An AC power system comprising a system for improving power factor of the AC power system by continuously variable, analog control of level of reactive current introduced into said at least one power conveying line (106, 197), wherein the AC power system includes an AC power source and an electrical load that are interconnected by said at least one power conveying line (106, 197) for conveying power in one or multiple phases from said AC power source to said electrical load; said electrical load being contained in a first circuit (104, 190, 191, 193, 196, 197) connected between said power conveying line and ground; the system for improving power factor of the AC power system comprising: a) a power factor-improving circuit including at least one channel (110, 120, 130, 140 and 150) coupled between the power conveying line and ground in parallel with the first circuit, each channel having a channel-level AC electron tube circuit arranged to have current level therein controlled in an analog, continuously variable fashion, each of said channel-level AC electron tube circuit comprising one bidirectional cold-cathode field-emission electron tube rated at medium to high voltage or two unidirectional cold-cathode field-emission electron tubes rated at medium to high voltage and connected in anti-parallel manner and at least one associated reactive impedance element interconnected in series manner (112, 122, 132, 142, 152); and b) each of said channel-level AC electron tube circuit being responsive to a control system configured to control a current in the control terminal of the channel-level electron tube in a continuously variable analog manner, the channel-level AC electron tube being configured to provide continuously variable, analog control of the level of reactive current in the at least one associated reactive impedance element (112, 122, 132, 142, 152) so that the foregoing level of reactive current changes, as necessary, in a continuously variable, analog manner to improve power factor in said power conveying line (106, 197); wherein the bidirectional cold-cathode field-emission electron tube and the two unidirectional cold-cathode field-emission electron tubes connected in anti-parallel manner are operative to conduct current in forward and reverse directions, toward or away from ground, based on a polarity of the AC power conveyed on the power line such that power factor improvement occurs over an entire cycle of AC power signals conveyed over the power conveying line. a) a power factor-improving circuit including at least one channel (110, 120, 130, 140 and 150) coupled between the power conveying line and ground in parallel with the first circuit, each channel having a channel-level AC electron tube circuit arranged to have current level therein controlled in an analog, continuously variable fashion, each of said channel-level AC electron tube circuit comprising one bidirectional cold-cathode field-emission electron tube rated at medium to high voltage or two unidirectional cold-cathode field-emission electron tubes rated at medium to high voltage and connected in anti-parallel manner and at least one associated reactive impedance element interconnected in series manner (112, 122, 132, 142, 152); and b) each of said channel-level AC electron tube circuit being responsive to a control system configured to control a current in the control terminal of the channel-level electron tube in a continuously variable analog manner, the channel-level AC electron tube being configured to provide continuously variable, analog control of the level of reactive current in the at least one associated reactive impedance element (112, 122, 132, 142, 152) so that the foregoing level of reactive current changes, as necessary, in a continuously variable, analog manner to improve power factor in said power conveying line (106, 197); wherein the bidirectional cold-cathode field-emission electron tube and the two unidirectional cold-cathode field-emission electron tubes connected in anti-parallel manner are operative to conduct current in forward and reverse directions, toward or away from ground, based on a polarity of the AC power conveyed on the power line such that power factor improvement occurs over an entire cycle of AC power signals conveyed over the power conveying line.