltage Tolerance

Per EN 50160 and BS EN 50160: $$V_{supply} = V_{nominal} \pm 10%$$

For 230V nominal: $207V \leq V_{supply} \leq 253V$

Why LV Matters for Distributed Generation

Most domestic and small commercial generation connects at LV level:

• Simpler protection requirements
• Lower cost interconnection
• G98/G99 regulations apply

230V 50Hz System Configuration

Single-phase supply consists of three conductors:

• Live (L): Carries AC current at 230V RMS to neutral
• Neutral (N): Return path, connected to earth at transformer star point
• Earth (E/PE): Safety conductor for fault current

Voltage Waveform

$$v(t) = V_m \sin(\omega t)$$

Where:

• $V_m = \sqrt{2} \times 230 = 325V$ (peak voltage)
• $\omega = 2\$pi f = 314.16 rad/s (at 50Hz)
• Period $T = 1/f = 20$ ms

RMS and Peak Relationship

$$V_{rms} = \frac{V_m}{\sqrt{2}} = \frac{V_{peak}}{\sqrt{2}}$$

Power Calculations

Resistive loads (unity power factor): $$P = V_{rms} \times I_{rms} = VI$$

Reactive loads (with power factor): $$P = VI\cos\phi \text{ (Real power in Watts)}$$ $$Q = VI\sin\phi \text{ (Reactive power in VAr)}$$ $$S = VI \text{ (Apparent power in VA)}$$

Power Triangle

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

Typical Domestic Capacity

UK domestic supplies typically:

• 60A or 80A main fuse (older properties)
• 100A main fuse (modern properties)
• Maximum demand: ~23kW at 100A

Fundamental Relationships

Three phases displaced by 120° (or 2π/3 radians): $$V_A = V_m\sin(\omega t)$$ $$V_B = V_m\sin(\omega t - 120°)$$ $$V_C = V_m\sin(\omega t + 120°)$$

The √3 Factor

Line voltage to phase voltage relationship: $$V_L = \sqrt{3} \times V_P$$

For EU systems: $V_L = \sqrt{3} \times 230V = 400V$

This factor arises from the vector sum of two phase voltages 120° apart.

Star (Wye) Connection

$$V_L = \sqrt{3} \times V_P$$ $$I_L = I_P$$

• Neutral available for single-phase loads
• Common for distribution systems

Delta Connection

$$V_L = V_P$$ $$I_L = \sqrt{3} \times I_P$$

• No neutral conductor
• Common for motors and transformers

Three-Phase Power

$$P_{3\phi} = \sqrt{3} \times V_L \times I_L \times \cos\phi$$ $$P_{3\phi} = 3 \times V_P \times I_P \times \cos\phi$$

Balanced System Property

In a balanced three-phase system: $$I_A + I_B + I_C = 0$$ (vector sum)

This means neutral current is zero for balanced loads.

Why Three-Phase for Larger Installations?

• More power for same conductor size
• Constant instantaneous power (no pulsation)
• More efficient for motors
• Required for generation >3.68kW single-phase

Definition

The Point of Common Coupling (PCC) is the interface point where a distributed energy resource connects to the utility distribution network. It's the electrical location where:

• Power quality measurements are taken
• Interconnection requirements are enforced
• Protection coordination is established
• Multiple customers may share the connection

Why PCC Matters for Distributed Generation

Power Quality Control:

• THD limits measured at PCC (typically <5%)
• Voltage regulation requirements apply at PCC
• Flicker limits (Pst, Plt) assessed at PCC

Voltage Impact: $$\Delta V_{PCC} = \frac{P \times R + Q \times X}{V_{PCC}}$$

Protection Coordination at PCC

IEEE 1547 voltage ride-through requirements:

Fault Current at PCC

Total fault current includes utility and DER contributions: $$I_{fault(total)} = I_{fault(utility)} + I_{fault(DER)}$$

Power Flow Direction at PCC

$$P_{PCC} = P_{generation} - P_{load}$$

• Positive $P_{PCC}$: Export to grid
• Negative $P_{PCC}$: Import from grid

Short Circuit Ratio at PCC

$$SCR = \frac{S_{SC}}{S_{DER}}$$

• SCR > 20: Stiff grid (small voltage impact)
• SCR < 10: Weak grid (significant voltage impact)

Grid Synchronization

Grid-tied inverters must precisely match the grid's voltage, frequency, and phase before connecting. Failure to synchronize properly causes large transient currents that can damage equipment and trip protection.

Synchronization Requirements

Three conditions must be met before closing the grid connection:

Phase-Locked Loop (PLL)

The PLL is the core synchronization mechanism. It continuously tracks the grid voltage and generates a reference signal locked to the grid phase:

$$\theta_{grid} = \int \omega_{grid} \, dt$$

The PLL uses feedback to minimize phase error:

$$e_{\phi} = \theta_{ref} - \theta_{measured}$$

A PI controller adjusts the internal oscillator frequency until $e_{\phi} \rightarrow 0$.

Synchronization Sequence

1. Monitoring: Measure grid V, f, φ continuously
2. Ramping: Adjust inverter output to match grid
3. Verification: Confirm all parameters within tolerance
4. Connection: Close contactor when synchronized
5. Current injection: Begin power export

The synchronization time typically ranges from 20ms to 5 seconds depending on grid stability and inverter design.

Grid-Following Inverter

Grid-following (also called grid-feeding) inverters treat the grid as a stiff voltage source and inject current synchronized to the grid voltage. This is the dominant topology for residential and commercial solar installations.

Operating Principle

The inverter acts as a controlled current source:

$$i_{inv}(t) = I_m \sin(\omega_{grid} t + \phi)$$

Where:

• $I_m$ = current amplitude (controlled by MPPT)
• $\omega_{grid}$ = grid angular frequency (from PLL)
• $\phi$ = phase angle (typically 0° for unity power factor)

Control Architecture

PV Array → DC-DC (MPPT) → DC Link → DC-AC Inverter → Filter → Grid
                            ↑                           ↓
                       DC voltage              Current control
                        control                   (PLL-based)

Power Control

Real and reactive power are controlled via current magnitude and phase:

$$P = V_{grid} \cdot I_{inv} \cdot \cos(\phi)$$ $$Q = V_{grid} \cdot I_{inv} \cdot \sin(\phi)$$

Limitations

• Cannot operate without grid: Requires grid voltage reference
• Stability concerns: High penetration can cause voltage/frequency issues
• No black start capability: Cannot energize a dead grid

Grid-following inverters comply with IEEE 1547 and G98/G99 requirements for anti-islanding - they must disconnect within 2 seconds of grid loss.

Grid-Forming Inverter

Grid-forming inverters create their own voltage and frequency reference, behaving as a voltage source rather than current source. They can operate independently or support weak grids.

Operating Principle

The inverter maintains a controlled output voltage:

$$v_{inv}(t) = V_m \sin(\omega_0 t + \delta)$$

Where:

• $V_m$ = voltage amplitude (regulated)
• $\omega_0$ = internal frequency reference
• $\delta$ = power angle (determines power flow)

Droop Control

Grid-forming inverters use droop characteristics to share load and maintain stability:

Frequency droop (P-f): $$f = f_0 - m_p (P - P_0)$$

Voltage droop (Q-V): $$V = V_0 - n_q (Q - Q_0)$$

Where $m_p$ and $n_q$ are droop coefficients (typically 2-5%).

Comparison Table

Virtual Synchronous Machine (VSM)

Advanced grid-forming control emulates synchronous generator behaviour:

$$J \frac{d\omega}{dt} = P_{ref} - P_{out} - D(\omega - \omega_0)$$

Where $J$ = virtual inertia, $D$ = damping coefficient.

This provides synthetic inertia to stabilize grid frequency during disturbances.

Maximum Power Point Tracking (MPPT)

Solar panels have a unique operating point where power output is maximized. MPPT algorithms continuously find and track this point as conditions change.

I-V and P-V Curves

A PV panel's output varies with voltage:

The maximum power point (MPP) occurs where:

$$\frac{dP}{dV} = 0$$

Since $P = V \times I$:

$$\frac{d(VI)}{dV} = I + V\frac{dI}{dV} = 0$$

At MPP: $\frac{dI}{dV} = -\frac{I}{V}$

Environmental Effects

Temperature coefficient (typical): $-0.4\%/°C$ for power.

MPPT Algorithms

Perturb & Observe (P&O):

• Simplest, most common algorithm
• Periodically changes $V$ and observes $\Delta P$
• If $\Delta P > 0$, continue same direction
• Oscillates around MPP (1-3% power loss)

Incremental Conductance:

• Compare $\frac{dI}{dV}$ with $-\frac{I}{V}$
• More accurate tracking
• Better performance under rapidly changing conditions

MPPT efficiency: $$\eta_{MPPT} = \frac{\int P_{actual} , dt}{\int P_{MPP,ideal} , dt} \times 100%$$

Typical MPPT efficiency: 98-99.5% for quality inverters.

Harmonics & Total Harmonic Distortion

Harmonics are integer multiples of the fundamental frequency (50Hz). Non-linear loads and switching inverters inject harmonic currents that distort the voltage waveform.

Harmonic Series

For a 50Hz fundamental:

Fourier Representation

Any periodic waveform can be decomposed:

$$v(t) = V_1 \sin(\omega t) + \sum_{h=2}^{\infty} V_h \sin(h\omega t + \phi_h)$$

Where $V_h$ = magnitude of harmonic $h$.

Total Harmonic Distortion (THD)

THD quantifies total harmonic content relative to fundamental:

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

For current: $THD_I = \frac{\sqrt{\sum_{h=2}^{\infty} I_h^2}}{I_1} \times 100\%$

Limits and Standards

Harmonic Effects

• Overheating: Transformers, cables, motors
• Resonance: With power factor correction capacitors
• Nuisance tripping: RCDs sensitive to high-frequency
• Meter errors: Older meters may read incorrectly

Inverters use output filters (L, LC, or LCL) to limit harmonic injection below regulatory limits.

Voltage Rise from Power Export

When distributed generation exports power, current flows "backwards" through the distribution network impedance, causing voltage to rise at the point of connection.

The Voltage Rise Problem

In a simple radial network:

Substation ──R+jX──┬── Load A
                   │
                   └── PV System (exporting)

Voltage at PV connection point:

$$V_{PCC} = V_{sub} + \frac{P \cdot R + Q \cdot X}{V_{PCC}}$$

For power export (P negative by convention, or positive export):

$$\Delta V \approx \frac{P_{export} \cdot R + Q \cdot X}{V_{nominal}}$$

Simplified Approximation

For LV networks where $R >> X$:

$$\Delta V \approx \frac{P \cdot R}{V}$$

Example: 4kW export, 0.5Ω line resistance, 230V: $$\Delta V = \frac{4000 \times 0.5}{230} = 8.7V \approx 3.8%$$

Voltage Limits

Mitigation Strategies

1. Reactive power control: Absorb Q to offset voltage rise $$Q_{absorb} = -\frac{P \cdot R}{X}$$ (if X significant)

2. Export limiting: Reduce P when V approaches limit

3. Volt-VAr mode: Automatic Q adjustment based on voltage $$Q = f(V) \text{ per programmed curve}$$

4. Network reinforcement: DNO upgrades cables/transformers

Modern inverters implement Volt-VAr and Volt-Watt response curves per G98/G99 requirements.

Power Factor in Grid-Tied Systems

Power factor describes the phase relationship between voltage and current, and the ratio of real power to apparent power.

Power Factor Definition

$$PF = \frac{P}{S} = \frac{P}{\sqrt{P^2 + Q^2}} = \cos(\phi)$$

Where:

• $P$ = Real power (W) - does useful work
• $Q$ = Reactive power (VAr) - energy storage in L/C
• $S$ = Apparent power (VA) - total current × voltage
• $\phi$ = Phase angle between V and I

Power Triangle

      S (VA)
     /|
    / |
   /  | Q (VAr)
  /φ  |
 ─────┘
  P (W)

$$S^2 = P^2 + Q^2$$

Displacement vs Distortion Power Factor

Displacement PF (fundamental only): $$PF_{disp} = \cos(\phi_1)$$

Distortion PF (due to harmonics): $$PF_{dist} = \frac{1}{\sqrt{1 + THD_I^2}}$$

True Power Factor: $$PF_{true} = PF_{disp} \times PF_{dist}$$

Grid Code Requirements

Inverter Capability

Modern inverters can operate across four quadrants:

Reactive power capability is limited by inverter VA rating: $$Q_{max} = \sqrt{S_{rated}^2 - P^2}$$

Voltage Flicker

Flicker is rapid, repetitive voltage fluctuation that causes visible light intensity changes. Human eyes are most sensitive to fluctuations around 8-10 Hz.

Causes of Flicker

• Cloud transients: Rapid irradiance changes on PV
• Inverter switching: Connection/disconnection events
• Motor starting: Large inrush currents
• Arc furnaces: Industrial loads with erratic current

Flicker Metrics

Short-term flicker severity ($P_{st}$):

• Measured over 10 minutes
• $P_{st} = 1.0$ means threshold of irritability
• Limit: typically $P_{st} < 1.0$

Long-term flicker severity ($P_{lt}$): $$P_{lt} = \sqrt[3]{\frac{1}{12}\sum_{i=1}^{12} P_{st,i}^3}$$

Measured over 2 hours (12 × 10-minute intervals).

Voltage Change Limits

Flicker from PV Systems

Cloud-induced ramp rates can be severe:

$$\frac{dP}{dt} \text{ up to } 100\%/\text{second}$$

Voltage change per power step: $$\Delta V = \frac{\Delta P \cdot R}{V}$$

Mitigation

1. Ramp rate limiting: Limit $dP/dt$ to 10-20%/minute
2. Energy storage: Buffer rapid power changes
3. Reactive power: Fast Q response to oppose ΔV
4. Network stiffness: Lower impedance reduces ΔV

Modern inverters include configurable ramp rate limits and Volt-VAr response to minimize flicker contribution.

Export Limiting

Export limiting restricts the maximum power that can be exported to the grid, regardless of generation capacity or load conditions.

Why Limit Export?

1. Grid capacity constraints: DNO network cannot accept more power
2. Connection agreement: G99 approval may specify export limit
3. Tariff restrictions: Some feed-in tariffs cap export
4. Network charges: Avoid capacity-based export charges
5. Self-consumption optimization: Maximize own use

Export Limit Calculation

At the meter point:

$$P_{export} = P_{generation} - P_{load}$$

Export limiting ensures:

$$P_{export} \leq P_{limit}$$

Therefore generation must be curtailed when:

$$P_{generation} > P_{load} + P_{limit}$$

Implementation Methods

Fixed export limit:

• Inverter configured with maximum export (e.g., 3.68kW for G98)
• Simple but may curtail unnecessarily

Dynamic export limiting:

• CT clamp measures actual export
• Real-time curtailment only when needed
• Maximizes generation within limits

G98/G99 Context

Some DNOs offer "flexible connections" with lower limits but faster approval.

Zero Export Systems

Zero export prevents any power flow to the grid, keeping all generated power within the premises. Required in some jurisdictions or where grid export is prohibited.

Use Cases

• No export permitted: Some countries/utilities prohibit export
• Complex metering: Avoid issues with non-bidirectional meters
• Off-grid backup: Systems that can island but normally grid-tied
• Demand charge reduction: Industrial sites avoiding export complications

Control Strategy

The system must satisfy:

$$P_{export} = 0 \Rightarrow P_{generation} \leq P_{load}$$

Control loop:

1. Measure $P_{grid}$ at meter point (CT clamp)
2. If $P_{grid} < 0$ (exporting): reduce inverter output
3. Target: $P_{grid} \geq 0$ with small margin

$$P_{inverter,setpoint} = P_{load} - P_{margin}$$

Typical margin: 50-200W to prevent accidental export.

Response Time Requirements

System Architecture

Grid ──[Meter]──┬── Main Loads
        ↑       │
       CT       └── [Inverter] ←── PV Array
        │              ↑
        └── Signal ────┘

The CT signal feeds directly to the inverter (Modbus, analog, or proprietary).

Limitations

• Wasted energy: Cannot export excess generation
• Battery recommended: Store excess for later use
• Rapid response needed: Fast communication essential
• Partial self-consumption: May not use all available solar

CT Clamp Monitoring

Current transformers (CTs) measure power flow at key points in the system, enabling intelligent control of generation and export.

CT Operating Principle

A CT is a transformer with the measured conductor as primary:

$$\frac{I_p}{I_s} = \frac{N_s}{N_p}$$

For a clamp-on CT with single primary turn ($N_p = 1$):

$$I_s = \frac{I_p}{N_s}$$

Example: 100A:50mA CT (2000:1 ratio)

• Primary current: 100A
• Secondary current: 50mA
• Turns ratio: 2000:1

Measurement Points

Grid ──[CT1]── Main Panel ──[CT2]── Sub-panel
                  │
             [CT3]└── Inverter ── PV

Power Calculation

With voltage reference:

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

For single-phase: $$P = V_{rms} \cdot I_{rms} \cdot PF$$

For three-phase balanced: $$P = \sqrt{3} \cdot V_L \cdot I_L \cdot PF$$

CT Specifications

Communication Protocols

Dynamic Curtailment

Dynamic curtailment adjusts generation in real-time based on grid conditions, maximizing output while respecting network constraints.

Curtailment Triggers

Volt-Watt Response

G98/G99 mandates Volt-Watt curtailment:

P(%)
100├────────┐
   │        │
   │        ╲
 20│         ╲
   │          ╲────
   └──────────────── V(%)
      100  106  110

$$P = \begin{cases} P_{max} & V < V_1 \ P_{max} \cdot \frac{V_2 - V}{V_2 - V_1} & V_1 \leq V \leq V_2 \ P_{min} & V > V_2 \end{cases}$$

Typical settings: $V_1 = 106\%$, $V_2 = 110\%$, $P_{min} = 20\%$

Frequency-Watt Response

For high frequency events:

$$\Delta P = -k_f \cdot \Delta f$$

Where $k_f$ = droop coefficient (typically 40%/Hz).

At $f > 50.5$ Hz: Begin reducing power At $f > 52$ Hz: Disconnect (protection)

Curtailment Calculation

Energy curtailed over period T:

$$E_{curtailed} = \int_0^T (P_{available} - P_{actual}) \, dt$$

Annual curtailment percentage: $$\text{Curtailment} = \frac{E_{curtailed}}{E_{potential}} \times 100%$$

Typical values: 0-5% for well-designed systems, up to 20% in constrained networks.

Economic Impact

Lost revenue from curtailment:

$$\text{Loss} = E_{curtailed} \times (\text{Export tariff} + \text{Avoided import})$$

Battery storage can capture otherwise-curtailed energy:

$$\text{Recovery} = \min(E_{curtailed}, E_{battery,available}) \times \eta_{battery}$$

Islanding

Islanding occurs when a distributed generator continues to power a section of the network after the grid supply has been disconnected. This creates a dangerous "island" of live conductors.

The Hazard

[Grid] ──X── [Local Network] ←── [DG]
       ↑              ↓
    Open         Still energized!
    breaker      

Dangers:

• Electrocution: Workers assume lines are dead after isolation
• Equipment damage: Voltage/frequency may drift outside limits
• Out-of-phase reconnection: When grid returns, severe transients
• Fire risk: Uncontrolled energy source

Islanding Conditions

For an island to persist, generation must match load:

$$P_{generation} \approx P_{load}$$ $$Q_{generation} \approx Q_{load}$$

The probability of exact balance is low, but the consequences are severe enough to require active prevention.

Non-Detection Zone (NDZ)

The NDZ defines the power mismatch range where islanding may go undetected:

$$\Delta P = P_{gen} - P_{load}$$ $$\Delta Q = Q_{gen} - Q_{load}$$

If $|\Delta P| < \Delta P_{threshold}$ AND $|\Delta Q| < \Delta Q_{threshold}$, detection may fail.

Regulatory Requirements

All grid-tied inverters must include anti-islanding protection as a fundamental safety feature.

Loss of Mains (LoM) Protection

Loss of Mains detection identifies when the grid connection has been lost, triggering immediate disconnection of the distributed generator.

Detection Philosophy

The inverter must detect grid loss even when:

• Local generation exactly matches local load
• Voltage and frequency remain within normal bounds
• No obvious transient occurs

LoM Detection Methods

G98/G99 Requirements

UK installations must implement:

1. Under-voltage: Trip if $V < 0.87 \times V_{nom}$ for > 0.5s
2. Over-voltage: Trip if $V > 1.10 \times V_{nom}$ for > 1.0s
3. Under-frequency: Trip if $f < 47.5$ Hz for > 0.5s
4. Over-frequency: Trip if $f > 52$ Hz for > 0.5s
5. RoCoF: Trip if $|df/dt| > 1$ Hz/s (adjustable)

RoCoF Calculation

$$RoCoF = \frac{df}{dt} = \frac{f(t) - f(t-\Delta t)}{\Delta t}$$

Measured over 100-500ms window. Normal grid RoCoF: < 0.1 Hz/s. Islanding RoCoF: typically > 0.5 Hz/s.

Reconnection Requirements

After LoM trip, reconnection only permitted when:

• Voltage within ±10% for > 60 seconds
• Frequency within ±0.5 Hz for > 60 seconds
• Minimum delay: 20 seconds (G98) to 3 minutes (some utilities)

Passive Anti-Islanding Detection

Passive methods monitor grid parameters without injecting any disturbance. They rely on natural changes when the grid disconnects.

Under/Over Voltage Protection (U/OVP)

Monitors RMS voltage against thresholds:

$$V_{min} < V_{measured} < V_{max}$$

Under/Over Frequency Protection (U/OFP)

Monitors grid frequency:

$$f_{min} < f_{measured} < f_{max}$$

Rate of Change of Frequency (RoCoF)

Detects rapid frequency excursions:

$$\left|\frac{df}{dt}\right| > RoCoF_{setting}$$

Typical setting: 0.5 - 1.0 Hz/s over 500ms window.

Advantages: Fast detection, simple implementation Disadvantages: May trip on genuine grid events

Vector Shift (Phase Jump)

Detects sudden phase angle changes:

$$\Delta\theta = \theta(t) - \theta(t - T)$$

Where $T$ = one cycle (20ms at 50Hz).

Trip if $|\Delta\theta| > 6°$ to $12°$ (adjustable).

Limitations of Passive Methods

All passive methods have a Non-Detection Zone where islanding can persist:

• Balanced load/generation
• High-Q resonant loads
• Multiple inverters on same island

This is why active methods are also required.

Active Anti-Islanding Detection

Active methods deliberately inject small disturbances and measure the grid's response. A stiff grid resists change; an island drifts.

Principle

Inject disturbance → Measure response → Grid present?
                                          ↓
      Minimal change ←─── Yes (stiff grid)
      Large drift ←───── No (island)

Impedance Measurement

Inject a small current at non-fundamental frequency and measure resulting voltage:

$$Z_{grid} = \frac{V_{response}}{I_{inject}}$$

Detection threshold: Typically 2-5× normal impedance.

Active Frequency Drift (AFD)

Also called Sandia Frequency Shift (SFS):

The inverter deliberately pushes frequency slightly:

$$f_{target} = f_{measured} + k \cdot (f_{measured} - f_{nom})$$

Where $k$ = positive feedback gain (typically 0.01-0.05).

• Grid connected: Grid holds frequency stable
• Islanded: Frequency drifts until U/OFP trips

Slip Mode Frequency Shift (SMS)

Phase is advanced when frequency exceeds nominal:

$$\theta_{inv} = \theta_{$$PLL} + k_{SMS} \cdot (f - f_{nom})

This accelerates frequency deviation during islanding.

Reactive Power Variation

Periodically vary Q output:

$$Q(t) = Q_0 + \Delta Q \cdot \sin(2\$$pi f_{probe} t)

Monitor voltage response at $f_{probe}$.

Comparison

Modern inverters combine multiple methods for robust detection across all scenarios.

G98: Small-Scale Generation

G98 (formerly G83) is the UK standard for connecting small-scale embedded generators to the low voltage distribution network. It provides a simplified "fit and notify" process for domestic installations.

Scope

The 3.68 kW limit derives from 16A × 230V = 3,680W.

Key Requirements

Equipment:

• Type-tested inverter to G98
• Protection settings factory-configured
• Installer cannot modify protection

Protection Settings (fixed):

Notification Process

1. Install: Complete installation per BS 7671
2. Notify: Submit notification to DNO within 28 days
3. Commission: Inverter self-tests on first power-up
4. Confirm: DNO may inspect (rarely for G98)

Notification is via DNO portals or the national MCS portal.

No Approval Required

Unlike G99, G98 installations do not require prior DNO approval. The installer simply notifies after completion.

G99: Larger-Scale Generation

G99 (formerly G59) covers larger embedded generation systems requiring DNO assessment and approval before connection.

Scope

Application Process

Application → DNO Assessment → Offer → Acceptance → Install → Commission
    ↓              ↓              ↓         ↓           ↓          ↓
 4 weeks      4-12 weeks     28 days   Sign + pay   Build    Witness test

Assessment includes:

• Fault level contribution
• Voltage rise calculation
• Thermal capacity check
• Protection coordination

Technical Requirements

Protection (Type A example):

Settings may be adjusted by DNO based on local network.

Additional Features (vs G98)

• Remote disconnection: DNO can disable generation
• Power quality monitoring: Continuous logging
• Witness testing: DNO attends commissioning
• Interface protection: Separate relay may be required

Export Limits

G99 applications often receive:

• Firm connection: Full export capacity guaranteed
• Flexible connection: Export limited during constraints
• Timed connection: Export only at certain times

DNO Notification Process

Distribution Network Operators (DNOs) manage the electricity network and must be informed of all generation connections.

UK DNOs

G98 Notification (Simple)

Information required:

• Site address and MPAN
• Installer details (MCS certified)
• Equipment make/model
• Installed capacity (kW)
• Single/three-phase
• Commissioning date

Timeline:

• Notify within 28 days of commissioning
• No response required (deemed acceptance)

G99 Application (Detailed)

Stage 1 - Budget Estimate (optional):

• Basic site info
• Approximate capacity
• Response: ~2 weeks

Stage 2 - Full Application:

• Detailed design
• Protection settings
• Single-line diagram
• Site plans
• Response: 45-65 working days

Application Fees

Additional costs for network reinforcement may apply.

Common Issues

• Voltage rise: Export may be limited
• Fault level: May require current-limiting inverter
• Protection coordination: Settings adjustment needed
• Reverse power flow: Transformer issues

Type Testing & Certification

Grid-connected equipment must be independently tested and certified before sale in the UK and EU.

Type Test Purpose

Demonstrates that a product design meets:

• Safety requirements
• Performance standards
• Grid code compliance
• EMC regulations

Individual units are not tested; the type (design) is certified.

G98/G99 Type Testing

Inverters must pass tests including:

Test Laboratories

UK-recognised test houses:

• DNV GL (KEMA)
• TÜV Rheinland/SÜD
• CSA Group
• Intertek
• SGS

Testing typically costs £10,000 - £50,000 per product variant.

Certification Marks

Product Documentation

Compliant inverters include:

• Type test certificate (reference number)
• G98/G99 compliance declaration
• Protection settings table
• Installation manual with grid code section

Installer responsibility: Verify equipment has valid type test certificate before installation.

G100 (Power Limiting)

New standard for power limiting devices:

• Tested separately from inverter
• Ensures export limits are enforced
• Required for flexible connections

Earthing Arrangements

The earthing system determines how fault currents return to source and how shock protection operates. UK domestic installations use three main arrangements.

TN-C-S (PME - Protective Multiple Earthing)

Most common in UK. The neutral and earth are combined in the supply cable, then separated at the premises.

Substation          Service          Consumer Unit
    │                  │                  │
N ──┼──────────────────┼──────────────────┼── N
    │    PEN conductor │                  │
E ──┴──────────────────┼──────────────────┼── E
                       ↓                  │
                 Separated here     Main earth

Characteristics:

• Low impedance earth path
• Earth potential can rise during faults
• Restrictions on earthing in some zones

PV considerations:

• Additional earth electrode may be required
• PME earthing restrictions for outdoor equipment

TN-S (Separate Earth)

Separate earth conductor from substation. Less common but considered superior.

Substation          Service          Consumer Unit
    │                  │                  │
N ──┼──────────────────┼──────────────────┼── N
    │                  │                  │
E ──┼──────────────────┼──────────────────┼── E
    │                  │                  │
   ═╧═               Cable             Main earth
  Earth             sheath
s```

**Characteristics**:
- True earth reference
- No neutral/earth rise issues
- Often found in older installations

### TT (Terra-Terra)

Earth electrode at premises; no earth from supply. Common in rural areas.

Substation Service Consumer Unit │ │ │ N ──┼──────────────────┼──────────────────┼── N │ │ │ ═╧═ None ═╧═ ← Local electrode Earth Premises earth

**Characteristics**:
- Higher earth impedance (< 200Ω required)
- RCD protection mandatory
- Suitable for PV installations

### Comparison Table

| Arrangement | Zs Typical | RCD Required? | PV Suitability |
|-------------|------------|---------------|----------------|
| TN-C-S (PME) | 0.35Ω | Recommended | Restrictions apply |
| TN-S | 0.8Ω | Recommended | Good |
| TT | 20-200Ω | Mandatory | Excellent |

![Earthing systems](https://upload.wikimedia.org/wikipedia/commons/8/80/Earthing_Systems_%28TN-S%2C_TN-C%2C_TN-C-S%2C_TT%2C_IT%29.svg)

RCD Protection

Residual Current Devices detect earth leakage and disconnect before dangerous shock or fire can occur. Essential for PV installations.

Operating Principle

An RCD sums the currents in live and neutral:

$$I_{residual} = I_L - I_N$$

Under normal conditions: $I_{residual} = 0$

If current leaks to earth: $I_{residual} = I_{fault}$

The RCD trips when $I_{residual} > I_{\Delta n}$ (rated sensitivity).

RCD Types

PV systems require Type B or Type A + upstream detection due to potential DC fault currents from inverter.

Sensitivity Ratings

For shock protection, trip time at 5× $I_{\Delta n}$:

• 30mA RCD: < 40ms at 150mA
• Limits energy: $I^2t < 40 \text{ A}^2\text{s}$

RCBO (RCD + MCB)

Combined device provides:

• Residual current protection (earth leakage)
• Overcurrent protection (overload, short circuit)

$$\text{RCBO rating: } I_n / I_{\Delta n} \text{ e.g., 32A/30mA Type A}$$

PV-Specific Requirements

BS 7671 requires:

• RCD on AC circuits supplied by inverter
• Type B if inverter doesn't have DC fault detection
• Type A acceptable if inverter has internal DC detection

Nuisance tripping: High-frequency leakage from long DC cables can cause unwanted trips. Solutions:

• Type B RCD (less sensitive to HF)
• Ensure DC cable capacitance is low
• Quality inverter with internal filtering

DC Isolation for PV Systems

Solar PV systems present unique DC hazards. Proper isolation ensures safe maintenance and emergency disconnection.

The DC Hazard

PV panels produce DC voltage whenever illuminated:

$$V_{OC,string} = V_{OC,module} \times n_{series}$$

Example: 10 panels × 45V = 450V DC (lethal!)

Unlike AC, DC arcs don't self-extinguish at zero-crossing. DC arc temperatures exceed 3,000°C.

Isolation Requirements

BS 7671 and EN 62446 require:

DC Isolator Ratings

Must be rated for PV service:

Warning: Standard AC isolators will fail catastrophically on DC!

Firefighter Safety Switch

Rapid shutdown requirement (increasing adoption):

• Reduces array voltage to < 30V within seconds
• Triggered by AC disconnect
• Module-level or string-level shutdown

$$V_{safe} < 30V \text{ DC within } 30 \text{ seconds}$$

Isolation Sequence

Safe shutdown procedure:

1. Switch off AC isolator (stops current flow)
2. Wait 5 minutes (capacitor discharge)
3. Switch off DC isolator
4. Verify with multimeter before touching

Never disconnect DC under load! Open-circuit voltage always present when illuminated.

Testing

Arc Fault Detection

DC arc faults in PV systems cause fires. Arc Fault Circuit Interrupters (AFCIs) detect and interrupt arcs before damage occurs.

Arc Fault Causes

• Loose connections: Corroded or poorly torqued terminals
• Damaged cables: Rodent damage, UV degradation, mechanical
• Connector faults: Mismatched or damaged MC4 connectors
• Water ingress: Tracking across wet insulation

Series vs Parallel Arcs

Series arc (in current path):

PV → ─╱╲─ → Load
     arc

• Current limited by load/PV characteristics
• Harder to detect (current may be normal)
• Most common type

Parallel arc (line to line/ground):

PV+ ─────┐
         ⚡ arc
PV- ─────┘

• High current, easier to detect
• Requires low impedance path
• Often causes immediate failure

Arc Signatures

DC arcs have characteristic signatures:

AFCI detection algorithm:

$$P_{arc} = \int_{f_1}^{f_2} |$$FFT(I(t))|^2 \, df

Trip if $P_{arc}$ exceeds threshold for sustained period.

AFCI Implementation

US NEC 690.11 requires AFCI for all new PV installations. UK currently recommends but doesn't mandate.

Limitations

• False positives: Inverter switching, poor connections
• Nuisance trips: During commissioning, testing
• Cost: Adds £50-200 per string
• Compatibility: Must work with specific inverter

Best Practice

Prevent arcs through good installation:

• Torque all connections to specification
• Use matched MC4 connectors only
• Protect cables from mechanical damage
• Regular thermographic inspection

System Sizing Methodology

Proper sizing balances generation, consumption, storage, and economics. Oversizing wastes money; undersizing misses potential.

Design Objectives

Different goals lead to different designs:

Sizing Process

1. Load Analysis → Annual kWh, daily profile, seasonal variation
       ↓
2. Site Assessment → Roof area, orientation, shading
       ↓
3. Generation Estimate → Expected yield (kWh/kWp/year)
       ↓
4. System Size → Match objectives and constraints
       ↓
5. Storage Sizing → If battery included
       ↓
6. Economic Analysis → Payback, ROI, NPV

Key Ratios

Self-consumption ratio (SCR): $$SCR = \frac{E_{consumed,direct}}{E_{generated}} \times 100%$$

Typical without battery: 25-40% With battery: 50-80%

Self-sufficiency ratio (SSR): $$SSR = \frac{E_{from,PV}}{E_{total,consumed}} \times 100%$$

Also called "autarky" - how much of your consumption comes from your system.

Specific yield: $$Y_{specific} = \frac{E_{annual}}{P_{rated}} \text{ kWh/kWp/year}$$

UK range: 800-1,000 kWh/kWp/year depending on location and orientation.

Rule of Thumb Sizing

Oversizing by 20-30% is common to account for:

• System losses
• Future consumption growth (EV, heat pump)
• Degradation over lifetime

Load Analysis

Understanding consumption patterns is essential for optimal system design. Analysis reveals how much energy is used, when, and by what.

Data Sources

Key Metrics

Annual consumption: $$E_{annual} = \sum_{i=1}^{12} E_{month,i} \text{ kWh}$$

UK domestic average: ~2,900 kWh (without electric heating)

Daily average: $$E_{daily,avg} = \frac{E_{annual}}{365} \text{ kWh/day}$$

Peak demand: $$P_{peak} = \max(P(t)) \text{ kW}$$

Typical domestic: 5-10 kW during cooking/kettle.

Load Profile Analysis

Half-hourly smart meter data reveals patterns:

Power (kW)
3│        ┌─┐
 │        │ │     ┌───┐
2│    ┌─┐ │ │     │   │
 │    │ │ │ │  ┌──┤   │
1│────┤ ├─┤ ├──┤  │   │
 │    │ │ │ │  │  │   │
0└────┴─┴─┴─┴──┴──┴───┴────
  0  6  12  18  24 hour
      Morning  Evening
      peak     peak

Baseload: Always-on consumption (fridge, standby, router)

• Typical: 100-300W continuous
• Annual: $P_{base} \times 8760 = 900-2,600$ kWh

Seasonal Variation

Load Categories

Load shifting potential: Moving flexible loads to solar generation hours increases self-consumption significantly.

Generation Estimation

Predicting annual yield requires understanding irradiance data, system losses, and site-specific factors.

Solar Resource

UK annual irradiation varies by location:

Orientation & Tilt Effects

Optimal UK orientation: South-facing, 30-40° tilt.

Dual-pitch (East-West): Common on modern roofs. Total yield ~85% but flatter generation curve improves self-consumption.

Generation Formula

$$E_{annual} = P_{rated} \times H_{POA} \times PR$$

Where:

• $P_{rated}$ = Array rated power (kWp)
• $H_{POA}$ = Plane-of-array irradiation (kWh/m²/year)
• $PR$ = Performance Ratio (typically 0.75-0.85)

Performance Ratio Components

$$PR = \eta_{temp} \times \eta_{soiling} \times \eta_{mismatch} \times \eta_{wiring} \times \eta_{inverter}$$

Combined PR: typically 0.75-0.85 for well-designed systems.

Monthly Distribution

UK generation varies dramatically by month:

Winter months produce ~10× less than summer months.

Shading Analysis

Even small shadows cause disproportionate losses:

$$P_{loss,shading} > \text{Area}_{shaded}$$

One shaded cell can limit entire string current. Tools for analysis:

• Sun path diagrams
• 3D modelling (PVsyst, SketchUp)
• On-site horizon measurement

Battery Storage Sizing

Batteries store excess generation for later use, increasing self-consumption and providing backup capability.

Sizing Objectives

Self-Consumption Sizing

Estimate daily excess generation:

$$E_{excess,daily} = E_{generated,daily} - E_{consumed,daytime}$$

Practical rule: Battery capacity = 50-100% of daily excess.

Example:

• 4 kWp system: ~11 kWh/day (summer average)
• Daytime consumption: 4 kWh
• Excess: 7 kWh
• Suggested battery: 5-7 kWh usable

Usable Capacity

Manufacturers quote total capacity; usable is less:

$$C_{usable} = C_{total} \times DoD_{max}$$

Cycle Life Consideration

Deeper cycles = fewer total cycles:

Annual cycles: ~250-350 (once daily average).

Expected lifetime: 10-15 years for quality lithium systems.

Power Rating

Battery power rating limits charge/discharge rate:

$$P_{battery} \text{ typically } 0.5C \text{ to } 1C$$

For 10 kWh battery at 0.5C: 5 kW max power.

Must cover:

• Peak export (to capture all excess)
• Peak consumption (to avoid grid import)
• Backup loads (if required)

Economic Sizing

Diminishing returns with larger batteries:

Sweet spot: Usually 1-1.5 × daily excess.

Backup Considerations

For backup power sizing:

$$C_{backup} = P_{critical} \times t_{autonomy} \times \frac{1}{\eta_{inverter}}$$

Example: 1 kW critical loads × 4 hours × 1.05 = 4.2 kWh minimum.

Smart Meters

Smart meters enable accurate billing, export payments, and detailed consumption data essential for optimizing solar + storage systems.

UK Smart Meter Rollout

Two generations deployed:

SMETS2 meters communicate via the Data Communications Company (DCC) network and work with any supplier.

Meter Configuration for Solar

Import/Export metering:

Grid ←──[Smart Meter]──→ Consumer Unit ←── Inverter ←── PV
          ↓                    ↓
     Measures:            Generation
     - Import (+)          meter
     - Export (-)         (separate)

The smart meter records:

• Import: Energy drawn from grid (you pay)
• Export: Energy sent to grid (you're paid)

Meter Modes

SEG (Smart Export Guarantee) requires actual export metering via smart meter or separate export meter.

Half-Hourly Data

Smart meters record consumption in 30-minute intervals:

$$E_{period} = \int_{t}^{t+30min} P(t) \, dt$$

This data enables:

• Accurate time-of-use billing
• Load profile analysis
• Self-consumption calculation
• System optimization

Data Access

Third-party apps (Loop, Hildebrand) can access data via CAD or DCC.

Generation Metering

Separate generation meter required for:

• Feed-in Tariff (FIT) legacy payments
• Renewable Energy Guarantees of Origin (REGOs)
• Some export tariffs

Must be MCS-certified meter, typically MID-approved.

Monitoring Systems

Monitoring systems track generation, consumption, and system health in real-time, enabling optimization and fault detection.

Monitoring Levels

System Architecture

Cloud Platform ←── Internet ←── Gateway/Logger
      ↓                              ↑
 Mobile App                    ┌────┴────┐
 Web Portal                    │         │
                            Inverter   Meter
                               ↑         ↑
                              PV      Grid CT

Communication Protocols

Monitoring Parameters

Generation metrics:

• Instantaneous power (W)
• Daily/monthly/annual yield (kWh)
• DC voltage and current per string
• AC voltage, current, frequency

Consumption metrics:

• Grid import/export (W, kWh)
• Self-consumption (W, kWh)
• Load breakdown (if circuit monitoring)

System health:

• Inverter status and alarms
• String performance comparison
• Temperature (ambient, module)
• Communication status

Popular Platforms

Third-Party Aggregators

Combine data from multiple sources:

• pvoutput.org: Free, community comparison
• Solar Analytics: Advanced diagnostics
• Home Assistant: DIY integration, local control

Data Logging

Systematic data collection enables performance analysis, fault detection, and long-term yield verification.

Logging Resolution

Typical systems log at 5-minute intervals with daily upload.

Essential Data Points

Minimum logging set:

• Timestamp (UTC or local with timezone)
• AC power output (W)
• Daily yield (kWh)
• Grid import/export (kWh)
• Inverter status code

Enhanced logging:

• DC voltage per string
• DC current per string
• AC voltage, current, frequency
• Power factor
• Temperature (inverter, ambient)
• Irradiance (if sensor installed)

Data Quality

Common issues and solutions:

Data validation checks: $$P_{max,expected} = G \times A \times \eta$$ Flag if $P_{measured} > 1.2 \times P_{max,expected}$

Storage Options

Data Export Formats

Retention Requirements

Performance Metrics

Key performance indicators (KPIs) quantify system health, enabling comparison against expectations and identification of issues.

Specific Yield

Energy produced per unit capacity:

$$Y_f = \frac{E_{out}}{P_{rated}} \text{ (kWh/kWp)}$$

Also called "final yield" or "capacity factor equivalent hours".

Performance Ratio (PR)

Actual vs theoretical output:

$$PR = \frac{E_{actual}}{E_{theoretical}} = \frac{E_{actual}}{H_{POA} \times P_{rated}}$$

Where $H_{POA}$ = plane-of-array irradiation.

Temperature-corrected PR: $$PR_{corr} = PR \times \frac{1}{1 + \gamma (T_{cell} - T_{STC})}$$

Where $\gamma$ ≈ -0.004/°C for crystalline silicon.

Capacity Factor

Utilisation of rated capacity:

$$CF = \frac{E_{actual}}{P_{rated} \times t_{period}}$$

For annual period: $CF = \frac{E_{annual}}{P_{rated} \times 8760}$

UK PV typical: 10-12% (vs 25-30% in sunny climates).

Self-Consumption Metrics

Self-consumption ratio: $$SCR = \frac{E_{self-consumed}}{E_{generated}} \times 100%$$

Self-sufficiency ratio: $$SSR = \frac{E_{from-PV}}{E_{total-demand}} \times 100%$$

Degradation Tracking

PV modules degrade over time:

$$P_{year,n} = P_{year,0} \times (1 - d)^n$$

Where $d$ = annual degradation rate (typically 0.3-0.7%/year).

Detecting abnormal degradation:

• Compare year-on-year performance
• Temperature-correct for fair comparison
• Flag if degradation > 1%/year

Fault Detection Metrics

Automated alerts: Set thresholds for email/SMS notification when KPIs fall outside expected ranges.