WO2014185921A1

WO2014185921A1 - Systems and methods for meter placement in power grid networks

Info

Publication number: WO2014185921A1
Application number: PCT/US2013/041403
Authority: WO
Inventors: Dimitri Marinakis; Kui WU; Sardar ALI; Kyle WESTON
Original assignee: Schneider Electric USA, Inc.
Priority date: 2013-05-16
Filing date: 2013-05-16
Publication date: 2014-11-20

Abstract

Systems and methods for placement of power meters in a power distribution network are disclosed. In one example, the method comprises modeling the power distribution network as a data-driven network comprising a plurality of nodes and a plurality of power links connecting individual nodes of the plurality of nodes, receiving at a computer system data pertaining to network topology and a number of power meters to be placed in the power distribution network, and calculating, by the computer system, placement of at least one power meter within the power distribution system.

Description

SYSTEMS AND METHODS FOR METER PLACEMENT IN POWER GRID

NETWORKS

BACKGROUND

Field of the Invention

At least one embodiment in accordance with the present invention relates generally to systems and methods for monitoring power networks, and more specifically, to systems and methods for optimizing placement of meters in power networks. Discussion of Related Art

Electrical power networks are one of the critical infrastructures of our society, which relies on reliable supply of electricity. Because of the essential nature of the power supply, there is a need to monitor operational and electrical characteristics of power networks. The ability to collect, analyze, and respond to information about the electrical power system can improve power quality, reliability, minimize equipment loss, decrease scrap, and ultimately save time and money. To that end, monitoring devices were developed to measure and report such information. Monitoring devices, such as power meters, are deployed in one or more segments of the power network to monitor and measure various characteristics of the power network. The various characteristics of the electrical signal, such as voltage, current, waveform distortion, power, passing through the conductors, and the data from each monitoring device is analyzed to evaluate potential quality-related issues.

SUMMARY

Power quality is a crucial part in the reliability of power distribution system. Due to the high cost of measurement devices, monitoring of power quality is essential to evaluating quality-related issues. According to various embodiments, systems and methods disclosed herein determine designated locations to deploy measurement devices on suitable power links to reduce the uncertainty of power quality values on non-monitored power links. According to at least one embodiment, one or more power networks are modeled as data-driven networks. Using entropy based measurements and the Bayesian network model, the various methods disclosed herein calculate the most suitable power links for power meter placement. The systems and methods, according to these embodiments, are simple, efficient, and significantly reduce the uncertainty of power quality values on non-monitored power links. According to one aspect, a method for placement of power meters in a power distribution network is disclosed. In one example, the method comprises modeling the power distribution network as a data-driven network comprising a plurality of nodes and a plurality of power links connecting individual nodes of the plurality of nodes, receiving at a computer system data pertaining to network topology and a number of power meters to be placed in the power distribution network, and calculating placement of at least one power meter within the power distribution system. In at least one example, the method further includes providing an indication of the placement of the at least one power meter to a display, the indication is based on the calculated placement.

In one example, the method further includes placing a power meter into the power distribution network in the location associated with the indication and receiving data related to power quality from the power meter. In some examples, the method further includes calculating placement of another power meter, different from the at least one power meter, within the power distribution system. In the method, the placement of the at least one power meter is configured to affect the placement of the another power meter. In the method, the network topology includes at least one of tree network topology, and line network topology.

In another example, the method further comprises coupling a communications network between a power monitoring system and the computer system and transferring data related to the power quality measured by the at least one power meter over the

communications network. In at least example, the method further comprises determining power quality distribution function of entropy for the plurality of power links. In some examples, for every node of the plurality of nodes, the method further comprises calculating uncertainty of power quality on the plurality of power links.

In one example, for every node the method further comprises calculating entropy for child power links in the plurality of links, and comparing the entropy with a maximum reduction value. In some examples, the method further comprises determining one power link of the plurality of power links that results in maximum entropy reduction in the power distribution network.

In another example, the method further comprises calculating a set of K samples using a Monte Carlo method for each power link within the power distribution network. In some example, the method comprises calculating a power quantity associated with at least one metered location using Monte Carlo simulation, and calculating a power quality associated with at least one non-metered locations as a function of the calculated power quantity observed at the at least one metered location. In at least one example, the method comprises comparing the metered power quantity with the non-metered power quantity to determine a comparison result, and calculating an error rate for each node of the plurality of nodes based on the comparison result. In some example, the method comprises sorting the error rate for the plurality of the nodes from highest error rate to lowest error rate. In one example, the method comprises determining placement of at least one power meter as a location associated with a node with the highest error rate.

According to another aspect, a system for placement of power meters in a power distribution network is disclosed. In one example, the system comprises a display, a power monitoring system having a plurality of power monitors coupled to components of the power distribution system, and a controller coupled to the power monitoring system and the display and configured to model the power distribution network as a data-driven network comprising a plurality of nodes and a plurality of power links connecting individual nodes of the plurality of nodes, receive data pertaining to network tree topology and a number of power meters to be placed in the power distribution network, determine placement of at least one power meter within the power distribution system, and provide an indication of the placement of the at least one power meter for the display.

In some examples, the controller is further configured to calculate placement of another power meter, different from the at least one power meter, within the power distribution system. In some example, the placement of the at least one power meter is configured to affect the placement of the another power meter. In the system, the network topology includes at least one of tree network topology, and line network topology.

In at least one example, the controller is further configured to receive data related to the power quality measured by the at least one power meter from a communications network. In another example, the controller further configured to determine power quality distribution function of entropy for the plurality of power links. In another example, the controller is further configured to calculate uncertainty of power quality on the plurality of power links, for every node of the plurality of nodes.

In one example, the controller is further configured to calculate entropy for child power links in the plurality of links for every node and compare the entropy with a maximum reduction value. In yet another example, the controller is further configured to determine one power link of the plurality of power links that results in maximum entropy reduction in the power distribution network. In some examples, the controller is further configured to calculate a set of K samples using a Monte Carlo method for each power link within the power distribution network. In the system, the controller is further configured to calculate a power quantity associated with at least one metered location using Monte Carlo simulation, and calculate a power quality associated with at least one non-metered locations as a function of the calculated power quantity observed at the at least one metered location.

In another example, the controller is further configured to compare the metered power quantity with the non-metered power quantity to determine a comparison result, calculate error rate for each node of the plurality of nodes based on the comparison result, sort the error rate for the plurality of the nodes from highest error rate to lowest error rate and determine placement of at least one power meter as a location associated with a node with the highest error rate.

According to another aspect a non-transitory computer readable medium for placement of power meters in a power distribution network having stored thereon sequences of instruction is disclosed. In one example, the instruction include instructions that will cause a processor to model the power distribution network as a data-driven network comprising a plurality of nodes and a plurality of power links connecting individual nodes of the plurality of nodes, receive data pertaining to network tree topology and a number of power meters to be placed in the power distribution network, calculate placement of at least one power meter within the power distribution system, and provide an indication of the placement of the at least one power meter for display.

In some examples, the non-transitory computer readable medium includes instruction that will cause the processor to calculate placement of another power meter, different from the at least one power meter, within the power distribution system. In some examples, the placement of the at least one power meter is configured to affect the placement of the another power meter. In the medium, the network topology includes at least one of tree network topology, and line network topology.

In at least one example, the non-transitory computer readable medium includes instruction that will cause the processor receive data related to the power quality measured by the at least one power meter from a communications network. In another example, the non- transitory computer readable medium includes instruction that will cause the processor to determine power quality distribution function of entropy for the plurality of power links. In another example, the controller is further configured to calculate uncertainty of power quality on the plurality of power links, for every node of the plurality of nodes.

In one example, the non-transitory computer readable medium includes instruction that will cause the processor to calculate entropy for child power links in the plurality of links for every node and compare the entropy with a maximum reduction value. In yet another example, the non-transitory computer readable medium includes instruction that will cause the processor to determine one power link of the plurality of power links that results in maximum entropy reduction in the power distribution network.

In some examples, the non-transitory computer readable medium includes instruction that will cause the processor to calculate a set of K samples using a Monte Carlo method for each power link within the power distribution network. In the medium, the non-transitory computer readable medium includes instruction that will cause the processor to calculate a power quantity associated with at least one metered location using Monte Carlo simulation, and calculate a power quality associated with at least one non-metered locations as a function of the calculated power quantity observed at the at least one metered location.

In another example, the non-transitory computer readable medium includes instruction that will cause the processor to compare the metered power quantity with the non- metered power quantity to determine a comparison result, calculate error rate for each node of the plurality of nodes based on the comparison result, sort the error rate for the plurality of the nodes from highest error rate to lowest error rate and determine placement of at least one power meter as a location associated with a node with the highest error rate.

Still other aspects, embodiments, and advantages of these exemplary aspects and embodiments, are discussed in detail below. Any embodiment disclosed herein may be combined with any other embodiment in any manner consistent with at least one of the objects, aims, and needs disclosed herein, and references to "an embodiment," "some embodiments," "an alternate embodiment," "various embodiments," "one embodiment" or the like are not necessarily mutually exclusive and are intended to indicate that a particular feature, structure, or characteristic described in connection with the embodiment may be included in at least one embodiment. The appearances of such terms herein are not necessarily all referring to the same embodiment. The accompanying drawings are included to provide illustration and a further understanding of the various aspects and embodiments, and are incorporated in and constitute a part of this specification. The drawings, together with the remainder of the specification, serve to explain principles and operations of the described and claimed aspects and embodiments.

BRIEF DESCRIPTION OF DRAWINGS

Various aspects of at least one embodiment are discussed below with reference to the accompanying figures, which are not intended to be drawn to scale. Where technical features in the figures, detailed description or any claim are followed by references signs, the reference signs have been included for the sole purpose of increasing the intelligibility of the figures, detailed description, and claims. Accordingly, neither the reference signs nor their absence are intended to have any limiting effect on the scope of any claim elements. In the figures, each identical or nearly identical component that is illustrated in various figures is represented by a like numeral. For purposes of clarity, not every component may be labeled in every figure. The figures are provided for the purposes of illustration and explanation and are not intended as a definition of the limits of the invention. In the drawings:

FIG. 1 is a block diagram of one example of a computer system with which various aspects in accord with the present invention may be implemented;

FIG. 2 is a schematic of one example of a distributed system including a power management system;

FIG. 3 is a block diagram of a power grid network in accordance with one embodiment;

FIG. 4 is a block diagram of a model of the power grid network in accordance with one embodiment;

FIG. 5 is a flow diagram of a method of power meter placement in accordance with one embodiment;

FIG. 6 is a flow diagram of another method of power meter placement in accordance with one embodiment;

FIG. 7 is a diagram of the power grid network modeled as a factor graph in accordance with one embodiment;

FIGS. 8A-8D are block diagrams of power grid networks in accordance with various embodiments; and

FIGS. 9A-9E are graphs illustrating error rate associated with devices in the power grid network in accordance with one embodiment. DETAILED DESCRIPTION

As discussed above, due to the society's dependence on electric power provided by large scale electric networks, the reliability of electric networks has become essential.

Reliability evaluation of large-scale power network is challenging due to the existence of multiple electric utilities and the potential of cascading failures of the power networks. One of the most influential factors impacting the reliability and energy saving of power networks is the power quality delivered to and experienced by critical electric equipment. Poor power quality, such as voltage sags, may lead to power outage and service interruptions. Hence, the monitoring of power quality is an important component of assessing and maintaining reliability in power networks.

To improve the reliability of power grid networks, power quality measurement devices, such as power meters, are deployed to closely monitor the power quality on underlying power links. However, it is appreciated that power meters can be expensive, making it impractical to deploy power meters to monitor every segment of the electric network. Instead, power quality in non- metered grid locations may be inferred given data obtained from the measured locations.

Systems and methods disclosed herein include iterative methods to identify network segments suitable for power meter placement. In some embodiments, the iterative methods use a fixed number of available power meters, which are selectively placed on predetermined segments of the network for monitoring, such that power quality can be inferred as accurately as possible in the remaining non-monitored segments of the network. During each iteration, the computer system identifies the network segment that suffers from the most unpredictable power quality given the meters deployed so far. The power meter is then deployed at that location.

The power meters deployed within the power grid network can be used to monitor and provide data that allows one or more systems to determine power quality of the power network. According to one embodiment, the power quality of a power network can be calculated to predict the propagation of power quality events through a power grid, as described in PCT Application No. PCT/US2011/065554, titled CO-LOCATION

ELECTRICAL ARCHITECTURE, filed on December 16, 2011, which is assigned to the assignee of the present application, and which is incorporated herein by reference in its entirety (referred to herein as "the PCT/US2011/065554 application"). The model described in the PCT/US2011/065554 application assumes that time is sliced into units of consistent duration and power quality is discretized into a specific class. The power quality assigned to each time slice is characterized at the most extreme event. The PCT/US2011/065554 application also introduces the concept of a device specific transfer function that specifies how a power quality event experienced at the input of an electrical component will propagates through the component.

Some of the concepts of device specific transfer functions described in the

PCT/US2011/065554 application are used in the methods and systems described herein to determine optimal placement of power meters. The power meters optimally placed within the power network can be used to calculate a Power Reliability Index (PRI), as described in the PCT/US2011/065554 application, which is a real-time metric that summarizes the overall risk or performance of reliability of the electrical network that can be calculated and configured to provide users. The optimal placement of power meters allows for monitoring and recording power quality results in more reliable power grid networks that are cost effective to implement and maintain.

The aspects disclosed herein in accordance with the present invention, are not limited in their application to the details of construction and the arrangement of components set forth in the following description or illustrated in the drawings. These aspects are capable of assuming other embodiments and of being practiced or of being carried out in various ways. Examples of specific implementations are provided herein for illustrative purposes only and are not intended to be limiting. In particular, acts, elements and features discussed in connection with any one or more embodiments are not intended to be excluded from a similar role in any other embodiments.

For example, according to one embodiment of the present invention, a computer system is configured to perform any of the functions described herein, including but not limited to, configuring, modeling and presenting information regarding specific data center configurations. Further, computer systems in embodiments may be used to automatically measure environmental parameters in a data center, and control equipment, such as chillers or coolers to optimize performance. Moreover, the systems described herein may be configured to include or exclude any of the functions discussed herein. Thus the invention is not limited to a specific function or set of functions. Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use herein of "including," "comprising," "having," "containing," "involving," and variations thereof is meant to encompass the items listed thereafter and equivalents thereof as well as additional items.

Computer System

Various aspects and functions described herein in accordance with the present invention may be implemented as hardware or software on one or more computer systems. There are many examples of computer systems currently in use. These examples include, among others, network appliances, personal computers, workstations, mainframes, networked clients, servers, media servers, application servers, database servers and web servers. Other examples of computer systems may include mobile computing devices, such as cellular phones and personal digital assistants, and network equipment, such as load balancers, routers and switches. Further, aspects in accordance with the present invention may be located on a single computer system or may be distributed among a plurality of computer systems connected to one or more communications networks.

For example, various aspects and functions may be distributed among one or more computer systems configured to provide a service to one or more client computers, or to perform an overall task as part of a distributed system. Additionally, aspects may be performed on a client-server or multi-tier system that includes components distributed among one or more server systems that perform various functions. Thus, the invention is not limited to executing on any particular system or group of systems. Further, aspects may be implemented in software, hardware or firmware, or any combination thereof. Thus, aspects in accordance with the present invention may be implemented within methods, acts, systems, system elements and components, using a variety of hardware and software configurations, and the invention is not limited to any particular distributed architecture, network, or communication protocol.

FIG. 1 shows a block diagram of a distributed computer system 100, in which various aspects and functions in accord with the present invention may be practiced. Distributed computer system 100 may include one more computer systems. For example, as illustrated, distributed computer system 100 includes computer systems 102, 104 and 106. As shown, computer systems 102, 104 and 106 are interconnected by, and may exchange data through, communication network 108. Network 108 may include any communication network through which computer systems may exchange data. To exchange data using network 108, computer systems 102, 104 and 106 and network 108 may use various methods, protocols and standards, including, among others, token ring, Ethernet, wireless Ethernet, Bluetooth, TCP/IP, UDP, Http, FTP, SNMP, SMS, MMS, SS7, Json, Soap, and Corba. To ensure data transfer is secure, computer systems 102, 104 and 106 may transmit data via network 108 using a variety of security measures including TSL, SSL or VPN among other security techniques. While distributed computer system 100 illustrates three networked computer systems, distributed computer system 100 may include any number of computer systems and computing devices, networked using any medium and communication protocol.

Various aspects and functions in accordance with the present invention may be performed on a plurality of different types of servers. For example, a server may be a physical server, a dedicated server, or a virtual server (or a cloud computing server). A physical server generally includes hardware where an operating system is run. A dedicated server generally includes a service application running on a physical server. For example, a dedicated server may include a web service or file transfer protocol (FTP) service on an operating system, where the service application can be coupled to the physical server. A virtual server can include a service that is independent of physical server hardware. For example, a virtual server may include a partitioning of a physical server into multiple servers, each having the appearance and capabilities as if they were running on their own dedicated server. In one embodiment, there can be one dedicated server operating system per physical server and multiple virtual servers per physical server. A virtual server can run concurrent with (e.g., on top of) a dedicated server.

Various aspects and functions in accordance with the present invention may be implemented as specialized hardware or software executing in one or more computer systems including computer system 102 shown in FIG. 1. As depicted, computer system 102 includes processor 110, memory 112, bus 114, interface 116 and storage 118. Processor 110 may perform a series of instructions that result in manipulated data. Processor 110 may be any commercially available processor, multiprocessor or controller. Some exemplary processors include commercially available processors such as an Intel Xeon, Itanium, Core, Celeron, or Pentium processor, an AMD Opteron processor, an Apple A4 or A5 processor, a Sun UltraSPARC or IBM Power5+ processor and an IBM mainframe chip, but may be any type of processor or controller as many other processors and controllers are available. Processor 110 is connected to other system elements, including one or more memory devices 112, by bus 114. Memory 112 may be used for storing programs and data during operation of computer system 102. Thus, memory 112 may be a relatively high performance, volatile, random access memory such as a dynamic random access memory (DRAM) or static memory (SRAM). However, memory 112 may include any device for storing data, such as a disk drive or other non- volatile storage device. Various embodiments in accordance with the present invention may organize memory 112 into particularized and, in some cases, unique structures to perform the aspects and functions disclosed herein.

Components of computer system 102 may be coupled by an interconnection element such as bus 114. Bus 114 may include one or more physical busses, for example, busses between components that are integrated within a same machine, but may include any communication coupling between system elements including specialized or standard computing bus technologies such as IDE, SCSI, PCI and InfiniBand. Thus, bus 114 enables communications, for example, data and instructions, to be exchanged between system components of computer system 102.

Computer system 102 also includes one or more interface devices 116 such as input devices, output devices and combination input/output devices. Interface devices may receive input or provide output. More particularly, output devices may render information for external presentation. Input devices may accept information from external sources.

Examples of interface devices include keyboards, mouse devices, trackballs, microphones, touch screens, printing devices, display screens, speakers, network interface cards, etc.

Interface devices allow computer system 102 to exchange information and communicate with external entities, such as users and other systems.

Storage system 118 may include a computer readable and writeable nonvolatile storage medium in which instructions are stored that define a program to be executed by the processor. Storage system 118 also may include information that is recorded, on or in, the medium, and this information may be processed by the program. More specifically, the information may be stored in one or more data structures specifically configured to conserve storage space or increase data exchange performance. The instructions may be persistently stored as encoded signals, and the instructions may cause a processor to perform any of the functions described herein. The medium may, for example, be optical disk, magnetic disk or flash memory, among others. In operation, the processor or some other controller may cause data to be read from the nonvolatile recording medium into another memory, such as memory 112, that allows for faster access to the information by the processor than does the storage medium included in storage system 118. The memory may be located in storage system 118 or in memory 112, however, processor 110 may manipulate the data within the memory 112, and then copies the data to the medium associated with storage system 118 after processing is completed. A variety of components may manage data movement between the medium and integrated circuit memory element and the invention is not limited thereto. Further, the invention is not limited to a particular memory system or storage system.

Although computer system 102 is shown by way of example as one type of computer system upon which various aspects and functions in accordance with the present invention may be practiced, aspects of the invention are not limited to being implemented on the computer system as shown in FIG. 1. Various aspects and functions in accord with the present invention may be practiced on one or more computers having a different architectures or components than that shown in FIG. 1. For instance, computer system 102 may include specially-programmed, special-purpose hardware, such as for example, an application- specific integrated circuit (ASIC) tailored to perform a particular operation disclosed herein. While another embodiment may perform the same function using several general-purpose computing devices running MAC OS System X with Intel processors and several specialized computing devices running proprietary hardware and operating systems.

Computer system 102 may be a computer system including an operating system that manages at least a portion of the hardware elements included in computer system 102.

Usually, a processor or controller, such as processor 110, executes an operating system which may be, for example, a Windows-based operating system, such as, Windows NT, Windows 2000 (Windows ME), Windows XP, Windows Vista or Windows 7 operating systems, available from the Microsoft Corporation, a MAC OS System X operating system or an iOS operating system available from Apple Computer, one of many Linux-based operating system distributions, for example, the Enterprise Linux operating system available from Red Hat Inc., a Solaris operating system available from Sun Microsystems, or a UNIX operating systems available from various sources. Many other operating systems may be used, and embodiments are not limited to any particular implementation.

The processor and operating system together define a computer platform for which application programs in high-level programming languages may be written. These component applications may be executable, intermediate, for example, C-, bytecode or interpreted code which communicates over a communication network, for example, the Internet, using a communication protocol, for example, TCP/IP. Similarly, aspects in accord with the present invention may be implemented using an object-oriented programming language, such as .Net, SmallTalk, Java, C++, Ada, or C# (C-Sharp). Other object-oriented programming languages may also be used. Alternatively, functional, scripting, or logical programming languages may be used.

Additionally, various aspects and functions in accordance with the present invention may be implemented in a non-programmed environment, for example, documents created in HTML, XML or other format that, when viewed in a window of a browser program, render aspects of a graphical-user interface or perform other functions. Further, various embodiments in accord with the present invention may be implemented as programmed or non-programmed elements, or any combination thereof. For example, a web page may be implemented using HTML while a data object called from within the web page may be written in C++. Thus, the invention is not limited to a specific programming language and any suitable programming language could also be used. Further, in at least one embodiment, the tool may be implemented using VBA Excel.

A computer system included within an embodiment may perform additional functions outside the scope of the invention. For instance, aspects of the system may be implemented using an existing commercial product, such as, for example, Database Management Systems such as SQL Server available from Microsoft of Seattle WA., Oracle Database from Oracle of Redwood Shores, CA, and MySQL from MySQL AB of Uppsala, Sweden or integration software such as Web Sphere middleware from IBM of Armonk, NY. However, a computer system running, for example, SQL Server may be able to support both aspects in accord with the present invention and databases for sundry applications not within the scope of the invention. Power Network Architecture

Some embodiments disclosed herein implement a power management system using one or more computer systems, such as the computer systems described below with reference to FIG. 1. FIG. 2 shows one example of distributed power network architecture 200. The power network architecture 200 may include a communications network 202, an electrical network 204, and a power management system 206. The electrical network 204 may be monitored by the power management system 206 though monitoring points disposed within the electrical network 204. The power meters and the power management system 206 may enable a user to monitor and store data/information from distribution points and assets. In one embodiment, the power meter placement methods 500 and 600 described below may be performed by the power management system 206. Alternatively, the power meter placement methods 500 and 600 may be performed by a stand-alone system and may produce one or more outputs to the power management system 206 which may be displayed on the display module 210.

The user, via a user interface of the power management system 206, may also control and manage various assets, run reports using information received, setup alarms, as well as perform other functions. The electrical network 204 and the power management system 206 may communicate via the communications network 202.

The electrical network 204 may include a plurality of devices organized into in a structured manner such as a tree topology, a line topology or other forms of topologies. In one example, the electrical network 204 may include multiple nodes and loops and may include connections or power links between the devices within the power grid network. A network of monitoring devices, shown as monitoring points M, may be included throughout the electrical network 204, which may be connected together by the communication network 202.

One example of a monitoring point is a smart meter such as the PowerLogic Energy and Power Quality Meter, provided by Schneider Electric. The entire electrical network 204 may be monitored by one of power management system, via the monitoring points M. In one embodiment, the monitoring and control systems comprise software programs,

communication gateways, metering, and digital protection devices, and can also interface with external monitoring devices.

In one example, the power management system 206 may have direct data access via the monitoring points M received via the communication network 202. In another example, the power management systems may be included embedded web pages, which may included into other monitoring or management systems. The power management system may include a combination of software and hardware.

FIG. 3 shows one example of the electrical network 204 which includes a root node 302, child nodes 304, and 306 and one or more monitoring points 308. In one example, the electric current in the tree structured electrical network 204 can flow from root node to the child nodes. Each of the child nodes can include one or more electronic components. In one example, the root node 302 may include a high voltage (HV) network loop and the child nodes in the electrical network 204 can provide power through a medium- voltage (MV) network loop. The child nodes in the MV network loop can provide power to one or more secondary distribution substations, generators and switch gear. The secondary distribution substations can provide power through a low voltage (LV) network loop to low power components and electrical equipment such as one or more Uninterruptible Power Supply (UPS) systems, with critical mechanical loads, electric switchboards, Heating, Ventilation, and Air conditioning (HVAC) systems, lighting and building loads, a remote power panels (RPP) and associated IT loads and Power Distribution Units (PDU). In some embodiments, enterprise level power grids such as are used in hospitals and data centers can employ have two utility feeds available as well as a independent emergency power source, with a dedicated set of redundant generators and associated Automatic Transfer Switch.

Referring again to FIG. 2, the power management system 206 can monitor utility feeds, including surge protectors, trip units, and transformers and can detect ground faults, voltage sags, voltage swells, momentary interruptions and oscillatory transients, as well as fan failure, temperature, and harmonic distortions in the output. The power management system 206 can also monitor generators, including outputs, protective relays, battery chargers, and sensors (for example, water, and fuel sensors). The power management system 206 can further detect generator conditions including reverse power, temperature, over voltage and under voltage conditions, over speed, ambient temperature. The power management system 206 can further monitor Transfer Switches (TS) including parallel switch gear, and Static Transfer Switches (STS) and can detect status change in the TS, as well as Silicon Controlled Rectifier (SCR) status, summary alarms, alarm condition, and test positions, among other information.

The power management system 206, via the display module 210, may display various display screens to the user relating to the electrical network 204. In one example, the display screens may include a dashboard screen, an electrical one-line screen, a power flow screen, a equipment detail screen and an alarm summary screen. The power management system may also produce various reports and may display them to the user via the display screen. For example, the reports may include power capacity, power incidents, power quality (PQ) events, and various trending statistics.

In one example, the display module 210 can display a representation of the electrical network 204 and the power meters M to be placed within the electrical network 204. In one example, the methods of determining placement of power meter can provide potential locations for one or more power meters, which can be displayed by the display module 210. The methods of determining meter placement, according to various embodiments, are data-driven and take advantage of smart meters that are capable of recording various power quality indicators at selected monitoring points. In addition, the power quality concepts can be further used to predict device outages and effectively schedule maintenance. For example, power quality numbers may be determined, when one of the power quality values for the PRI triggers an alert, system administrator and maintenance personnel can use the historical records of power quality vectors to find the critical components that should be maintained to avoid potential power outages. Network Model of Power Grid

According to one embodiment, to determine meter placement, the power grid network can be modeled as a data-driven network. FIG. 4 illustrates one example of a power grid network modeled as a data-driven network. The data driven network includes the electrical components of the network as network nodes such as the nodes 404, 406 and 408. As noted above, the electrical components can include primary and secondary distribution substations, generators, buses, transformers, Transfer Switches, including parallel switch gear, and Static Transfer Switches, UPS systems, with critical mechanical loads, electric switchboards, HVAC systems, lighting and building loads, a remote power panels and associated IT loads and PDU systems. The power links between the electronic components can be modeled as data links, the flow of power as data flow on the links, and the power flowing through links can be modeled as numeric data.

In one example, in the model, the power quality is assigned on a link at an instance in time as a discrete class (from c to c_n). The power quality class c can represent the best power quality while c_n can represent the worst power quality. Since power meters measure power quality continuously, a power quality class c, can be assigned to the power quality on a link as the worst power quality event measured on that link in the time interval. In every time slice a power quality class is assigned to each link where the smart meters are installed.

Moreover, in the model, the power flow through each node is established as a channel, such as the channels 410, 412, and 414 for nodes cl 404, c2 406, and cn 408. The input and output of this channel at each node comprises n power quality classes. And the probability that a power quality c_x will be received as c_y at the output of the channel at each device d is represented by the symbol

device d, the n x n matrix comprises the probability values

' ^{wmcn ma}Y be referred to herein as the power quality transition function, or the transition function. For a device (d) having multiple inputs/outputs, a power quality transition function is associated with each input/output pair. The power quality transition function can then be represented by Equation 1 as follows:

Equation (1) where

probability that the input quality c_x is received as cy at the output of device d. Note that every row in the above matrix should sum to 1. Another model for power quality propagation is described in Application PCT/US2011/065554. In one example, this power quality transition function may be probabilistic, potentially dynamic and can evolve over time. The power quality transition function may be impacted by many factors, including the maintenance schedule, age of components, and history of power quality events. Methods for Meter Placement

In at least one embodiment, an entropy based method of determining devices to be selected for meter placement is performed by a power management system, such as the power management system 206, discussed above with reference to FIG. 2. An example of a method of determining devices to be selected for meter placement is illustrated by FIG. 5.

In step 502, the distribution of power quality at the input to the power grid network is received by the power management system. In one embodiment, because the electrical utilities typically report on indices such as System Average RMS Variation Frequency Index (SARFI), the distribution of power quality at the input to the network, which is usually the utility feed, is a known quantity. The SARFI may comprise a count of the number of times the magnitude and duration of power quality falls below a threshold. Furthermore, there are independent bodies that gather statistics on power delivery service reliability that can also be incorporated into an estimate of power quality distribution. Therefore, the model assumes that the probability mass function pmf of power quality values at the input link to the root node is a known quantity. In step 504, the power management system receives the power quality transition function for each component. In one embodiment, the power quality transition function f(d) can be estimated for specific models of electrical components, through physical modeling or though the assessment of historical power monitoring data. Given a reasonable initial estimate, the transfer functions can be further refined through online learning techniques.

In step 506, the power management system receives the tree topology of the power grid, such as the example topology described in reference to FIG. 3, or the example topologies described with reference to FIG. 8A-8D. The power management system may also receive the number of meters to be place in the power grid. In one example, the tree topology information and the number of power meters may be input by a user via a user interface. In another example, the power management system may determine the tree topology from the information stored for the power grid network.

In step 508, for each device (d), the power management system determines the immediate parent device of node d, which is represented as d, the immediate child of a node d as d. It is appreciated that the device 1, which is the root of the network topology tree, has no parent device and therefore is represented by zero value.

In step 510, the power management system calculates the power quality distribution function of entropy for the link /₀ ^(d). In one example, the output link of a device d is represented as /₀ ^(d) while the input link to the same device is represented as /i_n ^(d) in. The probability distribution of power quality values (p^) at power link /₀ ^(d) is defined as f_x(d) which is the product of fx(d ) and the transition function f(d) of node d. Starting from the root node of the tree-structured power network, the power management system traverses nodes (devices) in level-order fashion to calculate the distribution functioned) as _x(d) =f_x(d) x /(d), and calculates the fx(d) =

V ⁼ 1, 2, ... . n.

In step 512, using the probability distribution of power at quality values power link /₀ ^(d), the power management system can calculate the uncertainty of power quality on a link using Shannon' s entropy measure. In one example, the determination is based on the principal power meters that are to be deployed on network links where the power quality values are most uncertain. Therefore, the entropy formula to determine uncertainty at the output link of a device d is determined as: π

Equation (2) where

the probability of getting power quality c; at the output link of device d.

In step 514, the power management system determines whether the uncertainly of power quantity has been calculated for every device (d). If no, in step 516, the power management system selects the next device in the power grid network. If yes, in step 518, the power management system determines output L, representing the list of devices to be selected for meter placement based on a determination of links having maximum uncertainty. In one example, the Algorithm 1 and method 500 can be used when there is no or negligible impact of one link on any other link in the network, for instance, if one node is producing a power quality Ci as output irrespective of the input quality (for example a stabilizer).

According to other embodiments, the network links are dependent on each other and therefore meter placement methods should consider the link dependency while calculating uncertainty of a link.

One example of an Algorithm for performing method 500 is illustrated in Algorithm 1:

Algorithm 1 A Simple Entropy Based Algorithm

Input: distribution function of input link to device 1 i.e., _x ⁽⁰⁾„ transition functioned), number of power meters N

Output: L (list of devices to be selected for meter placement)

begin tree) has no parent i.e., getParent(l) = 0 */

/* where pi (d) is the * component of _x(d) vector */

end

/* get N high entropy devices in vector H */

L _^getHighEntopyDevices(H,N)

end

In another embodiment, method 600 for determining power meter placement location using Monte Carlo predicted error method is illustrated in FIG. 6. The method 600 calculates the uncertainty of parent links conditioned on their child links and takes into the consideration the effect of every link under consideration on the other links in the network. Unlike the entropy-based method 500, method 600 for determining meter placement location selects high information locations for deploying power meters in the power grid network and uses Monte Carlo sampling and probabilistic inference approaches to indentify locations in the power grid which exhibit unpredictable power quality events. The problem is inherently challenging as the information received from a power meter flows not only in the forward direction from the root nodes toward the child nodes, but also in reverse or upstream direction toward the root node (utility main) and back to all other nodes in the network.

To allow for this type of information flow, the method 600 uses a Bayesian network and models the power grid using a factor graph. The method can use several message passing algorithms to help determine the optimal meter placement. The selected algorithm, in one example, includes the propagation or sum-product algorithm, which has been shown to work for general topologies (as opposed to a tree), and has several software libraries available. The method 600 is repeated for every power meter to be placed in the power grid network.

Similar to method 500, the method 600 can include the steps of receiving the topology

T of power grid, receiving the pmf of the input feed to first device i.e., f ° receiving the set of transition functions F = {/(d)}, Vd; and the number of power meters to place. Algorithm 2 illustrates one implementation of method 600:

Algorithm 2 Monte Carlo Predicted Error Algorithm

Input: The topology T of power grid; the pmf of the input feed to first device 1 i.e., x⁽⁰⁾ ; the set of transition functions F = {/(d)}, Vd; the number of power meters M to place; and the number of Monte Carlo samples to draw K

Output: L (list of devices to be selected for meter placement)

begin

foreach (power meter m) do

e, = 0, V links / G T;

foreach (Monte Carlo Sample k) do

c <- sample of instantaneous network state;

w <- metered sub-set of c;

z <- non-metered sub-set of c;

z <- predictPowerQuality(w, fj⁰⁾, F, T);

foreach ( link I £ z) do

if Z;= Z; then

/* Add to predicted error for this link */

et <- et + l/K;

end end

end

selectedLink <- max(e);

L.add( selectedLink);

end

end function predictPowerQuality(w, f , F, T)

begin

init pmf Ψ = { ψι} , V links / G T;

Ψ' <- BeliefPropogation given evidence w

foreach ( link I £ T, I w) do

z_/ <- max probability power quality class inferred in ψΊ ;

end

return Z = { z_/ }

end

In step 602, given the node transfer function F(d) of device d, the power management system uses a Monte Carlo (MC) method to obtain a set of K samples at each node. At each time slot I ... K, the power management system draws a sample c from the prior distribution of the utility feed. Then, for each node a pmfx_d ^l is calculated given its node transfer function and the sample obtained from its parent node d using x_d ^l = F(d) xg^l and the sample c _d ^l is drawn from x_d ^l . The power management system repeats this at each node of the tree starting from the root and ending at the leaves. The result is a set of K simulated samples C_d = {c_d, c_d, ... , c_d } for each of the N links in the power network.

In steps 604 and 606, the power management system simulates the network state at each metered and non-metered locations, respectively. In one example, the samples obtained by the MC simulation of power quality propagation contain consistent sets of power quality values at both metered and non-metered locations.

In step 608, the power management system uses Bayesian inference to infer the power quality at non-metered locations as a function of the simulated values observed at the metered locations. To determining the Bayesian inference, the power network is modeled as a factor graph. The belief propagation can then be used to calculate the inferred values of power quality at the output of each node using the (simulated) evidence obtained from the power meters.

FIG. 7 illustrates one example of the factor graph. The factor graph has conditional probability nodes t, including , t₂, and t^, equality nodes x, including xi, x₂ and X and evidence nodes y, including yi, y₂ and y - The t nodes can represent actual electrical devices with a known transition function. The x nodes can represent wired connections on the power grid network for which we have already obtained a set of samples using MC sampling. These nodes are constrained so that all edges connected to them are equal. The y nodes represent locations where a power meter could be placed. The non-metered nodes are initialized to a uniform pmf and the metered nodes are set to a trivial pmf with a probability of 1 at the true power quality event and a probably of 0 is set everywhere else. For each time slot the power management system determines the maximum likelihood that a power quality event that would appear at each node given the current meter configuration.

In step 610, the power management system compares the resulting predictions to the simulated value seen at the non-metered locations. The power management system can then calculate the error rate for each node in the network. If the determined event differs from the event given by the MC sample, the power management system can add 1=K for that sample.

In step 612, the power management system produces a relative indication of the predictive strength on each link of the network. At each round of the method the power management system conservatively chooses to place a power meter at the node with the highest error rate. The most poorly predicted non-metered locations, those having the highest error rate, are selected as the location for the next meter. The method 600 is repeated starting at step 602, until all meters have been placed.

Case Study

To test the meter placement method 600, two network topologies are used, including a line network of ten devices shown in FIG. 8 A and 8B and a tree network with 16 devices shown in FIG. 8C and FIG. 8D. It is appreciated that the method 600 may be applied to other network topologies. For each network topology, there are two device configurations tested, one with all identical devices (homogenous) and one with a mixture of different devices (heterogeneous). Table 1 illustrates a listing of the tested topologies and the corresponding device configurations. Network€∞iigwaik)is # Topology .Device CfcK¾ttraik*R

Tabfc I

ETWORKS USED I O«8 EXPERIMENTS

Table II illustrates a listing of the devices included in the network topologies 801-804, according to one example, including a bus, a switch, a transformer, and a UPS, and the corresponding transfer function as described above in reference to method 600. The transfer functions listed are assigned a prior on the utility feed of [0:9947 0:005 0:0002 0:0001 0:00001]. The utility feed assigned, in one example, is based on data reported by utility networks and provided by IEEE publications.

Tafe!s !!

(c) TiafisfisTfsser

The devices included in the network topologies 801-804 include a bus B 1-B 16, a switch SI -SI 2, a transformer T1-T13, and a UPS Ul-16. Power quality events can be assigned a number from 1-5 in order of severity in accordance with EPRI. Analysis of extremely reliable power delivery systems: A proposal for development and application of security, quality, reliability, and availability (sqra) modeling for optimizing power system configurations for the digital economy. CEIDS, 2002. These event types are listed in Table III along with their descriptions, ranging from event 1 associated with clean input having good power quality to event 5, associated with interruption of at least 5 minutes. E en* #

ί Good power qmsl Sy ftormsi

eksw 70% <sf rm i l voltage for greater ihm 0.02 secssads.

or below 80% of nosmnal voltage for pester thmi 0,5 seconds

3 Beio 70% of issmiBisi volisgs for mere t &a ill seconds

4 lBten¾piioti of iii kssf 1 se ond

5 foterrapiioo or^' a? leas* 3 minutes

sbie II

E ENT TYPES

For each network configuration K = 10000 samples were collected for each device using MC sampling. For the line networks 801 and 802, M = 5 meters were placed and for the tree networks 803 and 804, M = 10 meters were placed in order of importance. At each iteration of the meter placement method 600, the three highest error rate values along with their corresponding nodes and the meter placement decision were reported. These results are listed in Table IV shown below for each configuration shown in FIGS. 8A-8D. Table IV shows the error rate results for each round of power meter placement sorted based on the highest three error rates. It is appreciated that as a result of each iteration, the error rates may be changed based on the new information provided by the placed power meter. Therefore, the error rates associated with neighboring devices may be reduced as a result of the placement.

(a) ¾K «raiion !

Round orted Devices Sort d Error Ea¾es

c> CoRl g« .don 3

{ .) Cons iration 4

Table IV

RESULTS OR M CB ET ORK CONFIGURATION Testing Results for Homogeneous line network

The results obtained from a homogeneous line network (FIG. 8A) are considered for the configuration 801. As a result of the calculation of method 600, power meters are placed at the output of devices 10, 5, 3, 8 and 1, in that order, as shown in Table IV(a) and FIG. 8A. All devices share the same transfer function and each one adds a small degree of uncertainty to the resulting pmf, the last device is expected in the chain to have the highest degree of uncertainty. FIG. 9A illustrates the prediction error or the degree of uncertainty prior to placement of power meters. FIGS. 9B-9E illustrate the result on the degree of uncertainty as the power meters are placed at the output devices 10, 5, 3, 8 and 1. The first meter is expected to be placed at the end of the chain, or at the output of device 10, the location with the highest degree of uncertainty. As shown in FIG. 9B, once the first power meter is placed, the error rate for devices 7-11 is reduced. This error reduction is propagated toward the root or device 1. Based on the method 600, the second power meter is expected to be placed at the output of device 5, where the degree of uncertainty is highest after placement of the first power meter. As shown in FIG. 9C, once the second power meter is placed, the error rate for devices 4, 5, 6, 7 and 8 is reduced.

Subsequent meter placements are iteratively placed at the nodes farthest from the metered locations, which is consistent with the test results. As shown in FIG. 9D, the next power meter is placed at the output of device 3, resulting in the reduced error rate at devices 3, 4 and 5. As shown in FIG. 9E, the next power meter is placed on the output of device 8, resulting in the reduced error rate at the devices 8 and 9.

Testing Results for Heterogeneous line network

Considering the heterogeneous line network of FIG. 8B, the method 600 can place meters at device outputs 5, 9, 2, 7, 5, in that order. Meters are determined to be placed just before the two devices first, then after the remaining two. The fifth meter is determined to be placed before the second switch where the node distance from metered devices was greatest. As illustrated in Table VI (b), the buses and switches are both negatively active while transformers are both negatively and positively active. The devices can be placed in ascending order of expected entropy as bus, transformer, and switch. The UPS is a positively active device, which means that for any given input event, the probability of having a clean output event is high. However, in this case, the expected entropy is low only in the forward direction. If clean power is detected at the output of the UPS there is still a high degree of uncertainty regarding the input power quality. Therefore, placing meters at the inputs to the UPS devices is reasonable as initial meter placements.

Testing Results for Homogeneous tree network.

Considering the results obtained from the homogeneous tree network, as shown in FIG. IV( c), the meters one through six have been placed at the leaf nodes as expected and the subsequent meters have been placed along the main branches of the tree in midpoint locations.

Testing Result for Heterogeneous tree network

Finally, when considering the results obtained for the heterogeneous tree network shown in FIG. 8D it can be seen that the first three meters were placed at the bus outputs just before the UPS branches. The next three meters were placed at the output of the switches as would be expected. The last four meters were placed after the UPS outputs, suggesting that the error rate was low at the network segments feeding into the UPS devices.

As described above, methods 500, and 600 describe three approaches for placement of power meters in a power grid network. Method 500 defines an entropy-based method and method 600 defines a prediction error method. Experiments conducted using the prediction error approach suggest that the algorithm produces meter placement recommendations that are consistent with expectations based on numerical analysis.

It is appreciated that the methods described herein can be extended and scaled to estimate the pfm of the power quality at the metered locations and then, in a single step, derive a message passing algorithm for computing the resulting conditional entropy ( or expected prediction error ) at all non-metered locations.

Having thus described several aspects of at least one embodiment of this invention, it is to be appreciated various alterations, modifications, and improvements will readily occur to those skilled in the art. Such alterations, modifications, and improvements are intended to be part of this disclosure, and are intended to be within the spirit and scope of the invention. Accordingly, the foregoing description and drawings are by way of example only.

What is claimed is:

Claims

1. A method for placement of power meters in a power distribution network, the method comprising:

modeling the power distribution network as a data-driven network comprising a plurality of nodes and a plurality of power links connecting individual nodes of the plurality of nodes;

receiving at a computer system data pertaining to network topology and a number of power meters to be placed in the power distribution network; and

calculating, by the computer system, placement of at least one power meter within the power distribution system.

2. The method of claim 1, further comprising:

coupling a communications network between a power monitoring system and the computer system and transferring data related to the power quality measured by the at least one power meter over the communications network.

3. The method of claim 1, further comprising;

determining power quality distribution function of entropy for the plurality of power links.

4. The method of claim 3, further comprising:

for every node of the plurality of nodes, calculating uncertainty of power quality on the plurality of power links.

5. The method of claim 1, further comprising:

for every node, calculating entropy for child power links in the plurality of links; and

comparing the entropy with a maximum reduction value.

6. The method of claim 5, further comprising:

determining one power link of the plurality of power links that results in maximum entropy reduction in the power distribution network.

7. The method of claim 1, further comprising:

calculating a set of K samples using a Monte Carlo method for each power link within the power distribution network.

8. The method of claim 7, further comprising:

calculating a power quantity associated with at least one metered location using Monte Carlo simulation; and

calculating a power quality associated with at least one non-metered locations as a function of the calculated power quantity observed at the at least one metered location.

9. The method of claim 8, further comprising:

comparing the metered power quantity with the non-metered power quantity to determine a comparison result; and

calculating an error rate for each node of the plurality of nodes based on the comparison result.

10. The method of claim 9, further comprising:

determining placement of at least one power meter as a location associated with a node with a highest error rate.

11. A system for placement of power meters in a power distribution network, the system comprising:

a display;

a power monitoring system having a plurality of power monitors coupled to components of the power distribution system; and

a controller coupled to the power monitoring system and the display and configured to:

model the power distribution network as a data-driven network comprising a plurality of nodes and a plurality of power links connecting individual nodes of the plurality of nodes; receive data pertaining to network topology and a number of power meters to be placed in the power distribution network;

calculate placement of at least one power meter within the power distribution system; and

provide an indication of the placement of the at least one power meter for the display.

12. The system of claim 11, the controller further configured to:

receive data related to the power quality measured by the at least one power meter from a communications network.

13. The system of claim 11, the controller further configured to:

determine power quality distribution function of entropy for the plurality of power links.

14. The system of claim 13, the controller further configured to:

for every node of the plurality of nodes, calculate uncertainty of power quality on the plurality of power links.

15. The system of claim 14, the controller further configured to:

for every node, calculate entropy for child power links in the plurality of links; and

compare the entropy with a maximum reduction value.

16. The system of claim 15, the controller further configured to:

determine one power link of the plurality of power links that results in maximum entropy reduction in the power distribution network.

17. The system of claim 13, the controller further configured to:

calculate a set of K samples using a Monte Carlo method for each power link within the power distribution network.

18. The system of claim 17, the controller further configured to: calculate a power quantity associated with at least one metered location using Monte Carlo simulation; and

calculate a power quality associated with at least one non-metered locations as a function of the calculated power quantity observed at the at least one metered location.

19. The system of claim 18, the controller further configured to:

compare the metered power quantity with the non-metered power quantity to determine a comparison result;

calculate error rate for each node of the plurality of nodes based on the comparison result; and

determine placement of at least one power meter as a location associated with a node with a highest error rate.

20. A non-transitory computer readable medium for placement of power meters in a power distribution network having stored thereon sequences of instruction including instructions that will cause a processor to:

model the power distribution network as a data-driven network comprising a plurality of nodes and a plurality of power links connecting individual nodes of the plurality of nodes;

receive data pertaining to network topology and a number of power meters to be placed in the power distribution network;

determine placement of at least one power meter within the power distribution system; and

provide an indication of the placement of the at least one power meter for display.