Patent Publication Number: US-2012033473-A1

Title: Systems and methods for electrical power grid monitoring using loosely synchronized phasors

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Patent Application No. 61/363,643 filed Jul. 12, 2010 (entitled SYSTEMS AND METHODS FOR ELECTRICAL POWER GRID MONITORING USING LOOSELY SYNCHRONIZED PHASORS) which is related to the following applications: U.S. Provisional Patent Application No. 61/355,119 filed Jun. 15, 2010 (entitled GRID INTEGRATION OF PHOTOVOLTAIC INVERTERS WITH A NOVEL ISLAND DETECTION TECHNIQUE); U.S. Provisional Patent Application No. 61/363,634 filed Jul. 12, 2010 (entitled SYSTEMS AND METHODS FOR ISLANDING DETECTION, Attorney Docket No. 65564-8026.US01); and U.S. Provisional Patent Application No. 61/363,632 filed Jul. 12, 2010 (entitled SYSTEMS AND METHODS FOR DYNAMIC POWER COMPENSATION, SUCH AS DYNAMIC POWER COMPENSATION USING SYNCHROPHASORS, Attorney Docket No. 65564-8025.US01), each of which is also incorporated herein by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     This application is generally directed toward power generation systems. 
     BACKGROUND 
     An electrical power grid may include phasor measurement units (PMUs) at various locations of the electrical power grid. The PMUs measure characteristics of the electrical power (e.g., voltage and current) generated by or transmitted over the electrical power grid and produce phasors representative of the measurements. Such PMUs typically include a global positioning system (GPS) clock that uses a GPS signal that is accurate to approximately 1 microsecond (1 μs). The PMUs timestamp the phasors with the GPS-synchronized clock time. Phasors that are generated at the same, highly-accurate, time are known as synchrophasors. Synchrophasors can be analyzed, such as in real time, so as to monitor aspects of the electrical power grid. 
     One disadvantage to such a system is that a GPS clock and associated equipment (e.g., antenna) may add additional costs to the installation and use of a PMU. Such additional costs may preclude the installation of PMUs in certain locations where it would nonetheless be desirable to have information regarding the electrical power transmitted by the electrical power grid at such locations. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram illustrating a system for electrical power grid monitoring configured in accordance with an embodiment of the technology. 
         FIG. 2  is a block diagram illustrating components of a solar power inverter configured in accordance with an embodiment of the technology. 
         FIG. 3  is a flow diagram of a process for monitoring an electrical power grid in accordance with an embodiment of the technology. 
         FIGS. 4A and 4B  are flow diagrams of processes for analyzing grid and inverter phasors in accordance with an embodiment of the technology. 
     
    
    
     DETAILED DESCRIPTION 
     1. Overview 
     The inventor has recognized that the need exists for systems and methods that overcome the above disadvantage, as well as provide additional benefits. The present disclosure describes systems and methods for monitoring an electrical power grid using loosely synchronized phasors. The electrical power grid can include a PMU that is time synchronized to a highly-accurate time, such as a time provided by GPS signals. A solar power inverter can include a clock that is synchronized to a time that is less accurate than the time provided by the GPS signals. For example, the solar power inverter can synchronize its time to an Internet or Intranet time server and/or to a time signal broadcast over the radio spectrum. The solar power inverter can also include a PMU that generates phasors that are timestamped using the less-accurate inverter clock time. The solar power inverter can receive phasors from the electrical power grid PMU and analyze the grid and inverter phasors. For example, the solar power inverter can calculate a Pearson&#39;s correlation coefficient based on the grid and inverter phasors. As another example, the solar power inverter can calculate slip and acceleration quantities using the grid and inverter phasors. 
     The solar power inverter can use the analysis of the grid and inverter phasors (e.g., the Pearson&#39;s correlation coefficients, or the slip and acceleration quantities) to determine a state of the electrical power grid at the point of common coupling of the solar power inverter to the electrical power grid. Such information can enable the solar power inverter to take certain actions based upon the analysis. For example, if the analysis indicates that the solar power inverter is islanded from the electrical power grid, the solar power inverter can shut down (stop producing power). Alternatively, the solar power inverter can shift to an intentional island mode, in which a connection to the electrical power grid is opened and the solar power inverter produces power to support a local load. As another example, if the analysis indicates that the electrical power grid is stable but that certain grid support functionality may be useful, the solar power inverter can remain connected to the electrical power grid and provide such support functionality. 
     Certain details are set forth in the following description and in  FIGS. 1-4B  to provide a thorough understanding of various embodiments of the technology. Other details describing well-known aspects of power generation systems, solar power inverters, and phasors, however, are not set forth in the following disclosure so as to avoid unnecessarily obscuring the description of the various embodiments. 
     Many of the details, dimensions, angles and other features shown in the Figures are merely illustrative of particular embodiments. Accordingly, other embodiments can have other details, dimensions, angles and features. In addition, further embodiments can be practiced without several of the details described below. 
     In the Figures, identical reference numbers identify identical, or at least generally similar, elements. To facilitate the discussion of any particular element, the most significant digit or digits of any reference number refer to the Figure in which that element is first introduced. For example, element  100  is first introduced and discussed with reference to  FIG. 1 . 
     2. Systems and Methods for Electrical Power Grid Monitoring 
       FIG. 1  is a diagram illustrating a system  100  for monitoring an electrical power grid configured in accordance with an embodiment of the technology. The system  100  includes a utility grid portion  160  and multiple customer premises portions  120  and  140 . The utility grid portion  160  includes electrical power transmission lines  102  electrically connected to a transmission substation  104 . The electrical power transmission lines carry three phase alternating current (AC) generated by one or more electrical power generators. The transmission substation  104  steps down the voltage of the AC (e.g., from 345 kilo Volts (kV) to 69 kV, or from any particular voltage to a lower voltage) before transmission of the AC over electrical power transmission lines  108  to a distribution substation  110 . The distribution substation  110  further steps down the voltage of the AC (e.g., to 13.8 kV, or to any other voltage) prior to transmission over electrical transmission lines  112   a  to a first customer premises portion  120  and over electrical transmission lines  112   b  to a distribution device  114  and then to a second customer premises portion  140 . 
     The transmission substation  104  includes a phasor measurement unit (PMU)  105 . The PMU  105  measures characteristics of the AC at the transmission substation  104  and generates phasors based on the measured characteristics of the AC. The PMU  105  includes a Global Positioning System (GPS) antenna and clock that allow the PMU  105  to timestamp the generated phasors with a highly accurate time, e.g., on the order of +/−1 microsecond (1 μs). The phasors generated by the PMU  105  are thus associated with times that are accurate to a first degree of accuracy. The transmission substation  104  is networked via a communication channel  107  to a transceiver  106 . The transceiver  106  receives the phasors from the PMU  105  via the communication channel  107  and transmits the phasors. 
     The first customer premises portion  120  includes an industrial load  124 , one direct current (DC) from solar irradiance and provide the DC to the inverter  126 . The inverter  126  converts the DC into AC usable by the industrial load  124  or the electrical power grid. The inverter  126  is coupled to a transceiver  128 . As described in more detail herein, the transceiver  128  receives phasors transmitted from the transceiver  106  as well as time signals. The first customer premises portion  120  can also include a switch  122  near or at the point of common coupling (PCC)  166  of the inverter  126  to the electrical power grid. The switch  122  includes a transceiver  132 . The switch  122  can receive, via the transceiver  132 , information transmitted by the transceiver  106  and/or the transceiver  128 . 
     The second customer premises portion  140  includes a residential load  144 , an array  150  of photovoltaic cells, and an inverter  146 . The array  150  produces DC and provides the DC to the inverter  146 , which converts the DC into AC usable by the residential load  144  or the electrical power grid. The inverter  146  is communicably coupled to a transceiver  148 . As described in more detail herein, the transceiver  148  receives phasors transmitted from the transceiver  106  as well as time signals. The second customer premises portion  140  can also include a switch  142  at the PCC  168  of the inverter  146  to the electrical power grid. The switch  142  includes a transceiver  152 . The switch  142  can receive, via the transceiver  152 , information transmitted by the transceiver  106  and/or the transceiver  148 . 
     The system  100  also includes a time source  162  that includes a transceiver  164 . The time source  162  provides a time signal indicating time. For example, the time source  162  can include a Network Time Protocol (NTP) server. Such NTP servers may provide time accurate to within 10 milliseconds (1 ms) over the public Internet, and may achieve accuracies of 200 microseconds (200 μs) over a private Intranet. As another example, the time source  162  can include a National Institute of Standards and Technology (NIST) radio station that broadcasts a time signal. A clock that uses the NIST signal typically can maintain time accurate to approximately +/−1 second (1 s). As described in more detail herein, the inverters  126 / 146  receive the time signal from the time source  162  and use the time signal to synchronize their respective internal clocks. The time signals may indicate their degree of accuracy, or the inverter  126 / 146  may determine a degree of accuracy based upon the time signal and/or the time source  162 . For example, the inverter  126 / 146  may assume that time from an NTP server sourced over the public Internet is accurate to within 10 ms, or that time from an NIST signal is accurate to within 1 second. The inverter  126 / 146  may use other information to determine an accuracy of the time provided by the time source  162 . 
     As illustrated in  FIG. 1  the transceivers  106 / 128 / 132 / 148 / 152 / 164  are shown as wireless transmission and reception devices that transmit and receive information wirelessly. However, the transceivers  106 / 128 / 132 / 148 / 152 / 164  can be any suitable device for transmitting and receiving information over any suitable communication channel (e.g., a wireless network such as WiFi, WiMax, a cellular/GSM network, ZigBee, Advanced Metering Infrastructure (AMI), etc., a wired network such as a fiber network, an Ethernet network, etc., or any combination of wired and wireless networks). Accordingly, the techniques described herein are usable in conjunction with any suitable communication channel. 
     The system  100  can also include other components coupled to the electrical power grid that are not specifically illustrated. Such components can include other loads (e.g., inductive loads such as a transformer or motor), other electrical components (e.g., capacitor banks), other types of electrical power generation systems (e.g., wind power generation systems and/or other renewable power generation systems), and other components. Activity of loads or other components on the electrical power grid can cause voltage sags or swells and can be accompanied by reactive power flow, thereby resulting in less than ideal power to the load  124 / 144 , such as voltage that falls outside of a predetermined range that the load  124 / 144  utilizes, (e.g., ideally utilizes). Such out-of-range voltage can damage the load  124 / 144  and/or cause the load  124 / 144  to work harder. The activity of loads or other components on the electrical power grid can also cause overload conditions or other problems that are detectable at the PCCs  166 / 168  of the inverters  126 / 146  to the electrical power grid. As described in more detail herein, the inverters  126 / 146  can utilize loosely synchronized phasors to monitor the condition or state of the electrical power grid at the PCCs  166 / 168 . When the inverters  126 / 146  detect certain conditions at the PCCs  166 / 168 , the inverters  126 / 146  can perform appropriate actions in response to such conditions. 
       FIG. 2  is a block diagram illustrating components of the solar power inverter  126 / 146 . The solar power inverter  126 / 146  can also include components that are not illustrated in  FIG. 2 . The solar power inverter  126 / 146  includes a DC input component  245  that receives DC produced by the arrays  130 / 150 . The solar power inverter  126 / 146  also includes power generation component  220 , such as insulating gate bipolar transistors (IGBTs), which transforms DC into AC for output by an AC output component  250 . The solar power inverter  126 / 146  further includes various other electrical and/or electronic components  225 , such as circuit boards, capacitors, transformers, inductors, electrical connectors, and/or other components that perform and/or enable performance of various functions associated with the conversion of DC into AC and/or other functions described herein. The solar power inverter  126 / 146  also includes one or more data input/output components  230 , which can include the transceiver  128 / 148  and/or other components that provide data input/output functionality and/or connection to a wired or wireless network (e.g., an AMI device, a modem, an Ethernet network card, Gigabit Ethernet network card, etc.). 
     The solar power inverter  126 / 146  further includes a PMU  235  that measures characteristics of the AC produced by the power generation component  220  and generates phasors based on the measured characteristics. The PMU  235  can measure the characteristics of the AC at a location electrically proximate to the power generation component  220 . The solar power inverter  126 / 146  further includes a clock  255 . The solar power inverter  126 / 146  receives time signals via the transceiver  128 / 148  from the time source  162 . The clock  255  has a time that is set according to the time signals. Because the time signals from the time source  162  are less accurate than the GPS (or other high-accuracy) time signals used by PMU  105 , the time of the clock  255  is less accurate than the GPS clock time of the PMU  105 . The PMU  235  uses the clock time to associate times with the inverter phasors (timestamp the inverter phasors). Accordingly, the inverter phasors are associated with times that are accurate to a second degree of accuracy that is less than the first degree of accuracy of the times of the grid phasors. In some cases, the inverter phasors times may be one or more orders of magnitude less accurate than the grid phasors times. 
     The clock  255  can synchronize its time to the time source  162  time signals periodically (e.g., every hour, every 2 hours, every 24 hours, etc.). In some embodiments, the clock  255  synchronizes its time to a time in a grid phasor. In such cases, the accuracy of the clock  255  time would be dependent upon the latency of the connection between the PMU  105  and the inverter  126 / 146 . 
     In some embodiments, the solar power inverter  126 / 146  receives AC from the electrical power grid (for example, via the AC output component) that is used to power the solar power inverter  126 / 146 . In such embodiments, the PMU  235  can measure the characteristics of the received AC even if the inverter  126 / 146  is not generating AC. In some embodiments, the PMU  235  is external to the solar power inverter  126 / 146 . For example, the PMU  235  may be sited at the PCC  166 / 168  and can measure the characteristics of the AC at such location. A site may have multiple solar power inverters  126 / 146  with a single PCC  166 / 168  and a PMU  235  at the PCC  166 / 168 . The PMU  235  can measure the characteristics of the AC at the PCC  166 / 168  and transmit the synchrophasors to the multiple solar power inverters  126 / 146 . In such a configuration the solar power inverters  126 / 146  can act independently or collectively to monitor the electrical power grid using the synchrophasors from the PMU  105  (which may be referred to herein as reference synchrophasors) and synchrophasors from the PMU  235  (which may be referred to herein as local synchrophasors). 
     The solar power inverter  126 / 146  further includes a controller  215 , which includes a processor  205  and one or more storage media  210 . For example, the controller  215  can include a control board having a digital signal processor (DSP) and associated storage media. As another example, the controller  215  can include a computing device (for example, a general purpose computing device) having a central processing unit (CPU) and associated storage media. The storage media  210  can be any available media that can be accessed by the processor  205  and can include both volatile and nonvolatile media, and removable and non-removable media. By way of example, and not limitation, the storage media  210  can include volatile and nonvolatile, removable and non-removable media implemented via a variety of suitable methods or technologies for storage of information. Storage media include, but are not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, or any other medium (for example, magnetic disks) which can be used to store the desired information and which can accessed by the processor  205 . 
     The storage media  210  stores information  222 . The information  222  includes instructions, such as program modules, that are capable of being executed by the processor  205 . Generally, program modules include routines, programs, objects, algorithms, components, data structures, and so forth, which perform particular tasks or implement particular abstract data types. The information  222  also includes data, such as values stored in memory registers, which can be accessed or otherwise used by the processor  205 . The processor  205  can use the information  222  to perform various functions or cause various functions to be performed. The storage medium also stores phasor analysis information  224 . As described in more detail herein, the processor  205  can use the phasor analysis information  224  to, among other things, analyze grid and inverter phasors, determine a state of the electrical power grid based on the analysis, and/or to perform actions based on the state of the electrical power grid. 
       FIG. 3  is a flow diagram of a process  300  for monitoring an electrical power grid in accordance with an embodiment of the technology. The process  300  is described as performed by the controller  215  of the solar power inverter  126 / 146 . However, any suitable component of the solar power inverter  126 / 146  can perform the process  300 . Additionally or alternatively, any suitable apparatus or system with appropriate hardware (e.g., central processing unit (CPU), etc.), firmware (e.g., logic embedded in microcontrollers, etc.), and/or software (e.g., stored in volatile or non-volatile memory) can perform the process  300 . The controller  215  can perform the process  300  on a periodic or an ad-hoc basis. For example, the controller  215  can perform the process at the same rate at which the controller  215  receives phasors from the grid (described below). 
     The process  300  begins at step  305 , where the controller  215  receives phasors received by the data input/output component  230  (e.g., phasors transmitted by the transceiver  106 ). In  FIG. 1 , the transmission substation  104  includes the PMU  105  that generates phasors that the transceiver  106  transmits. Additionally or alternatively, other components of the utility grid portion  160  (e.g., the distribution substation  110 , the distribution device  114 , and/or electrical power generators) can include a PMU that generates phasors that are transmitted (e.g., wirelessly or by another suitable communication channel) to the solar power inverter  126 / 146 . Phasors derived from or generated based upon measurements taken of AC transmitted by the electrical power grid are referred to herein as grid phasors. The PMU  105  can measure characteristics of the AC and generate phasors at any suitable sampling rate, such as a sampling rate from approximately 5 Hz or more to approximately 120 Hz or more (e.g., approximately 5 samples per second to approximately 120 samples per second or more). The PMU  105  can transmit the samples at the same rate as the sampling rate. The controller  215  can receive phasors at the same rate as the sampling rate and perform the process  300  at the same rate. 
     At step  310  the controller  215  receives the phasors that are generated by the PMU  235  based on measurements of characteristics of the AC generated by the power generation component  220 . The PMU  235  can generate phasors at the same sampling rate as the PMU  105 . Phasors derived from or generated based upon measurements taken of AC generated by the power generation component  220  (or at an electrically proximate location) are referred to herein as inverter phasors. 
     As previously noted, the grid phasors generated by the PMU  105  of the transmission substation  104  can be timestamped with a highly-accurate time (e.g., to within 1 μs). The inverter phasors, however, are timestamped with a less accurate time (e.g., to within approximately 200 μs, to within 10 ms, or to within a second). Accordingly, the timestamping of the inverter phasors may be less accurate than the timestamping of the grid phasors. In some cases, the times of the inverter phasors may be one or more orders of magnitude less accurate than the times of the grid phasors. Such reduced accuracy may mean that the inverter phasors correspond to different AC cycles than the grid phasors. For example, in a 60 kHz system, if the inverter clock time is accurate to within 50 ms, then there could be up to three cycles of slip between the grid phasors and the inverter phasors (50 ms corresponds to 3 AC cycles in a 60 kHz system). However, despite these differences, it is still likely that analysis of the grid and inverter phasors can provide useful results, as described in more detail herein. 
     At step  315  the controller  215  analyzes the grid and inverter phasors.  FIG. 4A  is a flow diagram of a process  400  that the controller  215  can perform to analyze the grid and inverter phasors. The process  400  begins at step  405 , where the controller  215  aligns a set of grid and inverter phasors according to their timestamps (e.g., the controller aligns the grid and inverter phasors having timestamps at t 0 , t 1 , t 2 , and so on). At step  410  the controller  215  calculates the Pearson&#39;s correlation coefficient for the grid and inverter phasors. More details as to how the Pearson&#39;s correlation coefficient can be calculated using phasors can be found in the previously referred to U.S. Pat. App. No. 61/363,634 (entitled SYSTEMS AND METHODS FOR ISLANDING DETECTION, Attorney Docket No. 65564-8026.US01). The Pearson&#39;s correlation coefficient indicates a degree of correlation between the grid and the inverter phasors, which can be used to infer the state of the electrical power grid. For example, in an problem condition such as a line down or an overload, the grid and inverter phasors would likely be uncorrelated and such lack of correlation would be quantified by the Pearson&#39;s correlation coefficient. 
     Even though there may be several cycles of AC slip between the grid and inverter phasors due to the different time accuracies, the grid and inverter phasors are likely to be correlated as long as the electrical power grid is not experiencing a problem condition. Put another way, if the inverter  126 / 146  is truly islanded from the electrical power grid, the probability that the grid and the inverter phasors are uncorrelated is very high, regardless of whether there are multiple cycles of slip between the grid and the inverter phasors. The lack of such correlation, as indicated by the Pearson&#39;s correlation coefficient, would indicate a high probability that the state of the electrical power grid at the PCC  166 / 168  is abnormal, and thus that the inverter  126 / 146  should perform an appropriate action. After step  410 , the process  400  concludes. 
       FIG. 4B  is a flow diagram of a process  450  that the controller  215  can use to analyze the grid and inverter phasors in addition or as an alternative to the process  400  of  FIG. 4A . In general, the process  450  involves shifting the inverter phasors  215  over a time window or tolerance interval and calculating the Pearson&#39;s correlation coefficient for each possible shift in the time window or tolerance interval. The width of the time window or tolerance interval can be based upon the accuracy of the time of the inverter phasors. Decreasing accuracy of the time of the inverter phasors would tend to increase the width of the time window or tolerance interval. For example, where the accuracy of the time of the inverter phasors is to within 50 ms, the time window or tolerance interval over which the inverter phasors can be shifted is likely to be narrower than the time window or tolerance interval where the accuracy of the time of the inverter phasors is to within 1 second. 
     The process  450  begins at step  415 , where the controller  215  determines possible shifts in the time window of the grid and inverter phasors. At step  420  the controller aligns the grid and inverter phasors according to a first possible shifting. The controller  215  can hold the grid phasors constant and shift the inverter phasors. Alternatively, the controller  215  can shift the grid phasors relative to the inverter phasors. At step  425  the controller  215  calculates the Pearson&#39;s correlation coefficient for the grid and inverter phasors. At step  430  the controller determines if there is another possible alignment of the grid and inverter phasors. If so, the process returns to step  415 . If not the process  450  concludes. 
     The process  450  can result in multiple Pearson&#39;s correlation coefficients depending upon the number of shifts of the inverter phasors over the time window. If every Pearson&#39;s correlation coefficient that results from the process  450  indicates no correlation between the grid and inverter phasors over multiple consecutive iterations of the process  450 , then there is a high likelihood that there is a problem condition at the PCC  166 / 168  (e.g., such complete lack of correlation may indicate that the inverter  126 / 146  is islanded.) However, if there is at least one Pearson&#39;s correlation coefficient that indicates that the grid and inverter phasors are still correlated, then there is a low likelihood that there is a problem condition at the PCC  166 / 168  (e.g., at least one correlation may indicate that the inverter  126 / 146  is still connected to the electrical power grid and that the electrical power grid appears stable). 
     One advantage of the process  450  is that it can account for time signals from the time source  162  that are less accurate than other sources. For example, a time source  162  that transmits time that is only accurate to within 500 ms can result in a larger time window over which the controller  215  is to shift inverter phasors, and thus result in a larger number of calculations for the controller  215  to perform. However, the controller  215  can be selected so as have enough processing power to perform the necessary calculations within the necessary period of time. 
     After the processes  400  or  450  of  FIG. 4A  or  4 B conclude, flow returns to step  320  of  FIG. 3 , where the controller  215  determines a state of the electrical power grid based on the analysis of the grid and inverter phasors. The controller  215  can use the Pearson&#39;s correlation coefficients as a basis for determining a state of the electrical power grid. More details as to how the controller  215  can use the Pearson&#39;s correlation coefficients in this manner can be found in the previously referred to U.S. Pat. App. No. 61/363,634 (entitled SYSTEMS AND METHODS FOR ISLANDING DETECTION, Attorney Docket No. 65564-8026.US01). For example, certain states at the PCC  166 / 168  that the controller  215  can detect are: 1) the inverter  126 / 146  at the PCC  166 / 168  is islanded; 2) the electrical power grid appears stable, but certain support functions may be required such as low voltage ride through (LVRT) or volt-ampere reactive (VAR) corrections. Those of skill in the art will understand the controller  215  may be able to detect states other than those listed herein. 
     At step  325  the controller  215  performs an action and/or causes an action to be performed based on the state of the electrical power grid. For example, the controller  215  can cause the inverter  126 / 146  to shut down or switch to intentional island mode. As another example, the controller  215  can cause the inverter  126 / 146  to provide grid support functionality such as LVRT or VAR corrections. More details as to how the inverter  126 / 146  can provide grid support functionality can be found in the previously-referenced U.S. Pat. App. No. 61/363,632 (entitled SYSTEMS AND METHODS FOR DYNAMIC POWER COMPENSATION, SUCH AS DYNAMIC POWER COMPENSATION USING SYNCHROPHASORS, Attorney Docket No. 65564-8025.US01). Those of skill in the art will understand that the controller  215  may be able to perform actions and/or cause to be performed actions other than those listed herein. 
     At step  330 , the controller  215  determines whether the inverter  126 / 146  is still operating. If so, the process  300  returns to step  305 . If not, the process  300  concludes. Those skilled in the art will appreciate that the steps shown in any of  FIGS. 3 ,  4 A and  4 B may be altered in a variety of ways. For example, the order of the steps may be rearranged; substeps may be performed in parallel; shown steps may be omitted, or other steps may be included; etc. 
     Another technique for detecting an islanding condition using synchrophasors is referred to as “slip and acceleration.” Slip and acceleration uses a measure of the rate of change of the grid and inverter frequencies (slip) and a measure of the acceleration of the rate of change of the frequencies (acceleration). The controller  215  can use an analysis based on slip and acceleration in addition to or as an alternative to calculating the Pearson&#39;s correlation coefficient. For example, in steps  410  and  425 , instead of or in addition to calculating the Pearson&#39;s correlation coefficient, the controller  215  could calculate slip and acceleration of the grid and inverter phasors. The controller  215  would then determine a state of the grid based upon the calculated slip and acceleration values. Additionally or alternatively, the controller  215  could use other phasor-based techniques. 
     One advantage of the techniques described herein is that because the inverter  126 / 146  uses a time signal from an external time source to synchronize the clock  255  time, there can be no need to add the equipment required to obtain a high-accuracy time signal (e.g., a GPS clock and antenna). Since such equipment may be both high cost and difficult to place at certain inverter  126 / 146  sites, the ability to avoid using such equipment can be a significant advantage to solar power inverters configured as described herein. Another advantage is that a lack of correlation between grid phasors and inverter phasors can likely still be detected despite the inverter phasors having less accurate timestamps. This is because such lack of correlation is highly likely to show up even though the grid and inverter phasors may not be exactly aligned. 
     3. Conclusion 
     From the foregoing, it will be appreciated that specific embodiments of the invention have been described herein for purposes of illustration, but that various modifications may be made without deviating from the spirit and scope of the invention. For example, although the processes  400 / 450  are described as calculating the Pearson&#39;s correlation coefficient, correlation between the grid phasors and the inverter phasors can be calculated using other techniques. As another example, the elements of one embodiment can be combined with other embodiments in addition to or in lieu of the elements of other embodiments. Accordingly, the invention is not limited except as by the appended claims.