Supplementary
Engineering economics (dropped from NCEES Power 2020+), advanced PSA (state estimation), distribution reliability (SAIDI/SAIFI).
Lessons
Engineering economics — TVM, NPV, IRR, LCOE
Math of investment decisions. Six core TVM factors: (P/F), (F/P), (P/A), (A/P), (F/A), (A/F). NPV decision rule. IRR + its 3 limitations (multiple IRRs, NPV-ranking conflicts, reinvestment assumption — use MIRR). LCOE = PV-cost / PV-energy ($/MWh) — power-sector workhorse. MACRS 5/7/15/20-year property classes (solar PV is 5-yr). Fisher equation (real vs nominal). CRF + EAC for different-life alternatives + replacement analysis.
Power-system state estimation — WLS, observability, bad data, PMU
WLS minimises J(x) = Σ (z_i − h_i(x))² / σ_i² via Gauss-Newton: (Hᵀ R⁻¹ H) Δx = Hᵀ R⁻¹ r. State = |V|, θ at every bus (n = 2N−1). Observable iff rank(H) = n. Bad-data: χ²(m−n) test + |r_N,i| > 3 normalized residual. PMU (IEEE C37.118) measures V and θ directly → linear estimator. EMS workflow: SCADA + PMU → SE → CA → SCED → market clearing. Vendors: GE iDM / Siemens Spectrum / ABB-Hitachi.
Reliability indices — SAIDI / SAIFI / CAIDI / MAIFI / LOLE / EUE
Distribution (IEEE 1366): SAIFI = Σ N_i/N_total (sustained ≥ 5 min); SAIDI = Σ (U_i·N_i)/N_total; CAIDI = SAIDI/SAIFI; MAIFI for momentary. Typical US: SAIDI 60-300 min/yr; SAIFI 0.5-2.0. MED β-method excludes storms. Generation adequacy (NERC): LOLE ≤ 0.1 days/yr (1-in-10); EUE in MWh; PRM 15-20%. Capacity accreditation via ELCC. EEI benchmarking + PUC PBR. PSPS, microgrids, DERMS, resilience.