ESEGH cheat sheet

Power triangle: apparent power S (VA) = √(P² + Q²); real power P = S·cosφ; reactive power Q = S·sinφ. Power factor cosφ below ~0.9 increases line losses and may trigger utility penalties.

Three-phase power: P = √3 · V_LL · I_L · cosφ. For a balanced load, per-phase analysis uses phase voltage V_LN = V_LL/√3.

Per-unit system: Z_pu = Z_actual / Z_base, with Z_base = V_base² / S_base. Per-unit values are identical across transformer voltage levels, which is why fault and load-flow studies use them.

Synchronous generator swing equation: (2H/ω_s)·d²δ/dt² = P_m − P_e. Inertia constant H (s) sets frequency response speed; low-inertia grids with inverter-based resources have faster, larger frequency excursions (higher RoCoF).

Transmission line surge impedance loading: SIL ≈ V_LL² / Z_c, with Z_c ≈ √(L/C) (about 400 Ω overhead, ~40 Ω cable). Loading near SIL minimizes reactive absorption/export.

Transformer and line losses scale with current squared: P_loss = I²R. Doubling current quadruples resistive losses; voltage upgrade by factor k reduces losses by roughly k² for the same power.

Load flow (power flow) solves nodal complex power balance using bus types: slack (V, θ set), PV (P, V set), PQ (P, Q set). Newton-Raphson converges quadratically; Gauss-Seidel converges linearly.

Frequency droop control: Δf = −R·ΔP for a governor with droop R (e.g., 5% droop means 100% power change for 5% frequency change). Inverter-based resources emulate droop via grid-forming or fast frequency response.

Reliability metrics: SAIDI = Σ(customer-minutes interrupted)/total customers; SAIFI = Σ(customer interruptions)/total customers. N-1 contingency criterion requires the system to survive loss of any single element without cascading.

Wind power available in the wind: P = ½·ρ·A·v³. Power scales with the cube of wind speed and linearly with air density; a 10% wind-speed error produces roughly a 33% power error.

Betz limit: maximum fraction of kinetic energy extractable by an ideal rotor is 16/27 ≈ 0.593 of the incoming wind power. Practical turbines reach Cp ≈ 0.35–0.50.

Tip-speed ratio λ = ωR/v; turbines operate near an optimal λ (typically 6–8 for three-blade horizontal-axis machines). Cp depends on λ and blade pitch angle β.

Solar PV: module power depends on irradiance and cell temperature; power temperature coefficient is typically −0.3% to −0.45% per °C above 25 °C STC.

PV cell equivalent circuit: photocurrent source in parallel with a diode and shunt resistance, in series with series resistance. Fill factor FF = P_max/(V_oc·I_sc).

Solar geometry: solar declination δ ≈ 23.45°·sin[360°·(284 + n)/365]. Air mass AM = 1/cos(zenith); AM1.5 is the standard spectrum reference.

Concentrated solar power (CSP) with thermal storage (molten salt) provides dispatchable output; parabolic trough and power tower are the dominant designs.

Hydropower: P = ρ·g·Q·H·η. Head H and flow Q drive output; pumped storage has round-trip efficiency typically 70–80%.

Biomass and biogas: energy content depends on moisture and lower heating value (LHV). Anaerobic digestion yields methane-rich biogas (~50–70% CH4).

Energy efficiency ratio: EER = cooling output (Btu/h) / power input (W); COP = cooling output (kW) / power input (kW); COP ≈ EER/3.412.

Demand response categories: price-based (time-of-use, real-time pricing, critical-peak pricing) and incentive-based (direct load control, demand bidding, interruptible tariffs).

Load factor = average load / peak load over a period. Low load factor signals peaky consumption and higher per-kWh delivery cost.

Energy savings from variable-speed drives on fans/pumps follow affinity laws: flow ∝ speed, head ∝ speed², power ∝ speed³.

Lighting efficacy: LED ~100–200 lm/W, fluorescent ~60–100 lm/W, incandescent ~10–17 lm/W. Luminous efficacy converts electrical watts to lumens.

Building envelope: U-value (W/m²·K) is thermal transmittance; R-value = 1/U. Lower U-value means better insulation.

Peak demand reduction strategies include load shifting, thermal storage, behind-the-meter batteries, and automated demand response (OpenADR signaling).

Measurement and verification (M&V) per IPMVP options: Option A (retrofit isolation, key parameters), B (retrofit isolation, all parameters), C (whole facility), D (calibrated simulation).

Life-cycle assessment (LCA) stages per ISO 14040/14044: goal and scope definition, inventory analysis (LCI), impact assessment (LCIA), and interpretation.

Common impact categories: global warming potential (GWP, kg CO2e), acidification, eutrophication, ozone depletion, photochemical smog, and particulate matter.

GWP values are relative to CO2 over a time horizon; methane has GWP100 ≈ 28–30 (AR5, fossil) and N2O ≈ 265–298.

Environmental impact assessment (EIA) typically includes screening, scoping, baseline study, impact prediction, mitigation, and monitoring.

Cumulative impacts consider combined effects of multiple projects and past, present, and reasonably foreseeable actions.

Carbon footprint of electricity depends on the generation mix; grid emission factor = total emissions / total generation (kg CO2e/kWh).

Circular economy principles: reduce, reuse, recycle, recover. Material intensity of solar PV and wind includes critical minerals (lithium, cobalt, rare earths).

Water use: thermoelectric cooling (once-through vs. closed-loop) and hydropower evaporation are key water-intensity concerns for energy systems.

Levelized cost of energy (LCOE) = Σ[(I_t + O_t + F_t)/(1+r)^t] / Σ[(E_t)/(1+r)^t], where I is investment, O is O&M, F is fuel, E is energy, r is discount rate.

Feed-in tariffs (FiT) pay a fixed price per kWh; renewable portfolio standards (RPS) mandate a minimum renewable share; auctions/tenders set competitive prices.

Net metering credits exports at retail rate; net billing credits at avoided cost or wholesale rate.

Capacity markets pay for availability (kW) rather than energy (kWh); energy-only markets rely on scarcity pricing.

Merit order effect: low-marginal-cost renewables push down wholesale prices and displace higher-cost plants.

Discounting: present value PV = FV/(1+r)^n. Higher discount rates favor near-term cash flows and lower long-lived capital-intensive projects' apparent value.

Externalities (health, climate) can be internalized via carbon pricing: carbon tax (price-based) or cap-and-trade (quantity-based).

Regulatory frameworks: rate-of-return (cost-of-service) vs. performance-based regulation. Depreciation, rate base, and allowed return drive utility revenue.

GHG Protocol scopes: Scope 1 (direct combustion/process), Scope 2 (purchased electricity/heat), Scope 3 (value chain, upstream and downstream).

Scope 2 dual reporting: location-based (grid average emission factor) and market-based (contractual instruments such as RECs/PPAs).

Emission calculation: emissions = activity data × emission factor (e.g., kWh × kg CO2e/kWh; liters fuel × kg CO2/L).

Global Warming Potential converts non-CO2 gases to CO2-equivalent: CO2e = mass × GWP.

ISO 14064-1 specifies organizational GHG inventory principles: relevance, completeness, consistency, accuracy, transparency.

The GHG Protocol requires setting a base year, recalculating for structural changes (mergers, acquisitions, methodology changes) and using a significance threshold.

Direct measurement methods: continuous emissions monitoring systems (CEMS), stack testing, and flow meters; indirect methods use activity data and factors.

Verification: third-party assurance (limited vs. reasonable) checks inventory accuracy against a standard; materiality thresholds apply.

Avoided emissions and renewable energy certificates (RECs) must be reported separately from the inventory; RECs represent 1 MWh of renewable generation attributes.

Climate risk = hazard × exposure × vulnerability. Hazard is the physical event; exposure is assets/populations in harm's way; vulnerability is susceptibility to damage.

TCFD framework pillars: governance, strategy, risk management, and metrics/targets. Physical risks are acute (floods, storms) or chronic (sea-level rise, heat).

Transition risks: policy/legal, technology, market, and reputational risks arising from the shift to a low-carbon economy.

Climate scenarios: RCPs (Representative Concentration Pathways) and SSPs (Shared Socioeconomic Pathways); SSP5-8.5 is high-emissions, SSP1-2.6 is low-emissions.

Adaptation measures for energy systems: hardening substations, undergrounding lines, flood defenses, cooling-water resilience, and diversified generation.

Resilience metrics: robustness, rapidity, resourcefulness, redundancy. Grid resilience includes islanding capability and microgrids.

Stress testing: scenario-based analysis of assets under physical and transition risk, often using return periods (e.g., 100-year flood).

Stranded assets: fossil fuel reserves or infrastructure that may lose value under decarbonization policy and demand shifts.