Cable Parameter Influence and Compensation Measures of Long Distance Transmission High Voltage Power Supply
Long distance transmission of high voltage power from a supply to a remote load introduces effects from the cable parameters that are negligible at short distances. The cable resistance, inductance, and capacitance affect the voltage at the load, the power transfer capability, and the stability of the system. Understanding these effects and implementing compensation measures ensures effective power delivery over long cables.
Cable resistance causes voltage drop proportional to the current. The resistance depends on the conductor material, cross section, and length. For long cables, the resistance can be significant, causing substantial voltage drop at high currents. The load voltage is lower than the supply voltage by the product of current and cable resistance.
Resistance also causes power loss in the cable. The loss is proportional to the current squared and the resistance. This loss reduces the efficiency of power transmission and generates heat in the cable. For very long cables or high currents, the loss can be a significant fraction of the transmitted power.
Cable inductance causes voltage drop proportional to the rate of change of current. The inductance depends on the cable geometry and the magnetic permeability of the surrounding materials. For transient currents or AC power, the inductive reactance adds to the impedance. The inductive drop causes phase shift between voltage and current.
Cable capacitance causes charging current proportional to the rate of change of voltage. The capacitance depends on the cable geometry and the dielectric properties of the insulation. For DC power, the capacitance affects the transient response during voltage changes. For AC power, the capacitive charging current flows continuously.
The characteristic impedance of the cable is the square root of the ratio of inductance to capacitance. For cables long enough that the propagation time is significant compared to the signal frequencies, transmission line effects become important. Voltage and current propagate as waves along the cable, with reflections at impedance discontinuities.
For DC power transmission, the steady state effects are dominated by resistance. The voltage drop is the product of current and resistance. Compensation can be achieved by increasing the supply voltage to account for the drop, or by using remote sensing that measures the load voltage and adjusts the supply accordingly.
Remote voltage sensing measures the voltage at the load and feeds this information back to the supply. The supply adjusts its output to maintain the desired voltage at the load despite the cable drop. This approach requires separate sensing leads or communication of the measurement. The sensing must be accurate and fast enough for effective control.
For pulsed power transmission, the cable acts as a transmission line. The pulse propagates along the cable with a velocity determined by the inductance and capacitance. The pulse shape may be distorted by dispersion if different frequency components propagate at different velocities. Reflections occur if the load impedance does not match the cable characteristic impedance.
Impedance matching reduces reflections by making the load impedance equal to the cable characteristic impedance. This can be achieved with matching networks or resistive terminations. Matching eliminates reflections but may reduce the power delivered to the load if the matching involves dissipation.
Pulse shaping can pre distort the transmitted pulse to compensate for cable effects. If the cable response is known, the input pulse can be shaped so that the output pulse has the desired shape. This technique requires characterization of the cable response and may be sensitive to variations.
For very long cables, distributed compensation may be needed. Intermediate compensation stages along the cable can boost the voltage or correct the waveform. This approach is used in some power transmission systems but adds complexity.
Cable selection for long distance transmission considers the electrical parameters, the voltage rating, and the environmental requirements. Larger conductor cross section reduces resistance but increases cost and weight. Different cable constructions have different inductance and capacitance values. The insulation must be rated for the operating voltage. The cable must withstand the environmental conditions along the route.
