Abstract:
A power distribution unit (PDU) is disclosed wherein the PDU includes an interactive display and communications capability. The display is interactive. A touch screen allows a user to make selections of data, commands, and modes to view, as well as enter commands. Some versions include audio and video capability, allowing two people from distant locations to interact. Ports for USB, Ethernet, wifi, Bluetooth provide for various methods of interconnectivity. An energy metering and control board controls each PDU outlet and measures many parameters related to the power of each outlet. The data obtained is used to calculate the power of a three phase power source using no other hardware resources.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is related to commonly-owned U.S. patent application Ser. No. 12/177,881 submitted Jul. 22, 2008, by Christopher Verges, which application is incorporated herein in its entirety. 
     
    
     BACKGROUND 
       [0002]    Our society is using more and more electrical power for consumer electronics devices and even charging automobiles. So too, as private individuals and companies make growing use of the internet and other communications means, infrastructure facilities such as server farms and collocation facilities continue to use more electrical power with ever increasing complexity. The electrical needs of such facilities are often met using power distribution units (“PDUs”). 
         [0003]    This increased complexity is leading to more automation as a solution for managing power and dealing with installation and with problems, such as load balancing, load shedding, time of day and day of week scheduling, and problem avoidance and resolution. However human interaction with such systems is still required. This is somewhat frustrated by the counter forces of increasingly concentrated command and control but far reaching, geographically diverse power consuming centers. Users request more features, including more information from PDUs, a product which historically is relatively “dumb.” For example, users want to monitor power usage by individual outlet, thereby enabling assignment of cost on a per-user basis. Ideally the data should enable a determination of the total power taken from the grid, taking into account the various phases. The present art sometimes provides such information, but at a significant cost for the hardware to do so. 
         [0004]    In addition to the overall higher energy usage in datacenters, many facilities are now shared by multiple organizations. Colocation facilities, for example, are datacenters where disjoint parties locate their equipment, with the facilities infrastructure itself being run by a common third party. Corporate datacenters also are seeing a trend towards sharing datacenter resources across multiple business units. Yet with both scenarios, for management and billing purposes, energy usage must be allocated to each party or business unit. The classical model of having a single power meter at the building ingress does not lend itself to tackling this challenge. 
         [0005]    Because of the high number of devices being placed on the power grid&#39;s edge, it seems appropriate to have an equal number of meter devices. However, the classical meters are too expensive and cumbersome to install for each device in a datacenter. Instead, the power strip (a.k.a. “power distribution unit” or “PDU”) has been tapped with that task. 
         [0006]    What is needed is the addition of improved local human interfaces for monitor, control, intervention, and installation activities as well as human to human connectivity for these same purposes. Such a system should also provide improved information at a reasonable cost. 
       SUMMARY 
       [0007]    The present invention comprises equipment and methods which enable humans to better monitor system conditions in real time, either at the point of interest or remotely. In addition, the present invention provides for system command and control, including override, as well as communication between a person and remote equipment and between two or more persons. 
         [0008]    The present invention comprises communications and display capability in conjunction with power distribution units, utilizing many of today&#39;s communications means such as local area network, wifi, USB, RS-232, and Bluetooth to name a few. Such communications then provide the ability to logically combine physically diverse resources into virtual power distribution units, enabling a higher logical level of control. Virtual power distribution units (“VPDUs”) were disclosed in aforementioned U.S. patent application Ser. No. 12/177,881 and are not repeated in this application. 
         [0009]    The present invention also includes local displays for providing certain information to a human observer and enabling complex control commands. Displays plus sensors, such as a camera or microphone, enable the remote operation and/or verbal communication between two or more persons. Some displays also provide means for a person to request certain data and/or to enter requests, commands, or setup values for action by the system. In some embodiments individual and collective power use is also available for display or remote collection. Calculations based upon raw data enable these determinations without adding additional electronic components. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]      FIG. 1  is a level block diagram of an example system. 
           [0011]      FIG. 2  is one example of daisy chaining power distribution units using various communications means. 
           [0012]      FIG. 3  is an example of a display for local command and control input. 
           [0013]      FIG. 4  is a flow chart of logical steps for local command and control, using the display of  FIG. 3 . 
           [0014]      FIG. 5  is an example of power data presented on a local display. 
           [0015]      FIG. 6  is an example of a graphic data presented on a display. 
           [0016]      FIG. 7  is an example of a process for a user setting up system parameters using a touch sensitive display unit. 
           [0017]      FIG. 8  is an example of an alert message provided by a panel on a power distribution unit according to the present invention. 
           [0018]      FIG. 9  is an example of log information regarding a power distribution unit as presented on a local display. 
           [0019]      FIG. 10  is a flow chart of the logical steps for presenting and providing response capability regarding a system alert. 
           [0020]      FIG. 11  is an example of a system within a power distribution unit providing real time audio and video communication between two technicians involved with trouble shooting a power distribution system. 
           [0021]      FIG. 12  is an example of a system within a power distribution unit providing real time text communication between two technicians involved with trouble shooting a power distribution system. 
           [0022]      FIG. 13  is a schematic of an energy metering and relay control board. 
           [0023]      FIG. 14  is a schematic of a bank assembly including a plurality of energy metering and relay control boards similar to the board of  FIG. 13 . 
           [0024]      FIG. 15  is a schematic of a system formed from a plurality of bank assemblies similar to  FIG. 14 , including communication, display, and control elements. 
           [0025]      FIG. 16  defines the orientation parameters used by a sensor algorithm for determining the orientation of a power distribution unit. 
           [0026]      FIG. 17  is an illustration of a power triangle, showing the relationship between real, reactive, and apparent power. 
           [0027]      FIG. 18  illustrates the sum of electrical outlet apparent power vectors forming a bank apparent power vector. 
           [0028]      FIG. 19  is a schematic of a three phase Delta and Wye circuit. 
           [0029]      FIG. 20  shows the phase shift of three phase voltage waves. 
           [0030]      FIG. 21  is a three phase Wye circuit. 
           [0031]      FIG. 22  defines the phase relationships and symbols used in analyzing a three phase Wye circuit. 
           [0032]      FIG. 23  is a three phase Delta circuit. 
           [0033]      FIG. 24  defines the phase relationships and symbols used in analyzing a three phase Delta circuit. 
           [0034]      FIG. 25  shows the interaction of three phase Wye and Delta circuit waves. 
           [0035]      FIG. 26  is a flow chart of logical steps in determining and displaying input power parameters to an observer. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Definition of Some Terms 
       [0036]      
         [0000]    
       
         
               
               
             
           
               
                   
               
             
             
               
                 ADC 
                 Abbreviation for Analog to Digital Converter. 
               
               
                 Bluetooth 
                 An open wireless protocol for exchanging data over short distances with 
               
               
                   
                 fixed and mobile devices, thereby creating a personal area network. 
               
               
                 GUI 
                 Graphical User Interface. A visual presentation enabling a human user to 
               
               
                   
                 visualize and control a physical asset, such as a computer or a controller 
               
               
                   
                 controlling an outlet in a PDU. 
               
               
                 I/O 
                 Input/output. A term referring to how many input or output pins a 
               
               
                   
                 device provides. 
               
               
                 LAN 
                 Local Area Network. A computer network covering a small local area. 
               
               
                 LCD 
                 Liquid Crystal Display. A low power display technology. 
               
               
                 NIC 
                 Network Interface Card. An electronic circuit providing LAN connectivity to 
               
               
                   
                 an electronic appliance such as a computer or a PDU. 
               
               
                 OS 
                 Industry standard term for the operating system of a computing device, 
               
               
                   
                 such as a PC. 
               
               
                 Outlet 
                 A mechanical port to which a load may be connected. The load may be 
               
               
                   
                 an electrical appliance or a branch to another outlet or a plurality of 
               
               
                   
                 outlets. A load may be removable (unplugged) or hard-wired. Sometimes 
               
               
                   
                 called a “power terminal”, “electrical outlet”, “power outlet” and other 
               
               
                   
                 similar terms. 
               
               
                 PC 
                 Personal Computer. 
               
               
                 PDU 
                 Industry standard term for a power distribution unit. A PDU has electrical 
               
               
                   
                 outlets that may be turned ON or OFF. 
               
               
                 QVGA 
                 Quarter Video Graphics Array. A computer-like display with 320 × 240 
               
               
                   
                 pixel resolution. 
               
               
                 TRX 
                 Industry standard abbreviation for a transceiver. 
               
               
                 USB 
                 Universal Serial Bus, a serial communications technology standardized by 
               
               
                   
                 the USB Implementers Forum (USB-IFP). 
               
               
                 VPDU 
                 A virtual PDU. Sometimes referred to as a “logical PDU.” 
               
               
                 wifi 
                 Wireless local area network, based upon unlicensed spread spectrum 
               
               
                   
                 technology. 
               
               
                   
               
             
          
         
       
     
         [0037]    The present invention provides for human interface displays embedded within a power distribution unit. The display presents predetermined information, and in some embodiments includes the ability for a user to input data or commands, request certain information, or change configurations. Some embodiments include electronic communication such that two or more PDUs may be logically combined, thereby forming a virtual power distribution unit. In some embodiments the electronic communication capability is used to transport video, audio, status, control, or other information between two or more PDUs and/or a PDU or VPDU to a remote location. These communications are real time, such that system personnel may communicate to each other for the purposes of repair, troubleshooting, installation, configuration, and other obvious uses. 
         [0038]    Looking to  FIG. 1 , the dotted line defines those elements of the present invention  100  that are enclosed within a subject PDU. A given PDU may have all or less than all of the elements shown. An exemplary embodiment of the present invention  100  includes a microprocessor  102 . A microprocessor  102  controls the functions, including control, display, communication support, data collection, user interface, and calculations as needed. In some embodiments the microprocessor  102  includes sensors, for example a temperature sensor or an analog-to-digital converter. The microprocessor  102  may display information on a display  104 . In some embodiments the display  104  is a quarter VGA (QVDA). Other embodiments include a custom LCD display with predetermined symbols, an LCD module with alphanumeric capability, dot matrix LCDs or LEDs, or a panel with LEDs at certain positions associated with predetermined status words. In the interest of completeness this disclosure will assume a QVGA display, though a system including other display types is within the scope of the present invention. 
         [0039]    The microprocessor  102  receives user input from a touch screen  106 . In some embodiments the touchpad  106  is a keypad, slew switches, or positional switches. In one embodiment the touch screen  106  is transparent and is physically in front of the display  104  forming a single display and input unit  108 . A single unit  108  enables the dynamic display of selectable information or modes which a user may then touch to select. 
         [0040]    In some embodiments the microprocessor  102  is connected to a USB host port  110  for receiving or sending signals to a supported USB device  112 . Examples of USB devices  112  a video camera, digital camera, microphone, sensor data port, and others that are well known. 
         [0041]    In some embodiments the microprocessor  102  connects to a short range wireless transceiver  114 . Such transceivers  114  are often based upon the Bluetooth technology. The transceiver  114  communicates wirelessly with a wireless device  116 , such as a Bluetooth video camera, digital camera, microphone, or other sensor or interface device. 
         [0042]    The microprocessor  102  may be connected to a speaker  118 , thereby providing warning or status noises or prerecorded announcements. The speaker  118  may also carry audio from another person or annunciation element outside of the instant PDU via PDU-to-PDU communication, to be discussed hereinafter. 
         [0043]    The microprocessor  102  may be connected to a microphone  120  for receiving audio from a user. The microprocessor  102  may also be connected to a camera  122 . In some embodiments the camera  122  is a video camera, in other embodiments the camera  122  is a digital camera. The microprocessor  102  is connected to one or more power sensors and/or power management devices  124  for control or parameter sensing of the power outlets within the PDU (not shown). Multiple sensor or management devices are sometimes connected together and share or pass on data, forming a bank of such devices. 
         [0044]    Some embodiments include an accelerometer  126  for sensing the orientation of the PDU. Determining the orientation of the PDU allows the microprocessor  102  to orient the display on the graphics display  104  appropriately. In other embodiments, wherein the accelerometer  126  is not included, the system provides means for a user to select a display orientation. 
         [0045]    The connections to the various elements  104 ,  106 ,  108 ,  110 ,  114 ,  118 ,  120 ,  122 ,  124 ,  126  of the system  100  to the microprocessor are appropriate for the electronic interface of the individual element. The microprocessor  102  may include all of the electronic interfaces needed for a given complement of peripheral elements, or the microprocessor  102  may further have various external interface circuits to provide the needed interface. The connections are not discussed here, in that one of ordinary skill would be able to provide the appropriate interface. 
         [0046]    Looking to  FIG. 2 , a PDU  202  comprises a display and touch screen device  208  similar to the display  108  of  FIG. 1 ; a LAN connector  203  (not used in this example), two USB-A connection ports  205 ,  207  and a number of power outlets  209 . A second PDU  210  includes a USB-B port  211 . A USB A-B cable  204  connects the second PDU  210  with the first PDU  202 . Once the second PDU  210  is connected to the first PDU  202  the outlets of the second PDU  210  may be “seen” by the microprocessor  102  ( FIG. 1 ) of the first PDU  202 . In some embodiments the outlets  213  of the second PDU  210  are controlled by the microprocessor of the first PDU  202  and/or information associated with the PDU  210  and/or its individual outlets  213  presented on the display  208 . In embodiments wherein the display  208  includes a touch screen for control, a user may enter commands regarding an individual outlet amongst the complement of outlets  213  of the second PDU  210 . Of course such control would also be available amongst the outlets of the first PDU  202 . 
         [0047]    In similar fashion a second USB-A port  205  enables connection to a USB hub  250 , thereby providing connection to one or more PDUs  220 ,  230 ,  240  wherein the PDUs  220 ,  230 ,  240  include USB-B ports for connection using USB-AB cables  251 . 2  to  251 . n , wherein “n” indicates the number of USB equipped PDUs connected to the USB hub  250 . The hub may also provide for a connection to a non-PDU peripheral device  260  via USB-AB cable  251 . 1 . The non-PDU peripheral device  260  may, for example, be a camera, temperature sensor, or any other USB-equipped electronic device. As with the PDU  210 , the additional PDUs  220 ,  230 ,  240  may be logically controlled by the first PDU  202  to form a virtual PDU, as disclosed in detail in the aforementioned Verges &#39;881 application. In some embodiments the first PDU  202  provides display or control functions for it&#39;s USB-connected sister PDUs, but a virtual PDU is not formed. 
         [0048]      FIG. 3  is an example of how a user may receive information regarding a given physical or logical (eventually physical) outlet. For example, assume the touch screen  208  corresponds to the touch screen  208  of the first PDU  202  of  FIG. 2 . The display in the example provides identification, state, power, current, voltage, and power factor plus includes user input to turn the selected outlet ON, OFF, or to REBOOT it. REBOOT is a two step process of cycling outlet OFF, then back ON. Of course more, less, or different information may be provided on the screen  208 . The outlet of interest may be selected remotely from a central facility or may be selected based upon out of specification performance. In one embodiment a selection screen (not shown) is presented enabling the user to select the outlet of interest. 
         [0049]    Referring to  FIG. 1  to understand the supporting elements,  FIG. 4  is an example of a flow chart of the logic for controlling the display  108  and an associated outlet or device. A user touches  302  the display  108 . A touch screen  106  captures the input and provides X,Y coordinates  304  to the microprocessor  102 . The microprocessor compares the X,Y coordinates  306  with a map of coordinates that correspond to commands  308 . The command handler  308  has a library of command responses. One of the responses from the command handler  308  is the return that the area touched was not a touchable command area. That is, the area touched was not a “button” defined on the graphics display  104 , which is tested for at step  310 . If the touch was not in a valid area, the touch is simply disregarded  312  and the process again waits for a touch  302 . If the touch was within a valid area the event handler has provided the microprocessor with instructions, which the microprocessor puts into action in response to the decoded command  314 , then updates the display accordingly  316 , and returns to waiting for a new touch  302 . 
         [0050]      FIG. 3  is just one example of the data that a screen  108  may display.  FIG. 5  is an example according to  FIG. 3  wherein the input current in each phase and the neutral line of a three-phase Wye power input cord is shown. The information displayed is sometimes rotated amongst various predetermined presentations, changing every few seconds or in response to an event. In one embodiment a touch area  502  allows a user to interrupt the sequence, or to manually advance to the next screen. Arrows  504 ,  506  may also be used to enable navigation. 
         [0051]      FIG. 6  is another example of a data display. Sometimes the screen  108  supports color, including color graphics. 
         [0052]    In another example following  FIG. 3  (with element references to  FIG. 1 ),  FIG. 7  shows an example process of setting up the LAN settings of a PDU upon installation.  FIG. 7  is a sequence of questions, input enablement layouts, and example user inputs on the touch screen  108 . After getting into this configuration mode (not shown) the user is asked  702  if he wants to configure the instant PDU. Assuming a “YES” response, the user can select which LAN to be configured  704 . In this example there are two Ethernet and one wifi network selectable. Assuming ETHO was selected, the user is next asked to select between DCHP or manual setup  706 . In either case an IPv4 address is assigned (DCHP) or entered (manual)  708 . Manual entry is done using the keypad  709 . Once an IPv4 address is shown  721 , the user may cancel the entry  711  and try again; indicate “DONE”  713 ; navigate to the next  717  or previous  719  screen, or delete the previous character  715 . 
         [0053]    When the user touches the DONE area  713  the next screen allows entry of the subnet mask  710  in the same manner as the IPv4 address. The next step is to configure the IPv4 gateway  712 , then a summary of all configuration data is shown  714 . The user confirms “YES”  721  that the data entered is correct, the data is stored, and the system returns to step  702 . If the user responds with “NO” at step  714  the data is not saved prior to the system returning to step  702 . 
         [0054]    As has been seen, the use of a display screen  104  by the microprocessor  102  provides convenience and time savings as well as lower cost by enabling technicians to receive information and make responses where they are, without the need for a computer console, etc. Of course the display could be related to a PDU that is remotely located from the user; the display is at the PDU the user is using at the instant time. 
         [0055]    In another embodiment the system is designed to provide trouble alerts that override any other information of the moment (including none). For example,  FIG. 8  is an example of an alert message  800 . LEFT  802  and RIGHT  804  arrows allow the user to step through a list of alerts  800 . A message area  810  gives the reader information and sometimes instructions. A GOTO button takes the user to additional information and/or instructions. A DISMISS button  814  removes the alert from the alert list. In some embodiments an alert dismissal requires the user to enter a password that identifies him as having the authority to dismiss the alert. UP  806  and DOWN  808  arrows provide for scrolling the display to make additional text area available. 
         [0056]      FIG. 10  is an example of a flow chart illustrating the logical steps in support of alert displays. When the system detects an alert condition  1002 , the display (local or remote or both) updates to “pop up” the alert message  800 , overriding whatever else may have been previously displayed. The user is prompted for a response  1006 , which response is tested  1008 , looping until the touch is in a valid area  1007 . In this example only two command responses are allowed  1010 , other designs may allow more or different rezones. If the command GOTO is touched  1012  control passes to an appropriate page/procedure for response. If the user dismisses the alert  1014 , the alert changes to “Inactive” status and control/display return to the previous (pre-alert) condition  1016 . 
         [0057]    Similar to alerts,  FIG. 9  is an example of a display of a log of activities  900 . LEFT  1002  and RIGHT  1004  arrows enable stepping from one log page to another. An input area  906  may allow stepping to the next or previous log item. 
         [0058]      FIG. 11  is an example of audio and video links between two remotely located staff members enabling problem resolution. In a theoretical scenario, a staff member  1102  is located near a PDU  1101 , wherein the PDU  1101  is part of a system equipped according to the present invention. A video camera with audio support  1104  is connected to the PDU  1101  via a USB cable  1105  to a USB port  1106  on the PDU  1101 . Of course, as previously discussed, the video and audio support could connect to the PDU  1101  via a LAN connection, or the video camera and microphone could be built into the PDU  1101  (not shown). The video and audio feed is, for example, communicated to a remote staff member  1116  via a LAN connection  1110  through a LAN cable  1112 , the LAN cable  1112  further connected (directly or through an Ethernet connection) to a monitor  1114  at the remote location where there is a problem. Of course the monitor  1114  could be the screen of a PDU at the remote location, wherein the remote PDU is also equipped according to the present invention. Video and audio from the remote location is delivered via the same LAN connection  1110  back to the PDU  1101  and is presented to the local staff member  1102  on the screen  1108  of the PDU  1101 . From this and the previous description other configurations for communication will be obvious. The person in the display  1114  corresponds to the local staff member  110 - 2 , and the person in the other display  1108  corresponds to the remote staff member  1116 . 
         [0059]    In a similar situation, an example illustrated by  FIG. 12 , communication between the two staff members  1202 ,  1218  is based upon text. The local staff member  1202  types a request using a USB keyboard  1204 , wherein the USB keyboard  1204  is connected to a USB port  1208  via a USB cable  1206 . The USB port  1208  is associated with a PDU  1201  that is equipped according to the present invention. The text typing of the first staff member  1202  and the second staff member  1218  is shown on the display  1210  of the PDU  1201 . As previously discussed, text typing could also be done by presenting a keypad on the touch screen  1210  of the PDU  1201 . Text is sent to and from a remote display  1216  through a LAN port  1212  connected by a LAN cable  1214 , optionally through an Ethernet system. The display screen  1216  may be a standalone touch screen with the appropriate interface, or could be the screen on a PDU at the remote location. 
         [0060]    In some embodiments of the present invention a PDU includes the ability to collect and report parametric and performance data and to control one or more outlets. The data can be made available to a local user if a display is included in the local PDU, and to a remote user if communications is included. An example of support for this feature is the circuit of  FIG. 13 , an energy meter and relay control board  1300 . As will be discussed later, energy meter and relay boards  1300  can be combined within a defined bank of PDUs, as well as communicate outside the instant bank. 
         [0061]    The board  1300  comprises two sections: an analog section and a digital section. The analog section comprises a floating DC power supply  1402  ( FIG. 14 ) which provides DC voltage at pins V−IN  1302  and V+IN  1304 . The power supply  1402  may receive any electrical power, AC or DC, providing it can then supply a constant DC voltage offset against the floating (AC) ground AC HOT IN. V−IN  1302  is an AC signal used as a relative (floating) ground, and V+IN  1304  rides at a constant voltage, for example +5 volts, on top of VI−IN. V+IN is provided to “n” number of integrated circuits  1320 . n . Throughout this description we may use a reference number with “n” to mean any one or all such elements with the same reference number, but a different number for “n.” CAN controller  1332  and a CAN TRX  1328  have an isolated ground from V−IN. In  FIG. 14  the voltage signal V−IN is marked as “AC HOT GND” to make clear it is AC. AC HOT GND/V−IN is connected to the positive electrical connector in common with the power outlets of the PDU by a line  1303  to the electrical terminal  1306  labeled “AC HOT IN”, forcing the two to the same electrical potential. AC HOT IN may be a nominal 120 VAC, 208 VAC, or other voltages standard in varying countries. Regardless the value of AC HOT IN (and thereby AC HOT GND and V−IN), V+IN will be five volts above it, thereby providing a five volt supply for the electronic components of the board  1300 . Of course a different DC offset could be used to support an electronic design based upon other than five volts. 
         [0062]    ICn  1320 . n  is an integrated circuit which measures outlet parameters, for example voltage, current, power, and apparent energy. An example of such a device is an ADE7763 Single-Phase Active and Apparent Energy Metering IC, available from Analog Devices, 3 Technical Way, Norwood, Me. One skilled in the art will know of other products suitable for the measurements, such as a standard microprocessor with ADC input with appropriate firmware. The ICn  1320 . n  has a maximum input range for ADC conversion, so we scale the neutral line AC NEUTRAL IN  1308  to a value close to that of AC HOT IN. Scaling is done using a resistor divider comprised of R 10   1340  and R 11   1342 . For example, with AC HOT IN of approximately 170 volts (peak relative to neutral; typical of 120 volt RMS household current), R 10  ( 1340 )=1 Kohm, R 11  ( 1342 )=1 Mohm, the voltage on line  1313  will be approximately 0.1698 volts, well within the conversion range of the energy device ICn  1320 . n.    
         [0063]    AC HOT IN from terminal  1306  is distributed on a line  1315  and the scaled version of AC NEUTRAL IN from terminal  1308  is distributed on a line  1313 . Lines  1313  and  1315  are provided to the inputs V− and V+ respectively of all ICn  1320 . n  devices. The CAN controller  1332  provides control of the process. Many microcontrollers with adequate I/O would be suitable for this purpose. The operation of Channel “n” will be described; the other channels are controlled in the same manner. 
         [0064]    Assuming a given outlet connected to the Channel n AC HOT OUT terminal  1310 . n  is to be powered ON, CAN controller  1332  closes a SPST relay  1322 . n  by driving a control signal onto line  1317 . n . Relay  1322 . n  connects the voltage on pin  1310 . n  to the I+ input terminal on ICn  1320 . n . Current from pin  1310 . n  flows through a low value sense resistor Rn  1330  to the I− input terminal on the ICn  1320 . n . The value of voltage across the sense resistor Rn  1330  is measured by ICn  1320 . n , thereby determining the current by the formula 
         [0000]    
       
      
       I=E/R  
      
     
         [0000]    where “E” is the voltage measured across the sense resistor Rn  1330 . n ; and “R” is the value of the sense resistor Rn  1330 . n . Sense resistor Rn is a low value, for example 0.005 ohm, to develop a low voltage in response to the current provided by its associated channel current. Of course other current sensing components may be used in addition or instead of a sense resistor. 
         [0065]    The devices ICn convert the V+/V− input values to determine the voltage of the outlets in the PDU, taking into account that the V− value has been scaled down, again by the resistor divider formed by R 10   1340  and R 11   1342 . 
         [0066]    The board  1300  provides control and parameter measurements for an arbitrary number of outlets “n”, denominated as “n channels.” Each channel includes an electrical terminal  1310 . n , a relay  1322 . n , and a sense resistor Rn  1330 . n  or other current sensing device.  FIG. 13  shows an energy measuring ICn  1320 . n  for each channel. In some embodiments there are fewer energy measuring ICs, each with more input terminals than shown in the example of  FIG. 13 . In some embodiments a MUX reduces the number of energy measuring ICs  1310 . n . In the example of  FIG. 13 , each energy measuring IC  1320 . n  includes an interrupt pin INT, a chip select pin CS, a serial data clock SCLK, a shifted data output pin MOSI, and a shifted data in pin MISO. In this example using the aforementioned ADE7763 device, the ADE7763 device  1320 . n  continuously takes data. When data is ready the ADE7763  1320 . n  generates an interrupt on the pin INT. The CAN controller  1332  sometimes takes all data from all ADE7763 devices  1320 . n , other times samples the data from each ADE7763  1320 . n  per a schedule. To receive the data from a given ICn  1320 . n  the CAN controller  1332  drives the appropriate chip select CS pin, then toggles the clock line SCLK and receives the data serially from the MOSI data out terminal. The ADE7763 device  1320 . n  may optionally be configured for certain parameters and operating modes by serially shifting in commands/data/flags by selecting the appropriate chip select CS pin, toggling the clock SCLK, and shifting in the data on the data input terminal MISO. MISO and MOSI are as shown in  FIG. 13  rather than using the common terms for data input and output terminals to avoid confusion in that data “out” from a sender is date “in” to a receiver. 
         [0067]    The CAN controller  1332  provides data to the CAN TRX  1328  from a signal terminal CAN_TX through an optical isolator  1324  (for safety reasons) and receives data from the CAN TRX  1328  at a signal terminal CAN_RX, again protected by an optional optical isolator  1326 . The CAN TRX  1328  unit forms part of a system-wide CAN network on the digital section of the board  1300  by providing signals on the lines CANH  1312  and CANL  1314 . The digital section also provides power on a DC line  1316  and a ground line  1318 . Connectors  1350 ,  1352  provide interconnection means for connecting multiple energy meter and relay control boards  1300 , thereby passing through bias voltage  1316 , ground  1318 , CANH  1312  and CANL  1314  signals to all boards  1300  so connected. 
         [0068]    In some embodiments a plurality of energy meter and relay control boards  1300  are connected for form a larger local bank of control boards to support a larger number of outlets than a single energy meter and relay control board  1300  supports. An example of such a configuration is shown in  FIG. 14 , wherein three an energy meter and relay control boards  1300 . 1 ,  1300 . 2 ,  1300 . 3  are connected, powered by a single bias power supply  1402 , managing the connections and collecting data for multiple outlets  1404 . 
         [0069]    At a higher level of system integration,  FIG. 15  illustrates an exemplary configuration of three banks comprising BANK 1   1502 , BANK 2   1504 , and BANK 3   1506 . Bias power, chassis ground, CANH and CAHL signals are provided to all of the banks  1502 ,  1504 ,  1506  by a common connection line  1508 . The number of banks so connected is arbitrary. The connection line  1508  from the last bank in the system is connected to a CAN terminator. The connection line  1508  provides bi-directional CAN communications between the banks and a network interface card  1510 . A network interface card  1510  can include a variety of connection means, for example USB, Ethernet, RS-232, Firewire, Bluetooth, and the like. Some central units also include a touch screen  108 . In one embodiment the network interface card  1510  is incorporated into a PDU. 
         [0070]    The description of the display  108  hereinbefore has assumed a vertical (portrait) orientation of the display  108 . PDUs may be installed and used in any orientation. Some embodiments assume a static or user-selectable portrait display, others a static or user-selectable landscape display. In other embodiments, an accelerometer  126  is incorporated in a PDU according to the present invention. The accelerometer  126  provides means for determining the orientation of a PDU, thereby to present the data on the display  108  appropriately.  FIG. 16  defines a three dimensional coordinate system and the rotation angle theta (θ) for the following explanation. 
         [0071]    Define a relationship between θ and the display orientation: 
         [0000]      45°&lt;θ&lt;=135°=UP
 
         [0000]      135°&lt;θ&lt;=225°=LEFT
 
         [0000]      225°&lt;θ&lt;=315°=DOWN
 
         [0000]      315°&lt;θ&lt;=45°=RIGHT
 
         [0072]    The gravity vector is read from the accelerometer  126 , and the angle θ from the Y-Z plane determined. From the above relationships, we determine the orientation of the PDU. If the orientation is different than a previously stored orientation, the new orientation is saved as the instant “old” orientation and the display updated (that is, rotated) accordingly. Note that UP is defined as a vertical portrait orientation, and DOWN is an “upside down” version of UP. LEFT means that the landscape mode is counterclockwise relative to UP, and RIGHT means that the landscape mode is clockwise relative to UP. 
         [0073]    In some embodiments the accelerometer  126  provides acceleration data that is used to detect an earthquake, violent weather, movement of a semi-permanent building, etc, and the microprocessor may then decide to shut down all electrical outlets for safety. 
         [0074]    Per-outlet metering allows one to determine all energy parameters of both single phase and three phase systems. Each single phase load creates a unique power signature on the upstream distribution grid. By characterizing these power signatures, we can accurately predict the effects on the grid. 
         [0075]    The discussion to follow focuses on the techniques involved in characterizing single phase loads connected to a three phase grid, since the challenges posed by such a setup are a superset of the single phase case. 
         [0076]    A PDU acts as a junction point between a power grid and an edge device. Mathematical models describe the combined effects of the individual single phase loads on the grid itself, closing the loop and providing for an overall holistic approach to energy management. 
         [0077]    In the this discussion we use the following terminology and symbolic convention:
       {right arrow over (P)} is a vector named “P” with a given angle. The vector {right arrow over (P)} can be broken down into a magnitude P and an angle ∠θ.   φ is the phase shift (offset) between voltage waves in a three phase system.   θ is the phase shift (offset) between voltage and current waves in a single phase system.   The collective group of line-to-neutral phase angles (φ an , φ bn  and φ cn ) will be referred to as φ ln  where ln stands for “line-to-neutral.”   The collective group of line-to-line phase angles (φ ab , φ bc  and φ ca ) will be referred to as φ ll  where ll stands for “line-to-line.”   Similarly, any variable followed by a ln or ll subscript will refer to the line-to-neutral or line-to-line versions of the variable, respectively.   References hereinafter to a “bank” mean similar to a typical bank such as that of  FIG. 14 .       
 
       Single Phase Fundamentals 
       [0085]    Each single phase load is described by three components: the Apparent Power (S), the Real Power (P), and the Reactive Power (Q). The relationship between each is described in  FIG. 17 . Apparent Power is the power that the three phase distribution grid must generate to supply the single phase load. Real Power is the power that is actually consumed by the single phase load to perform the desired work. Reactive Power is the “overhead” (i.e. inefficiency) in the system for the given load. Equations (1), (2) and (3) mathematically describe this relationship. 
         [0000]      RealPower( W ) {right arrow over (P)}=   VI  cos θ=P∠0°   (1)
 
         [0000]      ReactivePower( VAR ) {right arrow over (Q)}=   VI  sin θ=Q∠±90°  (2)
 
         [0000]      ApparentPower( VA ) {right arrow over (S)}=   {right arrow over (P)}+{right arrow over (Q)}= ( V×I )∠0  (3)
 
         [0086]    Reactive Power cannot be measured directly, so most energy meters will measure Apparent Power and Real Power. Reactive Power can then be calculated by determining θ, the phase relationship between voltage and current waves. 
         [0087]    An ideal situation occurs when |cos θ|=1. In this case, Real Power and Apparent Power are identical, and the Reactive Power is equal to zero; no power is wasted in the delivery of the energy itself. 
         [0088]    Mathematically, the power components and current in a bank can be calculated. Note that in equation (7), the current for the bank is calculated by using the magnitude of the apparent power vector ({right arrow over (S)}) divided by the voltage of the bank. 
         [0000]      {right arrow over (P)}Bank=Σ i=1   n {right arrow over (P)} Outlet     —     i =P Bank ∠0°  4)
 
         [0000]      {right arrow over (Q)}Bank=Σ i=1   n   {right arrow over (Q)}   Outlet     —     i   =Q   Bank ∠±π°  (5)
 
         [0000]        {right arrow over (S)}   Bank   ={right arrow over (P)}   Bank   +{right arrow over (Q)}   Bank   =S   Bank ∠θ  (6)
 
         [0000]        I   Bank   =S   Bank   ÷V   Bank   (7)
 
         [0089]    Since each outlet&#39;s {right arrow over (Q)} could be either positive (+) or negative (−) in direction, the total effect of the reactive power can either be constructive or destructive. For example, consider two outlets on a bank such that {right arrow over (Q)} 1 =10∠+90° and {right arrow over (Q)} 2 =10∠−90°. When both outlets are drawing power, their reactive powers are equal in magnitude yet opposite in direction. This effectively cancels the reactive power on the bank. 
         [0090]    Due to this synergistic effect visualized in  FIG. 18 , the apparent power {right arrow over (S)} must be calculated using the individual vectors {right arrow over (P)} and {right arrow over (Q)} as described in equation (6). It may be found that the resulting vector {right arrow over (S)} has an improved power factor (cos θ). 
       Three Phase Fundamentals 
       [0091]    Three phase power circuits are of two types: Wye and Delta. Although similar in the power they provide, their analysis requirements are different.  FIG. 19  shows a Wye and a Delta circuit superimposed to highlight the similarities and the differences. Three phase power is comprised of three separate AC waves that are phase shifted by 120 degrees and superimposed. Each wave is defined by equation (8): 
         [0000]        f ( t )= A  sin(ω t+φ ))  (8)
 
         [0000]    where 
         [0092]    f(t) is the instantaneous voltage at a given time t, 
         [0093]    A is the peak amplitude, 
         [0094]    ω is the angular velocity given by 2πf, 
         [0095]    f is the frequency (in Hertz), and 
         [0096]    φ is the phase shift. 
         [0000]    The relationship between these phases is shown in  FIG. 20 . 
         [0097]    The set of line-to-neutral and line-to-line voltages can be described using vectors. For convention purposes, the phase shift of V an  is always equal to zero. Equations (9) thru (14) show both the mathematical definition as well as the ideal conditions (delineated by the operator ≈) for each equation. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             V 
                             -&gt; 
                           
                           an 
                         
                         = 
                         
                           
                             V 
                             an 
                           
                            
                           ∠ 
                            
                           
                               
                           
                            
                           
                             φ 
                             an 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             V 
                             an 
                           
                            
                           ∠0° 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       V 
                       -&gt; 
                     
                     bn 
                   
                   = 
                     
                    
                   
                     
                       
                         V 
                         bn 
                       
                        
                       ∠ 
                        
                       
                           
                       
                        
                       
                         φ 
                         bn 
                       
                     
                     ≈ 
                     
                       
                         V 
                         bn 
                       
                        
                       ∠120° 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       V 
                       -&gt; 
                     
                     cn 
                   
                   = 
                     
                    
                   
                     
                       
                         V 
                         cn 
                       
                        
                       ∠ 
                        
                       
                           
                       
                        
                       
                         φ 
                         cn 
                       
                     
                     ≈ 
                     
                       
                         V 
                         cn 
                       
                        
                       ∠240° 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       V 
                       -&gt; 
                     
                     ab 
                   
                   = 
                     
                    
                   
                     
                       
                         
                           V 
                           -&gt; 
                         
                         an 
                       
                       - 
                       
                         
                           V 
                           -&gt; 
                         
                         bn 
                       
                     
                     = 
                     
                       
                         
                           V 
                           ab 
                         
                          
                         ∠ 
                          
                         
                             
                         
                          
                         
                           φ 
                           ab 
                         
                       
                       ≈ 
                       
                         
                           V 
                           ab 
                         
                          
                         ∠30° 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       V 
                       -&gt; 
                     
                     bc 
                   
                   = 
                     
                    
                   
                     
                       
                         
                           V 
                           -&gt; 
                         
                         bn 
                       
                       - 
                       
                         
                           V 
                           -&gt; 
                         
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                     = 
                     
                       
                         
                           V 
                           bc 
                         
                          
                         ∠ 
                          
                         
                             
                         
                          
                         
                           φ 
                           bc 
                         
                       
                       ≈ 
                       
                         
                           
                             V 
                             bc 
                           
                            
                           ∠ 
                         
                         - 
                         
                           90 
                            
                           ° 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       V 
                       -&gt; 
                     
                     ca 
                   
                   = 
                     
                    
                   
                     
                       
                         
                           V 
                           -&gt; 
                         
                         cn 
                       
                       - 
                       
                         
                           V 
                           -&gt; 
                         
                         an 
                       
                     
                     = 
                     
                       
                         
                           V 
                           ca 
                         
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                         ∠ 
                          
                         
                             
                         
                          
                         
                           φ 
                           ca 
                         
                       
                       ≈ 
                       
                         
                           
                             V 
                             ca 
                           
                            
                           ∠ 
                         
                         - 
                         
                           210 
                            
                           ° 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
         [0098]    In the United States, the typical line-to-neutral voltage is 120 VAC, resulting in a line-to-line voltage of 208 VAC. In many European countries, the typical line-to-neutral voltage is 230 VAC, with a corresponding line-to-line voltage of 400 VAC. The ratio between these voltage pairs is identical: 
         [0000]    
       
         
           
             
               
                 208 
                  
                 
                     
                 
                  
                 VAC 
               
               
                 120 
                  
                 
                     
                 
                  
                 VAC 
               
             
             = 
             
               
                 
                   400 
                    
                   
                       
                   
                    
                   VAC 
                 
                 
                   230 
                    
                   
                       
                   
                    
                   VAC 
                 
               
               = 
               
                 3 
               
             
           
         
       
     
         [0099]    Each single phase bank is connected to the three phase vectors in one of two ways: a Wye (line-to-neutral) or Delta (line-to-line) configuration. 
       Three Phase Wye Circuits 
       [0100]      FIG. 21  shows a Wye circuit configuration, with the definitions of the various angles used in the following analysis shown in  FIG. 22 . 
       Calculating the Line Currents 
       [0101]    In a Wye system, each bank is connected between one of the lines (A, B or C) and neutral (N). For metering purposes, a Wye system is convenient, since simple vector math is adequate to determine the contribution of each bank to each line. 
         [0000]        {right arrow over (I)}   a =Σ i   {right arrow over (I)}   Bank     —     i where the absolute∠θ′ a =φ an +θ an   (15)
 
         [0000]        {right arrow over (I)}   b =Σ j   {right arrow over (I)}   Bank     —     j where the absolute∠θ′ b =φ bn +θ bn   (16)
 
         [0000]        {right arrow over (I)}   c =Σ k   {right arrow over (I)}   Bank     —     k where the absolute∠θ′ c =φ cn +θ cn   (17)
 
         [0000]      {right arrow over (V)} an ={right arrow over (V)} Bank     —     i  for any bank i that is connected between  {right arrow over (V)}   an   (18)
 
         [0000]      {right arrow over (V)} bn ={right arrow over (V)} Bank     —     j  for any bank j that is connected between  {right arrow over (V)}   bn   (19)
 
         [0000]      {right arrow over (V)} cn ={right arrow over (V)} Bank     —k     k  for any bank k that is connected between  {right arrow over (V)}   cn   (20)
 
         [0102]    By applying Kirchoff&#39;s laws, we are able gain additional information about the resulting three phase circuit. 
         [0000]        {right arrow over (I)}   a   {right arrow over (I)}   b   +{right arrow over (I)}   c   ={right arrow over (I)}   n   {right arrow over (I)}   n =0 when the loads are balanced  (21)
 
         [0000]      and 
         [0000]        {right arrow over (V)}   an   +{right arrow over (V)}   bn   +{right arrow over (V)}   cn =0  (22)
 
         [0103]    In equations (15), (16) and (17), we are able to calculate the relative angle θ ln  for each {right arrow over (I)} ln . However, equation (21) requires a vector that is referenced to an absolute zero degrees. As such, the angles θ′ ln , have been defined for each {right arrow over (I)} ln  with respect to the absolute φ ln . 
       Phase Angles 
       [0104]    Recalling that φ an =0° by definition, φ bn  and φ cn  must be measured or approximated. 
       Measuring φ ln    
       [0105]    Measuring φ is fairly straight-forward, but requires special hardware to monitor the zero-crossings of the sine wave. For example, using an analog-to-digital converter (ADC), we read the instantaneous value of V an . When this value crosses the X-axis (i.e. equals zero) and the last value was above the X-axis (i.e. positive), then the waveform is said to have a “negative” slope and a zero-crossing has occurred. The frequency (in Hertz) of the sine wave can be determined by dividing one by the amount of time between zero-crossings on the same wave. The phase shift between V an  and its related waves V bn  and V cn  can be found by dividing one by the amount of time between a zero-crossing of V an  and a zero-crossing of V bn  or V cn . 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                     = 
                     
                       1 
                       
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                     where 
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                     and 
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                     are 
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                     consecutive 
                      
                     
                         
                     
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                     of 
                      
                     
                         
                     
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                       V 
                       an 
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
             
               
                 
                   
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                     bn 
                   
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                      
                     ° 
                     × 
                     f 
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                             a 
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                     where 
                      
                     
                         
                     
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                         b 
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                      
                     
                         
                     
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                     before 
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                       t 
                       
                         a 
                          
                         
                             
                         
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                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
             
               
                 
                   
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                     cn 
                   
                   = 
                   
                     360 
                      
                     ° 
                     × 
                     f 
                     × 
                     
                       [ 
                       
                         
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                             a 
                              
                             
                                 
                             
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                       ] 
                     
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                     where 
                      
                     
                         
                     
                      
                     
                       t 
                       
                         c 
                          
                         
                             
                         
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                         1 
                       
                     
                      
                     
                         
                     
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                     occurs 
                      
                     
                         
                     
                      
                     before 
                      
                     
                         
                     
                      
                     
                       t 
                       
                         a 
                          
                         
                             
                         
                          
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
           
         
       
     
         [0106]    In the system described in the hereinbefore referenced Verges &#39;881 U.S. patent application, measuring these zero-crossings can be accomplished at the Network Interface Card (NIC) interface if each bank assembly notifies the NIC at its zero-crossing. Because the NIC  1510  provides a constant time reference apart from each bank assembly, it is able to make the calculations described in Equations (23), (24) and (25). 
       Estimating φ ln    
       [0107]    φ may also be approximated since it is a very tightly controlled fundamental parameter of three phase sources. Table 1 and Table 2 recommend values of φ. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Table 1 - Estimated Values of φ ln  for abc “Positive” Sequence 
               
             
          
           
               
                   
                 ∠ 
                 Value 
               
               
                   
                   
               
             
          
           
               
                   
                 φ an   
                 0° 
               
               
                   
                 φ bn   
                 −120° 
               
               
                   
                 φ cn   
                 −240° 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Estimated Values of φ ln  for acb “Negative” Sequence 
               
             
          
           
               
                   
                 ∠ 
                 Value 
               
               
                   
                   
               
             
          
           
               
                   
                 φ an   
                 0° 
               
               
                   
                 φ bn   
                 −240° 
               
               
                   
                 φ cn   
                 −120° 
               
               
                   
                   
               
             
          
         
       
     
         [0108]    Any error in φ ln  results in an error of {right arrow over (I)} ln . The individual vectors {right arrow over (I)} a , {right arrow over (I)} b  and {right arrow over (I)} c  will not be affected since they are calculated with respect to their voltage vectors {right arrow over (V)} ln . 
       Three Phase Delta Circuits 
       [0109]    Calculating the Line Currents 
         [0110]    Referring now to  FIG. 23  and  FIG. 24 , in a Delta system, each bank is connected between two pairs of the lines (A, B or C). 
         [0000]        {right arrow over (V)}   ab   ={right arrow over (V)}   an   −{right arrow over (V)}   bn where  {right arrow over (V)}   ab   ={right arrow over (V)}   Bank     —     i  for any bank i connected between  {right arrow over (V)}   ab   (26)
 
         [0000]        {right arrow over (V)}   bc   ={right arrow over (V)}   bn   −{right arrow over (V)}   cn where  {right arrow over (V)}   bc   ={right arrow over (V)}   Bank     —     j  for any bank j connected between  {right arrow over (V)}   bc   (27)
 
         [0000]        {right arrow over (V)}   ca   ={right arrow over (V)}   cn   −{right arrow over (V)}   an where  {right arrow over (V)}   ca   ={right arrow over (V)}   Bank     —     k  for any bank k connected between {right arrow over (V)} ca   (28)
 
         [0000]    See Equation (43) for a method to estimate {right arrow over (V)} ln  if it is not measured. 
         [0111]    Though we measure I ll , determining the line currents is much more difficult. Arthur Edwin Kennelly in “Equivalence of triangles and stars in conducting networks”,  Electrical World and Engineer, Volume  34, pp 413-414 in 1899 proposed a set of equations to convert the Delta system to a Wye system, which is simpler to solve. To compute I ln , st we must transform the Delta-based I ll  into its Wye-based equivalent. This is accomplished by using the resistance of each load. 
         [0000]    
       
         
           
             
               
                 
                   
                     R 
                     ab 
                   
                   = 
                   
                     
                       V 
                       ab 
                     
                     
                       I 
                       ab 
                     
                   
                 
               
               
                 
                   ( 
                   29 
                   ) 
                 
               
             
             
               
                 
                   
                     R 
                     bc 
                   
                   = 
                   
                     
                       V 
                       bc 
                     
                     
                       I 
                       bc 
                     
                   
                 
               
               
                 
                   ( 
                   30 
                   ) 
                 
               
             
             
               
                 
                   
                     R 
                     ca 
                   
                   = 
                   
                     
                       V 
                       ca 
                     
                     
                       I 
                       ca 
                     
                   
                 
               
               
                 
                   ( 
                   31 
                   ) 
                 
               
             
             
               
                 
                   
                     R 
                     an 
                   
                   = 
                   
                     
                       
                         R 
                         ab 
                       
                       × 
                       
                         R 
                         ca 
                       
                     
                     
                       
                         R 
                         ab 
                       
                       + 
                       
                         R 
                         bc 
                       
                       + 
                       
                         R 
                         ca 
                       
                     
                   
                 
               
               
                 
                   ( 
                   32 
                   ) 
                 
               
             
             
               
                 
                   
                     R 
                     bn 
                   
                   = 
                   
                     
                       
                         R 
                         bc 
                       
                       × 
                       
                         R 
                         ab 
                       
                     
                     
                       
                         R 
                         ab 
                       
                       + 
                       
                         R 
                         bc 
                       
                       + 
                       
                         R 
                         ca 
                       
                     
                   
                 
               
               
                 
                   ( 
                   33 
                   ) 
                 
               
             
             
               
                 
                   
                     R 
                     cn 
                   
                   = 
                   
                     
                       
                         R 
                         ca 
                       
                       × 
                       
                         R 
                         bc 
                       
                     
                     
                       
                         R 
                         ab 
                       
                       + 
                       
                         R 
                         bc 
                       
                       + 
                       
                         R 
                         ca 
                       
                     
                   
                 
               
               
                 
                   ( 
                   34 
                   ) 
                 
               
             
           
         
       
     
         [0112]    The current on each line can then be calculated using the conservation of apparent power. 
         [0000]    
       
         
           
             
               
                 
                   
                     I 
                     an 
                   
                   = 
                   
                     
                       V 
                       an 
                     
                     
                       R 
                       an 
                     
                   
                 
               
               
                 
                   ( 
                   35 
                   ) 
                 
               
             
             
               
                 
                   
                     I 
                     bn 
                   
                   = 
                   
                     
                       V 
                       bn 
                     
                     
                       R 
                       bn 
                     
                   
                 
               
               
                 
                   ( 
                   36 
                   ) 
                 
               
             
             
               
                 
                   
                     I 
                     cn 
                   
                   = 
                   
                     
                       V 
                       cn 
                     
                     
                       R 
                       cn 
                     
                   
                 
               
               
                 
                   ( 
                   37 
                   ) 
                 
               
             
           
         
       
     
         [0113]    Unfortunately, Kennelly&#39;s equations assume that current exists in each line-to-line connection. As I ll  approaches zero, the resistance R ll  approaches infinity. If the line-to-line load is severely unbalanced (meaning that I ll  is not split evenly between its two line-line-to-neutral components), there is no good od solution other than to measure the line currents individually. Blondel&#39;s Theorem indicates how many measurements will need to be made: N−1 where N is the number of lines. 
         [0114]    It may be adequate to assume that I ll  splits evenly. In this case, the line currents may be calculated using Equations (38), (39) and (40).  FIG. 25  visualizes the complex interaction between the line-to-line currents and the line-to-neutral currents (the waves with larger peaks are the line-to-neutral currents.) 
         [0000]        {right arrow over (I)}   an   ={right arrow over (I)}   ab   −{right arrow over (I)}   ca   (38)
 
         [0000]        {right arrow over (I)}   bn   ={right arrow over (I)}   bc   −{right arrow over (I)}   ab   (39)
 
         [0000]        {right arrow over (I)}   cn   ={right arrow over (I)}   ca   −{right arrow over (I)}   bc   (40)
 
       Phase Angles 
       [0115]    Like in the previous section on Wye circuits, φ plays a critical role in determining information here. In addition to the line-to-neutral φ that was described, we must also consider the line-to-line φ. We are faced with a choice of calculating, measuring or estimating φ ll . 
         [0000]    Calculating φ ll  from φ ln    
         [0116]    If one measures φ ln  and V ln , then φ ll  can be calculated very accurately using vector addition. See equations (26)(26), (27) and (28). 
       Measuring φ ll    
       [0117]    Like φ ln , φ ll  can be measured by calculating the time difference in zero-crossings of the voltage waves V ll . 
         [0000]      φ′ ll =360 °×f×[t   x1   −t   y1 ]  (41)
 
         [0118]    This time difference will result in φ′ ll , also known as the relative offset of φ ll . To calculate V ll , we need the difference in the relative offset and the absolute offset. 
         [0000]      φ offset =φ ll −φ′ ll   (42)
 
         [0119]    This offset can either be measured (by comparing the zero-crossings of V an  and V ab ) or estimated to thirty degrees for an abc sequence or minus thirty degrees for an acb sequence. 
       Estimating φ ll    
       [0120]    We can take advantage of the real-world commonality between most three phase systems and estimate φ. If we assume that the voltage in all V ll  is balanced within an acceptable threshold, then we can approximate a common voltage V zn  as described in Equation (43). 
         [0000]    
       
         
           
             
               
                 
                   
                     V 
                     zn 
                   
                   = 
                   
                     
                       1 
                       
                         3 
                       
                     
                      
                     
                       [ 
                       
                         
                           
                             V 
                             ab 
                           
                           + 
                           
                             V 
                             bc 
                           
                           + 
                           
                             V 
                             ca 
                           
                         
                         3 
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   43 
                   ) 
                 
               
             
           
         
       
     
         [0000]    V zn  can then be used to describe V an , V bn  and V ln . Because V ln  is then equal, φ ln  is then equal to the values presented in Tables 1 and 2. φ ll  can also be approximated using Table 3 and Table 4. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Estimated Values of φ ll  for abc “Positive” Sequence 
               
             
          
           
               
                   
                 ∠ 
                 Value 
               
               
                   
                   
               
             
          
           
               
                   
                 φ ab   
                 30° 
               
               
                   
                 φ bc   
                 −90° 
               
               
                   
                 φ ca   
                 −210° 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Estimated Values of φ ll  for acb “Negative” Sequence 
               
             
          
           
               
                   
                 ∠ 
                 Value 
               
               
                   
                   
               
             
          
           
               
                   
                 φ ab   
                 −30° 
               
               
                   
                 φ bc   
                 −150° 
               
               
                   
                 φ ca   
                 −270° 
               
               
                   
                   
               
             
          
         
       
     
       Three Phase Wye 
       [0121]    As an example, we calculate the individual line information for a three phase power distribution unit that contains twelve outlets, three banks, and one three phase input cord. For this example, assume that the outlets are evenly distributed across the banks; that is, four outlets per bank. Table 5 presents the measured outlet data. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 Example Outlet Data for Three Phase Wye PDU 
               
             
          
           
               
                 Bank 
                 Outlet 
                 V 
                 I 
                 θ 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 120 
                 1 
                 0° 
               
               
                   
                 2 
                   
                 2 
                 10° 
               
               
                   
                 3 
                   
                 0 
                 20° 
               
               
                   
                 4 
                   
                 3 
                 −10° 
               
               
                 2 
                 5 
                 117 
                 4 
                 −30° 
               
               
                   
                 6 
                   
                 8 
                 −20° 
               
               
                   
                 7 
                   
                 2 
                 60° 
               
               
                   
                 8 
                   
                 1 
                 10° 
               
               
                 2 
                 9 
                 112 
                 5 
                 80° 
               
               
                   
                 10 
                   
                 2 
                 30° 
               
               
                   
                 11 
                   
                 3 
                 −45° 
               
               
                   
                 12 
                   
                 6 
                 −20° 
               
               
                   
               
             
          
         
       
     
         [0122]    We now can find: 
         [0123]    {right arrow over (P)} Bank1 ≈711∠0°W from Equation (4) 
         [0124]    {right arrow over (Q)} Bank1 ≈21∠−90°VAR from Equation (5) 
         [0125]    S Bank1 ≈711VA from Equation (6) 
         [0000]    
       
         
           
             
               θ 
               
                 Bank 
                  
                 
                     
                 
                  
                 1 
               
             
             = 
             
               
                 
                   tan 
                   
                     - 
                     1 
                   
                 
                  
                 
                   ( 
                   
                     
                       
                         - 
                         21 
                       
                        
                       
                           
                       
                        
                       VAR 
                     
                     
                       711 
                        
                       
                           
                       
                        
                       W 
                     
                   
                   ) 
                 
               
               ≈ 
               
                 
                   - 
                   2 
                 
                  
                 ° 
               
             
           
         
       
     
         [0126]    I Bank1 ≈6A from Equation (7) 
         [0127]    {right arrow over (P)} Bank2 ≈1,517∠0°W 
         [0128]    {right arrow over (Q)} Bank2 ≈331∠−90°VAR 
         [0129]    S Bank2 ≈1,553VA 
         [0000]    
       
         
           
             
               θ 
               
                 Bank 
                  
                 
                     
                 
                  
                 2 
               
             
             = 
             
               
                 
                   tan 
                   
                     - 
                     1 
                   
                 
                  
                 
                   ( 
                   
                     
                       
                         - 
                         331 
                       
                        
                       
                           
                       
                        
                       VAR 
                     
                     
                       1 
                       , 
                       517 
                        
                       
                           
                       
                        
                       W 
                     
                   
                   ) 
                 
               
               ≈ 
               
                 
                   - 
                   12 
                 
                  
                 ° 
               
             
           
         
       
     
         [0130]    I Bank2 ≈13A 
         [0131]    {right arrow over (P)} Bank3 ≈1,264∠0°W 
         [0132]    {right arrow over (Q)} Bank3 ≈214∠90°VAR 
         [0133]    S Bank3 ≈1,282VA 
         [0000]    
       
         
           
             
               θ 
               
                 Bank 
                  
                 
                     
                 
                  
                 3 
               
             
             = 
             
               
                 
                   tan 
                   
                     - 
                     1 
                   
                 
                  
                 
                   ( 
                   
                     
                       
                         - 
                         214 
                       
                        
                       
                           
                       
                        
                       VAR 
                     
                     
                       1 
                       , 
                       264 
                        
                       
                           
                       
                        
                       W 
                     
                   
                   ) 
                 
               
               ≈ 
               
                 9 
                  
                 ° 
               
             
           
         
       
     
         [0134]    I Bank3 ≈11A 
         [0135]    {right arrow over (V)} an =120∠0° from Equation (18) and Table?? 
         [0136]    {right arrow over (I)} a =6∠−2° from Equation (15) 
         [0137]    {right arrow over (V)} bn =117∠−120° from Equation (19) and Table ?? 
         [0138]    {right arrow over (I)} b =13∠−12° from Equation (16) 
         [0139]    {right arrow over (V)} cn =122∠−240° from Equation (20) and Table?? 
         [0140]    {right arrow over (I)} c ={right arrow over (I)} Bank3 =11∠2° from Equation (17) 
       Three Phase Delta 
       [0141]    Next we calculate the individual line information for a three phase power distribution unit that contains twelve outlets, three banks, and one three phase input cord. Assume that the outlets are evenly distributed across the banks; that is, four outlets per bank. Table 6 contains the measured outlet data. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 Example Outlet Data for Three Phase Delta PDU 
               
             
          
           
               
                 Bank 
                 Outlet 
                 V 
                 I 
                 θ 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 207 
                 1 
                 0° 
               
               
                   
                 2 
                   
                 2 
                 10° 
               
               
                   
                 3 
                   
                 0 
                 20° 
               
               
                   
                 4 
                   
                 3 
                 −10° 
               
               
                 2 
                 5 
                 211 
                 4 
                 −30° 
               
               
                   
                 6 
                   
                 8 
                 −20° 
               
               
                   
                 7 
                   
                 2 
                 60° 
               
               
                   
                 8 
                   
                 1 
                 10° 
               
               
                 2 
                 9 
                 209 
                 5 
                 80° 
               
               
                   
                 10 
                   
                 2 
                 30° 
               
               
                   
                 11 
                   
                 3 
                 −45° 
               
               
                   
                 12 
                   
                 6 
                 −20° 
               
               
                   
               
             
          
         
       
     
         [0142]    Now we can find: 
         [0143]    {right arrow over (P)} Bank1 ≈1,226∠0°W from Equation (4) 
         [0144]    {right arrow over (Q)} Bank1 ≈36∠−90°VAR from Equation (5) 
         [0145]    S Bank1 ≈1,227VA from Equation (6) 
         [0000]    
       
         
           
             
               θ 
               
                 Bank 
                  
                 
                     
                 
                  
                 1 
               
             
             = 
             
               
                 
                   tan 
                   
                     - 
                     1 
                   
                 
                  
                 
                   ( 
                   
                     
                       
                         - 
                         36 
                       
                        
                       
                           
                       
                        
                       VAR 
                     
                     
                       1 
                       , 
                       226 
                        
                       
                           
                       
                        
                       W 
                     
                   
                   ) 
                 
               
               ≈ 
               
                 
                   - 
                   2 
                 
                  
                 ° 
               
             
           
         
       
     
         [0146]    I Bank1 ≈6A from Equation (7) 
         [0147]    {right arrow over (P)} Bank2 ≈2,736∠0°W 
         [0148]    {right arrow over (Q)} Bank2 ≈597∠−90°VAR 
         [0149]    S Bank2 ≈2,800VA 
         [0000]    
       
         
           
             
               θ 
               
                 Bank 
                  
                 
                     
                 
                  
                 2 
               
             
             = 
             
               
                 
                   tan 
                   
                     - 
                     1 
                   
                 
                  
                 
                   ( 
                   
                     
                       
                         - 
                         597 
                       
                        
                       
                           
                       
                        
                       VAR 
                     
                     
                       2 
                       , 
                       736 
                        
                       
                           
                       
                        
                       W 
                     
                   
                   ) 
                 
               
               ≈ 
               
                 
                   - 
                   12 
                 
                  
                 ° 
               
             
           
         
       
     
         [0150]    I Bank2 ≈13A 
         [0151]    {right arrow over (P)} Bank3 ≈2,165∠0°W 
         [0152]    {right arrow over (Q)} Bank3 ≈367∠90°VAR 
         [0153]    S Bank3 ≈2,196VA 
         [0000]    
       
         
           
             
               θ 
               
                 Bank 
                  
                 
                     
                 
                  
                 3 
               
             
             = 
             
               
                 
                   tan 
                   
                     - 
                     1 
                   
                 
                  
                 
                   ( 
                   
                     
                       367 
                        
                       
                           
                       
                        
                       VAR 
                     
                     
                       2 
                       , 
                       165 
                        
                       
                           
                       
                        
                       W 
                     
                   
                   ) 
                 
               
               ≈ 
               
                 9 
                  
                 ° 
               
             
           
         
       
     
         [0154]    I Bank3 ≈11A 
         [0155]    Since the voltages on all the banks are relatively close, we can use Equation (43) to estimate the line-to-neutral voltages and phase angles. 
         [0156]    {right arrow over (V)} an ≈121∠0° from Equation (43) and Table 1 
         [0157]    {right arrow over (V)} bn ≈121∠−120° from Equation (43) and Table 1 
         [0158]    {right arrow over (V)} cn ≈121≈−240° from Equation (43) and Table 1 
         [0159]    Assuming that the resistance of the line-to-line loads are roughly equal, we can estimate the current in each line. 
         [0160]    {right arrow over (I)} an ≈15∠0° from Equation (38) and Table 3 
         [0161]    {right arrow over (I)} bn ≈10∠−120° from Equation (39) and Table 3 
         [0162]    {right arrow over (I)} cn ≈19∠−240° from Equation (40) and Table 3 
         [0163]    The results of the above-described method may be displayed on the touch screen  108 , stored into a database, or both. Looking to  FIG. 26 , outlet energy meters  1300  send their data to the NIC  1510  via the CAN data link, as previously described  1602 . The NIC  1510  saves the data into a power data database  2604 . The database is stored in a mass storage device, for example a hard disc drive, or in other embodiments is stored in electronic memory, or both. The NIC then performs the above-described calculations  2606 . The data may optionally then be displayed to a viewer on a touch screen  108  or remotely on a monitor, either periodically or upon request. For an example wherein the data is presented on a touch screen  108 , the screen is divided into regions to display individual parametric data  2608 . Then for each region  2610  the description of the parameter  2612  and the value of the data found  2614  are displayed. The display may then sleep  2616  for a predetermined time, rerun upon request by the NIC  1510 , request by a viewer, request by a remote system, and the like. 
       RESOLUTION OF CONFLICTS 
       [0164]    If any disclosures are incorporated herein by reference and such incorporated disclosures conflict in part or whole with the present disclosure, then to the extent of conflict, and/or broader disclosure, and/or broader definition of terms, the present disclosure controls. If such incorporated disclosures conflict in part or whole with one another, then to the extent of conflict, the later-dated disclosure controls.