Frequency Response Estimation Following Large Disturbances using Synchrophasors Lucas Lugnani Daniel Dotta UNICAMP Campinas, Brazil Email:
[email protected] [email protected]
Joao M. F. Ferreira
Ildemar C. Decker
Joe H. Chow
RPI UFSC ONS Troy, NY Florian´opolis, Brazil Rio de Janeiro, Brazil Email:
[email protected] Email:
[email protected] Email:
[email protected]
Abstract—One new challenge, with the massive penetration of renewable generation (wind and solar), is the decline of the Electrical Power System’s (EPS) frequency response. In order to deal with this new scenario, the development of tools to estimate key valuable parameters for frequency response is imperative. The Wide Area Measurement Systems (WAMS) signals can be useful to estimate the EPS frequency response after large disturbances. The paper main goal is to estimate the frequency response of the Brazilian Interconnected Power System (BIPS) after large disturbances using synchrophasors. These events were recorded at outlet voltage by a synchronized phasor measurement prototype, the LVS (low voltage synchrophasor), with PMUs (Phasor Measurement Units) installed in 26 universities throughout Brazil. The results show that high penetration of wind generation contributes to change the inertial power system response. Index Terms—Inertial Response, Frequency Response, Electrical Power Systems, Phasor Measurement Units.
I. I NTRODUCTION Electrical Power Systems (EPSs) are complex systems with strict operation and stability requirements [1] [2]. Frequency stability is always a concern since large frequency fluctuations can damage consumer and power system devices and may lead to a partial or overall EPS outage. In traditional EPS the bulk spinning mass of synchronous generators (through its stored kinetic energy) naturally improves the stability of the system as it reduces the frequency deviation due to a disturbance (e. g., generation trip) [3]. The amount of time that a generator or group of generators can provide energy to the system solely through its rotor’s kinetic energy is known as Inertial Constant (H). Due to socio-environmental constraints, this classical configuration is suffering a structural transformation. This transformation brings about a higher penetration of intermittent generation (e. g., PV and wind farms) [4]. However, these new technologies lack an inherent kinetic energy within its generating capacity, thus depreciating the equivalent Heq of the system. Furthermore, given the intermittent nature of such new technologies, the synchronous generators component of the system becomes variable to ensure the demand for energy, making Heq variable as time passes [5]. Given this evolving perspective of EPSs, the BIPS also experiences such tendencies. In some cases, for instance, the Northeastern subsystem, the wind plant generation can reach a 60% of total
regional load [11]. Such as EPSs worldwide, the knowledge of the system’s Inertial Response becomes uncertain as it retains its importance to the assessment of the power system frequency stability. Several methods to monitor and estimate the Frequency Response can be found in the literature [3] [4] [8]. These methods make use of data measured mainly in interconnections and power plants. Each method also uses a different set of mathematical tools and parameters observed in order to estimate Heq . In [6], an estimation of the Inertial Frequency Response of several EPSs worldwide is realized through data gathered by frequency disturbance recorders of several events. The authors in [7] propose an on-line method for the estimation of time of disturbance and inertia using data from WAMS and active power with a proposed robustness to false disturbance detection (a threshold limit detection). Using data from PMUs connected to Transmission lines, [8] estimates the UK Inertial Frequency Response using the power swing equation. In this paper, the data extracted from PMUs connected to outlets is used to estimate frequency response after two severe disturbances with the method proposed in [9]. The main goal of this paper is identification of parameters of the frequency response using non-intrusive data. This paper is organized as follows. Section II presents the mathematical fundamentals. Section III presents the modeling and methodology proposed. Section IV presents the BIPS configuration and topology. Results are presented in section V, where the frequency response is estimated and the parameters of interest are presented. Section VI presents the conclusions. II. F UNDAMENTALS A. Inertial and Frequency Response The Inertial Response of a generator can be described as the kinetic energy (Ekin ) released by its rotating mass to oppose a frequency deviation on the system (such as to a power imbalance) [1]. Ekin =
1 J(2π∆fm )2 2
(1)
where J [kgm2 ] is the moment of inertia of the machine and ∆fm [Hz] its deviation from nominal frequency. It follows that the generator’s H is the total kinetic energy of the rotating mass
at nominal frequency rated at the nominal generator’s power and represents the amount of time the generator can feed the referred power only through its spinning mass stored kinetic energy: Ekin H= (2) SB SB [MVA] being the generator’s rated power. Considering that frequency deviations are usually small excursions (∆f ≈ 0) around the reference value and Pm − Pe is equal to the accelerating power (Pacc ), given a trip of generation (∆G), the frequency deviation with initial mechanical and electrical powers Pm0 and Pe0 is: 1 1 Pacc = [(Pm0 +∆Pm −∆G)−(Pe0 −D∆f )] 2Hs 2Hs (3) During steady-state operation Pm0 = Pe0 , those terms can be ignored, and considering that during the first seconds after a disturbance the primary frequency control does not act, ∆Pm will be zero as the machine’s governor will not open nor close to meet the electrical power imbalance. Furthermore, during the first cycles after the disturbance, due to very low-frequency deviation, the proportion of the load’s frequency response is negligible. Hence, the Inertial Response can then be described in terms of the swing equation of the synchronous generator as: 2HSB ˙ fm = (Pm − Pe ) (4) E˙ kin = fm ∆f =
In steady state, when Pacc = 0, the frequency deviation will be given as: 1 ∆f = ∆G (7) D + R1D Where D + R1D = β is the frequency response [9]. Equations (5) and (7) account for the initial cycles of the frequency response, that is, prior to any control action and will be used to estimate the BIPS frequency response in section IV. III. M ETHODOLOGY A. System modeling EPSs are complex and interconnected systems, the data recorded by the PMUs can be representative of events geographically and electrically far from the PMU’s location. In order to face such problems, an equivalent machine for the region studied is modeled with an aggregated Heq of the machines of that region as proposed in [1]. Thus, for the estimation of the Inertial and Frequency Response, the system is modeled as an Equivalent Machine vs Infinite Bus, as shown in Figure 2. In Figure 2 the PMU box represents
G jX
PMU E
δ
E 0º
where Pm is the generator’s mechanical power and Pe the electrical power required by the system. With this last identity, we ascertain a correlation between H and EPS parameters (fm and Pe ). Equation 4 becomes: ∆G (5) ∆f˙ = − 2H Where the machine’s rated power can be omitted if the power imbalance ∆G is considered in the same rated power and ∆f˙ is the machine’s Rate of Change of Frequency (ROCOF).
Pm 0 f
f0 + f
-
1/R D 1 + sTD
Pm
+-
+Pm
+
G
D
Pacc -
1 2Hs
f
Pe -
Pe 0
Fig. 1. Frequency response’s study model.
Equation (3) can be rewritten as the transfer function from ∆G to the frequency deviation ∆f, represented in Figure 1, as follows: 1 1 1 s∆f = (−∆G + ( + D)∆f ) (6) 2H RD 1 + sTG
Fig. 2. Equivalent machine vs Infinite Bus equivalent model.
each of the measuring unit connected to its respective location. E’ and δ are the equivalent machine’s voltage magnitude and angle and jX represents an equivalent system’s reactance. Note that despite being represented here, the equivalent machine’s magnitude and angle are disregarded, but rather the deviation values are used in the estimation process. Furthermore, as can be seen in equation (5), the knowledge of power deviation is also required. Given an event and the availability of generation or load loss information (i.e., amount of loss, location, time of disturbance), the methodology applied to frequency response estimation is: 1) The appropriate PMUs for the event are selected, i.e., a PMU recording a region that disconnected from the rest of the system and thus does not represent the disturbance’s frequency response, is disregarded; 2) The selected PMUs frequency measurements are filtered with a Butterworth 15th order low-pass filter and interpolated around the time of disturbance with the cubic spline method to attenuate instrument and communication noise; 3) The Rate of Change of Frequency (ROCOF) is calculated for each PMU frequency data set using a MATLAB function dif f for numerical differentiation;
4) With the first cycles after the disturbance, Pm becomes smaller (or bigger) than Pe and ROCOF increases in module. The inertial response releases energy on the grid so regional Heq estimation is carried using Equation (5); 5) f will reach the nadir as the ROCOF ∆f˙ = 0, thus nadir and steady-state frequency are identified; 6) As part of load is frequency-dependent (D), Pe will vary and so regional frequency response estimation with Equation (7). IV. S YSTEM ’ S C HARACTERISTICS AND T OPOLOGY The BIPS is divided into 4 regions: North, Northeast, Southeast-Midwest, and South. The main portion of the load is gathered in the South-Southeast compound region. Until recently the main generating portion of the system was also spread across the same region in the form of hydroelectric power plants. However, in recent decades new power plants have been installed in the North-Northeast region, making these regions energy deliverers to the South-Southeast compound in normal conditions. The BIPS has an installed capacity of approximately 150 GW [11], with 93% of total generated power being supplied by synchronous generators. The wind power generation installed capacity is around 12.3 GW, with future projections of installed capacity accounting for a rise of more then 50% until 2020 [11]. The daily average national demand rests around 65 GW [12], making it possible for the BIPS to operate with as much as 10% of electric energy production being supplied by wind power plants. Considering that most of the synchronous generators are located in the South-Southeast compound, this sub-system accounts for the Center of Inertia (COI). This compound will be called SEeq.
composed by 26 PMUs installed in universities in regional distribution systems throughout the country as seen in Figure 3. The central server is located in Southern Brazil and the data recorded by each PMU has a sampling frequency of 60 Hz. To use the data received by the server, a filtering process is required. Such filtering process seeks to eliminate the noise interference generated by the measuring, processing and transferring of data inherent to complex systems such as WAMS. The noise was modeled as white noise in order to apply the necessary techniques for the filtering and interpolating process. V. F REQUENCY R ESPONSE E STIMATION A. Brazilian 9-Bus Equivalent Simulation Using a 9-Bus equivalent of the BIPS proposed in [14], a disturbance was simulated in order to validate the algorithm. The BIPS equivalent is shown in Figure 4. Each subsystem was represented by an equivalent 6th order machine with frequency and voltage controls. Loads were also modeled as impedance equivalent concentrated ones. A trip of generation at 100 ms was applied to the Northern subsystem to evaluate resulting BIPS frequency response. The ANATEM software from CEPEL was utilized. The treated data was then numerically North Machine Equivalent
N Generation Trip
UNIR UFAM UFAC 1 UNIFAP UFT UNIR UFPA
PMUs
2000MW
Northeast Machine Equivalent
NE
2000MW
500 kV N1
UHE 1,800 MW
N3 N4
1500MW
500MW
NE2
N2
NE1
PMUs
NE3 W2 W1
N5
UNIPAMPA UFRGS UFSC UTFPR PTI
NE4
W3
USP-SC UNICAMP UFMS UNIFEI UFMG
UFJF UFRJ UFES UNB UFMT
UFBA UFPE UFC UFMA
SEeq
PMUs
Center of Inertia Equivalent
M1
Fig. 4. Power System Equivalent of BIPS. SE5 W4
SE4
SE3 SE1 SE2
SE7
SE6
Legend S5
S3 S1
Existent
S4
S2
Future
138 kV 230 kV 345 kV 440 kV 500 kV 750 kV + 600 kV cc PMU
Hydro Complex A Paraná B Paranapanema C Grande D Paranaíba E Paulo Afonso PDC
Fig. 3. PMUs locations for the synchrophasor low voltage measurement.
A. Low Voltage Wide Area Measurement System (LV-WAMS) In order to gather the necessary data for the analysis of such events, certain communication, measuring and processing technologies are required. The Brazilian LV-WAMS with its components and structure is presented in Figure 3. The LVWAMS used to gather the measurements in this work is
differentiated for the acknowledgment of the ROCOF of each subsystem. The resulting ROCOF for each Region at the first seconds are shown in Figure 5. With these informations, the subsystems Heq and β were calculated (SB = 100MVA) and are presented in Table I, with the respective relative error. TABLE I E STIMATED PARAMETERS - S IMULATED S YSTEM Heq (s) error (%) β (MW/0.1Hz) error (%) SEeq 4.878 2.12 173.1 0.69 N 2.995 1.15 175.3 0.57 Ne 4.018 1.80 172.7 0.92
B. Real Data Two real large disturbances are considered in this work: Under-Frequency and Over-Frequency (high wind penetration)
ROCOF PMUSEeq
0
PMUN PMUNE
Hz/s
-0.1 -0.2 -0.3 -0.4 -0.5 -0.6 0.095
0.1
0.105
0.11
0.115
0.12
0.125
0.13
Time (s)
Fig. 5. 9-Bus BIPS Equivalent simulated ROCOF
Disturbances. The system fundamental frequency was identified through Fast Fourier Transform in order to establish a threshold for a low-pass filter. The resulting threshold was set to 5 Hz in order to eliminate the noise present in the original signal but also regard event frequency dynamics. Given the determined cut-off frequency, a Butterworth filter was designed and the filter order was chosen aiming to cut abruptly the signal at the given threshold. Hence, the filter order was set to 15. It’s worth noting that while increasing the order of a Butterworth filter diminishes the slope of frequency cut-off, at unintended frequencies the oscillation amplitude might vary. Thus, the order choice must be judiciously made as a compromise between cut-off slope and amplitude variation of the frequencies of interest. After filtered, each selected frequency signal was interpolated with the cubic spline method. This method is appropriated for a smooth data set such as the filtered frequency signal. After interpolated, each frequency signal was then re-sampled. Event Frequency 60
Hz
59.9 59.8 Filt. Sig. - SEeq Filt. Sig. - N Filt. Sig. - NE Orig. Sig. - SEeq Orig. Sig. - N Orig. Sig. - NE
59.7 59.6 59.5
60
65
70
75
80
[3]) extend the data window to the last cycle prior to the event and the second cycle after. Such considerations are made due to filtering effects [3] or method convergence [13]. This work made use of the first two cycles after the disturbance given the smoothness of the ROCOF in the interval and to improve the data size. However, this criterion must be evaluated for each case given the variability of frequency response behavior for different possible events. The filtered frequency signals were then numerically differentiated.
85
Time (s)
Fig. 6. Original and Filtered Frequencies - Under-Frequency Event.
Equations (1) and (2) show that the inertial frequency response is dependent on Heq which is calculated for nominal steady-state operation regime (SB = 1000MVA). Considering this assumption, the estimation of Heq must take into account a quasi-steady region following the disturbance. This is due to the fact that as the system evolves after the event, frequency deviates and subsequently the generators rotor’s speed, as the machines deliver kinetic energy to the system. So, even though Heq is a constant value, it must be considered valid only on the first system’s cycle post-clutter. Some works in literature (e. g., [13], [4] and
1) First Event (Under-frequency): On 02/20/17 at 17h37min (UTC), a large hydro-power plant tripped out of the system resulting in 1,800MW of generation loss, as seen in Figure 4. The resulting filtered data (Figure 6) was used for ROCOF computing. The ROCOF of one of the PMUs for regions SEeq (USP-SC), NE (UFPE), N (UFT) for the period where the accelerating Power (Pacc ) is different from zero is presented in Figure 7. Note that, for illustration purposes,
Fig. 7. ROCOF calculated with PMU data - First Event.
Figure 7 presents 25 ROCOF samples, i.e. approximately the first half second after the disturbance, when Pacc is negative and the automatic generation control has not yet started. However, only the initial samples (i.e., cycles) can be considered for inertial response estimation [3] [7] [8]. The inertial frequency response was estimated with the presented information of the event and the data recorded [9], using Equation (5). The average ROCOF of the PMUs by region is presented in Table II. Their variance is 2.4 (mHz/s)2 , for a two cycle interval. Using equation (5), the detection of the start time for the fault is essential given that a 16 ms variation on the initial time can erroneously increase the ROCOF by up to 20% and the PMUs variance to 4.3 (mHz/s2 )2 , a 100% increase. Also with the recorded dataset, the frequency response (β) was calculated using the frequency of the system prior to the disturbance and the frequency’s nadir, with Equation (7) as shown in [9]. The estimated systems Heq and frequency response are presented in Table II: 2) Second Event (Over-Frequency): On 09/26/17 at 13h24min (UTC), two 345 kV transmission lines and a 345/88 kV transformer in S˜ao Paulo state disconnected from the BIPS, with a 574 MW loss of load rising the system’s frequency (Figure 8). Also, Figure 4 does neither represent the Second Event nor its power exchange, but rather the generation loss
and the Second Event had a 1.57/5.8 GW hydro/wind regional generation. The hydro generation decreased 30% and wind generation increased 130% in NE region.
TABLE II E STIMATED PARAMETERS - F IRST E VENT ROCOF (Hz/s) Heq (s) β (MW/0.1Hz) avg max avg avg SEeq -0.0603 -0.0759 6.473 978 N -0.0989 -0.0651 2.289 992 NE -0.0404 -0.1027 7.137 980
VI. C ONCLUSION
and power exchange of the First Event. During this event the Ne region was exporting 935 MW (Wind generation) to the SEeq compound. The same methodology was applied to the second event. Appropriate PMUs were selected and its data filtered and interpolated, as shown in III-A. The resulting treated frequency for 3 PMUs (one for each region is presented in Figure 8). ROCOF from the same three PMUs is displayed in Figure 9. The calculated ROCOF and estimated Heq and β are presented in Table III:
In this paper, the inertial constant and the frequency response of the BIPS regions were estimated through data collected from a WAMS. The estimation was carried out through a Machine vs Infinite Bus representation of the system, the determination of the system’s COI, signal filtering and numeric differentiation. Northeast region’s Heq showed a relevant variation, probably associated with high penetration of Wind generation. The estimate proved accurate to simulated values and of simple implementation. Regarding real measurements the method shown a tendency of change in the BIPS frequency response for the case of high wind penetration. However, a more substantial and detailed study considering a representative number of disturbance must be realized to verify accurrancy of the obtained estimations with real data. ACKNOWLEDGMENT The authors gratefully acknowledge FAPESP under grants no. 2016/08645-9 and 2015/18806-7 and FAEPEX under grant no. 519.292-1 for the financial support. R EFERENCES
Fig. 8. Original and Filtered Frequencies - Over-Frequency Event.
ROCOF 0.25
PMUSEeq PMUN
Hz/s
0.2
PMUNE
0.15 0.1 0.05 0 45.8
45.85
45.9
45.95
46
46.05
46.1
46.15
46.2
Time (s)
Fig. 9. ROCOF calculated with PMU data - Second Event. TABLE III E STIMATED PARAMETERS - S ECOND E VENT ROCOF (Hz/s) Heq (s) β (MW/0.1Hz) avg max avg avg SEeq 0.0833 0.0924 5.716 1,251 N 0.0921 0.0927 2.016 1,236 NE 0.1155 0.1196 5.691 1,189
It becomes evident a relevant variation of Heq for the Ne region between the First and Second Event. However, an analysis of power generation source for both events shows that First Event had a 2.25/2.5 GW hydro/wind regional generation
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