IEEE SIGNAL PROCESSING MAGAZINE [24] SEPTEMBER 2012
s an essential fixture of modern society, electricity is often taken for granted. In many cases, it becomes invisible or is ignored until it is not
there or it is time to pay the electric bill. Electricity has been around for well over a
century, and the march of industry and progress have creat-ed the most complex interconnected system in existence. In a delicate balancing act, the amount of electricity generation must track the amount consumed to prevent the system from collapsing, as there is only very limited storage capacity on the grid. The balance is maintained via a combination of predictions and control systems distributed across the grid. How well this balance is maintained produces signals that propagate across the entire system from the large generators to the wall outlets that are ubiquitous across the world. Observing these signals can provide a great deal of insight into the current status and operation of the power grid and can be done cheaply and accurately from inside a home or office.
INTRODUCTIONTraditionally, the power grid has been fairly opaque from a user perspective; the limited sensor data available to utilities has been closely guarded and restricted, mak-ing research into the area difficult and time consuming. Now, as the grid is transitioning from a centrally controlled architecture to one with increasingly diverse, smaller participants, the availability of data will also need to grow. The promise and goal of a smart grid is to enable a more intelligent, efficient, and reliable power grid with increasing user visibility and participation [1]. Technology has progressed to the point that it is possible for anyone to monitor the grid efficiently and cheaply. Simple signal processing techniques and inexpensive equipment could enable researchers from all over the world to observe local power grids in action from a large number of points. The additional visi-bility would promote new insights and improved understanding toward a more reliable efficient power grid.
A small network of sensors has been in place for several years as a frequency monitoring network (FNET) [2]. FNET con-sists of a consortium of universities, corporations and research entities, and is proving to be a valuable tool for researchers and industry. The concept embodied in FNET can be taken even further with even less expensive hardware, enabling grid sen-sors to be used for a much larger range of applications. Even the simplest sensors can provide significant insight into the operation of the power grid, either operating on their own or networked with other sensors. A cheap means of monitoring
Digital Object Identifier 10.1109/MSP.2012.2186763
[ Philip Top, Mark R. Bell, Ed Coyle, and Oleg Wasynczuk]
and reliable smart grid with increasing user visibility]
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the dynamic nature of the power grid has the potential to be used in distributed control systems, enabling automatic response to grid events. These types of controls will become ever more critical as electricity generation becomes more decentralized and custom-ers have increased ability to respond to changes. Widespread usage will increase openness and promote more resilient, secure, and efficient power grids around the world.
HISTORY OF THE GRIDTo understand complex systems, it is necessary to understand where the system came from and how it came to be in present form. This concept is especially true of the power grid in the United States. The first commercial power grid was created by Thomas Edison in 1882 on Pearl Street in New York City. This grid served wealthy clients with electric lighting. It was direct current (dc) system and took a tremendous amount of human energy and money to get started. In the next few decades, dc systems would give way to alternating current (ac) systems developed by Nikola Tesla and championed by Westinghouse. The original ac system operated on a single-phase of 133 Hz. Over the next 40 years, the capacity of the various U.S. electric systems increased from around 1 GW in 1900 to around 50 GW in 1940, and the frequency was standardized as 60 Hz. The expansion of the power grid was driven by the desire for increased profits; and, with that desire the progression of elec-trical services from the exclusive domain of the wealthy to pro-gressively lower income homes.
Up until 1896, power systems had mostly been local and sepa-rate. In 1896, the Niagara power plant began producing power and sending it down high-voltage wires some distance away. The new, cheap power source around Niagara created a high-tech corridor and enabled the aluminum industry as we know it. The grid began to grow and expand, sometimes at the will of extraordinary cap-tains of industry like Samuel Insull in Chicago. One major driving force to electric adoption was the radio in the 1920s. As is still observed today, entertainment drove technological advance and “must-have” devices drove the extension of the network to the edges. Many companies leveraged heavily in bids to expand during the boom years of the 1920s. During the depression, the high leverage led many companies to collapse. In the wake of these fail-ures, the increasing importance of the power grid led the federal and state governments to impose strict regulations on the power utilities, and in the case of the Tennessee Valley Authority, to run their own utility. The demands of war further solidified the gov-ernment’s role in regulating and managing the power grid. Initially, cities each had their own grids; but, over time, the grids became connected to cheaper generation centers and eventually to each other. The interconnections allowed the load centers to take advantage of cheaper generation elsewhere and also put off the need for expensive peak generation capacity locally, as power could be transferred from neighboring regions in times of high demand or emergencies. Eventually, the power grids become completely interconnected into three regions across the country. The state regulations kept the utilities in check and profitable through man-dated rates and energy costs.
In the 1990s, the status quo started to change. Several states began to deregulate the power industry, leading to the creation of energy markets. The hope was that this process would reduce the cost of electricity and spur innovation and competition. In spite of some trouble and difficulties in the early days of deregu-lation, lessons were learned and applied. Energy markets con-tinue to expand and are becoming an ever more important part of the power industry. New smart grid concepts and technolo-gies driven by market and legislative forces are generating faster changes to the grid than observed previously. A number of informative books have been written on the history of the power grid including The Grid by Schewe [3].
GRID COMPONENTSThe power grid in the United States and Canada is the most complex system ever devised. It spans the entire United States and most of southern Canada as well as a small part of Mexico. The power grid consists of a large number of components: generators, transformers, power lines, load compensators, and loads including everything that can be plugged into a wall outlet or runs off electricity. All these components are connected together, and together they determine the operation of the power grid. To understand the whole, it is nec-essary to gain an understanding of the pieces themselves.
A generator is any device that functions as a net producer of power to the electric grid. For the most part, generators are large, synchronous, rotating machines. These machines are powered by a variety of energy sources including nuclear reactors, coal or other fuel-fired steam, gas turbines, wind, and water. The total nameplate capacity of the generators in the United States as of 2009 is 1,121 GW. (The data is courtesy of the Energy Information Administration [4].)
Typically, generators are not located in the same location as the power consumers. This situation implies a need for trans-mission lines to send power over long distances. Transmission components serve as the connections between electricity gen-erators and consumers. Transmission lines can range from the low-voltage lines that connect individual houses to the mas-sive, high-voltage, overhead lines that link regions. As a gener-al rule, the farther the distance and the greater the power needed, the higher the voltage that is used. The physical implementation of the transmission lines consists of groups of wires and support structures. Typical high-voltage lines con-sist of a bundle of aluminum conductors surrounding a steel reinforced core. As of 2010, across the United States power grids, there are 169,000 mi (272,000 km) of high-voltage ac transmission lines [5].
These interconnections tie the major load and generation cen-ters together and allow for the sharing of generation and load between geographically separate regions.
Voltages at various points on the power grid are described by voltage phasors Vi / ui, where Vi is the magnitude of the voltage and ui is the phase of the voltage at bus i. The power flow through a transmission line is a function of the impedance of the transmis-sion line X, the voltages at the ends of the line Vi, Vj, and the sine of the phase difference between the two ends of the line
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Pi, j5ViVj
X sin 1ui2 uj 2 . (1)
If losses are included then the equation becomes
Pi, j5X
|Z |2ViVj sin 1ui2 uj2 1 R
|Z|2a X
|Z|2Vi
22 ViVj cos 1ui2 uj2b.
(2)
In these equations, Z5 R1 jX, where R is the loss term. Power generally flows from areas of leading phase to areas of lagging phase. Simplified models are presented here. For a more detailed treatment, several textbooks are available, such as [6] and [7].
LOAD FREQUENCY CONTROLSince there is only very limited storage capacity in the power grid, the generation must track the demand closely. If the generation PG is not matched to the load PL, the generators slow down, con-verting some of the kinetic energy from spinning motion into electric energy. The rate at which this occurs is dependent on the inertia of the system. This conversion is reflected in changes in the frequency at which the power grid operates. If not enough energy is produced, the frequency decreases; if too much is produced the frequency increases. In equation form the energy balance is
PL5 PG12Hf0
ddt
fD1 bfD. (3)
b is the frequency response of the system encompassing changes in generation with respect to frequency and changes in the load with respect to frequency. H is the per unit inertial constant of the system. The deviation of the frequency from the nominal value f0 is given by fD. If imbalances were allowed to continue unchecked the grid would quickly spin out of control. However, many genera-tors have speed governors that automatically increase the power output as the frequency declines. The change in power versus fre-quency is known as the regulation R of the generator; R has units of Hz/MW. The power generated is then given by
PG5 Pref21R
fD. (4)
In real generators, the regulation often has a deadband in which there is no change in power output for frequency deviations less than a certain threshold. The change in power takes a finite time period and can be described by a set of transfer functions with PD as the desired change,
PG 1s 2 5 DPG
DPD5
111 sTCH
. (5)
Typical values of TCH are around 0.2–0.5 s. Different types of gen-erators will have different equations, but the concept is the same. This time delay means that generators will respond to changes in frequency within a few seconds.
To maintain the frequency around a specific value, 50 or 60 Hz, a secondary control system is necessary. The grid itself is divided into several interconnects which are connected internally via ac transmission lines. The interconnects are divided into sev-
eral areas, known as balancing authorities. These areas are responsible for maintaining the stable operation of the grid and ensuring each area contributes its fair share. The control is accomplished via a signal known as the area control error (ACE). It is computed for each area by measuring the difference between actual power transmission Ta and scheduled transmission Ts and the deviation of the frequency from its scheduled value
ACE5 1Ta2 Ts 2 2 10BfD. (6)
The constant B represents the frequency response of the system and is related to the frequency response term in (3). B is typically specified in units of MW/0.1 Hz. In many control areas, this parameter is set as a constant, although it can be dynamically computed based on the current state of the system. The ACE acts as a control signal for adjusting Pref, the nominal generator out-put. One common mode of control is to use a PI controller as in
Pref 1t 2 5KP# ACE 1t 2 1KI3
t
0ACE 1x 2dx. (7)
These types of control systems are known as automatic generation control (AGC). Slower forms of control utilize forecasts of demand to achieve economic dispatching of generators to match the fore-cast loads.
RENEWABLE RESOURCESWind and solar energy are different than many other types of power generation in that they are not controllable. The wind can vary sig-nificantly from one part of the day to another, and even over the course of a few minutes the power output of a wind farm can change dramatically. This variability can have a significant impact on the operation of the power grid, and careful consideration of how to integrate renewable resources is needed [8]. In many ways, solar power is similar, it can experience sudden shifts in power out-put. For instance, a small cloud can reduce the output of a photo-voltaic solar farm for a few minutes and then raise it back to its previous level. The sudden changes in power production from renewable resources puts a strain on the frequency control systems in the grid. As the penetration level of these energy sources increas-es, the variability will have an impact on the frequency performance of the power grid. Renewable resources impact the grid in other ways as well. They are commonly connected via inverters instead of spinning generators, which means they do not have inertia to slow down the frequency change nor do they add to the regulation capa-bility. Thus, as the proportion of renewable energy goes up, the inertia of a system to resist changes in frequency goes down.
BASIC VOLTAGE WAVEFORMThe primary interaction of most users with the power grid is the common wall outlet. A wall outlet is a simple standardized mecha-nism which accepts the plug from innumerable devices. Most com-monly, the outlet is a power source, which enables much of what we consider to be modern society. It is also a window into the oper-ation of the much larger system behind it. The basic voltage wave-form is the commonly known 120 V 60 Hz sine wave in the United States, or 230 V 50 Hz in Europe, however, other common
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standards exist throughout the world. Going a little deeper, the sig-nal becomes more complex. An interesting feature is the presence of harmonics of the fundamental signal. These extraneous signals come from the various nonlinear devices on the system that feed back some energy into the system. Harmonics are produced by nonlinear loads such as switching dc power supplies, like those found in computers. New technologies such as plug-in electric vehicles [9] and wind generation [10] have the ability to create addi-tional harmonics on the grid that need to be monitored or reduced. Common harmonics can go out past the 35th harmonic. The impact of harmonics is felt through reduced power quality and reduced equipment lifespan. Beyond the basic harmonics, addition-al signals called interharmonics are also present on the system. These signals are much lower in amplitude than the harmonics but, nonetheless, can be observed. Some examples of voltage wave-forms are shown in Figure 1. Some of the signals are very clean and almost a perfect sinusoid, while others come close to a staircase.
While almost always close to 50 or 60 Hz, the frequency of the primary signal is continuously changing, reflecting current condi-tions on the grid. It is these small changes that give the most information about the operation of the grid. As described in the previous section, changes in frequency indicate mismatches between generation and load. The characteristics of these changes are indicative of the performance of the power grid.
MEASUREMENT HARDWAREThe hardware for measuring these changes can be made very inex-pensively. All that is required is a mechanism to get the voltage from wall outlet voltage levels to a level that an analog-to-digital converter can capture. The typical means of doing this is a trans-former, such as those in the power supplies of many dc-powered devices. Depending on the sampling rate of the ADC, an antialiasing filter should also be placed in the circuit along with a fuse for safety purposes. For a simple system to make measurements with little hardware or software development, and ADC solution with a USB interface and driver software can be purchased from companies such as National Instruments or Measurement Computing. A sam-ple generic schematic is shown in Figure 2. The values of C1 and R1 in the schematic depend on the properties of the antialiasing fil-ter desired. With a bit more effort, the system can be implemented directly on a microcontroller, as many modern microcontrollers include analog-to-digital converters, although care must to taken to ensure the voltages of the signal are of appropriate values, particu-larly if a single-ended ADC is used. Since the signal of interest has such a low frequency, the sampling rate can be correspondingly low. For instance, a great deal of usable data was collected using a 1,200 Hz sampling rate. Depending on how many harmonics are of interest, the sampling rate can be made even lower.
FREQUENCY ESTIMATION Once the data is in digital form, the measurements can be pro-cessed to estimate parameters of interest. A number of parameters can be estimated depending on the interest of the user, including voltage level, frequency, harmonic content, and others. If current conditions on the grid as a whole are of interest, then instanta-
neous frequency is of primary concern. Over the last few decades, many algorithms have been developed using a variety of tech-niques including: FFT-based algorithms [11], Kalman filter-based algorithms [12], zero-crossing algorithms [13], least-squares algo-rithms [14], [15], and modulation techniques [16], [17]. New tech-niques and modifications to extract the phasor and frequency measurements are continuously being developed. Such algo-rithms can tradeoff computational complexity for dynamic perfor-mance and work with three-phase systems [18]. For a more in-depth discussion of frequency estimation, the reader is encour-aged to read “Adaptive Frequency Estimation in Smart Grid Applications” by Xia, Douglas, and Mandic, which is also in this issue. With modern computational hardware, the differences in accuracy between the various methods become negligible in many circumstances. The decision to use a particular algorithm often lies in the tradeoff between various operating conditions. These tradeoffs can come in the form of system requirements for tran-sient settling time, start-up time, fault tolerance, measurement delay, stability, susceptibility to harmonics, noise performance, block or sample-by-sample processing, measurement range, algo-rithm complexity, available hardware, and measurement usage.
In-phase/quadrature demodulation is a common and robust technique. The algorithm is fairly tunable to specific applications, so it is worthwhile to examine the technique more closely since it is the algorithm used in the system that collected the data present-ed. The primary signal from a power outlet can be described by
v 1t 2 5 A sin 12pf0t1 u 1t 2 2 1 B cos 12pf0t1 u 1t 2 2 , (8)
where
u 1t 2 5 2p3t
2`
fD 1t 2dt, (9)
[FIG1] Examples of typical power outlet waveforms.
Vol
tage
Vol
tage
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
Vol
tage
[FIG2] Simple schematic of sensor hardware.
VAC
1
4
5
Fuse
Transformer
8
R1
C1
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and fD 1t 2 is the deviation from the nominal frequency with respect to time.
In a digital system, this signal is sampled at a specified rate. The sampling rate is denoted as Fa. The relationship between t and n is specified such that v 3n 45 v 1n/Fa 2 . Substituting this relationship into (8), we obtain
v 3n 45 A sina2pnf0
Fa1un 3n 4b 1 B cosa2pn
f0
Fa1un 3n 4b. (10)
The implementation of the in-phase, quadrature algorithm involves multiplying v 3n 4 by the in-phase and quadrature signals
ri 3n 45 cosa2pnf0
Fsb, (11)
and
rq 3n 45 sina2pnf0
Fsb. (12)
In an ideal system Fa5 Fs, however; in reality, the the actual sam-pling rate (Fa) does not match the assumed sampling rate 1Fs 2 , so we must account for this difference. However, it is reasonable to assume they are close. Multiplying the signal with the in-phase and quadrature components, using trig identities and low-pass fil-tering to remove the components near 2f0, leaves the remaining baseband signal
yi 3n 45 A2
sina2pnf0aFs2 Fa
FaFsb 1 un 3n 4b
1B2
cosa2pnf0aFs2 Fa
FaFsb 1 un 3n 4b, (13)
and
yq 3n 45 A2
cos a2pnf0aFs2 Fa
FaFsb 1 un 3n 4b
2B2
sin a2pnf0aFs2 Fa
FaFsb 1 un 3n 4b. (14)
Any number of low-pass filters can be used successfully in this application. For our application, we used a low-pass filter
H 1z 2 5N11 z21
12 1.4815z211 0.5625z22 , (15)
where N is a normalization constant so the filter has unity dc gain. In addition, a series of second-order infinite impulse response notch filters to filter out any residual signals at the har-monic frequencies were also used. The filter was chosen to obtain the required filtering and minimize the group delay around the baseband to prevent signal distortion. The signals yi 3n 4 and yq 3n 4 are the real and imaginary parts of a complex representation of the frequency deviation. The amplitude of the original signal can be extracted using
A0 3n 45"yi2 3n 41 yq
2 3n 4. (16)
The phase can be obtained using the 02 2p inverse tangent
un 3n 45 arg ayq 3n 4yi 3n 4 b 5 arg aA cos a2 B sin a
A sin a1 B cos ab , (17)
where
a5 2pnf0aFs2 Fa
Fa Fsb 1 un 3n 4. (18)
If we set b such that cos b52B/k and sin b5 A/k where k5"A21 B2 then (17) becomes
un 3n45 arg a k sinb cos a1 k cosb sin a
k sin b sin a2 k cos b cos ab . (19)
We note that tan b52A/B and hence b5 arg 12A/B 2 . Canceling the k terms, using sum-difference trig identities and the definition of tangent results in
un 3n 45 arg 1tan 1a1 b 22 5 2pnf0aFs2 Fa
Fa Fsb 1 un 3n 41 arga2A
Bb. (20)
We are looking to extract df 1t 2 , so we need to differentiate u 1t 2 with respect to t. However, since what is being measured is u 3n 4, we will start with an approximation to the derivative of u 1t 2 with respect to t
du 1t 2
dt<u 3n 42 u 3n2 1 4
1Fs
5 2pf0aFs
Fa2 1b 1 Fs 1u 3n 42 u 3n2 1 4 2 . (21)
It should be noted that the difference between u 3n 4 and u 3n 4 is in the presumed sampling rate for each of the terms. The sam-pling rate for u 3n 4 is actually Fa, and the rate for u 3n 4 is speci-fied as Fs. With this difference in mind, we can solve (21) for the quantity of interest,
df 1t 2 5 du 1t 2dt
< Fs 1u 3n42 u 3n2 14 212pf0a12 Fs
Fab. (22)
The second term in the equation is the error term and it goes to 0 if Fs5 Fa. It also allows for correction of the results if the exact sampling rate is not determined until after the fact.
Once the estimate is obtained, the output should be filtered to remove noise. Depending on the accuracy desired, complex output filters can be employed, such as Kalman filters or particle filters. However, for many applications a simple low-pass filter will remove most of the noise from the quantization and the numeric differentiation. The nature of the filter will depend on the desired output characteristics, such as the output frequency and data reporting rate. For example, common commercial synchrophasors output at a rate of up to 60 Hz. Such an output rate would imply an output filter with a cutoff of around 15 Hz.
TIME SYNCHRONIZATIONAs seen in (22), it is important to have accurate knowledge of the sampling clock so that the signal can be corrected after the fact, if
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necessary. To synchronize multiple sensors, absolute clock accura-cy is required. The most common method of synchronization is global positioning system (GPS) receivers. Many power grid sen-sors are now equipped with a GPS receiver to accurately time-stamp the data they collect, including commercial synchrophasors and the FNET sensors. GPS receivers typically require an outdoor-mounted antenna. Commercial sensor systems are typically mounted on major substations or transmission lines in the power grid allowing them to determine the exact phase difference between two measurements. Sensors at wall outlets have addition-al equipment between them, creating a small but unknown addi-tional phase delay. While the additional delay does not impact the frequency measurements in any meaningful way, it does make comparing the phase of the signal between any two points impos-sible, and only meaningful in a statistical sense for a large number of sensors across a large area.
Another means of synchronization is the radio station WWVB, which broadcasts from Fort Collins, Colorado, and uses an extreme-ly low-modulation frequency of 60 KHz. The signal propagates in a ground wave in areas within 1,500 km from the source. Beyond this range, the signal is propagated through a sky wave at the ionosphere boundary; meaning a single station can be used for the entire coun-try. The station uses a pulse amplitude modulated signal with a bit rate of 1 b/s. The time is broadcast over the course of a minute. The edge transitions occur on the second. The accuracy of the 60 KHz modulation is better than 10 parts in a billion, and a high-quality receiver using time averaging can estimate the time within 10 ms if the location of the receiver is known to a reasonable accuracy, i.e., better than 2 km. The signal strength varies with distance to the transmitter and time of day. Signal strength is reduced during the day due to ionospheric turbulence. Sunrise and sunset can pose sig-nificant problems receiving the signal due to solar interference, however, these periods are typically short. A few sensor platforms have been designed to use WWVB for geographically separated sen-sor networks, and they could provide a cheaper alternative to GPS [19]. WWVB is the signal that many autosetting clocks use. There are other similar stations such as DCF in Germany and JJY in Japan.
If the system doing the collection is connected to a network, the network time protocol (NTP) is another option. It is a program used to synchronize computer clocks. Mills [20] showed that NTP can achieve single-measurement time synchronization to about 4 ms across the Internet. With frequent sampling and additional processing, a higher accuracy can be achieved. In a local network, NTP can achieve somewhat better results, sometimes to 10 ms. This method requires a network connection and access to an NTP server. An evaluation of the protocol was undertaken with applica-bility to wide-area sensor networks for the power grid, and the protocol was found insufficient for highly synchronized applica-tions such as FNET [21]. Nonetheless, for many applications in which GPS is too expensive or not available or the accuracy requirements are not be as stringent, NTP is a viable alternative.
MEASUREMENT RESULTSOnce a system is running and collecting frequency data, there are a number of different observations that can be made. An interest-
ing aspect of the data is the presence of cycles of various periodic-ities in the frequency data. An examination of these periodicities was carried out using an average Fourier transform of the fre-quency data. Figure 3 shows the spectrum of the variations pres-ent during a day. The results were obtained by taking the Fourier transform of a days worth of frequency data, then doing a point-wise average of the data from many days. The resulting plot indi-cates three regions. The first is a very long period region with periodicities longer than 500 s. There is a significant peak at the point corresponding to a daily period and other spikes corre-sponding to intervals of time, such as an hour or 15 min, indica-tive of the scheduling in use. The second region seems to be an exponentially decaying region with periods of 10–500 s. The decaying region seems to indicate that the grid frequency could be modeled as a 1/f process, at least over a certain range of fre-quencies. The final region corresponds to periods shorter than 10 s. This region is marked by several peaks rising above what may be a noise floor in the frequency data. Figure 4 shows a zoomed-in view of this region. The broader peaks correspond to long-term resonances or oscillations in the power grid.
[FIG3] Average frequency variation spectrum.
10−5 10−4 10−3 10−2 10−1 10010−3
10−2
10−1
100
Variation Frequency (Hz)
Nor
mal
ized
Am
plitu
de
[FIG4] Short period variations in the power frequency.
0.25 0.3 0.35 0.4 0.45 0.5
10−2.9
10−2.8
10−2.7
10−2.6
10−2.5
10−2.4
10−2.3
Variation Frequency (Hz)
Nor
mal
ized
Am
plitu
de
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Over the long term, the probability density of the frequency can be determined. This density is reflective of the control strate-gies employed on the grid and the size of the grid. Figure 5 shows the probability densities for frequencies of the various U.S. inter-connects. The results indicate that the Western interconnect maintains a slightly tighter control than the Eastern interconnect, and that the Electric Reliability Council of Texas uses a different strategy and is smaller than the other two interconnects. A more detailed analysis could be done to determine the exact parameters of the distribution or track the changes over time.
Figure 6 shows the average frequency deviation over the course of a day. Some fascinating trends can be observed. Instead of being a smooth curve as one might initially expect, definite periodic patterns emerge. These patterns are the result of hourly changes in generation or power transfers between control areas. These changes in power flow or generation are the result of mar-
ket forces and human schedules. If the transfers were handled dif-ferently, then these patterns would change or disappear.
EVENT DETECTIONWhile averages and statistical patterns can give insight into the controls used and the operational characteristics of a specific grid, the instantaneous changes in frequency give insight into the cur-rent operational status of a grid. The range of variations from 60 Hz depends on the size and control of the particular grid. Frequencies too far from the nominal level can cause damage to equipment and are indicative of abnormal events. Large rapid fre-quency shifts are also indicative of specific problems occurring on the grid, such as a power plant going offline for some reason. Power grids are typically operated with reserves to handle any sin-gle event failure on the grid. Therefore, a single plant going offline, while a serious problem, does not typically threaten the stability of the power grid. These events are easily observable in the frequency data. For a number of years, utilities and transmission line opera-tors have been able to use data from phasor measurement units to assess the impact of large disruptions [22]. Similar observations can be made using data from power outlets. On 20 May 2006, two reactors shut down at the same time [23]; the result is shown in Figure 7. This event resulted in the loss of 2,258 MW from the grid. The frequency very quickly dipped by about 0.08 Hz. The initial fre-quency drop in frequency, typically 3 or 4 s is the period before the primary frequency response kicks. During this period the shortfall in generation is covered by converting the kinetic energy in the spinning generators into electrical energy. Calculating the maxi-mum rate of change of frequency and knowing the shortfall in energy would enable a rough calculation of the system inertia. In practice, measuring inertia in this way is somewhat error prone and depends on the proximity of the measurement to the source of the fault. A large set of faults was analyzed, in this manner, on the Western interconnect to determine the system inertia [24].
The system frequency response can also be calculated from the observations. As the frequency declines, the regulation of the gen-erators increases the power to the generators, eventually
[FIG5] Frequency densities of the U.S. interconnects.
−0.1 −0.05 0 0.05 0.1Frequency Deviation (Hz)
Rel
ativ
e P
roba
bilit
y
Eastern InterconnectWestern Interconnect
ERCOT
[FIG6] Average frequency over the course of a day.
00 02 04 07 09 12 14 16 19 21 00−20
−15
−10
−5
0
5
10
15
20
25
Hour of the Day (UTC)
Fre
quen
cy D
evia
tion
(mH
z)
[FIG7] The result of two reactors simultaneously shutting down: a 2,258 MW generator loss on 20 May 2006.
17:5
7:07
18:0
0:00
18:0
2:52
18:0
5:45
18:0
8:38
18:1
1:31
18:1
4:24
18:1
7:16
−0.1
−0.08
−0.06
−0.04
−0.02
0
0.02
Time
Fre
quen
cy D
evia
tion
(Hz)
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stabilizing the frequency. As there is some delay between the fre-quency dip and the governor, the frequency will ultimately dip to its nadir then recover slightly to a near constant value. The differ-ence between the frequency before the fault and the stable fre-quency before the secondary control algorithms can act is a measurement of the frequency response of the system. FERC has developed a standard to measure the frequency response, and this measurement can be done on data from a power outlet as well as data from the central measurement units. Researchers from Lawrence Berkeley National Lab used these methods to assess the performance of the U.S. interconnects and the potential for han-dling renewable resources [25], [26].
Other interesting events can also occur on the grid that do not necessarily relate directly to generator trips. Transmission lines can fail, or regions can separate from each other, known as island-ing. Figure 8 shows an example of an islanding event. In this instance, two sensors were located close together in the same city. Lightning struck a main line causing a glitch in the system and failure of some transmission lines. This event is shown as the spike in one of the sensors. This fault resulted in the islanding of a small region. Without the support the rest of the grid, the remaining generators had considerable difficultly maintaining the frequency. However, in this case they managed to recover the frequency enough such that they could resynchronize with the rest of the grid, potentially by shedding some load corresponding to the sharp increase in frequency. In this case, looking closely at the resynching data, it took a couple tries before the reconnection finally held. The proximity of these sensors, within a half mile of each other, demonstrates how small-scale events can be captured and the control steps analyzed.
If measurements are gathered over long time periods, then the probability of certain rare events can be obtained. Figure 9 shows a set of curves that represent the probability that the absolute fre-quency deviation of the power grid will exceed a certain level in a given day. While far from a definitive analysis, the number of events appears to be declining since 2005. Similar analysis could be done for other sorts of events, such as looking for rapid fre-quency shifts or limiting the events to slower excursions. The data is a very rich source of information on the operation of the power grid, and there is a great deal to be learned from such data. Further details on the data and measurements presented in this article can be found in [27].
DISCUSSIONThe power grid is a complex network filled with thousands of mov-ing parts covering a huge area. This enormous system reaches into almost every part of daily life in modern society. This ubiquity also allows a window into the operation of the system. By monitor-ing the frequency and voltage of the signal that comes out of a wall outlet, we can see how the system moves and behaves, how the control algorithms react and respond, and the frequency and severity of outages and other events that occur on the grid. And all this can be done from anywhere there is an electrical outlet.
Having such sensors online and continuously monitoring will establish a record of performance and allow changes and impacts to
be observed and studied, particularly as new technologies, renew-able generation, and other devices come online and start to have an impact on the operation of the power grid. Simple measurement devices can also monitor local voltage levels and if connected to a local control system could alert systems into standby mode or an automatic frequency response. Devices can be built cheaply enough that they could be incorporated into appliances as a trigger for very short-term demand response systems. Pacific Northwest National Labs has developed some devices that could be added to appliances to allow them to respond rapidly to events on the grid by detecting voltage and frequency [28]. Cheap monitors and sensors could be especially useful in territories with developing infrastructure, where they could allow businesses to rapidly respond to changing power conditions and have some warning if conditions were poor.
[FIG8] Grid islanding event.
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Researchers in those countries could also monitor the power con-ditions and develop mechanisms to improve it.
Some such measurement networks are already online, such as FNET [29]. FNET uses a network of devices that measure the fre-quency of the power grid through 120 V wall outlets. The data col-lected from this system has been used for event localization, disturbance monitoring, oscillation detection, and a number of other applications. The sensors themselves use GPS for time syn-chronization and report back to a central server.
The power grid is undergoing some major changes. At present, millions of smart meters have been deployed enabling people to have better insight into their own power consumption. New tech-nologies are being deployed; and the pace of change will continue to accelerate, driving toward a future smart grid that enables individu-als to impact the grid in ways that we are only now beginning to uncover. Simple mechanisms of electronics and signal processing that allow direct monitoring of some aspects of the behavior and status of the grid could be a key element of that interactive future.
AUTHORSPhilip Top ([email protected]) earned a B.S.E degree from Dordt College in Sioux Center, Iowa, in 2002, an M.S.E degree from Purdue University in 2004, and a Ph.D. degree from Purdue University in 2007 in the field of signal processing. Since 2007, he has been working as a research engineer at Lawrence Livermore National Lab in Livermore, California. His research interests include remote sensing technology, ultrawideband radar, data intensive computing, and power system dynamics and modeling.
Mark R. Bell ([email protected]) received the B.S.E.E. degree from California State University, Long Beach, in 1981 and the M.S.E.E. and Ph.D. degrees in electrical engineering from the California Institute of Technology (Caltech) in 1982 and 1988, respectively. From 1979 to 1989, he was employed by the Radar Systems Laboratory of Hughes Aircraft Company in Fullerton, California. While at Caltech, he was a Howard Hughes Doctoral Fellow. Since 1989, he has been on the faculty of Purdue University, West Lafayette, Indiana, where he is a professor in the School of Electrical and Computer Engineering.
Ed Coyle ([email protected]) received the B.S.E.E. degree from the University of Delaware, Newark, in 1978, and the Ph.D. degree in electrical engineering and computer science from Princeton University, New Jersey, in 1982. He currently serves as the Arbutus Professor of Electrical and Computer Engineering at Georgia Tech and is the director of the Arbutus Center for the Integration of Research and Education. His research interests include wireless networks, signal process-ing, and engineering education. He is a Fellow of the IEEE.
Oleg Wasynczuk ([email protected]) received the B.S.E.E. degree from Bradley University in 1976 and the M.S.E.E. and Ph.D. degrees from Purdue University in 1977 and 1979, respec-tively. Since 1980, he has been on the faculty of Purdue University, West Lafayette, Indiana, where he is a professor in the School of Electrical and Computer Engineering. His research interests are in the areas of electromechanical and power systems, including con-trol, power electronics, and computer analysis and simulation. He
received the 2008 IEEE Cyril Veinott Electromechanical Energy Conversion Award. He is a Fellow of the IEEE.
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