# Regulating the voltage at the end of a transmission line

#### ironring1

Joined Oct 18, 2019
3
Hello, all. I'm trying to develop a controller that will let me regulate the voltage at the end of a transmission line. I'm quite rusty on my control theory, so I'm looking for some help I'm not concerned about high-frequency behaviour, so I am modeling the transmission line as a first order low-pass filter fed by a variable voltage source. I'm also assuming that the voltage source will respond instantly to commands that I give it (again, at the frequencies of interest this should be a safe assumption). The power factor of the load is unity, so I can model it as a pure resistance in parallel with the capacitance of the line. So, I have a simple series RC circuit composed of Rt & Ct connected to a source Vs, with a load resistance R in parallel with Ct. Simple enough.

I would like the controller to command the source voltage Vs to vary so that the voltage across the capacitor Vc (which is the same as the voltage across the load) is held constant. At this point I'm not overly concerned with exact parameters such as steady state error, etc., I'm just having a hard time getting started (again, my control theory is rusty!).

The load resistance R is not fixed resistance. If it were, I could derive the following transfer function:
G(s) = Vc(s)/Vs(s) = (1/RtCt)/(s+(Rt+R)/(RtRCt)).

However, as the load current increases, the load "resistance" will decrease. If I replace R with a load current I(s), here is where I get stuck:
(s + 1/RtCt)Vc(s) = (1/RtCt)Vs(s) - I(s)
Clearly I(s) is a disturbance on the system, but I am not sure how to proceed beyond this point.

If it is not clear, my input is the source voltage Vs, and my output is the load voltage, which is the same as the voltage across the capacitor, Vc. I can measure the source current Is(c) directly. Although I am looking for a general solution, here are the expected values for the circuit parameters: Rt = 88 ohms, Ct = 44uF, target Vc = 300VDC. Output current will vary from 0 to about 3.5A.

Any advice on how to proceed would be greatly appreciated.

PS, I know that I could just slap a proportional controller on this, measure the response, call it a day and probably have it work out fine, but I want to do this properly with some rigour.

#### marcf

Joined Dec 29, 2014
257

#### ironring1

Joined Oct 18, 2019
3
I think you misunderstood my question. I am not looking for a way to measure the remote voltage. I don't have a spare pair for that (plus my transmission line is 3km long). All I have is a pair of conductors for power and fiber optics to communicate with the device powered at the other end (the FO are not available to send remote voltage sense data back to the power supply). All I can do is measure the power supply output voltage, output current, and command the power supply output voltage.

#### ronsimpson

Joined Oct 7, 2019
161
I would sent too much voltage and have a voltage regulator on the far end of the wire.

• Sensacell

#### AlbertHall

Joined Jun 4, 2014
8,512
I would sent too much voltage and have a voltage regulator on the far end of the wire.
Yes, that's the reliable method.

#### crutschow

Joined Mar 14, 2008
23,499
I see two ways to to this:

1. Use a regulator at the far end, as suggested, but that is not trivial with a 300V, 3.5A load.

2. If you know the transmission line resistance, than you can measure the current and adjust the supply voltage to cancel the calculated voltage drop in the line for that current.
Can the power supply voltage be adjusted electronically, or is it just a knob?
Does the power supply have inputs for remote load sense?

Last edited:

#### ronsimpson

Joined Oct 7, 2019
161
Use a regulator at the far end, as suggested, but that is not trivial with a 300V, 3.5A load.
We build power supplies of 1000 watts every day that set on the end of a wire that runs half way across the country.

Can be a buck with out isolation or a flyback with isolation. They flyback could have a Vin of 200 to 400V.
Input 300 to 400V
output: 300V @ 0 to 3.5A

I might try a 1000 watt off the power line type supply rated for 110 to 220VAC. Most of the 110-220 ac supplies will work just fine on dc.

#### MrAl

Joined Jun 17, 2014
6,610
Hello, all. I'm trying to develop a controller that will let me regulate the voltage at the end of a transmission line. I'm quite rusty on my control theory, so I'm looking for some help I'm not concerned about high-frequency behaviour, so I am modeling the transmission line as a first order low-pass filter fed by a variable voltage source. I'm also assuming that the voltage source will respond instantly to commands that I give it (again, at the frequencies of interest this should be a safe assumption). The power factor of the load is unity, so I can model it as a pure resistance in parallel with the capacitance of the line. So, I have a simple series RC circuit composed of Rt & Ct connected to a source Vs, with a load resistance R in parallel with Ct. Simple enough.

I would like the controller to command the source voltage Vs to vary so that the voltage across the capacitor Vc (which is the same as the voltage across the load) is held constant. At this point I'm not overly concerned with exact parameters such as steady state error, etc., I'm just having a hard time getting started (again, my control theory is rusty!).

The load resistance R is not fixed resistance. If it were, I could derive the following transfer function:
G(s) = Vc(s)/Vs(s) = (1/RtCt)/(s+(Rt+R)/(RtRCt)).

However, as the load current increases, the load "resistance" will decrease. If I replace R with a load current I(s), here is where I get stuck:
(s + 1/RtCt)Vc(s) = (1/RtCt)Vs(s) - I(s)
Clearly I(s) is a disturbance on the system, but I am not sure how to proceed beyond this point.

If it is not clear, my input is the source voltage Vs, and my output is the load voltage, which is the same as the voltage across the capacitor, Vc. I can measure the source current Is(c) directly. Although I am looking for a general solution, here are the expected values for the circuit parameters: Rt = 88 ohms, Ct = 44uF, target Vc = 300VDC. Output current will vary from 0 to about 3.5A.

Any advice on how to proceed would be greatly appreciated.

PS, I know that I could just slap a proportional controller on this, measure the response, call it a day and probably have it work out fine, but I want to do this properly with some rigour.
Hello,

If you are dealing with a true transmission line then i am guessing that the true answer to this is that it could be deemed uncontrollable. To be controllable you have to be able to measure the true state of the system and i dont think you can do that in this extreme case.
What you could do maybe is design an observer that measures the current and voltage on the close end and use that to predict the behavior at the far end. The far end will never be completely controllable, but at least you could get the steady state behavior close.
You'd have to check for extreme behavior though which would be like if the load resistance suddenly jumps up and that could cause the far end voltage to jump up or oscillate for a while before settling back down. Since as you probably know a transmission line has variation with both time and distance it would be hard to correct for this. Since you say you are going to model it as a pseudo transmission line considering capacitance and resistance only, that would have to be verified to work in practice with your particular line or you could be dealing with voltage spikes and sags on the far end before the close end even detects that anything has changed at all.

So in control jargon this would boil down to a feed forward system with a resistor and capacitor and load resistor plant, that's about it, and that means it has disadvantages as any feed forward system would have. You design a predictor to work as well as possible and put up with the somewhat lack of control at the far end.

#### ironring1

Joined Oct 18, 2019
3
So, running through a lot of the math on this over the weekend I've come to the conclusion that this is not controllable, but for a reason that I had not included in my original post (and had neglected up until now). The device at the end of the transmission line (an underwater robot) has transient suppression circuitry on its DC-DC converter front ends to protect them. Without communication, there is no way to know from the PSU end whether an increase in output current is due to the robot consuming more power in a useful way or if it is consuming more power due to its transient suppressors (MOV & TVS devices) starting to conduct.

As a result, I while I could tolerate lag in the response of the PSU increasing its output voltage, I cannot tolerate lag in the other direction as it would cause the transient suppressors to conduct, which would trigger the PSU controller to increase its output in response and the system would go unstable.

I reexamined my overall system and realized that I have a spare RS-232 (over fiber) communication channel. I'm going to design a variable dummy load that can sit at the end of the TL before the robot and that will draw excess power in order to keep the transient suppressors from conducting and then signal to the controller at the other end that it the PSU needs to reduce its output voltage. That means that I will have two controllers (one for the dummy load, one for the PSU, but because the former is making up for any lag in the response of the other I should be ok. In the event of a loss of communication (never underestimate the ability of an ROV operator to break the fibers in a tether...), we the PSU controller will set its output to a guaranteed safe level.

Thank you all for your commends and suggestions.

#### crutschow

Joined Mar 14, 2008
23,499
The device at the end of the transmission line (an underwater robot) has transient suppression circuitry on its DC-DC converter front ends to protect them. Without communication, there is no way to know from the PSU end whether an increase in output current is due to the robot consuming more power in a useful way or if it is consuming more power due to its transient suppressors (MOV & TVS devices) starting to conduct.
So I assume that means the maximum voltage required at the drive end for the maximum current is higher than the MOV voltage rating and would cause the MOVs to conduct if the load current were suddenly removed. (?)