This example shows how power flow control and deicing of a transmission line could be implemented using the Line Impedance Modulator (LIM) technology.
The Bundle-Controlled Line Impedance Modulator (LIM) is a distributed FACTS device that has the capability of increasing the impedance of high-voltage transmission lines. Using switches connected in series with each sub-conductors of a bundle, the LIM also allows concentrating each phase current into one sub-conductor at a time. It is then possible to de-ice each sub-conductor by the Joule effect, one after the other. This example shows how power flow control and line deicing could be implemented with a LIM. More information is available in the papers in reference.
This example shows two generators and a 10,000 MVA equivalent power system interconnected by three 735-kV transmission lines. Lines L1 and L2 are conventional 30- and 90-km long transmission lines. L3 is a 60-km long line with two switching modules installed at its mid-point. Line L3 with the two line segments forms a back-to-back LIM. Power outputs of generators 1 and 2 are respectively set at 2400 and 2500 MW. Given their respective loads, connected at the 13.8 kV for the sake of simplicity, they each supply 2000 MW to bus B1 and B2 respectively. Line L2 being much longer than L3, its normal power flow is only 1573 MW when the LIM's switches are all closed. Power flows on L1 and L3 are 415 and 2404 MW respectively. The impedance control command transmitted to the LIM is produced by a signal generator inside the LIM impedance Control block. The Z cmd signal ramps between 0.5 and 3 s from its minimum value 1.0 (when all four subconductors are used) to its maximum value 1.642 pu (when only one subconductor per bundle is used) . It then varies in steps after t= 4 s. As shown inside the LIM subsystem, a look-up table associates 58 combinations of 24 switch states to the requested impedance command. As explained in , these combinations have been selected to maintain negative- and zero-sequence currents at a level smaller or equal than observed when all switches are closed. The 58 switch combinations used in this example represent a very small subset of the 33752 switch combinations provided by a pair of BCL segments. Each line segment is represented by a 14-conductor Exact-Pi section . Line resistances, inductances and capacitances are provided in the power_LineImpedanceModulator_init.m file. The 14x14 impedance and admittance matrices are automatically loaded in the workspace (see File/Model Properties/Callbacks/PreloadFcn).
Run this example and observe the following sequence of events in Scope 1.
At t=0 s, all the LIM's switches are closed. Power flows in each line are annotated in blue in the example next to each transmission line.
At t=0.5 s, the impedance signal Zcmd ramps from 1 to 1.642 pu as shown by the yellow trace. For each values of Zcmd, the look-up table provides the corresponding switch combinations. The switch combinations transmitted to the switching modules are sampled here every 0.1 s. This gives the discretized impedance signal Zdisc (magenta).
At t=3 s, the LIM impedance is maximum. Note that power flows in L2 (magenta) and L3 (blue) are almost equal. Power flows at this point are annotated in red in the example.
At t=4 s, the LIM impedance is set to 1 pu which closes all switches. As a result, power flows in the lines vary abruptly within 1 cycle. This perturbation forces the synchronous generators governors to react and stabilize the power flows back to the initial values prevailing at t=0 s.
At t=5 s, the LIM impedance signal returns to 1.642 pu which again induces a power flow perturbation.
At 6.3 s, the LIM impedance is reduced down to 1 pu in three large steps.
As shown in the example, when the switches of the LIM are operated, impedance of line L3 progressively increases up to the point where only one switch remains closed per switching module. With only one conductor in service per bundle power flows in line L2 and L3 are nearly equals even though L2 is 50% longer than L3. Power flows in line L1 becomes almost zero. This shows that LIMs have the capability of reducing power flows of overloaded transmission lines. The step changes beyond t=4 s shows that LIMs can also quickly vary the line impedance if required. Scope 2 shows the bus B2 sequence voltages and the sequence currents flowing out of B2 toward line L3. This is the line current of the back-to-back LIM. It can be seen that for all switch combinations used, the negative- and zero-sequence voltages and currents remain lower than the initial values obtained with all switches closed. Hence LIMs can be operated to produce power ramping or power step without increasing negative- and zero-sequence levels. Scope 3 shows that the voltages across the switches of the phase A switching module located on the bus B2 side. It can be seen that transient voltages remain within 35 kV which allows the use of medium voltage switching devices. The maximum rms voltage in steady-state, visible at t = 3.9s, is 13.4 kV.
Scope 3 also shows the switch currents of the phase A switching module located on the bus B2 side. With all switches closed, switch currents are initially 465 A rms. With all but one switch opened at t=3.9 s, it can be seen that the switch current of subconductor 2 reaches 1533 A rms. Hence, although the power flow in line L3 has been reduced by 17%, the subconductor current has increased by a 3.3 factor. Such a current is large enough for simultaneously deicing by the Joule effect three subconductors (one per phase) in both 30-km BCL segments. Once a first subconductor is de-iced in each bundle of both BCL segments, three other switch combinations can be used to completely de-ice the transmission line. Note that the switch combination table provided in the example is appropriate for power flow control. Other switch combination tables would be used to force specific subconductor deicing sequence and avoid bundle rotation. Note that if line currents had initially been too low for reaching a deicing level, it could have been possible to open the switches of one 30-km segment only. The smaller impedance increase provided by one BCL segment would then lead to a higher current in the sub-conductors to de-ice. Also, accordingly to the concept of the smart power grid where each line would be equipped with switching modules [4-5], impedance of line L2 could be increased to divert even more current into line L3.
 P. Couture, J. Brochu, G. Sybille, P. Giroux and A. O. Barry, "Power flow and stability control using an integrated HV bundle-controlled line-impedance modulator", IEEE Trans. Power Del., vol. 25, no. 4, pp. 2940-2949, Oct. 2010.
 P. Couture, "Smart Power Line and Photonic de-icer concepts for transmission-line capacity and reliability improvement" Cold Reg. Sci. Technol. 65 (2011), Jan., 13-22.
 P. Couture, "Switching modules for the extraction/injection of power (without ground or phase reference) from a bundled HV line," IEEE Trans. Power Delivery, vol. 19, No3, pp. 1259-1266, July 2004.
 P. Couture, "Switching apparatus, control system and method for varying an impedance of a phase line", Patent pending, PCT/CA2011/00850, July 22, 2011.
 P. Couture, J. Brochu, B. Francoeur, R. Morin, D. H. Nguyen, K. Slimani, A. Turgeon and P. Van Dyke, "Smart Power Line (SPL) experimental research project," CIGRE 2014.
 J. Brochu and P. Couture, "Load Flow Modeling of the Integrated Bundle-controlled Line Impedance Modulator," IEEE Trans. Power Delivery, accepted and currently available on IEEExplore.