Patent Publication Number: US-7584066-B2

Title: Method for determining power flow in an electrical distribution system

Description:
This application claims the benefit of U.S. Provisional Patent Application No. 60/764,203, filed Feb. 1, 2006, which is incorporated herein by reference. 

   FIELD OF THE INVENTION 
   The present invention relates generally to methods of determining power flow in electrical distribution systems, and more particularly, to methods of providing power flow measurements useful for load scaling. 
   BACKGROUND OF THE INVENTION 
   Modeling the behavior of an electrical power network is important for ensuring reliable electrical service. The electrical power network consists of many interconnected elements, including power generation nodes, transmission systems, distribution systems and loads. Electrical power generators and distribution entities cooperate to achieve delivery of power upon demand. For example, electrical power generation and distribution entities may cooperate to facilitate to transmission of power from Arizona to a high need area in New York City at certain times of day or year, and to facilitate transmission of power from New York State to Arizona at other times of day or year. 
   In general, the electrical power network can be divided into two main elements, transmission systems and distribution systems. Transmission systems include transmission lines that deliver energy from power generating devices to power substations. Distribution systems are networks that distribute power from the power substations to the individual end-user loads. Distribution systems may also transfer power among themselves. 
   Transmission systems employ very high voltages, typically on the order of 110 kV to 500 kV AC, and have an interstate extent. Transmission systems transmit power in three phases, and tend to have balanced loads on all three phases. By contrast, distribution systems tend to employ lower distribution voltages (under 66 kV), and typically cover a confined geographical service such as a metropolitan area and its surrounds. While distribution systems are also three phase systems, the loads in distribution systems can be unbalanced due to the presence of two phase and single phase lines and distribution transformers. 
   Real-time modeling of transmission systems has been used to assist in the efficient allocation of power between power generators and the distribution substations. Real-time models may be generated multiple times per day to determine whether a reallocation in power is required. In the modeling of transmission systems, the distribution systems (i.e. represented by power substations and connected loads) are treated as balanced loads, and thus have composite electrical characteristics that are relatively easy to represent. Moreover, real-time power usage information at the subsystem level is readily available. 
   Modeling has also been used in distribution systems. However, for several reasons, modeling in distribution systems has typically been limited to non-real time or offline modeling. In particular, unlike transmission systems, real-time power flow measurements at individual loads are not readily available in distribution systems. While the usage of power at individual loads is typically metered (i.e. using electricity meters), the metered power information is typically not available in real time. More specifically, power measurement information from customer electricity meters is usually only retrieved at long intervals, for example, monthly. The lack of real-time power measurement information for the individual loads significantly complicates the development of real-time power flows in distribution systems. 
   Offline power flows, by contrast, do not require real-time measurement information. Instead, offline power flows employ assumptions about individual loads that suit the problem being addressed. For example, one offline power flow technique assumes full loading of all elements of the distribution network. Such a power flow may be used to identify areas of the distribution network in which increased capacity may be required to ensure proper operation during peak loading times. 
   Offline power flows, however, have limited usefulness in determining real time resource allocation. Resource allocation in distribution systems is dynamic, and is preferably updated several times per day. Thus, if power flow information is to be used in dynamic resource allocation, then power flows that use real-time power measurements are more desirable than offline power flows. 
   To satisfy this need, techniques have been developed that generate a real-time power flow in a distribution system using the limited real time power measurements that are available. However, because real-time power consumption information may not be available at all points throughout an electrical distribution network, historical usage information regarding individual loads of a distribution network may be used to estimate power usage based on available real-time power consumption information. For example, real-time power consumption information may be available at different locations on feeder lines, which at least provides some detail as to the power consumption of the distribution system. The historical consumption statistics of various loads connected to the feeders is then used to extrapolate out the measured power consumption to each of the various loads. 
   For example, consider a situation in which there are three loads on a feeder line, and that real-time measurement information is available for the feeder head. Also consider that two of the loads have roughly the same historical energy consumption record, and that the other load has twice the energy consumption of each of the first two loads. In such a case, the real-time measured energy of the feeder may be allocated at a ratio of 1:1:2. For example, if the real-time measured power on the feeder is 12 kW, it can be assumed that the first two loads are each consuming 3 kW and the third load is consuming 6 kW. This method of allocation in determining real-time power flow is known as scaling. Scaling factors are typically used to allocate measured power consumption at a supply node to individual loads connected to the node. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention is explained in the following description in view of the drawings that show: 
       FIG. 1  is a schematic representation of a portion of an exemplary electrical power network for which load scaling using current and power measurements may be accomplished in accordance with the present invention; 
       FIG. 2  is a vector diagram for an exemplary two feeder scaling solution; and 
       FIG. 3  is a vector diagram for an exemplary four feeder scaling solution. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 1  shows a schematic representation of a portion of an electrical power network  100  to which aspects of the present invention may be applied. The network  100  includes a transmission network  102 , a distribution network  104 , and at least one substation  106  in between the transmission network  102  and the distribution network  104 . The transmission network  102  includes high voltage transmission lines  110  and at least one three phase power generator  112 . Substation  106  connects to the transmission line  110  and may include one or more transformers  108 , such as a three phase transformer. Such transformer types, and their variants, are well known in the art. The distribution network  104  may include a number of feeders  114  emanating from the power substation  106  providing electrical power to one or more respective loads  116 . Power measurement devices  122  may disposed at various points throughout distribution network  104  to measure power and/or current flow. By way of example, the power measurement devices  122  may be connected to a Supervisory Control and Data Acquisition (“SCADA”) system, which is known in the art. 
   In operation, generator  112  generates power for transmission over the transmission line  110  at high voltage, for example 110 kV. The power substation  106  converts the voltage to a lower level, for example, 20 kV, for propagation over the feeders  114  to loads  116 . The transmission network  102  and distribution network  104  deliver energy in three phases, typically referred to as phase A, phase B and phase C. Each of the phases has a similar voltage magnitude, but has a different phase angle with respect to the other phases. 
   A power flow through the network  100 , as is known in the art, is a collection of values representative of a relatively detailed model of voltage, current and/or power flow values within an electrical power system. A real-time power flow is a power flow using real-time measured values to formulate the power flow. The real-time measured values may consist of voltages, active and reactive power, and/or current measurement value obtained at various points of the system, such as at the measurement devices  122 . For example, typical network power system measurements may include measurements of currents I 1 , I 2 , and I 3  taken at the heads of feeders  114  by measurement devices  122 . Such measurements are typically needed to ensure that feeder conductors are not current overloaded. In addition, because transformer overload limits are typically defined by apparent power provided at the transformer, measurements of injected power Pinj, Qinj, are typically taken, for example, by devices mounted on a circuit breaker associated with the substation transformer  108 . Accordingly, in a typical substation, measurement devices  122  configured for measuring current are used on feeders  114 , and measurement deices  122  configured for measuring injected power Pinj, Qinj are used on circuit breakers of substation transformer  108 . 
   Through the use of load scaling, it is possible to calculate a real-time power flow (details of power usage at each load  116 ) for a distribution network  100  having limited real-time measurement data on power consumption. For example, respective load scaling factors for allocating loads among feeders to determine power flow may be calculated according to the equations (1) and (2): 
   
     
       
         
           
             
               
                 
                   
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   In equation (1), SFP i  is the scaling factor for active power at feeder i, P meas  is a measured active power for the substation, P calc  is a calculated active power for the substation, and ΣP i  is the sum of the active powers at each feeder of the substation. In equation (2), SFQ i  is the scaling factor for reactive power at feeder i, Q meas  is a measured reactive power for the substation, Q calc  is a calculated reactive power for the substation, and ΣQ i  is the sum of the reactive powers at each feeder of the substation. Such load scaling may typically include changing a calculated active power P and calculated reactive power Q of the load(s)  116  to make these values equal to corresponding measured values. For example, in the case of the network  100  shown in  FIG. 1 , it is desired to make each calculated current I 1 (calc), I 2 (calc), and I 3 (calc) at each feeder  114  equal to the corresponding measured currents I 1 (meas), I 2 (meas), and I 3 (meas), while keeping calculated injected power Pinj(calc) and Qinj(calc) to equal to Pinj(meas) and Qinj(meas). Accordingly, a solution that simultaneously solves for P, Q, and I, is desired to provide improved generation of load scaling factors to more accurately estimate real time power flow, for example, among feeders  114  of a distribution network  100 . However, it is believed that conventional load scaling calculations are limited in accuracy because such solutions use only magnitudes of a measured current I. Without knowledge of the current angle, i.e. power factor angle, information, Pload and Qload of downstream loads cannot be accurately calculated to provide an estimate of real time power flow to enable determination of appropriate scale factors for the supply nodes. 
   The inventor of the present invention has developed an innovative load scaling method for a plurality of network feeders that provides a calculated feeder current Icalc equal to a measured feeder current Imeas, and simultaneously provides calculated injected power Pinj(calc) and Qinj(calc) equal to measured power Pinj(meas) and Qinj(meas). Accordingly, more accurate scaling factors can be determined using the calculated and measured values to produce an improved estimation of real-time power flow in the network  100 . 
   In an example embodiment, the method includes determining an apparent power S for each measured current Imeas of at least two power network feeders. Apparent power S may be calculated from Imeas using equation (3): as:
 
 S= √{square root over (3)} VI   meas   (3)
 
   Voltage V may be measured, for example at a feeder head busbar  120 , or may be estimated based on a nominal voltage at a substation  106 . Typically, voltage V is very close to a nominal voltage because substation transformers  108  are equipped with a Load Tap Changer (LTC). The LTC is a known type of local controller that keeps voltage at the busbar  120  equal to the desired value by changing transformer tap positions. 
   The method then includes determining the respective power factor angles φ of the feeder currents/responsive to the respective determined apparent power S and the active power Pinj and reactive power Qinj injected at the substation. For example, a system of equations (4) may be established for the substation node  118  using Kirchoff&#39;s first law and the know relationships that active power P is equal to apparent power times cosine of the power factor angle, P=S cos φ, and reactive power Q is equal to apparent power times sine of the power factor angle, P=S sin φ. Accordingly, the system of equations (4) defines each feeder&#39;s apparent power S with respect to injected power P and Q.
 
 P   inj   =S   1  cos φ 1   +S   2  cos φ 2   +S   3  cos φ 3   + . . . +S   n  cos φ n  
 
 Q   inj   =S   1  sin φ 1   +S   2  sin φ 2   +S   3  sin φ 3   + . . . +S   n  sin φ n   (4)
 
   The system of two equations (4) includes n unknown variables, φ 1 , φ 2 , φ 3′ . . . , φ n , where n is a number of feeders, and φ n  is the power factor angle for feeder n. Upon solving the set of equation (2) for φ 1 , φ 2 , . . . , φ n , the active and reactive powers for each feeder may be calculated as P feeder =S cos φ, Q feeder =S sin φ. By scaling the feeder loads according to the calculated P feeder , Q feeder  for each feeder, for example, using equations (1) and (2), the calculated values will be made equal to the measured values with regard to feeder currents I and injected power P, Q. 
   The power factor angles φ 1 , φ 2 , . . . , φ n  in the system of equations (4) may be calculated using a variety of techniques. For example, the case of n=1 is trivial. The case of n=2, i.e., there are two feeders connected to the substation, can be solved using known analytical techniques for two equations having two unknowns φ 1 , φ 2 . Accordingly, for n=2, the system reduces to the set of equations (5) below:
 
sin(φ 1 +α)=( P   inj   2   +Q   inj   2   +S   1   2   −S   2   2 )/(2 S   1 √{square root over ( P   inj   2   +Q   inj   2 )})
 
sin(φ 2 +α)=( P   inj   2   +Q   inj   2   +S   2   2   −S   1   2 )/(2 S   2 √{square root over ( P   inj   2   +Q   inj   2 )})  (5)
 
   where α=arccos(Q inj /√{square root over (P inj   2 +Q inj   2 )}) which can be solved directly. A graphical illustration of the vector diagram  200  where n=2 is depicted in  FIG. 2 . Three vectors, apparent injected power {right arrow over (S)}inj and respective feeder apparent powers {right arrow over (S)} 1 , {right arrow over (S)} 2  create a vector solution  202 , which can be built under a condition such that the magnitude of {right arrow over (S)}inj is less than the magnitude sum of {right arrow over (S)} 1 ,{right arrow over (S)} 2 . 
   When a number of feeders n is greater than 2, the system of equations (4) includes more variables than equations. Consequently, there is more than one combination of angles φ 1 , φ 2 , φ 3 , . . . , φ n  that satisfies the system of equations (4). This is illustrated in the vector diagram  300  of  FIG. 3  for four feeders, i.e. n=4. Each of the solutions  302 ,  304  will satisfy respective feeder current magnitudes I 1  . . . In, for example derived based on S 1  . . . Sn or S 1 ′ . . . Sn′ and injected power values Pinj and Qinj. 
   In the case of more than two feeders, power factor angles may be solved using iterative techniques, such as an iterative procedure built on equations (5). For example, for each feeder k of a set of n feeders and having a power factor angle φ k  as a variable, all other feeders of the set can be combined together to represent a second feeder. By reducing n to 2, analytic techniques can be used to calculate φ k  using equations (5). The calculated value of φ k  can then be used to calculate other power factor angles of other feeders by iteratively using the second feeder representation technique described above. In addition, because of multiple possible solutions for n&gt;2, additional conditions may be imposed on feeder power factors which may provide a more desirable or feasible solution. For example, feeder power factors that require minimal change in the load power factors for all loads scaled according to feeder P&#39;s and Q&#39;s may be used. 
   A processor  124  may be configured for implementing steps for performing the above described method. Processor  124  may take any form known in the art, for example, an analog or digital microprocessor or computer, and it may be integrated into or combined with one or more processors used for other functions related to power flow monitoring of the network  100 , such as an existing SCADA processor. The steps necessary for performing the method may be embodied in hardware, software and/or firmware in any form that is accessible and executable by processor  124  and may be stored on any medium that is convenient for the particular application. The processor  124  may receive input signals  126 ,  128 ,  130 ,  132  from the measurement devices  122  and process the signals according the above method to generate an output  134 , such as one or more power factor angles and/or active and reactive power of the feeders. 
   Based on the foregoing specification, the exemplary methods described for determining power flow in an electrical distribution network may be implemented using computer programming or engineering techniques including computer software, firmware, hardware or any combination or subset thereof. Any such resulting program, having computer-readable code means, may be embodied or provided within one or more computer-readable media, thereby making a computer program product, i.e., an article of manufacture, according to the invention. The computer readable media may be, for instance, a fixed (hard) drive, diskette, optical disk, magnetic tape, semiconductor memory such as read-only memory (ROM), etc. The article of manufacture containing the computer code may be made and/or used by executing the code by the processor. In an example application, the computer readable media may be used for upgrading an existing SCADA device. 
   One skilled in the art of computer science will easily be able to combine the software created as described with appropriate general purpose or special purpose computer hardware, such as a microprocessor, to create a computer system or computer sub-system embodying the method of the invention. An apparatus for making, using or selling the invention may be one or more processing systems including, but not limited to, a central processing unit (CPU), memory, storage devices, communication links and devices, servers, I/O devices, or any sub-components of one or more processing systems, including software, firmware, hardware or any combination or subset thereof, which embody the invention. 
   While various embodiments of the present invention have been shown and described herein, it will be obvious that such embodiments are provided by way of example only. Numerous variations, changes and substitutions may be made without departing from the invention herein. Accordingly, it is intended that the invention be limited only by the spirit and scope of the appended claims.