# Patent

## Title
Presettable transducer for electrical quantities

## Abstract

A presentable voltage sensor includes an electrode faced by an electric field probe and connected to a voltage source; a screening conductive shell wrapping the probe and connected to a reference potential; a dielectric material housed within the shell and interposed between the probe and the electrode; a conditioning circuit connected to an exit of the sensor and having a resistor of resistance Rm interposed between the probe and a second reference potential; and an integrator circuit formed from an RC network and having a resistor of resistance Ri, a capacitor of capacitance Ci, and a loss factor which, at a frequency of interest, is of an order of 10−4.

## Background
FIELD OF THE INVENTION
The present invention relates to a presettable voltage sensor for electrical quantities.
BACKGROUND OF THE INVENTION
Sensors are known devices for converting information, in the form of a physical quantity (of variable input) into a physical quantity (of variable output) of identical or different type, measurable in accordance with a defined law. These types of sensors generally include a sensor, i.e. a primary element of a measurement chain, configured to convert the variable input into a measurable signal, and a conditioning circuit, which receives the measurable signal as input and provides it as output transformed in accordance with a defined law, to make it available to the user.
Electrical systems are known to use current sensors and voltage sensors for various purposes, for example for energy measurements, for protection, for fault localization, etc.
U.S. Pat. No. 6,670,799 discloses a method and/or apparatus for measuring current in a high voltage current carrier and suggests a solution for the phase compensation of a Rogowski coil-based current transducer relied on the use of a proper passive circuit.
U.S. Pat. No. 5,473,244 discloses a different apparatus for measuring voltages and currents using non-contacting sensors.
WO99/54740 discloses a current measuring device comprising a Rogowski coil.
In particular, known voltage sensors consist of transformers or capacitive or resistive dividers, their purpose being generally to reduce the primary voltage to values compatible with the particular use for which they are intended. Known current sensors consist of current transformers or Hall effect sensors or anti-inductive shunts, their function being to reduce the primary current to values compatible with the particular use for which they are intended.
A basic requirement for a current or voltage sensor for the aforesaid uses is adequate precision, which is currently achievable only at the expense of sensor weight, overall size, cost, limitations on its field of application, and generally a series of limitations on its characteristics and/or performance, and the consequent need for the producer to compromise.
In particular, with regard to precision, a sensor must be able to provide as output an electrical quantity representative of the input quantity with phase and ratio errors contained within narrow predetermined limits.
SUMMARY OF THE INVENTION
An object of the invention is to provide a voltage sensor, which is without any of the drawbacks and limitations of known transducers.
Another object of the invention is to provide a voltage sensor, which can be adjusted to compensate its non-ideality deriving from the physical nature of the components, from parasite phenomena, and from the construction process.
These and other objects which will be more apparent from the ensuing description are attained, according to the invention, by an adjustable voltage sensor which includes a sensor connected to a voltage source to be measured and a conditioning circuit, connected to the exit of the sensor, and in which the sensor includes an electrode connected to the voltage source, an electric filed probe facing the electrode, a screening conductive shell wrapping the probe and connected to a reference potential, a dielectric material housed within the shell and interposed between the probe and the electrode, wherein the conditioning circuit includes a resistor that has a resistance Rm and that is interposed between the probe and a second reference potential, selected to satisfy the following conditions:



  
    
      R
      m
    
    ⁢
    
      <<
      
        
        
          
            R
            
              p
              ⁢
              
                
              
              ⁢
              2
            
          
          
            1
            +
            
              jω
              ⁢
              
                
              
              ⁢
              
                C
                2
              
              ⁢
              
                R
                
                  p
                  ⁢
                  
                    
                  
                  ⁢
                  2
                
              
            
          
        
        
      
    
  




  
    
      R
      m
    
    >>
    
      ω
      ⁢
      
        
      
      ⁢
      
        L
        pm
      
    
  




  
    
      R
      m
    
    ⁢
    
      <<
      
        
        
          1
          
            j
            ⁢
            
              
            
            ⁢
            ω
            ⁢
            
              
            
            ⁢
            
              C
              pm
            
          
        
        
      
    
  




  
    
      R
      m
    
    ⁢
    
      <<
      
        
        
          
            R
            
              p
              ⁢
              
                
              
              ⁢
              1
            
          
          
            1
            +
            
              j
              ⁢
              
                
              
              ⁢
              ω
              ⁢
              
                
              
              ⁢
              
                C
                1
              
              ⁢
              
                R
                
                  p
                  ⁢
                  
                    
                  
                  ⁢
                  1
                
              
            
          
        
        
      
    
  



and an integrator circuit formed from an RC network in which the resistor has a resistance Ri and the capacitor of capacitance Ci and a loss factor which, at the frequency concerned, is of the order of 10−4, such as satisfy the following relationship:





  
    
      arctan
      ⁡
      
        (
        
          
            -
            ω
          
          ⁢
          
            
          
          ⁢
          
            C
            i
          
          ⁢
          
            R
            i
          
        
        )
      
    
    +
    
      arctan
      ⁢
      
        
          ω
          ⁢
          
            
          
          ⁢
          
            R
            
              p
              ⁢
              
                
              
              ⁢
              1
            
            2
          
          ⁢
          
            R
            m
          
          ⁢
          
            C
            1
          
        
        
          
            
              R
              m
            
            ⁢
            
              R
              
                p
                ⁢
                
                  
                
                ⁢
                1
              
            
          
          +
          
            R
            m
            2
          
          +
          
            
              ω
              2
            
            ⁢
            
              R
              
                p
                ⁢
                
                  
                
                ⁢
                1
              
              2
            
            ⁢
            
              R
              m
              2
            
            ⁢
            
              C
              1
              2
            
          
        
      
    
  
  =
  0




in which:

ωRiCi>>1.




BRIEF DESCRIPTION OF THE DRAWINGS
The present invention is further clarified hereinafter in terms of a preferred embodiment thereof, provided by way of a non-limiting example with reference to the accompanying drawings, in which:
FIG. 1 is a schematic view of the sensor of a voltage sensor according to the invention,
FIG. 2 shows the equivalent electrical circuit of the sensor and of the integrator,
FIG. 3 shows the same equivalent electrical circuit without non-controllable parasitic elements,
FIG. 4 shows the vectorial diagram of the relevant sensor voltage, and
FIG. 5 shows the equivalent electrical circuit of the sensor in a different embodiment.



DETAILED DESCRIPTION OF THE INVENTION
With reference to FIGS. 1 and 2, a voltage sensor according to the invention is installed to provide at its output a voltage vo representative of an input voltage vi for example of a high, medium or low voltage cable 2, to which the sensor is connected.
In the same manner as traditional sensors, the voltage sensor according to the invention uses an electric field sensor comprising an electrode 4 and a probe 6 connected to a reference potential vref1, for example earth, via a resistance measurement resistor Rm, and is embedded in an insulating medium 8 wrapped by a screen 10 of conductive material connected to a reference potential vref. In reality, vo is connected to reference potential vref1 not only via the measurement resistor Rm, but also via its parasitic elements, identifiable as an inductance Lpm in series with Rm and as a capacitance Cpm.
An integrator circuit, consisting of an RC network with a resistor of resistance Ri and a capacitor of capacitance Ci, is connected to probe 6 of the electric field sensor and to resistor Rm.
Specifically, in the electrical circuit of FIG. 2:
C1 is the capacitance of that capacitor the plates of which are formed by the electrode 4 and probe 6, its dielectric being the insulating material 8, in which both are immersed,
C2 is the capacitance of that capacitor the plates of which are formed by the probe 6 and the metal shell 10 which enclose these and the dielectric which surrounds them,
Rp1 is the parasitic resistance of the capacitor of capacitance C1,
Rp2 is the parasitic resistance of the capacitor of capacitance C2,
Rm is the resistance of the measurement resistor interposed between the probe 6 and the reference potential vref,
Cpm is the parasitic capacitance of the resistor of resistance Rm,
Lpm is the parasitic inductance of the resistor of resistance Rm,
Ri is the resistance of the integrator circuit,
Ci is the capacitance of the capacitor of the integrator circuit,
Rpi is the parasitic resistance of the capacitor of capacitance C1.
In this circuit the parameters used for measurement are the capacitance C1 and the measurement resistor Rm, while all the other parameters (apart from resistance Ri and capacitance Ci) are parasitic and negatively influence the output signal vo.
To minimize the influence of these parasitic parameters, the value of the measurement resistor Rm must be chosen such that at the frequency concerned (for example 50 Hz) the following relationships are satisfied:




  
    
      
        
          
            R
            m
          
          ⁢
          
            <<
            
              
              
                
                  R
                  2
                
                
                  1
                  +
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    ω
                    ⁢
                    
                      
                    
                    ⁢
                    
                      C
                      2
                    
                    ⁢
                    
                      R
                      
                        p
                        ⁢
                        
                          
                        
                        ⁢
                        2
                      
                    
                  
                
              
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            R
            m
          
          >>
          
            ω
            ⁢
            
              
            
            ⁢
            
              L
              pm
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            R
            m
          
          ⁢
          
            <<
            
              
              
                1
                
                  jω
                  ⁢
                  
                    
                  
                  ⁢
                  
                    C
                    pm
                  
                
              
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              R
              m
            
            ⁢
            
              <<
              
                
                
                  Z
                  1
                
                
              
            
          
          =
          
            
            
              
                R
                
                  p
                  ⁢
                  
                    
                  
                  ⁢
                  1
                
              
              
                1
                +
                
                  jω
                  ⁢
                  
                    
                  
                  ⁢
                  
                    C
                    1
                  
                  ⁢
                  
                    R
                    
                      p
                      ⁢
                      
                        
                      
                      ⁢
                      1
                    
                  
                
              
            
            
          
        
      
    
    
      
        (
        1
        )
      
    
  




If these conditions are satisfied, then

V0(ω)≅jωRmC1Vi(ω)

and the voltage vo leads vi by π/2.
To then obtain the voltage vout in phase with the primary quantity vi the quantity vo must be integrated, this taking place in the integrator consisting of the RC network comprising the resistor Ri and the capacitor Ci.
By choosing the measurement resistor Rm such as to satisfy conditions (1) at the frequency concerned, the equivalent circuit of the sensor of FIG. 1 is transformed into the equivalent circuit of FIG. 3, i.e. it enables the sensor characterised by uncontrollable parameters (C2, Rp2, Lpm, Cpm) to be transformed into a sensor characterised by only controllable parameters. Moreover satisfying the conditions for C1 to have a low loss factor enables a substantially ideal integrator circuit to be obtained, in which the phase displacement between its input quantity vo and its output quantity vout can be controlled such as to have this latter in phase with the sensor input quantity v1.
In the case for example of an industrial frequency of 50 Hz, a convenient value for the measurement resistor Rm is of the order of 100 K′Ω, in that lesser values would penalize the signal/noise, whereas greater values would not enable the conditions (1) to be satisfied and would render the system uncontrollable.
In particular, the value Xc2 would be no longer negligible compared with Rm, meaning that the output voltage vout would be no longer in relationship with the derivative of the input voltage vi.
The RC network cutoff frequency must be such that at the relevant frequency the phase displacement introduced by it between vo and vout is equal to π/2. This is achieved by choosing high Ci and/or Ri values, such that the cutoff frequency is much less than 50 Hz, and is for example about 5 mHz.
The harmonic response of the integrator is




  
    
      H
      RC
    
    ⁡
    
      (
      jω
      )
    
  
  =
  
    1
    
      (
      
        1
        +
        
          jω
          ⁢
          
            
          
          ⁢
          
            R
            i
          
          ⁢
          
            C
            i
          
        
      
      )
    
  




hence if choosing

ωRiCi>>1

then




  
    
      
        H
        RC
      
      ⁡
      
        (
        jω
        )
      
    
    ≅
    
      1
      
        jω
        ⁢
        
          
        
        ⁢
        
          R
          i
        
        ⁢
        
          C
          i
        
      
    
  
  ,




this being the harmonic response frequency of an ideal integrator, in that it introduces a phase displacement between vo and vout of π/2.
However choosing high Ci and Ri values may not be sufficient, as at low frequency the equivalent circuit of the RC network also comprises a resistor Rpi, which takes account of the losses of the capacitor Ci. Consequently the harmonic response function of the real integrator is




  
    
      H
      RC
    
    ⁡
    
      (
      jω
      )
    
  
  =
  
    
      R
      pi
    
    
      
        
          R
          pi
        
        ⁡
        
          (
          
            1
            +
            
              jω
              ⁢
              
                
              
              ⁢
              
                R
                i
              
              ⁢
              
                C
                i
              
            
          
          )
        
      
      +
      
        R
        i
      
    
  




It follows that in the presence of the parasitic resistor Rpi of the capacitor of capacitance Ci, the phase displacement between the input voltage and the output voltage is not equal to

arctan(−ωCiRi)

but to




  arctan
  (
  
    -
    
      
        ω
        ⁢
        
          
        
        ⁢
        
          R
          pi
          2
        
        ⁢
        
          R
          i
        
        ⁢
        
          C
          i
        
      
      
        
          R
          pi
          2
        
        +
        
          
            R
            i
          
          ⁢
          
            R
            pi
          
        
      
    
  
  )




and tends to ∞ only if Rp is very high. This is obtained only if using a capacitor with a low loss factor, i.e. with tan δ of the order of 10−4.
Essentially the invention proposes to use a particular conditioning circuit (integrator) to compensate the effects of the parasitic parameters of the equivalent circuit of the electric field sensor, these effects appearing as a variation in the amplitude of the sensor output voltage vo compared with its rated value and, more importantly, in a phase displacement thereof from the source voltage vi.
This compensation takes place by acting on the electrical resistance values of the resistors of the conditioning circuit, either manually or by a suitable automatic presetting system connected to the sensor.
If a capacitor Ci with a low loss factor is chosen, either Ri or Ci can be varied to change the cutoff frequency of the RC network such that the phase displacement between the voltage vo and the voltage vi is not equal to π/2 but is less than that, as illustrated in FIG. 4, which shows that the voltage at the sensor exit leads the phase of the input voltage vi by an angle π/2−β. The value of β is related to parasitic resistance Rp1.
In this case, on the true assumption of being able to ignore the effects of all other parasitic components,




  
    
      V
      0
    
    ⁡
    
      (
      ω
      )
    
  
  =
  
    
      
        R
        m
      
      +
      
        j
        ⁢
        
          
        
        ⁢
        ω
        ⁢
        
          
        
        ⁢
        
          R
          
            p
            ⁢
            
              
            
            ⁢
            1
          
        
        ⁢
        
          R
          m
        
        ⁢
        
          C
          1
        
      
    
    
      
        R
        
          p
          ⁢
          
            
          
          ⁢
          1
        
      
      +
      
        R
        m
      
      +
      
        j
        ⁢
        
          
        
        ⁢
        ω
        ⁢
        
          
        
        ⁢
        
          R
          
            p
            ⁢
            
              
            
            ⁢
            1
          
        
        ⁢
        
          R
          m
        
        ⁢
        
          C
          1
        
      
    
  




in which case the phase displacement between vi and vo is given by




  arctan
  ⁢
  
    
      ω
      ⁢
      
        
      
      ⁢
      
        R
        
          p
          ⁢
          
            
          
          ⁢
          1
        
        2
      
      ⁢
      
        R
        m
      
      ⁢
      
        C
        1
      
    
    
      
        
          R
          m
        
        ⁢
        
          R
          
            p
            ⁢
            
              
            
            ⁢
            1
          
        
      
      +
      
        R
        m
        2
      
      +
      
        
          ω
          2
        
        ⁢
        
          R
          
            p
            ⁢
            
              
            
            ⁢
            1
          
          2
        
        ⁢
        
          R
          m
          2
        
        ⁢
        
          C
          1
          2
        
      
    
  




By the effect of resistance Rp1 the phase displacement between vi and vo (leading) is less than π/2, i.e. is equal to π/2−β; to bring vout into phase with vi, vout must be made to phase lag vo by a value less than π/2, i.e. π/2−β.
The integrator parameters must therefore be chosen such as to satisfy the relationship




  
    
      π
      2
    
    -
    β
  
  =
  
    arctan
    ⁢
    
      
        ω
        ⁢
        
          
        
        ⁢
        
          R
          
            p
            ⁢
            
              
            
            ⁢
            1
          
          2
        
        ⁢
        
          R
          m
        
        ⁢
        
          C
          1
        
      
      
        
          
            R
            m
          
          ⁢
          
            R
            
              p
              ⁢
              
                
              
              ⁢
              1
            
          
        
        +
        
          R
          m
          2
        
        +
        
          
            ω
            2
          
          ⁢
          
            R
            
              p
              ⁢
              
                
              
              ⁢
              1
            
            2
          
          ⁢
          
            R
            m
            2
          
          ⁢
          
            C
            1
            2
          
        
      
    
  




In short, the following must apply:




  
    
      arctan
      ⁡
      
        (
        
          
            -
            ω
          
          ⁢
          
            
          
          ⁢
          
            C
            i
          
          ⁢
          
            R
            i
          
        
        )
      
    
    +
    
      arctan
      ⁢
      
        
          ω
          ⁢
          
            
          
          ⁢
          
            R
            
              p
              ⁢
              
                
              
              ⁢
              1
            
            2
          
          ⁢
          
            R
            m
          
          ⁢
          
            C
            1
          
        
        
          
            
              R
              m
            
            ⁢
            
              R
              
                p
                ⁢
                
                  
                
                ⁢
                1
              
            
          
          +
          
            R
            m
            2
          
          +
          
            
              ω
              2
            
            ⁢
            
              R
              
                p
                ⁢
                
                  
                
                ⁢
                1
              
              2
            
            ⁢
            
              R
              m
              2
            
            ⁢
            
              C
              1
              2
            
          
        
      
    
  
  =
  0




Consequently if the value of Ci is fixed, Ri must be chosen at a value such as to satisfy the aforesaid relationship at the frequency concerned.
Again with reference to the vectorial diagram of FIG. 4, it can be seen that the voltage vo, which leads the voltage vi by π/2−β because of the non-ideality of the sensor, must be phase displaced in the opposite sense in the integrator, to be returned to phase with vi.
If Ci with a low loss factor (tan δ) is used, vout can be certainly set to lag behind vi and consequently, by suitably choosing Ri and Ci, it can be returned into phase with vi. If a capacitor with a low loss factor were not used, the voltage vout would be obtained lagging vi, and no adjustment of Ri or Ci would enable it to be brought into phase with vi.
The embodiment shown in FIG. 5 corresponds to the embodiment shown in FIG. 2, but instead of using an integrator circuit consisting of a RC network with a resistor of resistance Ri and a capacitor of capacitance Ci, it uses an active amplification device, consisting for example of an operational amplifier.
In such a case, in addition to all the aforelisted advantages, there is the additional advantage of substantial immunity from the effects of noise and of electrical and magnetic disturbances.
This is because the embodiment shown in FIG. 2 can be negatively affected by the effects of noise and electrical and magnetic disturbances both irradiated and conducted, originating from various sources such as the circuit power supply and the phases adjacent to the phase concerned, to which the sensor and the integrator circuit are connected. In this case the output voltage vout may not be linearly related to the input voltage vi, in which case it would be distorted.
From a physical viewpoint this phenomenon is described in terms of signal power, in the sense that if a signal is influenced by external disturbances, this signifies that it has low power and in the presence of such disturbances does not maintain its shape by mixes with them, to assume different shapes and hence undergo distortion. In contrast, a higher power signal is certainly more immune from the effect of these disturbances.
The embodiment shown in FIG. 5 solves this specific problem, in that it uses an amplifier which however does not require an external power supply for its operation.
With reference to FIG. 5, it can be seen that the integrator circuit powered by the input voltage comprises, as in the case of the integrator circuit of FIG. 2, the same components Ri, Ci and Rpi, and in addition an operational amplifier 12 which provides at its output a signal vout corresponding to the integral of the input voltage vi but having greater power compared with the voltage vo of the integrator circuit of FIG. 1, in that it is provided by the external power supply.
Based on the foregoing, it can be seen that a sensor according to the invention is more advantageous than traditional transducers, and in particular:
it is of limited overall size as it uses small lightweight components,
it presents high insulation as it uses an electric field, and is therefore not in direct contact with the voltage or current source,
it enables high precision to be achieved, certainly comparable with that achievable with the best and most costly commercially available sensors using passive components,
it is of low production cost, given its simple structure and the small number of components used, and
it can be integrated into a traditional electric isolator used as a support for conductors in electrical systems.

## Claims

1. A presettable voltage sensor comprising:
a sensor connected to a voltage source to be measured, the sensor comprising,
an electrode electrically connected to the voltage source,
an electric field probe facing the electrode,
a screening conductive shell enclosing the probe and connected to a reference potential,
a dielectric material housed within the shell and interposed between said probe and the electrode; and

a conditioning circuit connected to an exit of the sensor and comprising a resistor of resistance Rm interposed between the probe and a second reference potential, the conditioning circuit being configured to satisfy the following conditions:




  
    
      R
      m
    
    ⁢
    
      <<
      
        
        
          
            R
            
              p
              ⁢
              
                
              
              ⁢
              2
            
          
          
            1
            +
            
              j
              ⁢
              
                
              
              ⁢
              ω
              ⁢
              
                
              
              ⁢
              
                C
                2
              
              ⁢
              
                R
                
                  p
                  ⁢
                  
                    
                  
                  ⁢
                  2
                
              
            
          
        
        
      
    
  




  
    
      R
      m
    
    >>
    
      ω
      ⁢
      
        
      
      ⁢
      
        L
        pm
      
    
  




  
    
      R
      m
    
    ⁢
    
      <<
      
        
        
          1
          
            j
            ⁢
            
              
            
            ⁢
            ω
            ⁢
            
              
            
            ⁢
            
              C
              pm
            
          
        
        
      
    
  




  
    
      R
      m
    
    ⁢
    
      <<
      
        
        
          
            R
            
              p
              ⁢
              
                
              
              ⁢
              1
            
          
          
            1
            +
            
              j
              ⁢
              
                
              
              ⁢
              ω
              ⁢
              
                
              
              ⁢
              
                C
                1
              
              ⁢
              
                R
                
                  p
                  ⁢
                  
                    
                  
                  ⁢
                  1
                
              
            
          
        
        
      
    
  


in which:
C1 indicates capacitance of a first capacitor having first plates formed by the electrode and the electric field probe, the first plates being immersed in the dielectric material,
C2 indicates capacitance of a second capacitor having second plates formed by the electric field probe and the conductive shell, the dielectric, material surrounding the second plates,
Rp1 indicates parasitic resistance of the first capacitor,
Rp2 indicates parasitic resistance of the second capacitor,
Lpm indicates parasitic inductance of the resistor of resistance Rm, and
Cpm indicates parasitic capacitance of the resistor of resistance Rm; and

an integrator circuit formed from an RC network, the integrator circuit being connected to the exit of the sensor and comprising a resistor of resistance Ri, a capacitor of capacitance Ci, and a loss factor which, at a frequency of interest, is of an order of 10−4, such to satisfy the following relationship:





  
    
      arctan
      ⁡
      
        (
        
          
            -
            ω
          
          ⁢
          
            
          
          ⁢
          
            C
            i
          
          ⁢
          
            R
            i
          
        
        )
      
    
    +
    
      arctan
      ⁢
      
        
          ω
          ⁢
          
            
          
          ⁢
          
            R
            
              p
              ⁢
              
                
              
              ⁢
              1
            
            2
          
          ⁢
          
            R
            m
          
          ⁢
          
            C
            1
          
        
        
          
            
              R
              m
            
            ⁢
            
              R
              
                p
                ⁢
                
                  
                
                ⁢
                1
              
            
          
          +
          
            R
            m
            2
          
          +
          
            
              ω
              2
            
            ⁢
            
              R
              
                p
                ⁢
                
                  
                
                ⁢
                1
              
              2
            
            ⁢
            
              R
              m
              2
            
            ⁢
            
              C
              1
              2
            
          
        
      
    
  
  =
  0



in which:


ωRiCi>>1.

2. The sensor of claim 1, wherein the conditioning circuit also comprises an active amplification device for input signals of the integrator circuit.

3. The sensor of claim 2, wherein the amplification for the input signals device is an operational amplifier.