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Basics of Power Systems

Basics of Power Systems 22
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JuliyaMadenta,Philippines,Researcher
Published Date:15-07-2017
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Topic 1: Basics of Power Systems ECE 5332: Communications and Control for Smart Spring 2012 A.H. Mohsenian‐Rad (U of T) Networking and Distributed Systems 1Power Systems •The Four Main Elements in Power Systems: Power Production / Generation Power Transmission Power Distribution Power Consumption / Load  •Of course, we also need monitoring and control systems. Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 2Power Systems •Power Production: Different Types: Traditional Renewable Capacity, Cost, Carbon Emission Step‐up Transformers Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 3Power Systems •Power Transmission: High Voltage (HV) Transmission Lines Several Hundred Miles Switching Stations  Transformers Circuit Breakers Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 4Power Systems •Power Distribution: Medium Voltage (MV) Transmission Lines ( 50 kV) Power Deliver to Load Locations Interface with Consumers / Metering Distribution Sub‐stations Step‐Down Transformers Distribution Transformers Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 7Power Systems •Power Consumption: Industrial Commercial Residential Demand Response Controllable Load Non‐Controllable Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 8Power Systems Generation Load Transmission Distribution Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 9Power Grid Graph Representation Nodes: Buses Links: Transmission Lines Generator 10 MW 3 MW Load 7 MW Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 15Transmission Line Admittance •Admittance y is defined as the inverse of impedance z: z = r + j x                   (r: Resistance, x: Reactance) y = g + j b(g: Conductance, b: Susceptance) y = 1 / z Parameter g is usually positive Parameter b:  Positive: Capacitor Negative: Inductor Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 16Transmission Line Admittance •For the transmission line connecting bus ito bus k: Addmitance: y ik Example: y = 1 –j 4   (per unit) ik Note that, y is denoted by y and indicates: ii i  Susceptance for any shunt element (capacitor) to ground at bus i.  Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 17Y-Bus Matrix • We define: Y =  Y  where bus ij N Diagonal Elements: Y y y ii i ik k1,ki Off‐diagonal Elements:  Yy ij ij Note that Y matrix depends on the power grid topology  bas and the admittance of all transmission lines. N is the number of busses in the grid. Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 18Power Flow Equations •Let S denote the power injectionat bus i: i S = P + j Q i i i Active Power        Reactive Power •Generation Bus:  P  0 i •Load Bus:  P  0(negative power injection) i Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 21Power Flow Equations •Using Kirchhoff laws, AC Power Flow Equationsbecome: N P V V G cos( )B sin( ) k k j kj k j kj k j j1 N Q V V G sin( )B cos( )  k k j kj k j kj k j j1 •Do we know all notations here?  •If we know enough variables, we can obtain the rest of  variables by solving a system of nonlinear equations.  Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 22Power Flow Equations •The AC Power Flow Equations are complicated to solve. •Next, we try to simplify the equations in three steps.  •Step 1: For most networks, G  B. Thus, we set G = 0: N P V V B sin( )  k k j kj k j j1 N  Q V VB cos( ) k k j kj k j j1 Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 23Power Flow Equations  •Step 2: For most neighboring buses:                                  10 to 15 . i j Sin ( )  k j k j •As a result, we have:   Cos ( ) 1 k j  N  P V V B ( ) k k j kj k j j1 N  Q V VB k k j kj j1 Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 24Power Flow Equations •Step 3: In per‐unit, V is very close to 1.0 (0.95 to 1.05).  i V V1 •As a result, we have:                    .  i j N P B ( ) k kj k j j1 N N Q BB Bb  k kj kk kj k j1 j1, jk •P has a linear model and Q is almost fixed. k k Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 25Power Flow Equations •Step 3: In per‐unit, V is very close to 1.0 (0.95 to 1.05).  i V V1 •As a result, we have:                    .  i j DC Power Flow Equations N P B ( ) k kj k j j1 N N Q BB Bb  k kj kk kj k j1 j1, jk •P has a linear model and Q is almost fixed. k k Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 26Power Flow Equations •Given the power injection valuesat all buses, we can use N P B ( )  k kj k j j1 to obtain the voltage anglesat all buses.   •Let P denote the power flowfrom bus ito bus j, we have: ij P B ( ) ij ij i j Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 27Power Flow Equations •Example: Obtain power flow values in the following grid: g g P 2 pu P 2 pu 2 1 yj10 12 l P1 pu 2 yj10 yj10 yj10 23 14 13 yj10 34 g l P1 pu P 4 pu 4 3 Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 28Power Flow Equations •First, we obtain the Y‐bus matrix: bbbbbbb  1 12 13 14 12 13 14  b bbbbbb 21 2 21 23 24 23 24  Y j bus  bb bbbbb 31 32 3 31 32 34 34  bbb bbbb  41 42 43 4 41 42 43 B B B B  11 12 13 14   B B B B 21 22 23 24    j jB j  B B B B 31 32 33 34  B B B B  41 42 43 44 Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas Tech University 29