Patent Publication Number: US-7902813-B2

Title: Protective digital relay device

Description:
RELATED APPLICATION 
     This application is a divisional of U.S. patent application Ser. No. 11/400,087, entitled “Protective Relay Device, System and Methods for Rogowski Coil Sensors,” filed Apr. 7, 2006, now U.S. Pat. No. 7,638,999 the complete disclosure of which is hereby fully incorporated herein by reference. 
    
    
     BACKGROUND 
     This invention relates generally to electrical power systems, and more specifically to protective relay systems and controls therefor. 
     Electrical generation and power transmission networks include a large number of transformers, capacitor banks, reactors, motors, generators and other major pieces of electrical equipment. Such equipment is expensive, and each piece of equipment typically plays a vital role in the distribution of power to end users, such that an outage caused by the equipment being damaged or taken out of service for repair or replacement, may have costly consequences. As a result, such equipment is typically protected from potentially damaging overvoltages and overcurrents by protective components, such as relay devices that open and close portions of the system in response to actual operating conditions. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  schematically illustrates a protective relay system according to the present invention. 
         FIG. 2  illustrates a conventional iron-core current transformer equivalent circuit. 
         FIG. 3  illustrates a Rogowski coil equivalent circuit. 
         FIG. 4  is a comparison graph of voltage and current characteristics of the circuits shown in  FIGS. 2 and 3 . 
         FIG. 5A  illustrates waveforms of an original current waveform and a secondary Rogowski coil waveform according to the system of the present invention. 
         FIG. 5B  illustrates waveforms of an original current waveform and a Rogowski coil waveform of a conventional relay system. 
         FIG. 6  illustrates a data acquisition and processing block for a conventional relay system. 
         FIG. 7  illustrates a data acquisition and processing block for a relay system according to the present invention. 
         FIG. 8A  is an example waveform graph of a processed coil signal according to the present invention versus a conventional system in a symmetrical current fault condition. 
         FIG. 8B  is an example comparison root mean square current graph of processed signal according to the present invention and a test signal representing a symmetrical current fault condition. 
         FIG. 8C  is an example phase angle difference graph of a processed coil signal according to the present invention and a test signal representing a symmetrical current fault condition. 
         FIG. 9A  is an example waveform graph of a processed coil signal according to the present invention versus a test signal representing an asymmetrical current fault condition. 
         FIG. 9B  is an example comparison root mean square current versus of a processed signal according to the present invention a test signal representing an asymmetrical current fault condition. 
         FIG. 9C  is an example phase angle difference graph of a processed signal according to the present invention and a test signal representing asymmetrical current fault condition. 
         FIG. 10A  is an example waveform chart of a test signal representing a transformer inrush current. 
         FIG. 10B  is an example Rogowski coil secondary signal for the test signal shown in  FIG. 10A . 
         FIG. 10C  is an example root mean square current graph of a processed coil signal according to the present invention versus the test signal. 
         FIG. 10D  is an example phase angle difference graph of a processed coil signal according to the present invention versus the test signal. 
         FIG. 10E  is an example root mean square current graph of a second harmonic of the processed coil signal according to the present invention versus a second harmonic of the inrush current. 
         FIG. 10F  is an example phase angle difference graph of a processed coil signal according to the present invention versus a second harmonic of the inrush current. 
         FIG. 11A  is an example waveform graph of a processed coil signal according to the present invention versus primary transformer current in an asymmetrical current fault condition. 
         FIG. 11B  is an example waveform graph of a pre-processed coil signal according to the present invention versus primary transformer current in an asymmetrical current fault condition. 
         FIG. 11C  is an example current root mean square current graph of a processed coil signal according to the present invention versus primary transformer current in an asymmetrical current fault condition. 
         FIG. 11D  is an example phase angle difference graph of a processed coil signal according to the present invention versus primary transformer current in an asymmetrical current fault condition. 
         FIG. 12A  is an example waveform graph of a transformer inrush current versus a processed coil signal according to the present invention. 
         FIG. 12B  is an example waveform graph of a pre-processed coil signal according to the present invention versus transformer inrush current. 
         FIG. 12C  is digitally shifted coil waveform according to the present invention versus transformer inrush current. 
         FIG. 12D  is an example root mean square current graph of a processed signal according to the present invention versus transformer inrush current. 
         FIG. 12E  is a root mean square current graph of a fundamental harmonic of the processed coil signal according to the present invention versus a fundamental harmonic of the transformer inrush current. 
         FIG. 12F  is a phase angle difference graph of fundamental harmonics of the processed coil signal according to the present invention and the transformer inrush current. 
         FIG. 12G  is a root mean square current graph of a second harmonics of the processed coil signal according to the present invention and the transformer inrush current. 
         FIG. 12H  is a phase angle difference graph of second harmonics of the processed coil signal according to the present invention and the transformer inrush current. 
     
    
    
     DETAILED DESCRIPTION 
     Successful operation of network protection devices in an electrical power system is of course dependent upon accurate sensing and measurement of operating conditions. Microprocessor based equipment, such as digital relay devices, are increasingly being used in electrical power systems, and complex signal processing issues are raised, especially for phasor based relay systems, to provide input data to the relay devices for making control decisions. 
     In existing electrical power systems for electric utility companies and industrial facilities, current transformers (CTs) are utilized for measuring operation conditions of the system. The transformers may be connected to network protection devices, such as protective relays and circuit breakers, and signal outputs from the current transformers are input to the protective devices and are used to make control decisions by the network protection devices to open circuitry when fault conditions are detected, thereby protecting the power distribution network and associated equipment from damage. The output signals of the transformers, however, are vulnerable to distortion, and when used with digital equipment, such as modern digital relay devices, complex signal processing is required to convert the transformer output signals to a usable form that may be processed by the digital equipment to make control decisions. 
     Rogowski coils measure magnetic fields and provide a reliable means of sensing or measuring current flow at a given point in an electrical system, including detection of current flow through a primary winding of a transformer. Early Rogowski coils were not suitable for such current measurements because the coil output voltage and power were not sufficient to drive measuring equipment. With the advent of microprocessor-based protection and measurement equipment, however, Rogowski coils have become more suitable for use in electrical power systems. Signal processing issues, however, still remain to interface analog output signals of Rogowski coils to digital equipment for making control decisions. Complex analog or digital filters are typically required to determine the integral of the output signal of Rogowski coils over time, increasing the cost of such systems and introducing potential errors and reliability issues. 
     To overcome these and other disadvantages of existing devices, systems and methods, embodiments of protective relay devices, systems and methods are disclosed utilizing Rogowski coils as current detecting elements. Output signals of the Rogowski coils are used to represent current flow through a conductor in the frequency domain without determining integrals of the coil signals in the time domain that is common to known systems. Complex analog or digital filters in the time domain are therefore not required in embodiments of the present invention, while still providing an accurate indication of true current conditions in the conductor. A simpler, yet highly reliable, protective relay device, systems and methods are therefore provided. 
     For a full appreciation of the inventive aspects of exemplary embodiments of the invention described below, the disclosure herein will be segmented into sections. Basic components of the system are first discussed in Part I. including a discussion regarding construction and operation of Rogowski coils. Conventional devices and methods for measuring current in electrical power systems will be discussed and contrasted with Rogowski coils in Part II. Derivation of operating principles and schematic architecture of the present invention will be discussed in Part III. Validating examples of the invention will be described in Part IV. 
     I. System Introduction 
     As shown in  FIG. 1 , a protective relay system  100  according to an embodiment of the present invention includes a Rogowski coil  102 , a protective relay device  104 , an optional processing device  106 , and a circuit protector device  108 . The relay device  104  and or the processing device  106  are processor based devices that may be programmed to perform signal processing from the output of the Rogowski coil  100  according to the methods and algorithms explained below. The relay device  104  is operatively connected to a circuit protector device  108 , and depending upon the output signal v(t) of the Rogowski soil coil  102 , the relay device  104  causes the circuit protector device  108  to open or interrupt a current path when fault currents are detected. 
     The Rogowski coil  102  includes a conductive coil or winding  110 , fabricated from wire in one example, that is coiled or wound on a non-magnetic core  112  for a number of turns. The core  112  may be formed into a toroid shape, for example, as shown in  FIG. 1 , that defines a central opening  114  for the passage of a conductor  116  (shown in phantom in  FIG. 1 ) therethrough. To prevent nearby conductors carrying high currents from negatively influencing the output voltage v(t), the Rogowski coil  102  may include different windings  110  connected in the electrically opposite directions on the core  112 . The opposing windings  110  will accordingly cancel all electromagnetic fields coming from outside the coil loop. A similar effect may be accomplished by passing the end of a single windings  110  back through the core opening  114 . 
     The basic structure of the Rogowski coil is highly adaptable to meet different needs in use, and the present invention is equally applicable to a wide variety of Rogowski coils. For example, the core  112  may be fabricated from a flexible material such as coaxial cables, or relatively rigid materials such as straight rods connected to one another at their ends. Additionally, metering accuracy Rogowski coils may utilize printed circuit boards (PCBs) containing two imprinted coils wound in opposite directions (clockwise and counter-clockwise). This may be achieved by imprinting two windings on one PCB or using two PCBs located next to each other, each containing one imprinted winding. The PCBs may be multi-layered, and high precision is possible with computer controlled manufacturing process and control of the coil geometry. 
     The Rogowski coil  102  may be constructed with circular, oval, and rectangular shapes, for example, in different embodiments for different applications. Rogowski coils fabricated in oval or rectangular shapes are suitable, for example, to embrace all three-phases of a conductor  116  (for measurement of residual currents) or to embrace parallel conductors  116  that carry heavy currents. As those in the art will appreciate, the Rogowski coil  102  may also be fabricated with a split-core for installation to the conductor  116  without the need to electrically disconnect the conductor  116  from the circuit. 
     Operationally, the Rogowski coil  102  may be placed around one or more conductors  116  whose currents i(t) are to be sensed or measured. A primary current i p (t) flowing through the conductor(s)  116  generates a magnetic field that, in turn, induces a secondary voltage v(t) in the windings  110  of the Rogowski coil  102  as further explained below. The voltage output of the Rogowski coil  102  may be connected and input to the relay  104  via wireless communication, electrical wires or cables, fiber-optic cables, or in another manner known in the art. The relay  104  may be programmed to perform the signal processing techniques described below while avoiding the complexity of known signal processing techniques in conventional systems. 
     The protective relay device  104  may include a microprocessor  120 , an interface panel  122 , a display  124 , a memory  126 , and a communications module  128 . Control algorithms, parameters, and data may be stored in the microprocessor  120  and the memory  126  and utilized by the microprocessor  120  to execute the algorithms, respond to user inputs via the interface  122 , display information to users via the display  124 , collect and store data in the memory  126 , and communicate with other devices and systems, including but not limited to other protective relay devices. The relay device  104  may include various measuring and/or calculation devices (not shown) such as a voltage-measuring devices or current-calculating devices. Such devices may include, or be associated with, computer hardware or software for performing their respective functions. 
     The relay device  104  may be programmed in a known manner to detect overcurrent and undercurrent conditions, overvoltage and undervoltage conditions, voltage and current differentials, and conduct frequency analysis, power analysis, load shedding analysis and power signal analysis. Additionally, the relay device  104  may also perform event recording routines for data collection and analysis, signal synchronization procedures, and conduct equipment protection routines for specific devices (e.g., motors, transformers, generators, and capacitors). Suitable relay devices  104  for purposes of the present invention include the Edison® Idea™ of protective relays available from Cooper Power Systems, Inc. of Waukesha, Wis. 
     Optionally, the system  100  includes a second microprocessor based device  106 , separately provided from the relay device  104 , having a microprocessor  130  and a memory  132 . The voltage output v(t) of the coil  102  may be input to the second device  106  to perform the signal processing algorithms explained below, and also to extract and analyze data stored in the relay memory  126 . The second device  106  may optionally include an interface, display, and communications module for advanced functionality and user interaction as desired. The second device  106  may be, for example, another relay device, a laptop computer, a desktop computer or a workstation, or other electronic device having signal input, output and processing capabilities. 
     The protective device  108  is operatively connected to the relay  104  and is responsive thereto. The protective device  108  may be a circuit breaker, interrupter, switching element, or other circuit protection element for interrupting the measured current i(t) in the conductor  116  when fault conditions are detected, thereby preventing damage to equipment associated with the conductor  116 . 
     II. Current Transformers Versus Rogowski Coils 
     Historically, current transformers have been used for protection and measurement purposes of operating conditions in an electrical power system, and such transformers are prevalent in existing systems.  FIG. 2  illustrates an equivalent circuit of a conventional iron-core current transformer (CT) that is commonly found in existing medium and high voltage electrical systems. The CT impedance Z b , sometimes referred to as the CT burden, has a low value and the secondary current i s  of the transformer is nearly in phase with the primary current i p  However, due to a non-linear magnetizing branch, the secondary current i s  may be distorted if the CT saturates. If the secondary current i s  is being used for measurement purposes, distortion of the secondary current i s  may compromise proper operation of a protective device associated with the CT. 
       FIG. 3  illustrates an equivalent circuit of the Rogowski coil  102  shown in  FIG. 1 . In contrast to the CT circuit shown in  FIG. 2 , the burden Z b  of the Rogowski coil  102  has a high value so the coil output voltage V g  is shifted in phase nearly 90° relative to the measured current i p  and is proportional to the rate of change of measured current (di/dt) enclosed by the coil. Also in contrast to the CT circuit of  FIG. 2 , the Rogowski coil magnetizing branch is linear and the Rogowski coil secondary signal i s  is not distorted. Comparison of CT and Rogowski coil voltage/current characteristics is shown in  FIG. 4 , demonstrating the linearity of the Rogowski coil  102  and the non-linearity of the CT. Because of the linearity of the Rogowski coil  102  and its lower susceptibility to signal distortion, the Rogowski coil  102  is generally preferable to CTs for measurement and protection purposes. 
     Referring back to  FIG. 1 , the voltage v(t) induced in the windings  110  of the Rogowski coil  102  is governed by the following Equation: 
                 v   ⁡     (   t   )       =         μ   o     ⁢     μ   r     ⁢   nS   ⁢       ⅆ     i   ⁡     (   t   )           ⅆ     (   t   )           =     M   ⁢       ⅆ     i   ⁡     (   t   )           ⅆ     (   t   )               ,         
where μ o  is the magnetic permeability of free space, μ r  is the relative permeability (the ratio of the permeability of the coil  102  to the permeability of free space μ o ), n is the winding density (turns per unit length), S is the cross sectional area of the core  104  in the Rogowski coil, and M represents the mutual reactance or mutual coupling between the coil windings  110  and the conductor  116 .
 
     For an ideal Rogowski coil  102 , M is independent of the location of the conductor  116  within the opening  114 . As is evident from Equation 1, the Rogowski coil output voltage v(t) is proportional to the rate of change of the measured current i(t). To obtain signals proportional to the measured current i(t), the integral of the output voltage v(t) of the Rogowski coil  100  may be mathematically computed or otherwise determined, referred to herein as integration of the voltage signal, in a known manner. Conventionally, such integration may be performed, for example, at a location remote from the coil  102  (using known analog circuitry or digital signal processing techniques) or immediately at the coil location with an integrating circuit or other device. In a conventional protective relay system, integration of Equation (1) is represented by the following relationship: 
                 v   ⁡     (   t   )       =       M   RiCi     ⁢     i   ⁡     (   t   )           ,         
where R i  and C i  in Equation 2 represent an integrating resistor and capacitor.
 
     If the measurement of the current i(t) is restricted to a single sinusoidal current at a given frequency ω (e.g., 50 or 60 Hz), the coil output voltage v(t) will have a root mean square (RMS) value defined by Equation 3 and a phase shift nearly 90° versus the measured current i(t).
 
 V   rms   =Mω √{square root over (2)} Irms  
 
       FIG. 5   a  shows Rogowski coil output signals before and after integration of the output signals. As  FIG. 5   a  shows, the integrated and non-integrated signals are noticeably different. However,  FIG. 5   b  illustrates that the integrated signal accurately reproduces the waveform of the measured current in the conductor  116  (indicated as original primary current waveform in  FIG. 5   b ) recorded by a laboratory current sensor, and for this reason the integrated signal has been adopted and conventionally utilized in protective relay systems. 
       FIG. 6  is a block diagram of a data acquisition system  150  illustrating an analog signal flow from a conventional current transformer  152  into a conventional digital protective relay The system  150  includes a dielectric isolation element  154 , an anti-alias filtering element  156 , and an analog-to-digital converter  158 . Upon conversion to digital values, raw sample data is available to the relay logic. However, phasor-based protective relays require further signal processing to extract the power frequency signal in the form of a complex phasor having root mean square magnitude and phase angle to adequately represent the original signal (primary current i p ). As noted above, the Rogowski coil output signal v(t) is a scaled time derivative di/dt of the primary current i p . To use such signals with phasor-based protective relays, signal processing is required to extract the power frequency signal. This is typically achieved by integration  159  of the Rogowski coil output signal. As explained above, however, integration of the Rogowski coil output signal is not without difficulties. Complex analog or digital filters and/or signal processing techniques are typically required to integrate the output of Rogowski coils, increasing the cost of such systems and introducing errors at low frequencies and potential reliability issues. 
     One method commonly used to obtain the fundamental complex phasor value is to apply a discrete transform  160  to the raw sample data stream. As this transform represents a complete family of mathematical transforms there are multiple possible specific implementations which yield acceptable complex phasor outputs. Within the relay logic, it is also common to represent power system events as time-based oscillography, along with the corresponding actions determined by the logic (event recording). Such oscillography commonly utilizes the raw samples of the input signals, as well as the digitally filtered fundamental waveforms. These event recordings provide useful information to one skilled in the art of power systems analysis. 
     When the analog signal input to the sampling system is a linear scaled function of the original signal such as primary current i(t) measured by a current transformer, it is commonly only necessary to effect a magnitude correction  162  as a scalar multiplier to the resultant complex phasor. This magnitude correction may be performed to compensate for the scalar transformations between the original signal and the numerical output of the discrete transform. Thus, the resultant re-scaled complex phasor may be represented within the protective relay software in preferentially advantageous units. 
     III. Derivation OF Inventive Operating Principles 
     Unlike the previously described data acquisition system  150  shown in  FIG. 6  that requires integration of the raw data to provide useful data for the relay to make control decisions, a block diagram of a data acquisition system  170  according to the present invention is shown in  FIG. 7 . Notably, the system of  FIG. 7  does not utilize integration of the raw sample data stream, but rather provides a non-integrated Rogowski coil output signal that is used to determine the primary current flow i p  in a conductor  116  ( FIG. 1 ) that is detected by the Rogowski coil  102 . A simpler yet highly reliable system is therefore provided. 
       FIG. 7  illustrates an analog signal flow from the Rogowski coil  102  into the protective relay device  104 . The system  170  includes a dielectric isolation element  172 , an anti-alias filtering element  174 , and an analog-to-digital converter  176 . Thus, the raw data stream for the output voltage of the Rogowski coil  102  is digitized. Instead of integrating the raw data stream signal in the time domain as in conventional systems, the present invention utilizes signal processing in the frequency domain without integration of the signal. That is, in the system  170 , signal processing and corrections for both the magnitude and phase angle of the Rogowski coil output signal that are frequency dependent is performed. Theory of the frequency domain will now be explained. 
     The Rogowski coil output voltage with respect to the primary current is given by Equation 1, which can also be represented as follows.
 
 V ( s )=− sMI ( s )  (4a).
 
Recognizing that s is the Laplace operator jω in the frequency domain then Equation 4a may further be rewritten as
 
 V ( jω )=− jωMI ( jω )  (4b).
 
     To obtain the complex frequency representation of the measured primary current i p  that induces the voltage in the Rogowski coil  102 , it is necessary to perform a division in the frequency domain. 
                     I   ⁡     (   jω   )       =     -       V   ⁡     (   jω   )         jω   ⁢           ⁢   M                 (   5   )               
The complex number V(jω n ) is the output of the discrete cosine transform for the frequency of interest, ω n . When represented in single-frequency phasor form, the formula for calculating the primary current reduces to Equation 6:
 
     
       
         
           
             
               
                 
                   
                     I 
                     → 
                   
                   = 
                   
                     
                       
                         - 
                         
                           
                             V 
                             → 
                           
                           
                             j 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             M 
                           
                         
                       
                       ⇒ 
                       
                         
                           I 
                           n 
                         
                         ⁢ 
                         ∠ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         θ 
                       
                     
                     = 
                     
                       
                         
                           V 
                           n 
                         
                         ⁢ 
                         
                           ∠ 
                           ⁡ 
                           
                             ( 
                             
                               θ 
                               - 
                               
                                 90 
                                 ⁢ 
                                 ° 
                               
                             
                             ) 
                           
                         
                       
                       M 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     The scalar M of the Rogowski coil  102  may be advantageously determined at the fundamental power frequency, e.g. 60 Hz, and once the value of M is known, it may be used as a scalar multiplier to the voltage signal to determine the current according to Equation 6. In order to obtain properly scaled values of the original signal having an nth harmonic component of the fundamental frequency, it is necessary to incorporate the harmonic order n into Equation 6 as given by Equation 7: 
     
       
         
           
             
               
                 
                   
                     
                       I 
                       n 
                     
                     → 
                   
                   = 
                   
                     
                       
                         - 
                         
                           
                             
                               V 
                               n 
                             
                             → 
                           
                           
                             j 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             nM 
                           
                         
                       
                       ⇒ 
                       
                         
                           I 
                           n 
                         
                         ⁢ 
                         ∠ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         θ 
                       
                     
                     = 
                     
                       
                         
                           V 
                           n 
                         
                         ⁢ 
                         
                           ∠ 
                           ⁡ 
                           
                             ( 
                             
                               θ 
                               - 
                               
                                 90 
                                 ⁢ 
                                 ° 
                               
                             
                             ) 
                           
                         
                       
                       nM 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Equations 6 and 7 show that the Rogowski coil secondary signal is a voltage proportional to the primary current shifted 90°. Thus, for purposes of the present invention, the Rogowski coil secondary signal phase shift and scalar magnitude correction in the frequency domain may be utilized for making control decisions. By utilizing processing techniques in the frequency domain rather than in the time domain as conventionally employed, complex analog or digital filters in the time domain needed to integrate the signal are avoided, together with associated expense. By avoiding integration of the signal, reduced processing demands are experienced in the relay  104  and/or the external device  106  ( FIG. 1 ). Faster computing times are therefore possible in comparison to known systems. 
     The signal flow chart of  FIG. 7  is summarized by Equations 8a and 8b. 
                   I   ⁢           ⁢     ∠θ   ⁢     ⟶   RogowskiCoil     ⁢     v   ⁡     (   t   )       ⁢     ⟶   Digitizer     ⁢     v   ⁡     (   n   )       ⁢     ⟶   DigitalFourierTransform     ⁢   V     ⁢           ⁢     ∠   ⁡     (     θ   -     90   ⁢   °       )               (     8   ⁢   a     )                 V   ⁢           ⁢       ∠   ⁡     (     θ   -     90   ⁢   °       )       ⁢     ⟶   Correction     ⁢       V   ⁢           ⁢     ∠   ⁡     (     θ   -     90   ⁢   °     +     90   ⁢   °       )         M         =     I   ⁢           ⁢   ∠θ             (     8   ⁢   b     )               
Briefly, the measured primary current i p (t) (shown in  FIG. 1 ) in the conductor  116  passing through the Rogowski coil  102  is represented in the frequency domain as I∠θ translated by the Rogowski coil to v(t), which is a scaled time derivative of i p (t). The output signal v(t) of the coil  102  is digitized and processed through a known discrete transform algorithm, such as a Fourier Transform in one example, to determine the complex number representation of its one or more constituent frequency components. The one or more frequency components of interest, represented by the complex number output of the discrete transform algorithm  178 , are then modified by scalar multiplication and 90° phase shift  180  to obtain frequency domain representations of the original measured current i p (t). In one example, i p (t) may correspond to a sensed current in a primary winding of a current transformer, although other applications are contemplated as well.
 
     Traditionally, when using current transformers, or when performing integration of the Rogowski coil output signals inside the relay, event recording can provide true representation of the primary current waveform I(t). However, when using non-integrated signals from the Rogowski coil as described above, oscillographic recordings may provide the di/dt signals, but not readily utilized I(t) signals of the primary current. However, the di/dt raw sample data may be stored in the relay memory  126  ( FIG. 1 ), and event recording viewing may be performed offline at a location remote from the relay device  104  with another device  106  ( FIG. 1 ). Integration functions  182  on the raw sample data may also be run offline as desired to extract I(t) waveforms without burdening the relay device  104  with integration of the signal and necessary computations. Event recording software may be provided that includes integration of the Rogowski coil non-integrated signals as well as additional algorithms for final analysis, which may be run offline. 
     Using the system  170  shown in  FIG. 7 , the relay  104  may make control decisions based upon non-integrated signals from the Rogowski coil  102 . Specifically, based upon the phasor data obtained from the non-integrated Rogowski coil signal, a true representation of the current flow in the conductor  116  ( FIG. 1 ) may be provided. Once the representation of the current flow is obtained, the relay may identify fault conditions  182  in the conductor  116  ( FIG. 1 ) being monitored with the Rogowski coil  102  in a known manner. When fault conditions are identified, the relay device  104  may take appropriate corrective and protective action  184 , such as communicating with other devices and systems via the communications module  128  ( FIG. 1 ) and causing the protective device  108  ( FIG. 1 ) to interrupt the current path being monitored with the Rogowski coil  102  to protect associated equipment from damage. 
     Having now explained the theory and operating principles of the invention, it is believed that the data acquisition system  170  may be implemented using conventional programming techniques that are within the purview of those in the art. Further explanation of associated algorithms, methods and techniques associated with such programming is not believed to be necessary. Such programs, methods and techniques may be executable by the microprocessor based relay device  104  and/or the secondary device  106 . 
     IV. Validating Examples 
     Effectiveness of the inventive signal processing of the present invention, that avoids integration of signals in the time domain and instead processes signals in the frequency domain, has been tested and verified as will now be explained. 
       FIG. 8A  illustrates a symmetrical primary current and the Rogowski coil secondary signal shifted 90° compared to the primary current. Calculated RMS values for primary current and the RC secondary signal scaled to the primary are nearly identical after one cycle needed for phasor estimation algorithm to reach full accuracy ( FIG. 8B ). When the Rogowski coil phase angle of the secondary signal is digitally shifted 90°, the phase angle difference between the primary current and the Rogowski coil secondary signal becomes nearly zero ( FIG. 8C ). 
       FIG. 9A  shows primary current and the Rogowski coil secondary signal for asymmetrical current faults. As expected, the Rogowski coil secondary signal waveform differs from the primary current waveform since the DC component is attenuated and the signal is also shifted 90° However, calculated RMS values for primary current and the Rogowski coil secondary signal scaled to the primary become nearly identical after DC component attenuates in the primary current ( FIG. 9B ). The phase angle difference between the primary current and the Rogowski coil secondary signal digitally shifted 90° becomes nearly zero ( FIG. 9   c ). 
       FIGS. 10A and 10B  show primary current and the Rogowski coil secondary signal during a transformer energizing. Here again, the Rogowski coil secondary signal waveform differs from the primary current waveform since the primary current contains a large percent of the second harmonic component. However, calculated RMS values for primary current and the Rogowski coil secondary signal scaled to the primary become nearly identical ( FIG. 10C ). The phase angle difference between the primary current and the Rogowski coil secondary signal digitally shifted 90° is nearly zero ( FIG. 10D ). During a transformer energizing, the second harmonic component is pronounced and may be used for blocking the protection operation.  FIGS. 10E and 10F  show that both the amplitude and phase angle of the second harmonic component can be reliably calculated, and both the primary current and the Rogowski coil secondary signal are nearly identical. 
       FIG. 11A  shows primary current and the Rogowski coil secondary signal for asymmetrical current faults sampled at 16 samples per cycle in a protective relay system such as that shown in  FIG. 1 . The DC component of the primary current has been filtered by the relay consistently with  FIG. 7 . The Rogowski coil secondary signal waveform (before it was shifted 90°) and the primary current waveform are shown in  FIG. 11B . Calculated RMS values for primary current and the Rogowski coil secondary signal scaled to the primary are nearly identical ( FIG. 11C ). The phase angle difference between the primary current and the Rogowski coil secondary signal digitally shifted 90° becomes nearly zero ( FIG. 11D ). 
       FIG. 12A  shows primary current and the Rogowski coil secondary signal during a transformer energizing sampled at 16 samples per cycle in a protective relay system such as that shown in  FIG. 1 . The DC component of the primary current has been filtered by the relay consistently with the system of  FIG. 7 . The Rogowski coil secondary signal waveform (before it was shifted 90°) and the primary current waveform are shown in  FIG. 12B ). The phase angle difference between the primary current and the Rogowski coil secondary signal digitally shifted 90° becomes nearly zero ( FIG. 12C ). Calculated RMS values of all components for primary current and the Rogowski coil secondary signal scaled to the primary are nearly identical ( FIG. 12D ). Calculated RMS values and phase angles of the fundamental harmonic component (60 Hz) for primary current and the Rogowski coil secondary signal scaled to the primary are nearly identical ( FIGS. 12E and 12F ). Calculated RMS values and phase angles of the second harmonic components (120 Hz) for primary current and the Rogowski coil secondary signal scaled to the primary are also nearly identical ( FIGS. 12G and 12H ). 
     V. Conclusion 
     Embodiments of protective relay systems including Rogowski coils and signal processing techniques therefore are disclosed herein. Advantages of the invention include a simplified, yet highly effective and reliable, signal processing scheme wherein accurate representations of current flow may be provided at lower cost and in less time than conventional systems using more complex signal processing techniques and involving greater computational demands. 
     An embodiment of a protective system for a current path in a in an electrical power system is disclosed herein. The system comprises a Rogowski coil generating an output voltage signal corresponding to current flow in the current path; and a microprocessor based protection device receiving the output voltage signal. The microprocessor based protection device is responsive to the output voltage signal to cause the current path to be interrupted when a fault condition is detected, wherein the fault condition is detected without integration of the output voltage signal in the time domain. 
     Optionally, the voltage output signal may be processed in the frequency domain, and the phase of voltage output signal is digitally shifted by approximately 90 degrees The voltage output signal may further be multiplied by a scalar. The microprocessor based device may comprise a digital relay device, and the relay device may be configured to detect the fault condition. A second microprocessor based device may be separately provided from the protective device, and the second microprocessor based device may be configured to detect the fault condition, and may also be configured to integrate the voltage output signal to extract power analysis information. A circuit protector may be operatively connected to the protective device, with the protective device causing the circuit protector to open the current path in response to the output voltage signal. 
     An embodiment of a protective relay system for a current path in an electrical system is also disclosed herein. The system comprises a Rogowski coil generating an output voltage signal proportional to a time derivative of a current flow in the current path, and a microprocessor based relay device receiving a non-integrated output voltage signal of the Rogowski coil. The relay device causes the current path to be interrupted when a fault condition is detected using the non-integrated output voltage signal. 
     Optionally, the fault condition is detected without integration of the output voltage signal in the time domain. The voltage output signal may be processed in the frequency domain. The phase of the non-integrated voltage output signal may be digitally shifted by approximately 90 degrees, and the voltage output signal may be multiplied by a scalar. The relay may comprise a microprocessor and a memory, with the microprocessor and memory configured to detect the fault condition. A second microprocessor based device may be separately provided from the relay device, and the second microprocessor based device may process the non-integrated output voltage signal. A circuit protector may be operatively connected to the relay device, with the relay device causing the circuit protector to open the current path in response to the output voltage signal. 
     An embodiment of a protective relay system for managing an electrical system is also disclosed herein. The system comprises a conductor defining a current path in the electrical system, a Rogowski coil receiving the conductor and generating an analog output voltage signal proportional to a time derivative of current flow in the current path, and a digital relay device receiving the analog output voltage signal. The relay device is configured to digitize the signal and process the signal in the frequency domain to represent the current flow without integration of the output voltage signal in the time domain. The relay device causes the current path to be interrupted when a fault condition is detected using the represented current flow. 
     Optionally, the phase of the non-integrated voltage output signal may be digitally shifted by approximately 90 degrees, and the voltage output signal may be multiplied by a scalar. The relay may comprise a microprocessor and a memory, with the microprocessor and memory configured to detect the fault condition. A circuit protector may be operatively connected to the relay device, with the relay device causing the circuit protector to open the current path in response to the output voltage signal. 
     In an another embodiment, a digital relay device responsive to an output voltage signal of a Rogowski coil is disclosed. The relay device comprises a processor and a memory, wherein the processor and memory are configured to execute a control algorithm whereby the output voltage signal is processed in the frequency domain without integration of the output voltage signal in the time domain to determine a current signal corresponding to the output voltage signal. 
     Optionally, the processor and memory are further configured to detect a fault condition using the determined current signal. A circuit protector may be provided, with the relay causing the circuit protector to open a circuit path when the fault condition is detected. The output voltage signal may be multiplied by a scalar to determine the current signal, and the phase of the output voltage signal may be digitally shifted to determine the current signal. The output voltage of the Rogowski coil may be an analog signal, and the relay may comprise an analog to digital converter to digitize the output voltage signal. 
     A method of processing an output voltage signal of a Rogowski coil for control of a current path with a protective relay device is also disclosed. The method comprises obtaining the output voltage signal; digitizing the output signal; and determining a current signal corresponding the output voltage signal without integration of the output voltage signal in the time domain. 
     Optionally, determining the current signal may comprise applying a discrete transform algorithm to the digitized output signal, digitally shifting the phase of the digitized output signal, and multiplying the digitized signal by a scalar. The method may further comprise comparing the determined signal to a predetermined fault current signal, and detecting a fault condition based upon the compared determined signal and fault current signal. The method may also comprise causing a circuit protector to interrupt a current path extending through the Rogowski coil. Still further, the method may comprise storing in the relay device data relating to the determined current over time, extracting the data from the relay device, and integrating the extracted data with a microprocessor based device separate from the relay device. 
     An embodiment of a protective system for an electrical network is also disclosed. The system comprises a Rogowski coil monitoring a current path in an electrical system, and means for processing an output voltage signal of the Rogowski coil to provide a current signal corresponding to a time derivative of current flow in the current path. The means for processing provides the current signal while avoiding integration in the time domain of the output voltage signal. 
     Optionally, the means for processing may comprise a digital relay device. The system may also include means for interrupting the current flow in the current path when the provided current signal corresponds to a fault condition, means for storing data relating to the provided current signal over time, and means for extracting the stored data and analyzing the data. 
     While the invention has been described in terms of various specific embodiments, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the claims.