ECE 685 / Interactive course platform
Power Systems Design
From generation planning to power flow. Learn, explore, and calculate, one lecture at a time.
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Course & power-system overview
2 lecturesCourse Orientation & Logistics
People, course expectations, tools, assessments, and the power-system design workflow.
Course Orientation & Logistics 课程介绍与安排 People, course expectations, tools, assessments, and the power-system design workflow. 认识课程团队、学习要求、工具与考核，了解电力系统设计流程。 Meet your instructor Research Mission Meet your teaching assistant Course overview Course goals Reading Course outline Suggested problems Course logistics Getting help Course tools Grading Workload and practice Early-semester dates Final-month dates Problems and late work Final Project Responsible AI use Prohibited AI use Three-phase foundations Prerequisite check Power-system history Physical power system Grid transformation Reliability challenge Design workflowPower-System Evolution and Symbolic Representation
Trace the physical power system, construct a one-line diagram, and reconcile real and reactive power.
Power-System Evolution and Symbolic Representation 电力系统演进与符号表示 Trace the physical power system, construct a one-line diagram, and reconcile real and reactive power. 梳理电力系统的物理路径，建立单线图，核对有功与无功功率平衡。 Two views of the same power system From local service to interconnection National grid Network reliability Smart-grid layers Traditional and evolving grids Generation mix Resource geography Variable generation and net load Starting problem Physical path Generator Bus Transformer Transmission line Load Shunt Six symbols Three-phase system, one drawn path Plant to campus Define voltage zones Preserve endpoints and roles Complete the one-line Given data and sign convention Real-power balance at Bus 3 Reactive power at Bus 3 Line sending-end power Generator output System reconciliation System-data recordGeneration mix planning
2 lecturesOptimal Fuel Mix Analysis I
Demand, energy, capacity factor, planning reserve margin, and load-duration curves.
Optimal Fuel Mix Analysis I 最优燃料组合分析 I Demand, energy, capacity factor, planning reserve margin, and load-duration curves. 区分需求、能量与容量，学习容量因子、规划备用裕度和负荷持续曲线。 Two parts of today's lecture Demand is a power rate Power over time gives energy use Capacity is generation capability Rule: do not mix energy and power Capacity factor measures generation utilization Capacity factor example - interpret utilization Planning reserve margin is the capacity-planning metric PRM gives a target, not a complete resource plan Planning example - identify the capacity gap First check the current reserve margin Then calculate the capacity needed to reach 15% PRM is a primary metric for U.S. resource-adequacy planning Chronological demand Load-duration curve Same demand, new order Daily and annual LDCs use different source records Construct an annual LDC from hourly demand LDC construction Worked-example data LDC example - Step 1 LDC example - Step 2 LDC example - Step 3 LDC example - Step 4 One LDC block: energy Daily-energy check From LDC peak to capacity target A brief link to the Final Project SummaryGeneration Mix Planning II
Build screening curves, find cost crossovers, form net load, and check a generation portfolio.
Generation Mix Planning II 发电组合规划 II Build screening curves, find cost crossovers, form net load, and check a generation portfolio. 建立成本筛选曲线、求交点、计算净负荷，并检验发电组合。 One capacity target, many possible mixes Planning questions Why build a screening curve? One technology, one screening curve Concept 1: annual fixed-cost coefficient Example 1: annual fixed cost Concept 2: variable operating cost Example 2: variable operating cost Concept 3: build one screening curve Concept 4: curve crossover Example 3: simple cycle vs. combined cycle Four technologies for the case From load to net load Case inputs Place wind and solar Form the NLDC Recall the GT–CC crossover Map crossover to MW Round CC units Round GT units for peak load Check every load block Add PRM after load matching Repeat the planning loop How the two lectures connect SummarySingle-phase AC circuits
3 lecturesSingle-Phase AC Circuits I
Map sinusoidal waveforms to RMS phasors; convert and add polar and rectangular representations.
Single-Phase AC Circuits I 单相交流电路 I Map sinusoidal waveforms to RMS phasors; convert and add polar and rectangular representations. 在正弦波形与 RMS 相量之间转换，练习极坐标、直角坐标和相量加法。 Lecture outline Starting problem Starting-problem solution Sinusoid Waveform magnitudes Frequency and period What phase means Read phase from the time curve Phase difference RMS RMS derivation Three equivalent representations Time domain to polar form Polar form to time domain Polar form to rectangular form Rectangular form to polar form Choose polar or rectangular form Before adding, confirm compatibility Phasor addition is component addition Phasor addition as vectors CE-2A setup CE-2A Step 1 CE-2A Step 2 CE-2A Step 3 CE-2A Step 4 CE-2A Step 5 CE-2A Step 6 Practice problem Rectangular addition Polar reconstruction RMS waveform reconstruction Phasor summarySingle-Phase AC Circuits II
Calculate real, reactive, complex, and apparent power with consistent load and generator signs.
Single-Phase AC Circuits II 单相交流电路 II Calculate real, reactive, complex, and apparent power with consistent load and generator signs. 按统一的负荷与发电机符号约定，计算有功、无功、复功率和视在功率。 Lecture outline Starting problem Starting-problem solution Instantaneous power Average real power P Reactive power Q Recap: complex and apparent power Power triangle Power factor Load and generator sign conventions Reactive power of loads and generators Example setup CE-2B Step 1 CE-2B Step 2 CE-2B Step 3 CE-2B Step 4 Complex-power summarySingle-Phase AC Circuits III
Determine target reactive power, shunt compensation, and capacitance for power-factor correction.
Single-Phase AC Circuits III 单相交流电路 III Determine target reactive power, shunt compensation, and capacitance for power-factor correction. 从目标功率因数计算目标无功、并联补偿容量与电容值。 Lecture outline Load and generator sign conventions Capacitor power and power balance Shunt compensation Power-factor correction Step 1: Target reactive power Step 2: Required compensation Step 3: Capacitance Step 4: Verification Worked example: the L06 load Example: Step 1 Example: Step 2 Example: Step 3 Example: Step 4 Correction summaryThree-phase AC circuits
3 lecturesThree-Phase AC Circuits I
Balanced sets, phase sequence, symmetrical components, and wye/delta voltage and current relations.
Three-Phase AC Circuits I 三相交流电路 I Balanced sets, phase sequence, symmetrical components, and wye/delta voltage and current relations. 学习平衡三相相量、相序、对称分量，以及星形和三角形的电压电流关系。 Lecture outline Why three phases: constant total power Why three phases: economical conductors Why three phases: a rotating magnetic field Balanced source Phasor-to-waveform mapping Sequence rule Positive abc geometry Negative acb geometry Phase angles and peak times Time-order test Three forms of a complex number Balanced phasor sum Example: positive-sequence phasors Example: negative-sequence phasors Example: instantaneous voltage checks Shifted reference Three sequence basis vectors Why do the weighted sums isolate one sequence? Finding the three sequence coefficients Example: symmetrical components Wye source Orientation before arithmetic Wye voltage: complex subtraction Component triangle Other two line voltages Line-to-line rating Example: two voltage reference choices Current relation Balanced neutral current Delta phase voltage Current notation in delta Delta branch currents from voltage From voltage to line current at terminal A All three line currents from voltage A-line current: algebra from voltage A-line current: voltage geometry Balanced delta current result Positive-sequence delta current phasors Negative-sequence connection shifts Wye and delta: one reference table Wye and delta: visual summary Example: balanced 13.8-kV delta Example: delta branch-current calculation Example: line current from rectangular KCL Example: branch and line current setsThree-Phase AC Circuits II
Use per-phase equivalents to calculate three-phase power and reconcile source, line, and load.
Three-Phase AC Circuits II 三相交流电路 II Use per-phase equivalents to calculate three-phase power and reconcile source, line, and load. 利用每相等值电路计算三相功率，核对电源、线路与负荷的功率平衡。 Lecture outline Identify the source, line, and load first Start with a balanced Y–Y network Extract one phase, then reconstruct three A Y source feeding a Δ load Compare Y and Δ at the same terminals Derive the balanced impedance relation Use the balanced Δ↔Y conversion Start from the Y–Y diagram: one-phase power Sum the three Y-connected load branches Change the load connection: Y versus Δ Derive both phase and line forms Three-phase power: phase and line forms From load power to feeder power balance Why line power uses |I_A|^2 Source, line, and load power balance Example: complex power of one delta leg Example: power of the 13.8-kV delta Example A: 480-V wye feeder Example A: per-phase circuit Example A: solve the phase current Example A: line voltage drop Example A: load phase voltage and KVL Example A: load line-to-line voltage Example A: load complex power Example A: complete power balance Example A: independent checks Example B: 4.16-kV delta feeder Example B: delta-to-wye load conversion Example B: source reference and phase circuit Example B: solve the line current Example B: load voltage and KVL Example B: load terminal line voltage Example B: physical delta branch currents Example B: source complex power Example B: line and load absorption Example B: source, line, and load powers Example B: independent reconstruction checks A complete balanced three-phase solutionThree-Phase AC Circuits
Worked examples on phase sequence, wye/delta conversion, branch currents, and feeder power balance.
Three-Phase AC Circuits 三相交流电路例题 Worked examples on phase sequence, wye/delta conversion, branch currents, and feeder power balance. 通过例题练习相序、星形与三角形变换、支路电流及馈线功率平衡。 Lecture map Balanced set and phase sequence Example 1: a positive-sequence voltage set Example 1, Q1: positive-sequence B and C voltages Example 1, Q2: all three voltages after a +30° shift Example 1, Q3: shifted voltages in rectangular form Example 1, Q4: balance verification after the shift Y connection: phase and line quantities Example 2: a balanced Y-connected load Example 2, step 1: line voltage to phase voltage Example 2, step 2: complete the phase-voltage set Example 2, step 3: solve the phase-A current Example 2, step 4: other line currents and neutral Example 2, step 5: rebuild and verify line voltages Delta connection: branch quantities and line currents Example 3: balanced 13.8-kV delta load Example 3, step 1: branch-voltage set Example 3, step 2: branch-current set Example 3, step 3: line current from KCL Example 3, step 4: complete current set and checks Balanced Y–Delta transformation Y–Delta: terminal and branch quantities Example 4: an equivalent delta for a Y load Example 4, Q1: Y-to-delta impedance conversion Example 4, Q2: delta branch currents Example 4, Q3: line-current comparison Example 4, Q4: delta-to-Y conversion Balanced three-phase power Source, line, and load power Example 5: power with line impedance Example 5: the source–line–load circuit Example 5, step 1: line current Example 5, step 2: source complex power Example 5, step 3: three-phase line absorption Example 5, step 4: load power by two routes Example 5, step 5: check the power balance Complete solution workflowTransformer modeling
3 lecturesTransformer Modeling I
Derive ideal voltage and current ratios, power conservation, and impedance referral.
Transformer Modeling I 变压器建模 I Derive ideal voltage and current ratios, power conservation, and impedance referral. 推导理想变压器的电压、电流比，功率守恒和阻抗折算关系。 Lecture outline Transformers in the power system Transformers in Power Systems How a transformer works Winding variables and units Core material and geometry Magnetizing current Zero winding resistance Ideal assumption 1 Zero leakage flux Ideal assumption 2 Infinite core permeability Ideal assumption 3 Zero core loss Ideal assumption 4 Ideal model and reference directions Flux linkage in an ideal winding Equal flux per turn Induced winding voltage Voltage ratio Ampere-turn balance Current ratio Power quantities and units Complex-power conservation Load impedance referred to H Impedance referred to L Low-voltage-side equivalent circuit Equivalent circuit referred to H Example setup Example: Step 1 Example: Step 2 Example: Step 3 Example: Step 4 Example: Step 5 Example: Step 6 Direct high-side impedance Apparent-power check Ideal-transformer summaryTransformer Modeling II
Add winding resistance, leakage reactance, excitation, and checked equivalent-circuit approximations.
Transformer Modeling II 变压器建模 II Add winding resistance, leakage reactance, excitation, and checked equivalent-circuit approximations. 引入绕组电阻、漏抗和励磁支路，检验等值电路的近似。 Lecture outline Ideal-model limitation Ideal transformer equivalent circuit Winding resistance Leakage flux Why resistance and leakage reactance? Finite core permeability Core loss Why R_c and j X_m? Exact equivalent circuit Why referral and approximation? Referral: replace the boxed network Refer low-side quantities to H Referral derivation Equivalent circuit referred to H Excitation current Why the excitation branch can move Input-shunt approximation Equivalent series impedance Approximate circuit with excitation Neglecting excitation current Neglecting winding resistance Limits of the steady-state model Example: data and required quantities Example: circuit referred to H Example: load current Example: required input voltage Example: results and circuit checkTransformer Modeling III
Infer transformer parameters from open- and short-circuit tests; calculate regulation and efficiency.
Transformer Modeling III 变压器建模 III Infer transformer parameters from open- and short-circuit tests; calculate regulation and efficiency. 从开路与短路试验确定模型参数，计算电压调整率和效率。 Lecture outline Determining model parameters The model established in L11 Parameters to determine Open-circuit condition Why energize LV for the OC test? Open-circuit test Meter readings and RMS phasors Inferring the current phase OC formulas: resolve the measured current OC formulas: identify the core-loss branch OC formulas: identify the magnetizing branch Example: OC measurements Example: excitation-current components Example: core-loss resistance Example: magnetizing reactance Short-circuit condition Why energize HV for the SC test? Short-circuit test SC formulas: identify impedance and resistance SC formulas: identify leakage reactance Example: SC measurements Example: SC current phasor Example: series impedance magnitude Example: series resistance Example: leakage reactance Putting both test results on HV The L11 model with measured parameters Operation at rated load Voltage regulation: no-load and full-load Voltage regulation: series voltage drop Example: voltage regulation Losses in the operating circuit Efficiency: real-power balance Summary: tests, regulation, and efficiencyPer-unit systems
3 lecturesPer Unit System I
Choose coherent bases and normalize voltage, current, impedance, admittance, and power.
Per Unit System I 标幺值系统 I Choose coherent bases and normalize voltage, current, impedance, admittance, and power. 选择相容的基准值，对电压、电流、阻抗、导纳和功率进行标幺化。 Lecture outline What is a per-unit system? Why use per unit? Per unit makes voltage levels comparable One network, several voltage levels The same equipment in per unit Equipment operating quantities in per unit Voltage, current, and power along a line Four coupled electrical quantities Circuit laws couple the four quantities Two independent bases determine the rest Convert all four quantities One impedance base for Z, R, and X Admittance and its reciprocal base One power base for P, Q, and S Coherent bases preserve circuit laws Two independent bases for Y and delta Y branch quantities and voltage references Y branch: calculating the bases Y branch: normalized circuit laws Delta branch quantities and current directions Delta branch: calculating the bases Delta branch: normalized circuit laws Checking the delta–Y relationship Normalization workflow Per-unit calculation and recovery Example: circuit data and specified bases Step 2: Derive the current base Step 2: Derive the impedance base Step 3: Normalize the given data The circuit ready for per-unit calculation Step 4: Calculate the line current Step 4: Calculate the load voltage Step 4: Calculate the circuit powers Step 5: Recover current and voltage Step 5: Recover the circuit powers Check: the recovered physical circuit Per-unit summaryPer Unit System II
Propagate bases through transformers and apply change of base across a multi-voltage network.
Per Unit System II 标幺值系统 II Propagate bases through transformers and apply change of base across a multi-voltage network. 通过变压器传递基准值，在多电压等级网络中应用基准变换。 Lecture outline The ideal transformer and local bases Transformer per-unit base rules The current and impedance bases on each side Voltage normalization cancels the turns ratio Current normalization cancels the inverse ratio The ideal per-unit circuit Approximate circuit referred to H Equivalent impedance before and after normalization The series per-unit circuit The complete physical circuit Normalization of the excitation branch The complete per-unit circuit Transformer normalization: summary The goal: one complete per-unit circuit The supplied component bases are incompatible System bases for every component Change of base Voltage and current Impedance Admittance Power System application Example circuit Step 1: select corresponding voltage bases Step 2: calculate both impedance bases Step 3: normalize directly on the 120-V side Step 4: verify from the 480-V side The per-unit result on both sides The transformer series circuit in per unit Recovering quantities on the correct side The same transformer on new system bases The new bases preserve the physical impedance SummaryPer Unit System III
Complete single-phase transformer and three-phase wye/delta normalization examples.
Per Unit System III 标幺值系统 III Complete single-phase transformer and three-phase wye/delta normalization examples. 完成单相变压器及三相星形、三角形电路的标幺化例题。 Lecture outline Part 1: single-phase voltage levels Example 1: circuit and data Example 1: questions Example 1 workflow: bases and current Example 1 workflow: voltages and power E1 Step 1: single-phase bases E1 Step 1: normalized data E1 Step 2: PU circuit E1 Step 2: network impedance E1 Step 2: total impedance E1 Step 2: series current E1 Step 3: T1 drop E1 Step 3: bus B2 E1 Step 3: line drop E1 Step 3: bus B3 E1 Step 3: bus B4 E1 Step 3: voltage check E1 Step 3: load voltage E1 Step 3: actual currents E1 Step 3: voltage results E1 Step 4: source power E1 Step 4: absorbed powers E1 Step 4: power balance Example 1: final answer Part 2: three-phase Y–Δ normalization Example 2: circuit and data Example 2: questions Example 2 workflow: connection and bases Example 2 workflow: solve and restore E2 Step 1: Y–delta conversion E2 Step 1: equivalent Y load E2 Step 2: three-phase bases E2 Step 2: source phase voltage E2 Step 2: normalized data E2 Step 2: delta on the same base E2 Step 2: equivalent PU circuit E2 Step 3: line current E2 Step 3: equivalent phase voltage E2 Step 3: load line voltage E2 Step 4: delta branch voltages E2 Step 4: delta branch currents E2 Step 4: line-current check E2 Step 4: load power in pu E2 Step 4: Y–delta power check Example 2: circuit answer Two examples: base conventionsExam 1 practice & review
2 lecturesExam 1 Practice
Practice the first-exam topics with the current lecture's worked problem sequence.
Exam 1 Practice 考试 1 练习 Practice the first-exam topics with the current lecture's worked problem sequence. 按照当前讲义的例题顺序，练习第一次考试涉及的课程内容。 Exam 1 format and timing Exam materials and conduct Answer format and grading Practice topics RMS phasors and complex power Example 1: sinusoidal voltage and current Solution 1: phasors and power Balanced three-phase circuits Example 2: balanced delta load Solution 2: branch and line currents Solution 2: power and equivalent Y Power-factor correction: the L07 method Example 3A: single-phase correction Solution 3A: target power and capacitor rating Solution 3A: capacitance and current check Parallel loads: combine powers first Example 3B: combine parallel loads Solution 3B: combined power and compensation Ideal transformer ratios Transformer tests and referral Example 4A: SC test and referral Solution 4A: impedance on both sides Open-circuit test Example 4B: open-circuit measurements Solution 4B: excitation parameters Per-unit bases Example 5A: transformer on rated bases Solution 5A: current and impedance bases Solution 5A: normalized impedance Changing the per-unit base Example 5B: changing the power base Solution 5B: new base and physical check Planning: screening cost and capacity Example 6: cost and required capacity Solution 6: screening and capacityExam 1 Review
Review the first course block and connect circuit calculations with design checks.
Exam 1 Review 考试 1 复习 Review the first course block and connect circuit calculations with design checks. 复习第一阶段知识，将电路计算与设计核查联系起来。 Review outline Starting problem RMS phasors Time domain to RMS phasors Complex-number forms Complex power uses the current conjugate Impedance power check Power-factor correction Positive-sequence set Wye line voltage Delta line current Three-phase power Example: feeder data Example: solution route Example: voltage reference Example: delta equivalent Example: line current Example: sending voltage Example: total load power Example: feeder loss Transformer quantities Practical transformer model Example: short-circuit test Example: test solution Single-phase per-unit bases Practice: referral and base Practice: referral answer Review error checks Core review summary Demand, energy, capacity Load-duration curve Screening curves Renewable shares Feasible generation mix Planning extension: data Planning: installed capacity Planning: peak adequacy Planning: result summaryThree-phase transformers
2 lecturesThree-Phase Transformers I
Build three-phase banks and distinguish winding, line, and bank relationships.
Three-Phase Transformers I 三相变压器 I Build three-phase banks and distinguish winding, line, and bank relationships. 建立三相变压器组，区分绕组量、线量与变压器组关系。 Lecture outline Starting problem Three identical single-phase units Winding and bank conventions Wye connection quantities Delta winding Delta current factor Wye and delta factors Y–Y bank Δ–Δ bank Y–Δ bank Delta on H, wye on L Bank voltage and current ratios Neutral and grounding Example: data Example: solution route Example: winding currents Example: wye–wye voltages Example: wye–wye power Example: delta–wye voltages Example: delta–wye power Example: solution check Practice: model and calculation Practice: solution Connection-factor summary Closing checkThree-Phase Transformers II
Apply phase conventions and delta–wye terminal relationships to transformer phasors.
Three-Phase Transformers II 三相变压器 II Apply phase conventions and delta–wye terminal relationships to transformer phasors. 应用相位约定和三角形—星形端口关系分析变压器相量。 Lecture outline Starting problem Textbook phase convention Angle conventions Delta-wye terminal relationships H-side delta phasors L-side wye phasors Dot correspondence Positive sequence L-side line voltage Remaining L-side voltages Sequence and phase displacement Per-unit base Bank impedance and winding impedance Example setup Example: solution route Example: two voltage ratios Example: winding phasors Example: low-side line voltage Example: tap angle Example: impedance base Example: rated currents Example: no-load model Practice: model and calculation Practice: solution Summary Closing checkTransmission-line parameters
4 lecturesTransmission-Line Parameters I
Relate conductor geometry and series-line physics to per-length resistance and inductance.
Transmission-Line Parameters I 输电线路参数 I Relate conductor geometry and series-line physics to per-length resistance and inductance. 从导线几何和线路物理关系推导单位长度的电阻与电感。 Lecture outline Starting problem Series-line physics Per-length quantities Area and outer radius Differential slice Area Temperature Resistance factors Unit ladder Inductance Amp ere's law Net gap field External flux linkage Internal current distribution Internal shells Ideal internal inductance Conductor and loop inductance Example: data Example: solution route Example: resistance rate Example: temperature correction Example: route resistance Example: magnetic components Example: total inductance Example: reactance Example: conductor and loop Practice: model and calculation Practice: solution Summary Closing checkTransmission-Line Parameters II
Use conductor GMR, tower geometry, and phase spacing to calculate line inductance.
Transmission-Line Parameters II 输电线路参数 II Use conductor GMR, tower geometry, and phase spacing to calculate line inductance. 利用导线 GMR、杆塔几何和相间距离计算线路电感。 Lecture outline Starting problem Series-parameter carry-forward GMR substitution Conductor GMR Tower geometry Equal spacing Unequal spacing Complete transposition Phase rotation Distance table Why GMD is a geometric mean Balanced-current simplification Reactance formula Example: data Example: solution route Example: position spacings Example: distance matrix Example: transposition cycle Example: geometric mean Example: self-distance ratio Example: phase inductance Example: route reactance Example: independent checks Practice: model and calculation Practice: solution Summary Closing checkTransmission-Line Parameters III
Derive line capacitance from electric fields, potential difference, and conductor geometry.
Transmission-Line Parameters III 输电线路参数 III Derive line capacitance from electric fields, potential difference, and conductor geometry. 从电场、电位差和导线几何推导线路电容。 Lecture outline Starting problem Series and shunt line parameters Gauss's law Potential difference Two-conductor capacitance Ideal pair Balanced phase charge Complete transposition Potential-reference cancellation Phase capacitance Capacitance to susceptance Unit check Charging current Capacitive reactive power Nominal-π shunt split Example: data Example: solution route Example: electric distance ratio Example: capacitance rate Example: susceptance rate Example: route shunt totals Example: charging current and power Capacitance checks Practice: model and calculation Practice: solution Summary Closing checkTransmission-Line Parameters IV
Calculate bundled-conductor parameters using bundle geometry and consistent line notation.
Transmission-Line Parameters IV 输电线路参数 IV Calculate bundled-conductor parameters using bundle geometry and consistent line notation. 采用一致的线路符号，根据分裂导线的几何计算参数。 Lecture outline Starting problem Carry-forward notation Phase bundle Equal bundle members Two-subconductor bundle notation Bundle GMR Electric bundle radius Physical totals Example setup Example: solution route Example: phase-center GMD Example: bundle GMR Example: electric bundle radius Example: bundle resistance Example: phase reactance Example: phase capacitance Example: shunt susceptance Example: full circuit totals Example: charging power Example: common-base record Bundle effects Double-circuit scaling Verification checks Practice: model and calculation Practice: solution Summary Closing checkTransmission-line models
3 lecturesTransmission-Line Models I
Construct the short-line model with declared terminal-current reference directions.
Transmission-Line Models I 输电线路模型 I Construct the short-line model with declared terminal-current reference directions. 在明确的端口电流参考方向下建立短线路模型。 Lecture outline Starting problem Physical line record Short-line model Short-line current Reference directions Short-line equations Three-phase conversion Receiving complex power Sending-end voltage Voltage regulation Sending-end power Example: complete input data Example: solution route Example: phase-voltage reference Example: receiving power Example: load current Example: route impedance Example: complex voltage drop Example: sending voltage Example: sending power Example: real-power efficiency Example: voltage regulation Example: checks Practice: model and calculation Practice: solution Summary Closing checkTransmission-Line Models II
Build the nominal-π circuit from series impedance and split shunt admittance.
Transmission-Line Models II 输电线路模型 II Build the nominal-π circuit from series impedance and split shunt admittance. 利用串联阻抗与两端分配的并联导纳建立标称 π 型电路。 Lecture outline Starting problem Nominal-π circuit Reference arrows Total shunt and terminal halves Receiving shunt current Series branch Series KVL Sending terminal ABCD constants ABCD cascade Nominal- π ABCD constants No-load voltage and regulation ABCD checks Example setup Example: solution route Example: receiving load current Example: receiving shunt current Example: series current Example: sending voltage Example: sending current Example: sending complex power Example: real-power balance Example: reactive-power balance Example: ABCD constants Example: cross-check Practice: model and calculation Practice: solution Summary Closing checkTransmission-Line Models III
Derive distributed long-line equations, propagation constants, and terminal relationships.
Transmission-Line Models III 输电线路模型 III Derive distributed long-line equations, propagation constants, and terminal relationships. 推导长线路分布参数方程、传播常数和端口关系。 Lecture outline Starting problem Spatial coordinate Segment KVL Segment KCL Coupled first-order equations Propagation constant Characteristic impedance General spatial solution Apply receiving-end conditions Exact ABCD constants Shared physical data Exact equivalent-π Surge-impedance loading Example setup Example: solution route Example: total line data Example: propagation and impedance Example: exact ABCD constants Example: exact sending quantities Example: equivalent-pi parameters Example: nominal-pi solution Example: short-line solution Example: output comparison Model selection Practice: model and calculation Practice: solution Summary Closing checkExam 2 review
1 lecturesExam 2 Review
Review transformer models, per-unit bases, three-phase banks, and transmission-line topics.
Exam 2 Review 考试 2 复习 Review transformer models, per-unit bases, three-phase banks, and transmission-line topics. 复习变压器模型、标幺基准、三相变压器组和输电线路知识。 Review outline Starting problem Transformer ratios Practical transformer model Per-unit bases Change of base Three-phase bank ratios Phase displacement Line-parameter data Line-model selection Signs and directions Integrated review case Complete input record Example: solution route Example: transformer base Example: bank and winding ratios Example: transposed reactance Example: shunt capacitance Example: common-base line Example: load current Example: bank voltage and loading Example: receiving line terminal Example: sending line terminal Example: complete power balance Line-model comparison Engineering interpretation Practice: common-base record Practice: base solution Practice: equipment loading Practice: loading solution Exam 2 summary Closing checkPower-flow analysis
5 lecturesPower Flow I
Identify power-flow inputs, bus types, unknowns, net injections, topology, and operating limits.
Power Flow I 潮流分析 I Identify power-flow inputs, bus types, unknowns, net injections, topology, and operating limits. 识别潮流输入、节点类型、未知量、净注入、拓扑与运行限值。 Lecture outline Starting problem Models already established Inputs and outputs Specifications and limits Topology and status Scope of the study Bus type Net bus injection Slack bus Slack real-power balance PV bus PQ bus Zero-injection junction Bus-type reference table Reactive capability Example: network and schedules Example: branch models Example: bus data and limits Example: solution workflow Example: known and unknown Example: voltage unknowns Preview: solved bus quantities Preview: real-power balance Practice: bus classification Practice: classification answers Practice: a PV limit Practice: limit answer SummaryPower Flow II
Assemble Y-bus from series branches, line charging, fixed shunts, and transformer taps.
Power Flow II 潮流分析 II Assemble Y-bus from series branches, line charging, fixed shunts, and transformer taps. 由串联支路、线路充电、固定并联元件和变压器分接头组装节点导纳矩阵。 Lecture outline Starting problem Bus 1 current balance Collecting the voltage terms The bus-admittance equation Series-branch terminal currents Series-branch stamp Impedance to admittance Nominal-pi line Fixed bus shunt Transformer tap convention Tap current referral Transformer branch stamp Matrix checks Example: network data Example: assembly workflow Example: admittance 1–2 Example: stamp 1–2 Example: admittance 1–3 Example: add branch 1–3 Example: add branch 2–3 Example: symbolic Y-bus Example: conductance and susceptance Example: independent row check Example: zero row sum Practice: line charging Practice: charging answer Practice: line 2–3 outage Practice: outage answer A diagonal-only difference Angle reference SummaryPower Flow III
Form polar power equations, choose the state, calculate mismatches, and apply a stopping tolerance.
Power Flow III 潮流分析 III Form polar power equations, choose the state, calculate mismatches, and apply a stopping tolerance. 建立极坐标功率方程，确定状态量，计算不平衡量并应用收敛容差。 Lecture outline Starting problem Current from a voltage state Complex power at a bus Combining current and power Polar notation Expanding one coupling term Real-power injection Reactive-power injection Angle difference and real power Active equations by bus type State and equation counts The three-bus state Mismatch convention PV reactive power Residual norm Example: complete input record Example: initial voltage state Example: calculation workflow Example: bus-3 current Example: bus-3 power Example: bus-3 mismatch Example: bus-2 power Example: PV-bus mismatch Example: complete mismatch Example: stopping test Tolerance in physical units Stored values and display rounding Practice: mismatch and stopping Practice: mismatch answer SummaryPower Flow IV
Run Gauss–Seidel PQ and PV updates, restore PV magnitude, and check reactive-power capability.
Power Flow IV 潮流分析 IV Run Gauss–Seidel PQ and PV updates, restore PV magnitude, and check reactive-power capability. 执行高斯—赛德尔 PQ、PV 更新，恢复 PV 电压幅值并检查无功能力。 Lecture outline Starting problem The PQ-bus equation Isolating the diagonal term The indexed PQ update Bus order within a sweep PV-bus update PV magnitude projection Example: PQ then PV Example: declared procedure Example: network matrix Example: initial mismatch Example: first-sweep workflow Step 1: PQ power term Step 1: neighbor subtotal Step 1: new PQ voltage Step 2: required PV reactive power Step 2: capability check Step 3: provisional PV voltage Step 3: restored PV magnitude Step 4: completed-sweep mismatch Step 4: progress toward balance Example: convergence history Example: convergence curve Example: converged voltages Example: final reactive capability Optional: relaxation factor Practice: stale neighbor voltage Practice: stale-value answer Practice: tighter reactive limit Practice: limit-enforcement answer Common update errors SummaryPower Flow V
Use Newton's Jacobian and corrections, then validate convergence, branch flows, and operating limits.
Power Flow V 潮流分析 V Use Newton's Jacobian and corrections, then validate convergence, branch flows, and operating limits. 利用牛顿法雅可比矩阵与修正量，检验收敛、支路潮流和运行限值。 Lecture outline From sequential to coupled updates A scalar Newton step Linearizing the power equations Jacobian blocks Use radians for angle corrections Two-bus example Two-bus equations Two-state Jacobian Flat start First Newton correction State update Recalculate the original powers First residual check Second Jacobian Optional: second Newton correction Optional: second residual check Two-bus convergence history Two-bus solved voltage Two-bus power balance Two-bus operating checks Common case: data and initial state Common case: Jacobian order Reference: off-diagonal derivatives Reference: diagonal derivatives Common case: Newton system Common case: first correction Common case: convergence history Common case: solved bus records If the PV reactive limit binds Branch-flow sign convention Example: power on branch 2–3 Common case: real-power paths Common case: flows and ratings Common case: independent power balance Common case: operating checks Stored precision and displayed precision Practice: change one branch rating Practice: rating-change answer Optional: comparing the methods Complete power-flow workflowComprehensive final review
1 lecturesComprehensive Final Review
Connect generation planning, AC circuits, transformers, line models, and power flow in a complete review.
Comprehensive Final Review 期末综合复习 Connect generation planning, AC circuits, transformers, line models, and power flow in a complete review. 综合复习发电规划、交流电路、变压器、线路模型和潮流分析。 Course review outline Starting problem Demand, energy, and capacity Portfolio constraints RMS phasors and complex power Balanced three-phase relations Transformer models and tests Per-unit bases and conversion Transformer connection conventions Line parameters Transmission-line models Network matrix and bus types Power-flow iteration Example: complete network data Example: solution route Example: portfolio checks Example: load specification Example: physical line parameters Example: common-base records Example: network admittance Example: initial mismatch Example: initial Jacobian Example: first Newton update Example: mismatch convergence Example: converged bus records Example: branch terminal powers Example: total power balance Example: portfolio acceptance Example: network acceptance Practice: load and transformer Practice: cross-topic solution Practice: a tighter source limit Practice: capability decision Scope of the conclusions Course summary Closing checkOutline source：ECE685_Course_Package_v2/01_lectures