Mathcad-Based Education on Modern Transmission Systems

Size: px

Start display at page:

Download "Mathcad-Based Education on Modern Transmission Systems"

Shannon Perry
6 years ago
Views:

1 Mathcad-Based Education on Modern Transmission ystems 3rd and 4th International MAINELIE Workshops on Prime Movers and hip Automation and Control Pavlos Georgilakis, George Korres chool of Electrical and Computer Engineering National Technical University of Athens, Greece

2 Introduction (I) Modern transmission systems are undergoing continuous changes and restructuring. The regulatory constraints on transmission expansion have pushed transmission systems closer to their stability and thermal limits. To achieve both operational reliability and financial profitability, it is clear that more efficient utilization and control of the existing transmission system infrastructure is required. This can be effectively tackled by the introduction of high power electronic controllers for the flexible regulation of power flows and voltages in AC transmission systems, whereby the changes can be accommodated easily without stressing the system. MAINELIE 01, Athens /15

3 Introduction (II) Power electronic based systems and other static equipment, which provide controllability of power flows and voltages, are termed flexible AC transmission systems (FACT). The basic applications of FACT controllers are: power flow control, increase of transmission capability, voltage control, reactive power compensation, stability improvement, power quality improvement, and interconnection of renewable and distributed generation. In the fast changing electricity market environment, teaching transmission lines and FACT controllers is a challenge. The article demonstrates how Mathcad software can be used as a major advancement for teaching flexible AC transmission systems (FACT). MAINELIE 01, Athens 3/15

4 MATHCAD (I) Mathcad software is widely used for electrical engineering topics. The students learn how to use Mathcad in a short time with limited practice. Its use is much easier than learning a programming language and has many built-in functions that facilitate its use in many textbook applications. Its main advantage is that the equations appear in similar format as in handwriting. The Mathcad feature of what-you-see-is-what-you-get, allows students to see if they have entered a problem correctly or not. MAINELIE 01, Athens 4/15

5 MATHCAD (II) Another significant advantage is the integration of the units of measurement, which means that the students are free from keeping track of the units used. The students have only to indicate the units for each input data and ask for the answer in any particular unit, while Mathcad automatically performs all the unit transformations. Taking advantage of the computational power and speed of Mathcad, instructors and students can quickly cycle through problem scenarios, observing changes in the behavior of transmission lines and FACT controllers. MAINELIE 01, Athens 5/15

6 FACT Course Content and yllabus (I) One of the seventh semester elective courses, of the five-year NTUA undergraduate curriculum for Electrical and Computer Engineers, is on Transmission Lines and FACT Controllers. It covers the following subjects: Introduction to Mathcad; Electrical characteristics of transmission lines (TL); Equations and equivalent circuits of small, medium, and long TL; Generalized circuit ABCD constants and two-port circuits of TL; TL shunt and series compensation; TL power, losses, and efficiency; MAINELIE 01, Athens 6/15

7 A sample of MATHCAD Environment MAINELIE 01, Athens 7/15

8 FACT Course Content and yllabus (II) Introduction to FACT; FACT with thyristor based controllers (C - tatic Ar compensators, TCC -, thyristor controlled series capacitors, and P - phase shifters); FACTs controllers with voltage- or current-sourced converters (TACOM - static synchronous compensators, C - static synchronous series compensators, UPFC - unified power flow controllers); High voltage direct current (HDC) transmission systems; The role of FACT in deregulated electricity markets. MAINELIE 01, Athens 8/15

9 Conventional thyristor-based FACT controllers MAINELIE 01, Athens 9/15

10 Converter-based FACT controllers MAINELIE 01, Athens 10/15

11 Power Flow Control with C P + jq X 1 T X P + jq A B I C A B P = X sin δ E P = X sin δ E Q = ( ) cosδ E X Q = ( ) cosδ E X E T = 1± T = Esin δ + cosδ MAINELIE 01, Athens 11/15

12 ariation of P, Q, and Q for T =0.6 pu and capacitive mode 3.0 Q (pu) P (pu) Q (pu) -3.0 transmission angle δ (degrees) MAINELIE 01, Athens 1/15

13 MATHCAD Code for Power Flow Control with C Definition pu : = 1. 0 Input Data X : = 1.0 pu X 1 : = X X X : = δ : = 90 deg : = 1.0 e j δ pu : = 0.97 e j0 pu T : = 0.6 pu (Capacitive) Calculations E : = 1+ ( ) ( ) + cos( δ) T P : = X sin ( δ) E esults E = pu P = pu MAINELIE 01, Athens 13/15

14 MATHCAD Code for Power Flow Control Calculations with C Problem: Calculation of T for the capacitive or inductive operation mode ( T =0.6 pu ) and the uncompensated mode ( T =0.0 pu ) for δ in the interval (-45 0, ) i : = 0, n : = 0, 1.. T n : = n : = ( 45 + i) deg δ i E i, n : = 1+ ( ) ( ) + cos( δ ) T n i T ( ) i, n : = E i, n sin δ i MAINELIE 01, Athens 14/15

15 atio of transmitted power over maximum power (T) for capacitive mode ( T =0.6 pu), uncompensated mode ( T =0.0 pu) and inductive mode ( T =0.6 pu) T (pu) capacitive uncompansated 0.5 inductive transmission angle δ (degrees) MAINELIE 01, Athens 15/15

16 MATHCAD Code for Power Flow Control with C Problem: Calculation of the values of δ in the interval (-45 0, 5 0 ) where T becomes zero, for T =0.6 pu (inductive operation mode) Calculation T0 1+ ( ) ( ) ( ) + cos x sin ( x) solve, x = 0 assume, x = ealange π 5π, MAINELIE 01, Athens 16/15

17 Conclusions An effective approach to education in the field of transmission lines and FACT has been presented. The proposed teaching methodology uses Mathcad, a powerful tool for performing calculations. The advantages of the proposed approach are: the students write the equations in the familiar textbook format; the students interest is significantly increased because the problems are interactively solved in a computer-equipped classroom; the students concentrate on the meaning of what they learn, they analyze results and draw conclusions, thus enhancing their learning ability. Mathcad can been ideally used for teaching courses in power flow, short circuit and protection analysis, for electric shipboard electric power systems. MAINELIE 01, Athens 17/15

THE UNIVERSITY OF NEW SOUTH WALES. School of Electrical Engineering & Telecommunications FINALEXAMINATION. Session

Name: Student ID: Signature: THE UNIVERSITY OF NEW SOUTH WALES School of Electrical Engineering & Telecommunications FINALEXAMINATION Session 00 ELEC46 Power System Analysis TIME ALLOWED: 3 hours TOTAL