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Appendix A to Interim Report No. 5:

The Load Flow Problem and Technical Aspects of Power Electronics

WV Electric Industry Restructuring Group

5A.0 The Load Flow Problem and Technical Aspects of Power Electronics

A given set of loads can be supplied by a given set of generators in a number of ways. A load flow analysis is used for planning and to determine the transmission constraints in the existing networks. A mathematical/computer model of the interconnected network is used to describe the relationship between powers and the voltages. Power flows in all the transmission lines are calculated by solving the equations numerically, subject to some power and voltage constraints. The load flow solution gives information about the magnitude and phase angle of the voltage at each bus and real and reactive power flows in each line for given generation, load and transmission network data.

The maximum amount of power that can be transmitted through a transmission line depends on voltages at both ends of the line and the line parameters. The four parameters of a transmission line are resistance, inductance, capacitance, and conductance. The leakage current over the insulators of the overhead line and through the insulation of a cable is determined by the conductance. Since the leakage current is very small, the conductance parameter of the transmission line is neglected. Transmission lines at voltages greater than 230 kV have more than one conductor per phase. Table 5.1 shows typical parameters of transmission lines from 230 kV to 1100 kV.

Table 5.1 Typical overhead transmission line parameters.

The line losses decease at higher voltages due to decrease in resistance of the line. The surge impedance(Z_c ) of the line varies from 380 ohms to 230 ohms. Surge impedance loading(SIL) of the lines varies from 140 MW to 5260 MW. The power transfer capability of a transmission line is usually expressed in terms of SIL. For example, a 200 miles line can be loaded to 1.25 SIL.

The power transfer capability of the transmission line can be increased by the use of power electronics if the line has not been loaded to the thermal limit. Most of the EHV transmission lines in the United States today are not loaded to their thermal limit. They are loaded to lower limits due to voltage and stability considerations. Table 5.2 shows the typical surge impedance loading and the thermal rating of the EHV lines.

Table 5.2 Surge impedance loading (SIL) and typical thermal rating for voltage levels 230 kV to 1100 kV.

5A.1 Power Electronic Devices and Systems

Some examples of power electronics devices and systems which can increase the efficiency of use of existing transmission lines are reviewed below.

5A.1.1 Static Var Compensator

Figure 5.5 shows a single line diagram of a Static Var Compensator. The power through a simple transmission line model depends on voltage magnitude, transmission line reactance, and phase angle difference between the sending end and the receiving end voltages. Power electronic switching devices such as thyristors and gate turn-off thyristors (GTO) can be used to control voltage, line reactance, and phase angle. A Static Var Compensator (SVC) can increase power transmission significantly by maintaining constant voltage during steady state and dynamic operating conditions. A SVC consists of switchable capacitors and thyristor controlled reactors. A capacitor supplies reactive power and raises the voltage of the transmission line. An inductor absorbs reactive power and lowers the voltage of the transmission line. A number of utilities have applied SVC to enhance their transmission systems. A SVC can modulate reactive power to improve the dynamic and transient stability of power system.

(Figure 5.5 not available at this time)

Figure 5.5: A Single-line Diagram of a Static Var Compensator

5A.1.2 Series Controlled Capacitor

Figure 5.6 shows a single line diagram of a series controlled capacitor. Power transfer through a transmission line can be increased by decreasing reactance of the line. The reactance of the line can be decreased by adding capacitors in series with the line. Series compensation has mostly been used in the Western U.S. power system to increase transmission capacity in long transmission lines. The addition of series capacitors may cause subsynchronous resonance problems and damage the shaft of a turbine generator. However, a thyristor-based controller has been developed to damp the subsynchronous oscillations.

General Electric demonstrated the operation of a three-phase thyristor controlled series capacitor in a 500 kV line at Slatt Substation of Bonneville Power Administration (BPA) system. It consists of six 1.33 ohm modules connected in series. Each module consists of a series capacitor group in parallel with a series connected reactor and a thyristor unit. This installation has a continuous current rating of 2900 amperes and a short-term overload rating of 4350 amperes. The use of thyristor controlled series capacitor will allow control over the level of series compensation and can improve the damping of the power system.

(Figure 5.6 not available at this time)

Figure 5.6 : Single Line Diagram of a Series Controlled Capacitor

5A.1.3 Static Condenser

Figure 5.7 shows a one-line diagram of a Static Condenser or STATCON. An inverter generates three-phase voltages in phase with the ac system voltages. The current lags if the inverter voltage is less than the system voltage and leads if the inverter voltage is greater than the system voltage. The reactive power delivered by STATCON is a function of voltage and current. This device can deliver reactive power under reduced voltage condition and has a better performance than a Static Var Compensator. A 100 MVA SATCON has been installed at Sullivan substation in TVA power system to demonstrate its operation.

(Figure 5.7 not available at this time)

Figure 5.7: One-line Diagram of Static condenser (STATCON)

5A.1.4 Unified Power Flow Controller

Figure 5.8 shows a one-line diagram of a unified power flow controller. This controller allows the control of real and reactive power through the transmission line. The unified power flow controller allows the injection of a variable voltage magnitude and phase angle in series with the phase voltage. American Electric Power is planning to install a 320 MVA unified power flow controller at its Inez Station in eastern Kentucky to fully utilize the high capacity of this new 138 kV line. In the first phase of the project a ±160 MVA shunt voltage source inverter is installed at the Inez substation. This controller will provide reactive power and dynamic voltage control in the Inez area. Other power electronics devices are Thyristor Controlled Phase Angle Regulator and Thyristor Controlled Dynamic Brake. The thyristor controlled dynamic brake can damp subsynchronous oscillations if the power transfer capability of the transmission network is limited due to concern of subsynchronous resonance. Mechanically switched devices are less expensive and slower in response compared to electronically switched devices. A combination of mechanical and electronic devices may provide a least cost solution to give the desired steady state and dynamic response for the transmission system.

   (Figure 5.8 not available at this time)

Figure 5.8: One-line Diagram of a Unified Power Flow Controller

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