energies

Article Impacts of Power Grid Deviation on Error of Synchronous Electric and Worldwide Power System Practices on Time Error Correction

Yao Zhang 1,*, Wenxuan Yao 1, Shutang You 1 ID , Wenpeng Yu 1, Ling Wu 1, Yi Cui 1 and Yilu Liu 1,2

1 Department of Electrical Engineering & Computer , The University of Tennessee, Knoxville, TN 37996, USA; [email protected] (W.Y.); [email protected] (S.Y.); [email protected] (W.Y.); [email protected] (L.W.); [email protected] (Y.C.); [email protected] (Y.L.) 2 Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA * Correspondence: [email protected]; Tel.: +1-865-566-4173

Received: 7 July 2017; Accepted: 25 August 2017; Published: 29 August 2017

Abstract: Synchronous electric utilize power grid frequency as their timing reference. Power grid frequency deviation away from its nominal value results in synchronous electric clocks running fast or running slow (also known as the time error). In this article, statistical analysis on time error of synchronous electric clocks around the world is firstly presented using the power grid frequency measurements recorded by the wide-area frequency monitoring network FNET/GridEye. Then, the time error correction (TEC) process provided by electric utilities is analyzed and the worldwide TEC practice is investigated. Eventually, regions of the world where electric utilities provide TEC service are differentiated from those without TEC services. Analytical results demonstrate that the average time error of synchronous electric clocks in North America seems to be less than five seconds, and it has not changed very much over the few years. On the other hand, the identification results that up to the end of 2016, many electric utilities around the world, especially in North America and Europe, provided the TEC service to periodically remove the accumulative time error of synchronous electric clocks.

Keywords: power grid frequency; synchronous electric clock; time error; time error correction (TEC); timekeeping accuracy; wide-area measurement system (WAMS)

1. Introduction A synchronous electric clock is powered by and synchronous to the power line frequency. It was first constructed around the 1910s and became one of the most widely used clocks after the rapid development of industry in the 1930s [1]. A synchronous electric clock does not contain a timekeeping oscillator such as a , but instead it keeps the time through counting the of the waveform from its wall plug [2]. An important reason for the popularity of synchronous electric clocks around the world is that the power grid frequency, as a clock timing source with almost zero cost, reliable performance and high accuracy, is generally accessible anywhere and anytime, as long as there are power transmission lines in service [3]. Nowadays, there are still many synchronous electric clocks using power grid frequency as their timing sources [4], for example, traffic lights, electricity meters and programmable household appliances. Therefore, the timekeeping ability of synchronous electric clock is important for people’s daily life. However, power grid frequency is not always a constant (also known as the nominal frequency, it is 60 Hz in North and South America, but 50 Hz in most other countries). Electric utilities usually

Energies 2017, 10, 1283; doi:10.3390/en10091283 www.mdpi.com/journal/energies Energies 2017, 10, 1283 2 of 15 keep the power grid frequency running in a very small range. The frequency deviation away from its nominal value results in synchronous electric clocks running fast or running slow. If a power grid frequency is above its nominal value, the clock will run fast. Otherwise, it will run slow. Therefore, the fluctuation of power grid frequency might cause a time error of a few seconds during the period of one day [5]. This time error would not completely cancel out by its own. As time goes by, this error gradually accumulates and finally tends to cause a large time drift of synchronous electric clocks in the long term. As discussed above, the stability of a power grid frequency has great influence on the timekeeping ability of synchronous electric clock. In fact, the frequency stability is considered as a critical issue for secure power system operation [6]. Therefore, a large number of studies on power system frequency stability have been performed over the last ten years, for example, frequency stability evaluation and control [7], the determination of frequency stability border of power system operation [8], the enhancement strategies to improve power system frequency stability [9,10], and the impact of renewable energy generation on frequency stability [11–13]. Although the frequency stability has been studied for many years, these studies mentioned above are primarily concerned with the ability of power system to maintain the steady frequency after a severe disturbance [14]. Up to now, there is a good deal of research focusing on the impacts of power system frequency deviation on the time error of synchronous electric clock. In this paper, we used frequency measurements collected by the wide-area frequency monitoring network, FNET/GridEye, to carry out the detailed statistical analysis on the time error of synchronous electric clocks in both North American and worldwide power grids. As a pilot wide-area measurement system (WAMS) system, FNET/GridEye has been monitoring the U.S. power grids and other worldwide power grids for more than a decade. Using those valuable measurements, the time error correction (TEC) service provided by electric utilities was investigated through the data-driven approach. The TEC practice around the world was also analyzed. FNET/GridEye, as an independent observer, identified regions of the world where electric utilities are providing TEC services from those without TEC services. Considering that TEC services would end soon in North America [5], our research would be helpful to reveal the impacts of TEC services on the time error and provide valuable guidance for the development of synchronous clocks. Finally, the long-term power system frequency distribution pattern was studied and its statistical characteristics were identified. To the best of our knowledge, it is the first effort to analyze the time error of synchronous electric clock in worldwide power grids and investigate the worldwide practice of the time error correction service provided by electric utilities. The other sections of this paper are organized as follows. Section2 presents a brief introduction of the wide-area frequency monitoring network FNET/GridEye. Statistical analysis on the time error of synchronous electric clock is shown in Section3. Section4 discusses two common types of TEC services and the worldwide TEC practice. Then, the long-term frequency distribution patterns in worldwide power grids are provided in Section5. Finally, this paper is concluded in Section6.

2. Wide-Area Frequency Monitoring Network FNET/GridEye Obtaining the frequency measurement of power transmission line is a prerequisite for analyzing the timekeeping accuracy of synchronous electric clocks. The power grid frequency dataset used in this paper is provided by FNET/GridEye. As a pioneering WAMS, FNET/GridEye was originally developed in 2003 and is now operated by the University of Tennessee, Knoxville (UTK), and Oak Ridge National Laboratory (ORNL) [15]. FNET/GridEye, an internet-based WAMS, has been continuously monitoring the power grid for over ten years [16]. It can measure power grid frequency, voltage magnitude and voltage angle with low-cost, reliable performance and high accuracy (±0.0005 Hz for grid frequency and ±0.0002 rad for voltage angle) [17]. Since the FNET/GridEye went online in 2003, more than 15 TB of data have been collected. Based on these real-time measurements, a variety of online and offline applications have Energies 2017, 10, 1283 3 of 15 been developed to monitor power system dynamic behaviors, such as location estimation [18], inter-area mode identification [19], and adaptive data-driven damping control [20]. The frequency disturbance recorder (FDR), a single-phase variant of the phasor measurement unit (PMU), is the main sensor of the FNET/GridEye [21]. In comparison with the conventional PMU, which requires high production and installation cost, the FDR measures from a normal single-phase electrical outlet at the 120 V distribution level [22]. These measurements are then synchronized by Global Positioning System (GPS)-based timestamps and transferred through Internet to the phasor data concentrator (PDC) for data processing and long-term storage [23]. After over ten years of development, more than 200 FDRs have been deployed in main interconnection systems of North America [24]. Figure1 shows the location of FDRs deployed in North America up to now. On the other hand, the FNET/GridEye also serves other interconnection systems around the world. Up to now, over 50 FDRs have been deployed worldwide, for example, China, Europe and Japan [24]. Figure2 demonstrates the FNET/GridEye sensor deployment around the world. In this study, we select 12 FDRs deployed in different Interconnection systems around the world. Table1 gives the basic information of all selected FDRs. For example, the first three FDRs record the frequency of Eastern Interconnection (EI), Western Electricity Coordinating Council (WECC) and Electric Reliability Council of Texas (ERCOT) systems in North America, respectively. The FDR deployed in Aalborg, Denmark collects the frequency of the synchronous grid of Continental Europe.

Table 1. Basic information of the selected FDRs in this study.

FDR Location Nominal Frequency Energies 2017, 10, 1283 1 USA, Seattle 60 Hz 3 of 15 2 USA, Matton 60 Hz The frequency 3disturbance Sweden,recorder Stockholm(FDR), a single-phase variant 50 Hzof the phasor measurement unit (PMU), is the 4main sensor of USA, the SanFNET/Gri AngelodEye [21]. In comparison 60 Hz with the conventional PMU, which requires5 high production Brazil, and Itajub instalá lation cost, the FDR60 Hz measures from a normal single-phase electrical6 outlet at the Japan, 120 Karuizawa V distribution level [22]. These 60 Hz measurements are then synchronized by Global7 Positioning UK, System Sheffield (GPS)-based timestamps 50 Hz and transferred through Internet to the phasor8 data concentrator Denmark, (PDC) Aalborg for data processing and 50 long Hz -term storage [23]. After over ten years of development,9 more China, than Shanghai 200 FDRs have been deployed 50 Hz in main interconnection systems of North America10 [24]. Figure Australia, 1 shows Brisbane the location of FDRs deploy 50 Hz ed in North America up to now. On the other11 hand, the FNET/GridEye India, Kanpur also serves other interconnection 50 Hz systems around the 12 Latvia, Riga 50 Hz world. Up to now, over 50 FDRs have been deployed worldwide, for example, China, Europe and Japan [24]. Figure 2 demonstrates the FNET/GridEye sensor deployment around the world.

Figure 1. FNET/GridEye sensor deployment in North America. The red point shows the frequency Figure 1. FNET/GridEye sensor deployment in North America. The red point shows the frequency disturbance recorder (FDR) location. disturbance recorder (FDR) location.

Energies 2017, 10, 1283 3 of 15

The frequency disturbance recorder (FDR), a single-phase variant of the phasor measurement unit (PMU), is the main sensor of the FNET/GridEye [21]. In comparison with the conventional PMU, which requires high production and installation cost, the FDR measures from a normal single-phase electrical outlet at the 120 V distribution level [22]. These measurements are then synchronized by Global Positioning System (GPS)-based timestamps and transferred through Internet to the phasor data concentrator (PDC) for data processing and long-term storage [23]. After over ten years of development, more than 200 FDRs have been deployed in main interconnection systems of North America [24]. Figure 1 shows the location of FDRs deployed in North America up to now. On the other hand, the FNET/GridEye also serves other interconnection systems around the world. Up to now, over 50 FDRs have been deployed worldwide, for example, China, Europe and Japan [24]. Figure 2 demonstrates the FNET/GridEye sensor deployment around the world.

EnergiesFigure2017, 101. ,FNET/GridEye 1283 sensor deployment in North America. The red point shows the frequency4 of 15 disturbance recorder (FDR) location.

Figure 2. FNET/GridEye sensor deployment around the world. The colorful region indicates the area monitored by FNET/GridEye.

3. Statistical Analysis on Time Error of Synchronous Electric Clock

3.1. Time Error Calculation In this study, we assume an ideal synchronous clock using power grid frequency, which means there is no time error inside this ideal clock. Then, we only consider the impact of the frequency deviation on its time error. The instantaneous time error at time t caused by frequency deviation can be written as: f − f ∗ ∆T = t × τ, (1) t f ∗ ∗ where f is the nominal frequency (60 Hz in North America), ft is the real-time frequency recorded by FNET/GridEye at time t. τ is the temporal resolution of frequency measurements. In this paper, τ = 0.1 because the FDR records power line frequency every 0.1 s. Then, the accumulative time error up to time t can be calculated by: ∆T = ∑ ∆Tt, (2) t According to Equations (1) and (2), if power line frequency has been running 2 mHz high (i.e., 60.002 Hz), a synchronous clock using this frequency as its timing reference would run fast 1.2 s after 10 h (i.e., 2 mHz/60 Hz × 10 h × 3600 s/h = 1.2 s).

3.2. Time Error Analysis in North America Figure3 shows the change of the time error over one month in EI system of North America. This time error is displayed by an ideal synchronous clock. To compute the time error reasonably, the median time error over one month is set as the time reference of this ideal synchronous clock. If the time error gives a positive value, the clock runs fast. On the contrary, the negative time error indicates that the clock runs slow. From Figure3a, it can be seen that the time error went up and down many in one month. Although the maximum time error once reached up to about +18.38 s, the average time error was only +00.78 s, meaning the synchronous clock could likely run very well in EI system. Energies 2017, 10, 1283 5 of 15 s, the average time error was only +00.78 s, meaning the synchronous clock could likely run very well in EI system. Figure 3b presents the probabilistic distribution of time error in one month. From Figure 3b, it can be observed that the possibility of running fast seems to be quite close to the possibility of running slow. Figure 4 presents the change of the time error in October 2016 for WECC system of North America. From Figure 4, it can be observed that the results of WECC system are similar to those of EI Energies 2017, 10, 1283 5 of 15 system shown in Figure 3. The accumulative time error changed from −09.58 to +11.14 s. From the times, the erroraverage distribution time error depicted was only in +00.78 Figure s, 4b,me aningit can thebe synchronousfound that if clockthe clock could uses likely the run WECC very frequencywell in EI system.as its timing Figure reference, 3b presents the possibilitythe probabilis of runningtic distribution fast and of running time error slow in isone quite month. close. From The averageFigure 3b, time it errorcan be was observed about +00.16 that thes. possibility of running fast seems to be quite close to the possibilityFigure of 5 showsrunning the slow. time error change in ERCOT system of North America with the same period of FiguresFigure 3 and4 presents 4. Compared the change with EIof and the WECCtime error systems, in October ERCOT 2016system for is WECC a minor system interconnection of North EnergiessystemAmerica.2017 because From, 10, 1283 Figureit only 4,covers it can most, be observed but not that all, ofthe Texas. results From of WECC Figure system 5a, it canare similarbe observed to those that5 of of the EI 15 timesystem error shown did notin Figure change 3. sharply The accumulative over one month. time errorThe maximum changed fromfast time −09.58 error to +11.14is +07.15 s. Froms and the maximumtime error slowdistribution time error depicted is −05.68 in Figures. On the 4b, other it can hand, be found the time that error if the distribution clock uses in the Figure WECC 5b Figuredemonstratesfrequency3b presents as its that timing thethe probabilistic possibility reference, theof distribution running possibility fast of of timeis running nearly error equalfast in one and to month. therunning possibility From slow Figure is of quite running3b, close. it can slow. The be observedTheaverage average time that time error the possibilityerror was overabout one of +00.16 running month s. fastis +00.58 seems s, tovery be quiteclose closeto zero. to the possibility of running slow. Figure 5 shows the time error change in ERCOT system of North America with the same period of Figures 3 and 4. Compared with EI and WECC systems, ERCOT system is a minor interconnection system because it only covers most, but not all, of Texas. From Figure 5a, it can be observed that the time error did not change sharply over one month. The maximum fast time error is +07.15 s and the maximum slow time error is −05.68 s. On the other hand, the time error distribution in Figure 5b demonstrates that the possibility of running fast is nearly equal to the possibility of running slow. The average time error over one month is +00.58 s, very close to zero.

(a) (b)

Figure 3.3.Time Time error error change change over over one one month month in Eastern in East Interconnectionern Interconnection (EI) system (EI) ofsystem North of America. North (America.a) Time-series (a) Time-series curve of time curve error of time in October error in 2016; October (b) Probabilistic 2016; (b) Probabilistic distribution distribution function of function time error of intime one error month. in one The month. blue color The presentsblue color the presents fast time the error. fast time The orangeerror. The color orange indicates color the indicates slow time the error.slow time The greyerror. line The shows grey line the estimatedshows the probabilityestimated probability density of timedensity error. of time error.

Figure4 presents the change of the time error in October 2016 for WECC system of North America. (a) (b) From Figure4, it can be observed that the results of WECC system are similar to those of EI system shownFigure in Figure 3. Time3. The error accumulative change over time one error month changed in East fromern Interconnection−09.58 to +11.14 (EI) s. system From theof North time error distributionAmerica. depicted (a) Time-series in Figure curve4b, of ittime can error befound in October that 2016; if the (b clock) Probabilistic uses the distribution WECC frequency function of as its timingtime reference, error in theone possibilitymonth. The of blue running color presents fast and the running fast time slow erro isr. quite The close.orange The color average indicates time the error was aboutslow time +00.16 error. s. The grey line shows the estimated probability density of time error.

(a) (b)

Figure 4. Time error change over one month in Western Electricity Coordinating Council (WECC) of North America. (a) Time-series curve of time error in October 2016; (b) Probabilistic distribution function of time error in one month. The blue color presents the fast time error. The orange color indicates the slow time error. The grey line shows the estimated probability density of time error.

(a) (b)

FigureFigure 4. TimeTime error error change change over over one one month month in in Wester Westernn Electricity Electricity Coordinating Coordinating Council Council (WECC) (WECC) of ofNorth North America. America. (a) ( aTime-series) Time-series curve curve of of time time error error in in October October 2016; 2016; (b) ProbabilisticProbabilistic distributiondistribution

functionfunction ofof timetime errorerror inin oneone month.month. TheThe blueblue colorcolor presentspresents thethe fastfast timetime error.error. TheThe orangeorange colorcolor indicatesindicates thethe slowslow timetime error.error. TheThe greygrey lineline showsshows thethe estimatedestimated probabilityprobability densitydensity of of time time error. error.

Figure5 shows the time error change in ERCOT system of North America with the same period of Figures3 and4. Compared with EI and WECC systems, ERCOT system is a minor interconnection system because it only covers most, but not all, of Texas. From Figure5a, it can be observed that the time error did not change sharply over one month. The maximum fast time error is +07.15 s and the maximum slow time error is −05.68 s. On the other hand, the time error distribution in Figure5b demonstrates that the possibility of running fast is nearly equal to the possibility of running slow. The average time error over one month is +00.58 s, very close to zero. Energies 2017, 10, 1283 6 of 15 Energies 2017, 10, 1283 6 of 15

(a) (b)

Figure 5. Time error changechange overover oneonemonth month in in Electric Electric Reliability Reliability Council Council of of Texas Texas (ERCOT) (ERCOT) system system of ofNorth North America. America. (a) Time-series(a) Time-series curve curve of the timeof the error time in Octobererror in 2016; October (b) Probabilistic 2016; (b) Probabilistic distribution distributionfunction of timefunction error of over time one erro month.r over Theone bluemonth. color The indicates blue color the indicates fast time the error. fast The time orange error. color The orangepresents color the slowpresents time the error. slow The time grey error. line showsThe grey the line estimated shows probabilitythe estimated density probability of time density error. of time error. 3.3. Time Error Tendency in Recent Years 3.3. Time Error Tendency in Recent Years Next, we analyze the changing tendency of time error over the past few years. In this subsection, Next, we analyze the changing tendency of time error over the past few years. In this three statistical indicators are calculated for each month and then their changes are used to study the subsection, three statistical indicators are calculated for each month and then their changes are used time error trend. These three indicators include: to study the time error trend. These three indicators include: • Maximum Error (i.e., the maximum running fast time error over a specified period); • Maximum Error (i.e., the maximum running fast time error over a specified period); • Minimum Error (i.e., the maximum running slow time error over a specified period); • Minimum Error (i.e., the maximum running slow time error over a specified period); • • Average ErrorError (i.e.,(i.e., thethe averageaverage timetime errorerror overover aa specifiedspecified period).period). Note thatthat thethe maximummaximum error error always always takes takes a positivea positive value value and and the minimumthe minimum error error always always takes takesa negative a negative value. value. The average The average error can error be eithercan be positive either positive or negative. or negative. Figure6 presentsFigure 6 thepresents monthly the monthlychange of change the above of the three above indicators three forindicators EI system for fromEI system January from 2014 January to April 2014 2017. to Note April that 2017. the Note time thaterror the of time each error month of haseach the month same has time the reference. same time The reference. time error The of time next e monthrror of next would month cumulative would cumulativeupon the latest upon time the error latest of time previous error month. of previous From Figuremonth.6 ,From it can Figure be seen 6, that it can the be maximum seen that error the maximumseems to be error gradually seems increasing to be gradually over the increasing past few years.over the In 2014,past thefew monthly years. In maximum 2014, the errormonthly was maximumgenerally less error than was +05.00 generally s. However, less than it +05.00 has climbed s. However, up to above it has +10.00climbed s since up to 2016. above By +10.00 contrast, s since the 2016.monthly By contrast, minimum the error monthly shows minimum a downward error trend show ins recenta downward years. Itstrend value in decreasedrecent years. from Its nearlyvalue decreased−10.00 s in from 2014 nearly to about −10.00−05.00 s in s 2014 in 2017. to about On the −05.00 other s hand, in 2017. we On also the observe other thathand, the we variation also observe range thatof time the errorvariation has a range tendency of time to become error has large a tendency in recent to years. become Nevertheless, large in recent the average years. Nevertheless, error did not thechange average too mucherror did from not 2014 change to 2017 too and much its valuefrom 2 was014 alwaysto 2017 lowerand its than value± 3.50was s,always meaning lower that than the ±3.50clock s, can meaning still work that very the clock well. can Another still work interesting very well. observation Another isinteresting that there observation was a turning is that point there for wasthe average a turning error point in Septemberfor the average 2015. error Before in thisSeptem turningber 2015. point, Before the monthly this turning average point, error the was monthly always averagenegative. error After was this always point, however, negative. the After average this errorpoint, turned however, to be the a positive average value, error which turned means to be the a positivesynchronous value, clock which was means more the likely synchronous to run faster clock than wa thes standardmore likely time. to run faster than the standard time.

Energies 2017, 10, 1283 7 of 15 Energies 2017, 10, 1283 7 of 15 Energies 2017, 10, 1283 7 of 15

Figure 6. Monthly change of the time error for Eastern Interconnection (EI) system of North America Figure 6. Monthly change of the time error for Eastern Interconnection (EI) system of North America Figure 6.from Monthly 2014 to 2017.change The of blue the bar time shows error the formaximum Eastern time Interconnection error (positive value, (EI) i.e.,system running of Northfast time America from 2014 to 2017. The blue bar shows the maximum time error (positive value, i.e., running fast time from 2014error) to 2017.in this Themonth. blue The bar orange shows bar the presents maximum the minimum time error time (positiveerror (negat value,ive value, i.e., i.e., running running fast time error) inslow this time month. error) Thein this orange month. bar The presents grey line indicates the minimum the average time time error error (negative over one month. value, i.e., running error) in this month. The orange bar presents the minimum time error (negative value, i.e., running slow time error) in this month. The grey line indicates the average time error over one month. slow timeTexas error) produces in this themonth. most The wind grey power line ofindicates any stat thees inaverage the USA. time [25]. error Wind over power one month. generation accounted for 12.63% of the total electricity generation in Texas during 2016. Figure 7 demonstrates Texasthe yearly produces change the of mostmost the time windwind error powerpower for ERCOT ofof anyany system statesstates from inin the the2008 USA.USA. to 2017. [[25].25 In]. Windeach year, power a typical generation accountedmonth forfor 12.63%is12.63% selected ofof the asthe a total totalreference electricity electricity for calculating generation genera tionsome in in Texasstatistics Texas during duringof the 2016. time 2016. Figureerror, Figure including7 demonstrates 7 demonstrates the the yearlythe yearly changemaximum, change of theminimum, of timethe time errormedian error for time ERCOT for error ERCOT and system their system fromquartiles. 2008from In toeach2008 2017. month, to In2017. eachthe medianIn year, each time a year, typical error a typical month over this month is set as the time reference. As shown in Figure 7, although the annual wind power ismonth selected is selected as a reference as a reference for calculating for calculating some statistics some ofstatistics the time of error,the time including error, theincluding maximum, the minimum,generation median has time tripled error from and2008 their(16,225 quartiles. GWh) to 2016 In each(57,551 month, GWh) in the Texas median [26], which time may error have over this maximum,negative minimum, impacts onmedian power timesystem e rrorfrequency and theirstability quartiles. because of In wind each power month, fluctuation the median [27], there time error monthover this isseems setmonthas to thebe is no timeset obvious as reference. the timechanges reference. As for shown these As intime Figureshown error 7statistics. ,in although Figure This 7, the althoughmight annual be because windthe annual powerthe ERCOT wind generation power hasgeneration tripledcontinues has from tripled to 2008 provide (16,225from TEC 2008 GWh)services (16,225 to to 2016 blackGWh) (57,551 out to the2016 GWh)accumulated (57,551 in TexasGWh) time [ 26errorin ],Texas whichwhen [26], it may arises. which have More may negative have impactsnegativeinformation onimpacts power on about system power TEC frequency systemservice is frequency presented stability inbecausestabi Sectionlity of 4.because The wind accumulative power of wind fluctuation powertime error fluctuation [was27], generally there [27], seems there to beseems no obvioustolower be nothan changes obvious ±10.00 fors. changesMoreover, these time for the errorthese average statistics.time time e rrorerror This statistics.did might not change beThis because toomight much thebe over ERCOTbecause the past continuesthe ten ERCOT to years and its value was always lower than ±02.00 s. providecontinues TEC to servicesprovide toTEC black services out the to accumulated black out the time accumulated error when ittime arises. error More when information it arises. aboutMore TECinformation service isabout presented TEC service in Section is presented4. The accumulative in Section time4. The error accumulative was generally time lower error thanwas generally±10.00 s. Moreover,lower than the ±10.00 average s. Moreover, time error the did average not change timetoo error much did overnot change the past too ten much years andoverits the value past wasten alwaysyears and lower its value than ±was02.00 always s. lower than ±02.00 s.

Figure 7. Yearly change of the time error for Electric Reliability Council of Texas (ERCOT) system of North America from 2008 to 2017. One typical month is selected to represent every year. The box-plot depicts the maximum and minimum time error (the ends of the whiskers), the first and third quartiles (the bottom and top of the box), and the mean time error (the band inside the box).

Figure 7. Yearly change of the time error for Electric Reliability Council of Texas (ERCOT) system of Figure 7. Yearly change of the time error for Electric Reliability Council of Texas (ERCOT) system of North America from 2008 to 2017. One typical month is selected to represent every year. The box-plot depicts thethe maximummaximum and and minimum minimum time time error error (the (the ends ends of the of whiskers), the whiskers), the first the and first third and quartiles third (thequartiles bottom (the and bottom top of and the top box), of andthe box), the mean and the time mean error time (the error band (the inside band the inside box). the box).

Energies 2017, 10, 1283 8 of 15

3.4. Time Error Analysis around the World In addition to the three interconnection systems in North America discussed above, the time error of the synchronous clock using power grid frequency in worldwide power grids are also analyzed in this subsection. Table2 shows some important statistics of the monthly time error around the world. From Table2, it can be observed that the time error is usually less than ±30.00 s in most countries. Moreover, power grid frequency, as a timing source with almost zero-cost, stable performance and high accuracy, is generally accessible and available anywhere, anytime as long as there are power transmission lines in service. Another interesting observation in Table2 is that the average time error is positive for most countries except for India and Latvia, meaning that the synchronous clock is more likely to run fast. This also indicates that the long-term power grid frequency is slightly higher than its nominal value. More information about the long-term power system frequency distribution pattern is shown in Section5. In Table2, we also find some countries with the time error larger than one minute, such as Brazil and China. This is because these countries might not provide TEC service. More information about TEC service is presented in Section4.

Table 2. Statistical analysis of the monthly time error around the world.

Maximum Time Error Minimum Time Error Average Time Error Location (Run Fast, Seconds) (Run Slow, Seconds) (Seconds) USA, Seattle +11.14 −09.58 +00.16 USA, Matton +18.38 −08.05 +00.78 Sweden, Stockholm +20.52 −12.11 +02.97 USA, San Angelo +07.15 −05.68 +00.58 Brazil, Itajubá +80.39 −00.00 +43.02 Japan, Karuizawa +07.59 −06.75 +00.04 UK, Sheffield +16.72 −16.10 +03.34 Denmark, Aalborg +17.88 −10.81 +01.07 China, Shanghai +333.94 −00.00 +180.70 Australia, Brisbane +04.43 −05.16 +00.08 India, Kanpur +00.00 −144.76 −69.83 Latvia, Riga +02.17 −35.85 −17.37

4. Time Error Correction Practice around the World

4.1. Time Error Corretion Provided by Untilities Electric utilities keep the grid frequency running in a very small range, however, the fluctuations in the grid frequency might cause the time error of a few seconds during the period of one day [5]. This time error would not completely cancel out by its own. If electric utilities do not provide an additional time correction service, this error would accumulate over time and finally tend to cause a large time drift in the long term. To periodically remove the time error, electric utilities provide the time error correction (TEC) service [28]. When the time error accumulates to a predefined value, the time monitor sends a notice to all balancing authorities to offset the scheduled frequency by a small number (e.g., 20 mHz) [29]. This offset will be maintained for several hours until the time error has dropped below the satisfied value. Two typical TEC services provided by electric utilities in North America are introduced as follows.

4.1.1. Fast Time Error Correction Fast TEC service is provided for a positive accumulative time error. Figure8 gives an illustrative example of fast TEC process in EI system of North America. From Figure8a, it can be observed that the accumulative time error went up to +08.41 s at 04:00 p.m. on 24 October 2016. Then, electric utilities started to provide the TEC service and the accumulative time error began dropping since that time. In this case, the TEC service lasted about 16 hours and stopped working at 08:00 a.m. on Energies 2017, 10, 1283 9 of 15

Energies 2017, 10, 1283 9 of 15 25 October 2016. Figure8b illustrates the change of the average system frequency with the same periodthe same of Figureperiod8 ofa. FromFigure Figure 8a. From8b, it Figure can be 8b, observed it can be that observed the average that the system average frequency system was frequency above 60.000was above Hz before60.000 andHz before after the and fast after TEC the service. fast TE However,C service. However, the average the frequency average frequency dropped todropped 59.985, 15to mHz59.985, lower 15 mHz than lower 60.000 than Hz, when60.000 electric Hz, when utilities electric provided utilities fast provided TEC services. fast TEC The declineservices. of The the averagedecline of frequency the average is mainly frequency because is mainly the scheduled because the frequency scheduled has frequency been offset has by been a small offset number by a duringsmall number the TEC during process. the Consequently, TEC process. this Consequently offset away, fromthis offset the nominal away from frequency the nominal (60.000 frequency Hz) leads to(60.000 a rapid Hz) decline leads to of a the rapid accumulative decline of timethe accumulative error in several time hours. error in several hours.

(a) (b)

Figure 8.8. IllustrativeIllustrative exampleexample of of fast fast time time error error correction correction (TEC) (TEC) process process in Easternin Eastern Interconnection Interconnection (EI) system(EI) system of North of North America: America: (a) Time (a) Time error error change change from from 24 October 24 October 2016 2016 07:00 07:00 a.m. toa.m.25 to October 25 October 2016 01:002016 01:00 p.m.; p.m.; (b) Power (b) Power system system frequency frequency change change during during the same the same period period of (a ).of The (a). greyThe grey vertical vertical line indicatesline indicates the starting/stoppingthe starting/stopping point point of theof the TEC TEC process. process. The The red red solid solid line line indicatesindicates thethe averageaverage systemsystem frequencyfrequency before,before, duringduring andand afterafter thethe TECTEC process.process.

4.1.2. Slow Time Error Correction 4.1.2. Slow Time Error Correction Slow TEC service is used for a negative accumulative time error. Figure 9 presents an Slow TEC service is used for a negative accumulative time error. Figure9 presents an illustrative illustrative example of slow TEC process in EI system. From Figure 9a, it can be observed that the example of slow TEC process in EI system. From Figure9a, it can be observed that the accumulative accumulative time error went up to −08.47 s. Then, electric utilities started to provide the slow TEC time error went up to −08.47 s. Then, electric utilities started to provide the slow TEC service and the service and the accumulative time error began dropping since that time. In this case, the TEC process accumulative time error began dropping since that time. In this case, the TEC process lasted about lasted about 10 h from 01:00 a.m. to 11:00 a.m. on 11 May 2015. From Figure 9b, it can be seen that the 10 h from 01:00 a.m. to 11:00 a.m. on 11 May 2015. From Figure9b, it can be seen that the average average frequency increased to 60.017, 17 mHz higher than 60.000 Hz, when electric utilities frequency increased to 60.017, 17 mHz higher than 60.000 Hz, when electric utilities provided slow provided slow TEC services. It indicates that the scheduled frequency was offset by a small number TEC services. It indicates that the scheduled frequency was offset by a small number during the TEC during the TEC process. Then, this offset away from 60.000 Hz leads to a rapid elimination of the process. Then, this offset away from 60.000 Hz leads to a rapid elimination of the accumulative time accumulative time error in several hours. error in several hours. Recently, there are ongoing proposals to stop TEC services, since TEC services may negatively Recently, there are ongoing proposals to stop TEC services, since TEC services may negatively affect power system stability. This could have impacts on the timekeeping accuracy of synchronous affect power system stability. This could have impacts on the timekeeping accuracy of synchronous clocks. According to the analysis results in [5], it is believed that the time error of synchronous clocks clocks. According to the analysis results in [5], it is believed that the time error of synchronous clocks would significantly increase on the EI system. Nevertheless, it is still unknown what will be affected would significantly increase on the EI system. Nevertheless, it is still unknown what will be affected by the cancelation of TEC services since no one is quite sure how many clocks are using power line by the cancelation of TEC services since no one is quite sure how many clocks are using power line frequency as their timing sources. This topic is also outside of the scope of this paper and needs more frequency as their timing sources. This topic is also outside of the scope of this paper and needs more research in future. research in future.

Energies 2017, 10, 1283 10 of 15 Energies 2017, 10, 1283 10 of 15

(a) (b)

Figure 9. Illustrative example of slow time error correction (TEC) process in Eastern Interconnection Figure 9. Illustrative example of slow time error correction (TEC) process in Eastern Interconnection (EI) system of North America: (a) Time error change from 10 May 2015 07:00 p.m. to 11 May 2015 (EI) system of North America: (a) Time error change from 10 May 2015 07:00 p.m. to 11 May 2015 07:00 p.m.; (b) Power system frequency change during the same period of (a). The grey vertical line b a 07:00indicates p.m.; ( )the Power starting/stopping system frequency point of change the TEC during process. the The same red period solid line of ( indicates). The grey the verticalaverage line indicatessystem the frequency starting/stopping before, during point and ofafter the the TEC TEC process. process. The red solid line indicates the average system frequency before, during and after the TEC process. 4.2. Worldwide Practices on Time Error Correction 4.2. WorldwideApart Practices from three on Timeinterconnection Error Correction systems in North America, other interconnection systems Apartaround from the threeworld interconnectionare also providing systems TEC services in North at America, this time. other Figure interconnection 10 presents an systemsillustrative around example of the TEC process in the Japanese Western Interconnection system. Figure 10a gives the the world are also providing TEC services at this time. Figure 10 presents an illustrative example of change of time error over one month. From Figure 10a, it can be observed that Japanese utilities also the TEC process in the Japanese Western Interconnection system. Figure 10a gives the change of time provide the TEC service similar to that of North American utilities. Once the accumulative time error errorhas over reached one month. a predefined From value, Figure TEC 10 servicesa, it can start be work observeding to thatcancel Japanese out this time utilities error. also However, provide it the TEC serviceseems that similar compared to that with of NorthNorth American utilities, utilities. the Once threshold the accumulative to start TEC service time error is set has to be reached a a predefinedlow value value, in Japanese TEC servicesutilities, startusually working 6–7 s. Another to cancel observation out this timeis that error. Japanese However, utilities it provide seems that comparedTEC services with North more Americanfrequently than utilities, North the American threshold utilities. to start According TEC service to the istime set error to be distribution a low value in Japanesedepicted utilities, in Figure usually 10b, 6–7the maximu s. Anotherm time observation error is about is that +7.59 Japanese s, the minimum utilities time provide error TECis nearly services more− frequently6.75 s, and the than average North time American error is close utilities. to zero According. Thus, the tosynchronous the time error electric distribution clock using depicted power in Figureline 10 b,frequency the maximum could likely time run error very is aboutwell in +7.59 Japan. s, the minimum time error is nearly −6.75 s, and the average time error is close to zero. Thus, the synchronous electric clock using power line frequency could likely run very well in Japan. On the other hand, we also find that there are some Interconnection systems not providing TEC services for synchronous electric clocks. An illustrative example is the Brazil Interconnection system, as shown in Figure 11. From Figure 11a, it can be observed that the time error kept going up over this month. TEC services usually cause to a continuous decrease of the accumulative time error. However, such phenomenon was never found in Figure 11a of Brazil Interconnection system. Finally, the time error accumulated to a significant value (+80.39 s). The above observation is also confirmed by the probability distribution of power grid frequency shown in Figure 11b. From Figure 11b, it can be seen that power grid frequency( followsa) the normal distribution very well. But,(b) the mean frequency is 2 mHz higherFigure than 10. Time the nominalerror change frequency over one month (60 Hz). in Karuizawa, This deviation Janpa. ( isa) theTime-series main reason curve of why time the clock finally accumulatederror in October to a2016; large (b) timeProbabilistic error atdistribution the end function of one month.of time error Thus, in one the month. synchronous The blue clock in Brazil wouldcolorvery presents likely the fast have time a bigerror. time The orange drift in color the indicates long term. the slow time error. The grey line shows the estimated probability density of time error.

Energies 2017, 10, 1283 10 of 15

(a) (b)

Figure 9. Illustrative example of slow time error correction (TEC) process in Eastern Interconnection (EI) system of North America: (a) Time error change from 10 May 2015 07:00 p.m. to 11 May 2015 07:00 p.m.; (b) Power system frequency change during the same period of (a). The grey vertical line indicates the starting/stopping point of the TEC process. The red solid line indicates the average system frequency before, during and after the TEC process.

4.2. Worldwide Practices on Time Error Correction Apart from three interconnection systems in North America, other interconnection systems around the world are also providing TEC services at this time. Figure 10 presents an illustrative example of the TEC process in the Japanese Western Interconnection system. Figure 10a gives the change of time error over one month. From Figure 10a, it can be observed that Japanese utilities also provide the TEC service similar to that of North American utilities. Once the accumulative time error has reached a predefined value, TEC services start working to cancel out this time error. However, it seems that compared with North American utilities, the threshold to start TEC service is set to be a low value in Japanese utilities, usually 6–7 s. Another observation is that Japanese utilities provide TEC services more frequently than North American utilities. According to the time error distribution depicted in Figure 10b, the maximum time error is about +7.59 s, the minimum time error is nearly

Energies−6.75 s,2017 and, 10 the, 1283 average time error is close to zero. Thus, the synchronous electric clock using power11 of 15 line frequency could likely run very well in Japan.

Energies 2017, 10, 1283 11 of 15

On the other hand, we also find that there are some Interconnection systems not providing TEC services for synchronous electric clocks. An illustrative example is the Brazil Interconnection system, as shown in Figure 11. From Figure 11a, it can be observed that the time error kept going up over this month. TEC services usually cause to a continuous decrease of the accumulative time error. However, such phenomenon(a ) was never found in Figure 11a of Brazil Interconnection(b) system. Finally, the time error accumulated to a significant value (+80.39 s). The above observation is also confirmedFigure by 10.10. the TimeTime probability error error change change distribution over over one one month ofmonth power in Karuizawa,in Karuizawa,grid frequency Janpa. Janpa. (a shown) Time-series(a) Time-series in Figure curve curve11b. of time From of errortime Figure 11b, inerrorit can October in be October seen 2016; that (2016;b) Probabilisticpower (b) Probabilistic grid distribution frequency distribution functionfollows function ofthe time normal of errortime indistributionerror one in month. one month. very The bluewell. The color blueBut, the meanpresentscolor frequency presents the fastis the 2 time fastmHz error.time higher error. The orange thanThe orange the color nominal color indicates indicates frequency the slow the slow time(60 time error.Hz). error. This The The greydeviation grey line line shows is shows the the main the estimated probability density of time error. reasonestimated why the probability clock finally density accumulated of time error. to a large time error at the end of one month. Thus, the synchronous clock in Brazil would very likely have a big time drift in the long term.

(a) (b)

Figure 11. Time error change over one month in ItajubItajubá,á, Brazil.Brazil. (a) Time-series curve of time error in October 2016; (b) ProbabilisticProbabilistic distributiondistribution function of thethe system frequency in oneone month.month. The blue color presents the fast time error. The orange color indicates the slow time error. The grey line shows the estimatedestimated probability probability density density of powerof power grid grid frequency. frequency. The verticalThe vertical dashed dashed line presents line presents the average the frequencyaverage frequency of this month. of this month.

Using the frequency measurements collected by worldwide FDRs in FNET/GridEye, we Using the frequency measurements collected by worldwide FDRs in FNET/GridEye, we analyze analyze the TEC practice around the world and identify regions of the world where electric utilities the TEC practice around the world and identify regions of the world where electric utilities provide provide TEC services from those without TEC services according to measurements collected in 2016. TEC services from those without TEC services according to measurements collected in 2016. In this In this study, if the average time error (absolute value) over one typical month of 2016 is larger than study, if the average time error (absolute value) over one typical month of 2016 is larger than 10.00 s, 10.00 s, this interconnection system would be considered to not provide TEC services. Otherwise, it this interconnection system would be considered to not provide TEC services. Otherwise, it would be would be considered to provide TEC services. Figure 12 demonstrates the identification result of considered to provide TEC services. Figure 12 demonstrates the identification result of TEC practices TEC practices around the world. From Figure 12, it can be observed that the countries providing around the world. From Figure 12, it can be observed that the countries providing TEC services are TEC services are concentrated in North America and Europe. In Asia and South America, however, concentrated in North America and Europe. In Asia and South America, however, most countries do most countries do not provide TEC services. Therefore, synchronous electric clocks installed in these not provide TEC services. Therefore, synchronous electric clocks installed in these countries usually countries usually tend to have a large time drift in the long term. tend to have a large time drift in the long term.

Energies 2017, 10, 1283 12 of 15 Energies 2017, 10, 1283 12 of 15

Figure 12. Time error correction (TEC) practice around the world. The green region indicates the Figure 12. Time error correction (TEC) practice around the world. The green region indicates the countries providing TEC service. The orange region indicates the countries not providing TEC countries providing TEC service. The orange region indicates the countries not providing TEC service. service. 5. Power System Frequency Distribution Pattern Analysis 5. Power System Frequency Distribution Pattern Analysis As discussed above, the long-term average of power grid frequency has great influence on the As discussed above, the long-term average of power grid frequency has great influence on the accumulative time error of synchronous electric clocks. Specifically, as demonstrated in Figure 11b, accumulative time error of synchronous electric clocks. Specifically, as demonstrated in Figure 11b, the monthly average frequency higher than the nominal value by only 2 mHz could eventually the monthly average frequency higher than the nominal value by only 2 mHz could eventually lead lead to a significant time drift (+80.39 s) at the end of one month. On the other hand, according to to a significant time drift (+80.39 s) at the end of one month. On the other hand, according to Equations (1) and (2), if the accumulative time error ∆T is forced to be zero, the following equation Equations (1) and (2), if the accumulative time error ∆ is forced to be zero, the following equation can be derived can be derived T 1 ∗ f = ∑ ft = f , (3) T 1 ̅ t=1 ∗ = = , (3) ∗ where f is the long-term average of system frequency and f is the nominal frequency. As shown by Equationwhere ̅ (3),is the a necessarylong-term conditionaverage of for system the accumulative frequency and time ∗error is the being nominal zero frequency. is that the long-termAs shown averageby Equation frequency (3), shoulda necessary be equal condition to the nominal for the frequency. accumulative Therefore, time iterror is believed being thatzero the is long-term that the averagelong-term of average power grid frequency frequency should and itsbe distributionequal to thepattern nominal is frequency. also very valuable Therefore, for statisticalit is believed analysis that ofthe the long-term time error. average To do of so, power power grid system frequency frequency and its distribution distribution patterns pattern are is studiedalso very in valuable this section for andstatistical the differences analysis of between the time countries error. To providing do so, andpower not system providing frequency TEC services distribution are also patterns compared. are studiedFigure in this13 presents section theand probability the differences density between function countries (PDF) of providing power grid and frequency not providing in countries TEC providingservices are TEC also services.compared. The PDF curve is depicted by the kernel density estimator [30,31] using the frequencyFigure 13 measurementspresents the probability of one year density (2016). functi Fromon Figure (PDF) 13of ,power it can begrid observed frequency that in the countries yearly PDFproviding curve TEC appears services. to be The a standard PDF curve normal is depicted distribution by the [ 32kernel]. Another density observation estimator [30,31] is that using different the interconnectionfrequency measurements systems haveof one different year (2016). frequency From Fi deviations.gure 13, it can EI, be WECC, observed ERCOT that the and yearly European PDF systemscurve appears have very to be small a standard frequency normal deviations distributi (fromon− 0.05[32]. HzAnother to 0.05 observation Hz). As shown is that in Figuredifferent 13, althoughinterconnection the frequency systems distribution have different pattern frequency varies fordeviations. these countries EI, WECC, providing ERCOT TEC and services, European their averagesystems frequencyhave very deviationssmall frequency (shown deviations by numbers (from in − brackets)0.05 Hz to are 0.05 all Hz). less thanAs shown±0.10 in mHz. Figure Thus, 13, thealthough synchronous the frequency clock using distribution power gridpattern frequency varies infor these these countries countries could providing likely runTEC very services, well in their the longaverage term. frequency deviations (shown by numbers in brackets) are all less than ±0.10 mHz. Thus, the synchronousFigure 14 clock shows using the yearlypower PDFgrid curvesfrequency of power in these grid countries frequency could in countries likely run not very providing well in TEC the services.long term. The yearly PDF curves of Russia and Brazil are close to standard normal distributions. On the contrary,Figure the 14 PDF shows curve the of yearly China PDF looks curves like aof saddle power (a grid roughly frequency bimodal in countries distribution), not providing which may TEC be causedservices. by The the yearly dead-band PDF ofcurves governors of Russia [32]. and For Brazil the three are systemsclose to shownstandard in Figurenormal 14 distributions., their frequency On deviationsthe contrary, are the all veryPDF smallcurve and of China usually looks vary fromlike a− saddle0.05 Hz (a to roughly 0.05 Hz. bimodal However, distribution), compared with which the may be caused by the dead-band of governors [32]. For the three systems shown in Figure 14, their frequency deviations are all very small and usually vary from −0.05 Hz to 0.05 Hz. However,

Energies 2017, 10, 1283 13 of 15 Energies 2017, 10, 1283 13 of 15 Energies 2017, 10, 1283 13 of 15 countriescompared shown with the in Figurecountries 13, theshown average in Figure frequency 13, th deviationse average frequency are all very deviations large in these are all countries very large not providingcomparedin these countries TECwith services.the notcountries providing Then, shown frequency TEC in Figureservices. deviations 13, Then,th graduallye average frequency accumulatefrequency deviations deviations over gradually time are and all finallyaccumulate very causelarge ainover big these time time countries and drift finally of synchronous not cause providing a big clocks time TEC indrif services. thet of long synchronous Then, term. frequency clocks indeviations the long term.gradually accumulate over time and finally cause a big time drift of synchronous clocks in the long term.

(a) (b) (a) (b) Figure 13.13. Probability distribution of power system frequencyfrequency in countries providing the time error correctionFigure 13. inProbability 2016.2016. ( a) distribution Three major of interconnectioninterconnection power system freq systemsuency in in NorthNorth countries America;America; providing ((b)) InterconnectionInterconnection the time error systemscorrection aroundaround in 2016. thethe ( world.aworld.) Three Figures Figures major in interconnectionin brackets brackets denote denote systems the the average average in North frequency frequency America; deviation deviation (b) Interconnection away away from from the nominalsystemsthe nominal around frequency. frequency. the world. Figures in brackets denote the average frequency deviation away from the nominal frequency.

Figure 14. Probability distribution of power system frequency in countries not providing the time error correction in 2016. Figures in brackets denote the average frequency deviation away from the Figure 14. Probability distribution of power system frequency in countries not providing the time nominal frequency. error correction in 2016. Figures in brackets denote the average frequency deviation away from the nominal frequency. 6. Conclusions

6. Conclusions In this paper, we used the power grid frequency measurements coming from the wide-area frequency monitoring network FNET/GridEye to carry out statistical analysis on the time error of In this paper, wewe usedused thethe powerpower gridgrid frequencyfrequency measurementsmeasurements coming from the wide-areawide-area synchronous electric clock. The time error correction (TEC) service provided by electric utilities was frequency monitoring network FNET/GridEye to to carry carry out out statistical statistical analysis analysis on on the the time error of investigated and then the worldwide power system practices on TEC services were analyzed. The synchronous electric electric clock. clock. The The time time error error correctio correctionn (TEC) (TEC) service service provided provided by electric by electric utilities utilities was regions of the world where electric utilities provide TEC services are identified from those without wasinvestigated investigated and then and thenthe worldwide the worldwide power power system system practices practices on TEC on TECservices services were were analyzed. analyzed. The TEC services. The following conclusions can be drawn from the analytical results. Theregions regions of the of theworld world where where electric electric utilities utilities provid providee TEC TEC services services are are identified identified from from those those without Firstly, the synchronous clock using power line frequency as its timing source usually run very TEC services. The following conclusions can be drawn fromfrom thethe analyticalanalytical results.results. well if utilities provide TEC services. Secondly, in order to periodically remove the accumulative Firstly, thethe synchronoussynchronous clock using power line frequency as its timing source usually run very time error, many electric utilities around the world are providing the TEC service through offsetting well if utilitiesutilities provideprovide TECTEC services.services. Secondly, in order to periodicallyperiodically remove thethe accumulativeaccumulative timethe scheduled error, many frequency electric utilitiesby a small around number. the worldThirdly, are according providing to the frequency TEC service measurements through offsetting in 2016, theanalytical scheduled results frequency present by that a small the number.countries Thirdly, providing according TEC servicesto frequency are concentratedmeasurements in in North 2016, analytical results present that the countries providing TEC services are concentrated in North

Energies 2017, 10, 1283 14 of 15 time error, many electric utilities around the world are providing the TEC service through offsetting the scheduled frequency by a small number. Thirdly, according to frequency measurements in 2016, analytical results present that the countries providing TEC services are concentrated in North America and Europe. In Asia and South America, however, most countries do not provide TEC services. Finally, the TEC service provided by electric utilities contributes to maintain the long-term average grid frequency at its nominal value. However, for the countries not providing TEC services, their long-term average frequency usually has a significant deviation from the nominal frequency.

Acknowledgments: This work was supported primarily by the Engineering Research Center Program of the National Science Foundation and the Department of Energy under NSF Award Number EEC-1041877 and the CURENT Industry Partnership Program. Author Contributions: Yili Liu, Wenpeng Yu and Yao Zhang conceived and designed the experiments; Yao Zhang performed the experiments; Yao Zhang, Yi Cui and Ling Wu analyzed the data; Wenxuan Yao and Shutang You carried out the theoretical analysis of the system; Yilu Liu contributed materials and analysis tools; Yao Zhang wrote the paper; all authors revised and approved the manuscript. Conflicts of Interest: The authors declare no conflicts of interest.

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