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Power system responses to geomagnetic disturbances recognized using phasor measurement recordings
Electrical Power and Energy Systems 113 (2019) 932–940
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Power system responses to geomagnetic disturbances recognized using phasor measurement recordings☆
T
⁎
Jian Chena, Chunming Liua, , Maohai Wangb, Tong Wanga a b
School of Electrical and Electronic Engineering, North China Electric Power University, Beijing 102206, China North China Branch of the State Grid Corporation of China, Beijing 100053, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Excitation current Geomagnetically induced current (GIC) Phasor measurement unit (PMU) Reactive power Response Wide area measurement system
Geomagnetically induced currents (GICs) flowing through transformers result in a DC bias, which poses a threat to safe and stable power grid operation. To evaluate the influence of geomagnetic storms on power systems, it is necessary to study actual power system responses. In this paper, the power system response is represented separately using current and reactive power measurements acquired using phasor measurement units (PMUs). On the basis of the data obtained from a wide-area measurement system, the power system responses to geomagnetic disturbances at Yangquan Substation, Shanxi, China were obtained. By employing the plane wave method, the data acquired during two mild magnetic storms at the Shisanling Geomagnetic Observatory were used to calculate the electric field and GIC at Yangquan Substation. The response variables and calculated GIC results agreed well, and the response variables were thus applied to assess the GIC level in the power system. The results show that the fluctuations in the PMU measurements were caused by GICs in the power system, laying the foundation for a significantly more detailed geomagnetic storm risk monitor.
1. Introduction During magnetic storms, geomagnetically induced currents (GICs) flow through transformers and increase the reactive power and highorder harmonics, which may result in power system accidents including voltage sags, reactive power variations, protective equipment malfunctions, and nuisance equipment tripping. Thus, properly managing a GIC is becoming increasingly important for ensuring power grid safety and stability [1,2]. Many magnetic storms that led to protective equipment malfunction, nuisance equipment tripping, and even serious disruption of electrical power service were discussed in [3–7], including a severe power failure in Quebec in 1989 that was mainly related to secondary transformer disturbances such as the reactive power and harmonics caused by a GIC. Modern power systems in the future will likely require GMD protection which will include (PMU) algorithms which rapidly identify potentially damaging GIC currents. In recent years a new power grid GIC protective device was developed, tested in a live power grid, and installed for continuous operation on a HV transformer in the American Transmission Co. (ATC) power grid in northern Wisconsin, USA. This
neutral GIC blocking device has reportedly been in operation for over three years and has automatically switched into its GIC blocking mode over thirty (30) times when GMDs were detected [7]. Our paper addresses a new refined data processing assessment for characterizing potentially harmful GMD events so that appropriate automatic control actions can be applied in future HV power systems. To realize the fast assessment of the impacts of geomagnetic disturbances (GMDs) on power grids, many research projects have been conducted in the past 10 years. This research has focused on two major topics concerning GMD’s; namely creating a numerical GIC model [8–12] and capturing transformer GIC data in real time [13–17]. These studies have involved a GIC evaluation to assess the potential effects on power grids; however, the GIC is influenced by the real-time operation of the power grid in question, various transformer parameters, the station location, etc. Thus, even if a numerical GIC model is sufficiently precise to enable the assessment of the risks faced by a transformer, it is still difficult to perform precise calculations for entire power grids. In addition, the calculations are usually based on certain assumptions since some information such as the practical grounding configuration of every transformer substation is unknown. Furthermore, GIC monitoring equipment has not been installed widely which also makes it difficult to
☆
This work was supported by the National Key Research and Development Plan (2016YFC0800103) and the National Natural Science Foundation of China (51677068, 51577060). ⁎ Corresponding author. E-mail address: [email protected] (C. Liu). https://doi.org/10.1016/j.ijepes.2019.06.027 Received 18 February 2019; Received in revised form 23 April 2019; Accepted 12 June 2019 Available online 20 June 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.
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the fundamental components under normal operation, an analysis of the fundamental components of the electrical variables with the effects of a GIC is given below. The excitation current i(t) without the effects of the GIC can be expressed as
assess the effects of GICs on power grids, especially in real time. Although the effects of GMD are stronger in high latitudes, power grids in mid-low latitudes may suffer damages due to GIC as well [18,19]. Large GICs also have been found at some Chinese substations [20], and the interactions of GICs with the various HV grid levels have been revealed [21]. These studies have proven that magnetic storms will pose serious threats to the large-scale power grid in China. In recent years, the State Grid Corporation of China, Chinese Academy of Engineering, and several other organizations have been focusing on assessing the influences of geomagnetic storms on the power system, which has become an urgent problem. In 2016, the geomagnetic storms impact on the oil and gas pipeline networks and grids were included in the “National Public Security Risk Prevention and Control Technology and Emergency Technology Equipment” national special research and development program. The defense of power grid disasters is one research objective of this program [22]. The use of a wide-area measurement system has been rapidly growing in China. Phasor measurement units (PMUs) have been installed in all the 500-kV substations in China. Specifically, by the end of June 2016, 240 PMUs had been installed in the North China power grid, covering all the power plants and substations with voltage levels of 500 kV and higher. The wide application of PMU data provides the data necessary for the real-time monitoring of the dynamic processes of the components [23,24], off-line power system emulation [25], and disaster situation awareness [26–28]. In this study, we investigated the power system responses to two geomagnetic storms by analyzing the current and reactive power data acquired during the storms using PMU measurements. In addition, the relations between the response variables and the calculated GICs were also verified on the basis of the data acquired and GIC detailed modeling calculations.
(1)
i (t ) = inm (t ) = Is sin ωt
As shown in Fig. 1, when the GIC appears, the excitation current can be represented as
i (t ) = inm (t ) + IGIC + ia (t ), where inm(t) is the normal current, IGIC is the DC current, and ia(t) is the additional distortion currents caused by IGIC which can be expressed as
ia(t ) =
k1 − k2 (Is sin ωt + Idc − Is ) k2
(2)
Let Ks = k1/k2 and Kdc = Idc/Is, then we have
ia (t ) =
{
(Ks − 1) Is (sin ω t − 1 + K dc ), 0
θ<ω t<π−θ (3)
Eq. (3) can also be derived from Eq. (4) in Ref. [30]. Applying Fourier analysis to (3), we obtain the DC component Iad, fundamental component ia1 and harmonic component iah of ia(t), as follows:
Iad =
(Ks − 1) Is [2 cos θ + (Ks − 1)(π − 2θ)] 2π
(4)
ia1 =
(Ks − 1) Is π 1 ⎡ − θ − sin 2θ⎤ sin ω t π 2 ⎣2 ⎦
(5)
iah = An cos n ω t + Bn sin n ω t
(6)
where An and Bn are coefficients (not given here). Therefore, the excitation current iex can be represented as
2. Analysis of the effects of GICs on transformers
iex = inm + IGIC + Iad + ia1 + iah
The GIC flowing through a transformer results in a DC bias, and the characteristics of the transformer excitation current are shown in Fig. 1 as described by Walling [29]. The symbols in Fig. 1 are defined as follows. G is the knee point, below which the curve is linear and above which it reaches saturation; Is is the saturation current; Φs is the saturation flux; k1 is the gradient in the linear region, and k2 is the gradient in the saturation region of the magnetizing curve; and θ = arcsin (1 – Kdc) is the minimum angle in one cycle at Φ = Φs. Afshin Rezaei-Zare [30] and [31] provide similar analytical methods based on a piecewise model of the iron core and analysis of the harmonics and reactive power consumption characteristics under the effects of the DC bias. Since the PMUs in a power system only measure
(7)
It can be shown (see Appendix A) that ia1 is greater than zero during the positive half-cycle of iex, which indicates that ia1 increases owing to the DC bias. And Iex represents the RMS of iex, to express the reactive power consumption caused by the increase in Iex, the fundamental reactive power is defined as
Qm = UN ·Iex
(8)
where UN is the rated voltage of the transformer. 3. PMU measurement responses to GMDs As mentioned in Section 2, the reactive power and excitation current increase during a GMD event. Dispatchers focus on the effects of GICs on power grids; however, the uncertainty in the GICs in different areas and the variety of transformer types, together with the variable operation, make it difficult to assess the effects of GICs on power grids in real time. Several methods have been proposed for GIC/GMD detection using phasor measured data [32]. However, this approach relies on knowledge of the relationship between GIC and the reactive power being known in advance. In contrast, we propose methods to recognize the grid responses on the basis of PMU measurements. Three-winding transformers are widely used in the power grids. Electric power is transferred between the high- and mid-voltage sides, while the low-voltage side is connected to reactive power compensation devices. PMUs usually measure the electrical variables on the high- and mid-voltage sides but not on the low-voltage side. During GMDs, the GICs flowing through power grids cause responses of the electrical variables in the transformers, including increased excitation current and reactive power as well as harmonics. However, GICs are unlikely to cause transformer breakdown or destruction immediately; thus, the transient data is not usually recorded by PMUs in such situations. The measured current, voltage, and reactive
Fig. 1. Excitation characteristic curve. 933
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transformer is greatly affected by the load current fluctuation on the mid-voltage side. However, the excitation current has a stable response because it is only affected by the DC bias and measured directly by PMUs. According to Fig. 2, the relation between the excitation and load currents can be expressed as
Iṁ = I1̇ − I2̇ / k12 − I3̇ / k13
Fig. 2. Equivalent circuit of a three-winding transformer.
power are all stable, which implies that the harmonics produced by GICs in transformers are not recognized using PMU data. In the study described in [15], the relations between the reactive power consumption and the GIC were investigated, and the GIC was calculated from reactive power measurements obtained with a twowinding transformer. However, three-winding transformers have some differences. In this study, the fluctuations in the electrical variables of a three-winding transformer under the effects of a GIC were fully analyzed considering the PMU measurement characteristics.
k12 =
Iex ≈ |I1̇ − I2̇ / k12 |
(9)
where Qb is the total reactive power consumption; Q′1, Q′2, and Q′3 are the flux leakage reactive powers on the high-, mid-, and low-voltage sides, respectively; and Q1, Q2L, and Q3L are the reactive powers on the high-, mid-, and low-voltage sides, respectively. (Note: Q1 and Q2L can be obtained by PMUs.) Note that the reactive power measured on the mid-voltage side is the reactive power of the load. Q1 and Q2L in (9) are the PMU measurements from which the response can be calculated. The response variable Q0 is defined as the difference between Q1 and Q2L:
(14)
4. GIC calculation at Yangquan Substation 4.1. Two GMDs in 2016 On May 9, 2016, the National Space Science Center of the Chinese Academy of Sciences issued a bulletin that the geomagnetic activity reached the levels of light, medium, and heavy magnetic storms for 12 h, 9 h, and over 6 h, respectively, owing to a coronal hole high-speed flow from 08:00 on May 8 to 11:00 on May 9 Beijing time (Universal Time (UT) + 8) [33]. Another event occurred between 14:00 on October 13 and 17:00 on October 14 Beijing time when the geomagnetic activity reached the levels of medium and light magnetic storms for 9 h and 12 h, respectively. The Kp indices of the two events are shown in Fig. 3. The geomagnetic data recorded by the Meridian Project in China include the north–south (H), east–west (D), and vertical (Z) components. The GMDs were analyzed using all three geomagnetic components from 00:00 to 24:00 UT on May 8 and from 00:00 to 24:00 UT on October 13, as shown in Fig. 4(a) and (b), respectively. The data were obtained at Shisanling Geomagnetic Observatory, Beijing, China (40.3° N, 116.2° E). In general, the GIC through a power grid significantly depends on the rate of change of the H-component of the geomagnetic variation. This is evident in Fig. 4(a) and (b). It is seen in Fig. 4(a) that the Hcomponent rapidly changed between 00:00 and 24:00 UT on May 8. Meanwhile, on October 13, the H-component decreased slowly to its
(10)
When the reactive power Q3L at X′3 is neglected, we have
Q0 = Qb
(13)
where all of the variables on the right side are known on the basis of measurements, and | · | represents the modulus. Since the neutral point voltage U0 is stable when the reactive power compensation is determined, the fluctuations in I3̇ can be neglected. Thus, the excitation current fluctuations in the presence of a GIC can be identified by measuring I1̇ and I2̇ . Both (9) and (14) can be used to recognize the response of a power system due to a GMD from PMU measurements. However, the excitation reactive power (Qm) is affected by two factors: low-voltage side reactive power (Q3L) and the flux leakage reactive powers (Q′1, Q′2, and Q′3). That is to say a transformer is also a source of reactive power because it absorbs or consumes reactive power on the flux leakage. The excitation current (Im) is only affected by the low-voltage side current (I3). In China, the 3-winding 500 kV transformers are usually connected to reactive power compensation devices on the low-voltage sides, which results in only small fluctuations of I3. Therefore Eq. (14) may be more suitable to recognize the impact of GIC on a system.
The equivalent circuit of a three-winding transformer is shown in Fig. 2, where the reactive power consumption of the transformer includes two parts: the excitation reactive power Qm in the excitation branch and the flux leakage reactive power generated by the load currents flowing in the leakage reactances. A PMU measures the reactive power separately on the high- and mid-voltage sides. The total reactive power consumption of the transformer can be expressed as
Q0 = Q1 − Q2L = Qb + Q3L
∑ U1 ∑ U2
The excitation current Iṁ and load current I3̇ on the low-voltage side are reactive power currents. Their phases can be deemed consistent or have a difference of 180°; thus, the amplitude of the sum of Iṁ and I3̇ on the low-voltage side is equal to the sum of their amplitudes. The response variable Iex can be defined and calculated as follows:
3.1. Reactive power response of a transformer to GIC
Qm + Q1′ + Q2′ + Q3′ = Q1 − Q2L − Q3L ⏟ Qb
(12)
where Iṁ is the excitation current; I1̇ , I2̇ , and I3̇ are the currents on the high-, mid-, and low-voltage sides, respectively; I1̇ and I2̇ can be obtained by PMUs; and k12 and k13 are the transformer ratios of the high- and mid- voltage sides and the high- and low- voltage sides, respectively, and can be calculated as follows:
(11)
When the load current on the low-voltage side is stable, Q3L can be treated as a constant. Moreover, the reactive power change due to the leakage inductances X′1 and X′2 can be neglected when the load current on the mid-voltage side varies only slightly. Then, the fluctuations in Q0 reflect the changes in Qm, which indicates that the transformer reactive power consumption in the presence of a GIC can be recognized through PMU measurements of Q1 and Q2L. If the Q0 and GIC waveforms are similar, the changes in Q0 can be regarded as the response of the reactive power to the GIC. It is noted that in general, if the load current has large fluctuations, the reactive power on the low-voltage side cannot be ignored. In this condition, the magnitude of the change in Qb is not the only parameter determined by the GIC. 3.2. Excitation current response of a transformer to a GIC The analysis above indicates that (9) has a strict constraint when it is used to recognize the effects of a GIC because the reactive power of a 934
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Fig. 3. Kp indices of two magnetic storms (UT).
Fig. 5. Wiring diagram of a 500-kV power grid in Shanxi province.
the power grid responses to GMDs. The 500-kV network containing Yangquan Substation is shown in Fig. 5, and was used to calculate the GIC at that Substation. Here, the typical parameters of the 500 kV transformers of Yangquan Substation are provided in Table 1. To calculate the geoelectric field from the geomagnetic data, a onedimensional (1D) layered earth conductivity model was established according to the geological structure and electromagnetic sounding data in [22,33]. The conductivities at different depths in Yangquan City are listed in Table 2. The GIC in a power grid is greatly affected by factors such as the grid topology and network parameters [34]. When the power grid topology and parameters are defined, the GIC amplitude mainly depends on dH/dt. After analyzing the geomagnetic data in Fig. 4, we calculated the geoelectric field and GIC at Yangquan Substation using the geomagnetic data acquired from 02:00 to 07:00 UT on May 8 and from 16:00 to 20:00 UT on October 13. These results are shown in Fig. 6. 5. Recognizing power system responses to GMDs from PMU measurements According to the analysis introduced above, the GIC flowing through a power grid will result in a response that can be identified in PMU measurements. The GICs calculated at Yangquan Substation during the two aforementioned magnetic storms were employed in this study to confirm the power system response to each GMD.
Fig. 4. Variations in the geomagnetic components during two magnetic storms (a) from 00:00 to 24:00 UT on May 8, 2016 and (b) from 00:00 to 24:00 UT on October 13, 2016.
5.1. Reactive power response to a GMD lowest point from 06:00 to 16:00 UT, as shown in Fig. 4(b). Eq. (9) provides a method of recognizing the reactive power response by performing calculations using PMU measurements, based on which the reactive power consumed by a transformer during each of the
4.2. GIC calculation based on geomagnetic data The PMU data were obtained at Yangquan 500 kV Substation (37.97° N, 113.63° E), which serves as the connection between the Hebei and Shanxi power grids, and is approximately 300 km away from the Shisanling Geomagenetic Observatory. To verify the power system response to a GMD, the GIC impacts should be recorded. However, GIC monitoring data are not available for that substation because GIC monitors are not widely applied in the power grids in China. Since a numerical method for calculating the GIC based on geomagnetic data has been developed [8–12], the calculated GICs can be used to verify
Table 1 Typical parameters of the 500 kV transformers in Yangquan Substation.
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Parameters
Value
Core construction Voltage ratings Power ratings Impedance percent Winding connections
3-single-phase-three leg 525 kV/230 kV/36 kV 1000 MVA/1000 MVA/300 MVA 15.7 (H-M), 60.3 (H-L), 40 (M-L) Yyn0d11
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Table 2 Layered-earth conductivity structure in Yangquan City. Depth (km)
Conductivity (S/m)
0–31 31–41.51 41.51–47.34 47.34–68.96 > 68.96
0.0670 0.0021 0.1653 0.0001 0.1269
Fig. 7. Comparison of the currents on the high- and mid-voltage sides at Yangquan Substation during the GMDs on (a) May 8, 2016, and (b) October 13, 2016.
Fig. 6. Calculated geoelectric fields and GICs at Yangquan Substation during the GMDs on (a) May 8, 2016, and (b) October 13, 2016.
aforementioned magnetic storms was calculated. In the calculations, the influence of the load current on the reactive power must be taken into account. The currents measured by the PMUs on the high- and midvoltage sides are presented separately in Fig. 7. In Fig. 7(a), which depicts the currents measured during the magnetic storm on May 8, the current on the high-voltage side is quite different from that on the mid-voltage side, demonstrating the load current fluctuation during the geomagnetic storm. In Fig. 7(b), which depicts the currents during the magnetic storm on October 13, the currents on the high- and mid-voltage sides are almost the same, which demonstrates that the load current experienced little fluctuation in that case. It should be noted that the electricity load was heavy during the magnetic storm on May 8 from 10:00 to 17:00 Beijing time and light during the magnetic storm on October 14 from 00:00 to 04:00 Beijing time. Kazerooni et al. [35] PMU data to validate a geomagnetic disturbance model, which makes a good reference. Based on the knowledge that an approximate linear relationship exists between the reactive power and the GIC for a single-phase transformer [15,35], we performed regression analysis to verify the Q0 response to each GIC and obtained the results shown in Fig. 8. As Fig. 6 (b) shows, there is a large difference in the GIC effect on the grid prior to and around 19:00. Thus,
Fig. 8. Results of a regression analysis between the reactive power and the GIC for the GMDs occurring on (a) May 8, 2016 and (b) October 13, 2016.
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Table 3 Correlations between the calculated GICs and Q0. Date
Variable 1
Variable 2
Statistic
R
Sig.
May 8
∼ IGIC ∼ IGIC
∼ Q0 ∼ Q0
Pearson
0.768
0.00
Pearson
0.833
0.00
October 13
a model comprising two segmented and piecewise linear regression analysis was considered more suitable for the verification, as shown in Fig. 8(b). Next, a Pearson correlation analysis was applied to the two variables after removing the mean value of each:
∼ ⎧ Q0 = Q0 − Q¯ 0 ∼ ⎨ IGIC = IGIC − I¯GIC ⎩
(15)
Then, the correlation coefficient of the two variables is
Rge =
∼ ∼ 〈Q0, IGIC 〉 ∼ ∼ ||Q0 || ||IGIC ||
(16)
The correlation results for the two geomagnetic storms are presented in Table 3. According to Table 3, the correlation coefficients of the variables during the magnetic storms on May 8 and October 13 are 0.768 and 0.833, respectively, and the results pass the significance test, which illustrates a strong correlation between Q0 and the GIC. Thus, the reactive powers measured by the PMUs are responses to the GICs. It is mentioned that the response is affected by the load current in that the correlation coefficient for the event on May 8 is less than that for the event on October 13. To illustrate the relation between the GIC and Q0 more clearly, they are both depicted in Fig. 9 using a double coordinate system, where the GIC and Q0 peaks appear at almost the same times during the magnetic storms. The measured reactive power and GIC agree well during the two magnetic storms; thus, the response of a power system to a geomagnetic storm can be described using the reactive power. Obvious differences between Q0 and GIC can also be seen in Fig. 9. One reason for that is the uncertainties in the calculated GIC which come partly from spatially varying earth conductivity and partly from spatially varying magnetic field variation; another possible reason is the reactive power loss of a transformer can be influenced by the variation of the load. For example, the shift of Q loss in Fig. 9(a) around 4:00 is caused by the reactor connected to the tertiary winding which was put into use during that time.
Fig. 9. Comparison of the transformer reactive power and calculated GIC at Yangquan Substation during the GMDs on (a) May 8, 2016 and (b) October 13, 2016. All of the measurements in this figure were obtained by removing the mean values from the original data.
principle, the projection of the vector x onto the vector y can be described as
||→ xL || = ||→ x ||·cosθ x ||·R = ||→ xy
=
〈→ x ,→ y〉 ||→ y ||
(18)
Thus, the projection coefficient is defined as
||→ x || Km = →L || y ||
5.2. Excitation current response to a GMD
(19)
In the same coordinate system, the two vectors can be represented as According to (11), the transformer excitation current could also be employed to analyze responses to GMDs using PMU measurements. To verify the excitation current responses, the mean values of the relevant variables are examined first, i.e.,
∼ ⎧ Iex = Iex − I¯ex ∼ ⎨ IGIC = IGIC − I¯GIC ⎩
→ → ⎧ xL = Km· x → ⎨ y ⎩
(20)
As shown in Fig. 10, the peaks in the excitation current and GIC waveforms agree well during each magnetic storm, which illustrates that the excitation current can also be used to describe the power system responses to GMDs.
(17)
where IGIC is the absolute value of GIC, I¯ex and I¯GIC are the mean value of Iex and IGIC, respectively. Considering that the relation between the excitation current and the GIC is approximately a piecewise linear function rather than a linear function, a linear correlation analysis is not suitable for these variables. Thus, the method of waveform comparison was employed to analyze the relation between them. Verification could be performed by analyzing the peak times. The waveforms of I¯GIC and I¯ex during the two magnetic storms are shown separately in Fig. 10. To show two vectors of the same length clearly in a single figure, the projection coefficient was introduced. On the basis of the projection
6. Analysis and discussion With the rapid development of power systems, the status of power system operations are becoming increasingly complex, making safety and stability more critical issues. However, effective power system control remains a major problem. To study the effects of GMDs on power grids, the actual responses of power grids need to be recognized. In this study, the response at Yangquan Substation, as represented by PMU measurements, was taken as a practical example, and the calculated GICs were employed for response verification. Since the response 937
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On the contrary, the excitation current alone can be utilized as the response quantity since its fluctuations mainly depend on the GIC. In practical dispatching, the fluctuations in the electrical quantities attract more attention than GICs. Therefore, the excitation current is a suitable response quantity, even though the correlation between the excitation current and the GIC cannot be calculated owing to the nonlinearity of the excitation current. In terms of power grid security and stability, risk assessment is becoming increasingly important, particularly with regards to the effects of natural disasters. In previous research, some efforts have been made to perform risk assessment on the basis of GIC calculations. However, it is difficult to employ GIC calculations throughout a power grid and even more difficult to perform GIC calculations in real time. It is also necessary to develop a more precise GIC calculation model in future work because the GIC accuracy is important when studying the mechanisms which impact power grid electrical equipment. 7. Conclusion The actual power grid responses during two geomagnetic storms were investigated in this study. Response quantities obtainable through PMU measurements were verified using GIC calculations. On the basis of comparisons of the response quantities and calculated GICs, the following conclusions can be drawn: (1) The waveforms of the reactive power and excitation current response quantities both agree with the GICs, which demonstrates that power grids experience responses during GMDs. (2) The excitation current is the most suitable quantity for assessing power grid responses to geomagnetic storms. Moreover, the correlation results indicate that not all reactive power fluctuations are caused by GMDs. (3) The two practical examples analyzed in this study demonstrate that a power grid can experience a response even during a small geomagnetic event. Thus, PMU measurements can be employed to assess the risks of future geomagnetic storm impacts on power grids.
Fig. 10. Comparison between the excitation current and calculated GIC at Yangquan Substation during the GMDs on (a) May 8, 2016 with Km = 0.145 and (b) October 13, 2016 with Km = 0.30. All of the measurements in this figure were obtained by removing the mean values from the original data.
quantities, i.e., Q0 and Iex, both agreed well with the GICs, we consider them to represent the actual dynamic power system responses to the GMDs. In the waveform results in Figs. 9 and 10, both Q0 and Iex calculated from the PMU measurements display obvious responses during the two investigated geomagnetic storms. However, the reactive power alone cannot be employed as the response quantity since it is sensitive to the load current. In general, the load current exhibits significant randomness; thus, when the reactive power is used to analyze the power grid response to a GMD, it is also necessary to analyze the correlation between the measured reactive power and the calculated GIC to ensure that the reactive power fluctuations are mainly caused by the GIC. Furthermore, our results show that GIC calculations should be necessary in future power systems.
The responses represented by PMU measurements in this paper can provide data indicating the actual state of a power grid flexibly and in real time and the robustness of the grid. In future work, power grid risk prediction will be realized by employing PMU measurements together with geomagnetic data. Acknowledgment The authors would like to thank the geomagnetic network of the Meridian Project of China for the geomagnetic data (http://www.sepc. ac.cn/), and the North China Branch of the National Power Dispatching & Control Center for the PMU data.
Appendix A Since the PMUs in a power system measure the fundamental components under normal operation, we show below that the fundamental component of excitation current increases under the influence of GIC. The excitation current i(t) without the effects of the GIC can be expressed as
i (t ) = inm (t ) = Is sin ωt
(1)
When the GIC appears, the excitation current can be represented as
i (t ) = inm (t ) + IGIC + ia (t ),
(2)
where
ia (t ) =
{
(Ks − 1) Is (sin ω t − 1 + K dc ), 0
θ<ω t<π−θ (3)
Within θ < ωt < π-θ, applying Fourier analysis to (3), we obtain the DC component Iad, fundamental component ia1, and harmonic component iah 938
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of ia(t), as follows:
Iad =
A0 2
(4)
ia1 = A1 cos ω t + B1 sin ω t
(5)
iah = An cos n ω t + Bn sin n ω t
(6)
where An and Bn are undetermined coefficients, which can be solved by (3) and Fourier equations.
A0 =
1 π
A1 =
1 π
∫θ
B1 =
1 π
∫θ
∫θ
π−θ
π−θ
π−θ
C1 sin x + C2 dx =
2C1 C cos θ + 2 (π − 2θ) π π
(7)
(C1 sin x + C2) cos x dx = 0 (C1 sin x + C2) sin x dx =
(8)
C1 C (π − 2θ + sin 2θ) + 2 2 cos θ 2π π
(9)
In (7)–(9),
ωt = x C1 = (Ks − 1) Is ⎨ ⎩C2 = (Ks − 1) Is (K dc − 1) ⎧
In order to prove that the fundamental component of excitation current is increased under the influence of GIC, we simply need to prove that ia1 is increased.
ia1 = ⎛ ⎝
Ks − 1 π 1 ⎞ ⎡ − θ − sin 2θ⎤ Is sin ωt . π ⎠⎣ 2 2 ⎦
(10)
Obviously, Ks > 1, sin ωt > 0. Let,
g (θ) =
π 1 − θ − sin 2θ 2 2
Consider the situation at 0 < IGIC < Is, and the offset angle at 0 < θ < π/2 (The same is true of other cases.), we have,
π g ⎛ ⎞ = 0, g ′ (θ) = −cos 2θ − 1 < 0 ⎝2⎠ which explains that for any θ ∈ [0, π/2], g (θ) > g
( ) = 0. Thus, the fundamental component of excitation current is increased. π 2
Space Weather 2014;12(1):76–91. [14] Marti L, Rezaei-Zare A, Narang A. Simulation of transformer hotspot heating due to geomagnetically induced currents. IEEE Trans Power Del 2013;28(1):320–7. [15] Marti L, Berge J, Varma RK. Determination of geomagnetically induced current flow in a transformer from reactive power absorption. IEEE Trans Power Del 2013;28(3):1280–8. [16] Overbye TJ, Hutchins TR, Shetye K, Weber J, Dahman S. Integration of geomagnetic disturbance modeling into the power flow: a methodology for large-scale system studies. In: North American Power Symp. (NAPS), Champaign, USA, pp. 1–7. [17] Demiray T, Beccuti G, Andersson G. Risk assessment of the impact of geomagnetic disturbances on the transmission grid in Switzerland. In: 2013 IEEE Power & Energy Society General Meeting (PES), Vancouver, BC; 2013. p. 1–5. [18] Gaunt CT, Coetzee G. Transformer failures in regions incorrectly considered to have low GIC-risk. 2007 IEEE Lausanne Power Tech 2007:807–12. [19] Marshall RA, Gorniak H, Van Der Walt T, et al. Observations of geomagnetically induced currents in the Australian power network. Space Weather 2013;11(1):6–16. [20] Liu CM, Liu LG, Pirjola RJ. Geomagnetically induced currents in the high-voltage power grid in China. IEEE Trans Power Del 2009;24(4):2368–74. [21] Guo S-X, Liu L-G, Pirjola RJ, Wang K-R, Dong B. Impact of EHV power system on geomagnetically induced currents in UHV power system. IEEE Trans Power Del 2015;30(5):2163–70. [22] Liu C, Wang X, Wang H, Zhao H. Quantitative influence of coast effect on geomgnetically induced currents in power grid; a case study. J Space Weather Space Clim 2018;8, [Article A60, 21, December 2018]. [23] Brahma S, Kavasseri R, Cao H, Chaudhuri NR, Alexopoulos T, Cui Y. Real-time identification of dynamic events in power systems using PMU data, and potential applications models, promises, and challenges. IEEE Trans Power Del 2017;32(1):294–301. [24] Pignati M, Zanni L, Romano P, Cherkaoui R, Paolone M. Fault detection and faulted line identification in active distribution networks using synchrophasors-based realtime state estimation. IEEE Trans Power Del 2017;32(1):381–92. [25] Castillo MRM, London JBA. Off-line detection, identification and correction of branch parameter errors using SCADA and synchronized phasor measurements. In: 2014 IEEE PES Transmission & Distribution Conference and Exposition-Latin America (PES T&D-LA). pp. 1–5. [26] Basu C, Padmanaban M, Guillon S, de Montigny M, Kamwa I. Combining multiple sources of information for situational awareness of geomagnetic disturbances. In: Proc. IEEE Power Energy Society General Meeting, Denver, CO, USA, July 2015.
References [1] Albertson VD, Thorson JM, Clayton RE, Tripathy SC. Solar-induced-currents in power systems: cause and effects. IEEE Trans Power App Syst 1973;PAS92(2):471–7. [2] Molinski TS. Why utilities respect geomagnetically induced currents. J Atmos SolTerr Phys 2002;64(16):1765–78. [3] Kappenman JG. Geomagnetic storms and their impact on power systems. IEEE Power Eng Rev 1996;16(5):5–8. [4] Bolduc L. GIC observations and studies in the Hydro-Quebec power system. J Atmos Sol-Terr Phys 64(16);2002:1793–802. [5] Wik M, Viljanen A, Pirjola RJ, Pulkkinen A, Wintoft P, Lundstedt H. Calculation of geomagnetically induced currents in the 400 kV Power grid in southern Sweden. Space Weather 2008;6(7):11. [6] Vakhnina VV, Shapovalov VA, Kuznetsov VN, Kretov DA. The influence of geomagnetic storms on thermal processes in the tank of a power transformer. IEEE Trans Power Del 2015;30(4):1702–7. [7] Faxvog FR, Fuchs G, Jensen W, Wojtczak D, Marz MB, Dahman SR. HV power transformer Neutral Blocking Device (NBD) operating experience in Wisconsin. MIPSYCON Conference November 7, 2017. [8] Boteler DH, Pirjola RJ. Modelling geomagnetically induced currents produced by realistic and uniform electric fields. IEEE Trans Power Del 1998;13(4):1303–8. [9] Pirjola RJ. Geomagnetically induced currents as ground effects of space weather. In: Cuesta HJM, editor, Space Science, InTech, 2012, Ch. 2, pp. 27–44. [Online] Available: < http://www.intechopen.com/books/space-science/geomagneticallyinduced-currents-as-ground-effects-of-space-weather > . [10] Viljanen A, Pirjola RJ, Wik M, Ádám A, Prácser E, Sakharov Y, et al. Continental scale modelling of geomagnetically induced currents. Space Weather Space Climate 2012;2(1):A17–28. [11] Horton R, Boteler D, Overbye TJ, Pirjola RJ, Dugan RC. A test case for the calculation of geomagnetically induced currents. IEEE Trans Power Del 2012;27(4):2368–73. [12] Viljanen A, Pirjola RJ, Prácser E, Ahmadzai S, Singh V. Geomagnetically induced currents in Europe: characteristics based on a local power grid model. Space Weather 2013;11(10):575–84. [13] Fiori RAD, Boteler DH, Gillies DM. Assessment of GIC risk due to geomagnetic sudden commencements and identification of the current systems responsible.
939
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J. Chen, et al.
China. [32] Kamwa I, Beland J, Trudel G, Grondin R, Lafond C, McNabb D. Wide-area monitoring and control at Hydro-Quebec: past, present and future. In: 2006 IEEE Power Engineering Society General Meeting, Montreal, Que, Canada. [33] Zhang JJ, Wang C, Tang BB. Modeling geomagnetically induced electric field and currents by combining a global MHD model with a local one-dimensional method. Space Weather 2012;10:S05005. [34] Zheng K, Boteler D, Pirjola RJ, Liu LG, Becker R, Marti L, et al. Effects of system characteristics on geomagnetically induced currents. IEEE Trans Power Del 2014;29(2):890–8. [35] Kazerooni M, Hutchins T, Overbye T, Zhu H. Use of PMU data for geomagnetic disturbance model validation. North American Synchrophasor Initiative; 2015.
p. 1–5. [27] Kamwa I, Beland J, Trudel G, Grondin R, Lafond C, McNabb D. Wide-area monitoring and control at Hydro-Quebec: past, present and future. In: 2006 IEEE Power Engineering Society General Meeting, Montreal, Que., Canada, June 2006, p. 1–12. [28] Birchfield AB, Gegner KM, Xu T, Shetye KS, Overbye TJ. Statistical considerations in the creation of realistic synthetic power grids for geomagnetic disturbance studies. IEEE Trans Power Syst 2017;32(2):1502–10. [29] Walling R, Khan A. Exciting current characteristics of transformers under GICs. IEEE Trans Power Del 1991;6(4):1707–14. [30] Rezaei-Zare Afshin. Behavior of single-phase transformers under geomagnetically induced current conditions. IEEE Trans Power Del 2014;29(2):916–25. [31] Yao J, Liu M, Li C, Li Q. Harmonics and reactive power of power transformers with DC bias. In: 2010 Asia-Pacific Power and Energy Engineering Conf., Chengdu,
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Contents lists available at ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Power system responses to geomagnetic disturbances recognized using phasor measurement recordings☆
T
⁎
Jian Chena, Chunming Liua, , Maohai Wangb, Tong Wanga a b
School of Electrical and Electronic Engineering, North China Electric Power University, Beijing 102206, China North China Branch of the State Grid Corporation of China, Beijing 100053, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Excitation current Geomagnetically induced current (GIC) Phasor measurement unit (PMU) Reactive power Response Wide area measurement system
Geomagnetically induced currents (GICs) flowing through transformers result in a DC bias, which poses a threat to safe and stable power grid operation. To evaluate the influence of geomagnetic storms on power systems, it is necessary to study actual power system responses. In this paper, the power system response is represented separately using current and reactive power measurements acquired using phasor measurement units (PMUs). On the basis of the data obtained from a wide-area measurement system, the power system responses to geomagnetic disturbances at Yangquan Substation, Shanxi, China were obtained. By employing the plane wave method, the data acquired during two mild magnetic storms at the Shisanling Geomagnetic Observatory were used to calculate the electric field and GIC at Yangquan Substation. The response variables and calculated GIC results agreed well, and the response variables were thus applied to assess the GIC level in the power system. The results show that the fluctuations in the PMU measurements were caused by GICs in the power system, laying the foundation for a significantly more detailed geomagnetic storm risk monitor.
1. Introduction During magnetic storms, geomagnetically induced currents (GICs) flow through transformers and increase the reactive power and highorder harmonics, which may result in power system accidents including voltage sags, reactive power variations, protective equipment malfunctions, and nuisance equipment tripping. Thus, properly managing a GIC is becoming increasingly important for ensuring power grid safety and stability [1,2]. Many magnetic storms that led to protective equipment malfunction, nuisance equipment tripping, and even serious disruption of electrical power service were discussed in [3–7], including a severe power failure in Quebec in 1989 that was mainly related to secondary transformer disturbances such as the reactive power and harmonics caused by a GIC. Modern power systems in the future will likely require GMD protection which will include (PMU) algorithms which rapidly identify potentially damaging GIC currents. In recent years a new power grid GIC protective device was developed, tested in a live power grid, and installed for continuous operation on a HV transformer in the American Transmission Co. (ATC) power grid in northern Wisconsin, USA. This
neutral GIC blocking device has reportedly been in operation for over three years and has automatically switched into its GIC blocking mode over thirty (30) times when GMDs were detected [7]. Our paper addresses a new refined data processing assessment for characterizing potentially harmful GMD events so that appropriate automatic control actions can be applied in future HV power systems. To realize the fast assessment of the impacts of geomagnetic disturbances (GMDs) on power grids, many research projects have been conducted in the past 10 years. This research has focused on two major topics concerning GMD’s; namely creating a numerical GIC model [8–12] and capturing transformer GIC data in real time [13–17]. These studies have involved a GIC evaluation to assess the potential effects on power grids; however, the GIC is influenced by the real-time operation of the power grid in question, various transformer parameters, the station location, etc. Thus, even if a numerical GIC model is sufficiently precise to enable the assessment of the risks faced by a transformer, it is still difficult to perform precise calculations for entire power grids. In addition, the calculations are usually based on certain assumptions since some information such as the practical grounding configuration of every transformer substation is unknown. Furthermore, GIC monitoring equipment has not been installed widely which also makes it difficult to
☆
This work was supported by the National Key Research and Development Plan (2016YFC0800103) and the National Natural Science Foundation of China (51677068, 51577060). ⁎ Corresponding author. E-mail address: [email protected] (C. Liu). https://doi.org/10.1016/j.ijepes.2019.06.027 Received 18 February 2019; Received in revised form 23 April 2019; Accepted 12 June 2019 Available online 20 June 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.
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the fundamental components under normal operation, an analysis of the fundamental components of the electrical variables with the effects of a GIC is given below. The excitation current i(t) without the effects of the GIC can be expressed as
assess the effects of GICs on power grids, especially in real time. Although the effects of GMD are stronger in high latitudes, power grids in mid-low latitudes may suffer damages due to GIC as well [18,19]. Large GICs also have been found at some Chinese substations [20], and the interactions of GICs with the various HV grid levels have been revealed [21]. These studies have proven that magnetic storms will pose serious threats to the large-scale power grid in China. In recent years, the State Grid Corporation of China, Chinese Academy of Engineering, and several other organizations have been focusing on assessing the influences of geomagnetic storms on the power system, which has become an urgent problem. In 2016, the geomagnetic storms impact on the oil and gas pipeline networks and grids were included in the “National Public Security Risk Prevention and Control Technology and Emergency Technology Equipment” national special research and development program. The defense of power grid disasters is one research objective of this program [22]. The use of a wide-area measurement system has been rapidly growing in China. Phasor measurement units (PMUs) have been installed in all the 500-kV substations in China. Specifically, by the end of June 2016, 240 PMUs had been installed in the North China power grid, covering all the power plants and substations with voltage levels of 500 kV and higher. The wide application of PMU data provides the data necessary for the real-time monitoring of the dynamic processes of the components [23,24], off-line power system emulation [25], and disaster situation awareness [26–28]. In this study, we investigated the power system responses to two geomagnetic storms by analyzing the current and reactive power data acquired during the storms using PMU measurements. In addition, the relations between the response variables and the calculated GICs were also verified on the basis of the data acquired and GIC detailed modeling calculations.
(1)
i (t ) = inm (t ) = Is sin ωt
As shown in Fig. 1, when the GIC appears, the excitation current can be represented as
i (t ) = inm (t ) + IGIC + ia (t ), where inm(t) is the normal current, IGIC is the DC current, and ia(t) is the additional distortion currents caused by IGIC which can be expressed as
ia(t ) =
k1 − k2 (Is sin ωt + Idc − Is ) k2
(2)
Let Ks = k1/k2 and Kdc = Idc/Is, then we have
ia (t ) =
{
(Ks − 1) Is (sin ω t − 1 + K dc ), 0
θ<ω t<π−θ (3)
Eq. (3) can also be derived from Eq. (4) in Ref. [30]. Applying Fourier analysis to (3), we obtain the DC component Iad, fundamental component ia1 and harmonic component iah of ia(t), as follows:
Iad =
(Ks − 1) Is [2 cos θ + (Ks − 1)(π − 2θ)] 2π
(4)
ia1 =
(Ks − 1) Is π 1 ⎡ − θ − sin 2θ⎤ sin ω t π 2 ⎣2 ⎦
(5)
iah = An cos n ω t + Bn sin n ω t
(6)
where An and Bn are coefficients (not given here). Therefore, the excitation current iex can be represented as
2. Analysis of the effects of GICs on transformers
iex = inm + IGIC + Iad + ia1 + iah
The GIC flowing through a transformer results in a DC bias, and the characteristics of the transformer excitation current are shown in Fig. 1 as described by Walling [29]. The symbols in Fig. 1 are defined as follows. G is the knee point, below which the curve is linear and above which it reaches saturation; Is is the saturation current; Φs is the saturation flux; k1 is the gradient in the linear region, and k2 is the gradient in the saturation region of the magnetizing curve; and θ = arcsin (1 – Kdc) is the minimum angle in one cycle at Φ = Φs. Afshin Rezaei-Zare [30] and [31] provide similar analytical methods based on a piecewise model of the iron core and analysis of the harmonics and reactive power consumption characteristics under the effects of the DC bias. Since the PMUs in a power system only measure
(7)
It can be shown (see Appendix A) that ia1 is greater than zero during the positive half-cycle of iex, which indicates that ia1 increases owing to the DC bias. And Iex represents the RMS of iex, to express the reactive power consumption caused by the increase in Iex, the fundamental reactive power is defined as
Qm = UN ·Iex
(8)
where UN is the rated voltage of the transformer. 3. PMU measurement responses to GMDs As mentioned in Section 2, the reactive power and excitation current increase during a GMD event. Dispatchers focus on the effects of GICs on power grids; however, the uncertainty in the GICs in different areas and the variety of transformer types, together with the variable operation, make it difficult to assess the effects of GICs on power grids in real time. Several methods have been proposed for GIC/GMD detection using phasor measured data [32]. However, this approach relies on knowledge of the relationship between GIC and the reactive power being known in advance. In contrast, we propose methods to recognize the grid responses on the basis of PMU measurements. Three-winding transformers are widely used in the power grids. Electric power is transferred between the high- and mid-voltage sides, while the low-voltage side is connected to reactive power compensation devices. PMUs usually measure the electrical variables on the high- and mid-voltage sides but not on the low-voltage side. During GMDs, the GICs flowing through power grids cause responses of the electrical variables in the transformers, including increased excitation current and reactive power as well as harmonics. However, GICs are unlikely to cause transformer breakdown or destruction immediately; thus, the transient data is not usually recorded by PMUs in such situations. The measured current, voltage, and reactive
Fig. 1. Excitation characteristic curve. 933
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transformer is greatly affected by the load current fluctuation on the mid-voltage side. However, the excitation current has a stable response because it is only affected by the DC bias and measured directly by PMUs. According to Fig. 2, the relation between the excitation and load currents can be expressed as
Iṁ = I1̇ − I2̇ / k12 − I3̇ / k13
Fig. 2. Equivalent circuit of a three-winding transformer.
power are all stable, which implies that the harmonics produced by GICs in transformers are not recognized using PMU data. In the study described in [15], the relations between the reactive power consumption and the GIC were investigated, and the GIC was calculated from reactive power measurements obtained with a twowinding transformer. However, three-winding transformers have some differences. In this study, the fluctuations in the electrical variables of a three-winding transformer under the effects of a GIC were fully analyzed considering the PMU measurement characteristics.
k12 =
Iex ≈ |I1̇ − I2̇ / k12 |
(9)
where Qb is the total reactive power consumption; Q′1, Q′2, and Q′3 are the flux leakage reactive powers on the high-, mid-, and low-voltage sides, respectively; and Q1, Q2L, and Q3L are the reactive powers on the high-, mid-, and low-voltage sides, respectively. (Note: Q1 and Q2L can be obtained by PMUs.) Note that the reactive power measured on the mid-voltage side is the reactive power of the load. Q1 and Q2L in (9) are the PMU measurements from which the response can be calculated. The response variable Q0 is defined as the difference between Q1 and Q2L:
(14)
4. GIC calculation at Yangquan Substation 4.1. Two GMDs in 2016 On May 9, 2016, the National Space Science Center of the Chinese Academy of Sciences issued a bulletin that the geomagnetic activity reached the levels of light, medium, and heavy magnetic storms for 12 h, 9 h, and over 6 h, respectively, owing to a coronal hole high-speed flow from 08:00 on May 8 to 11:00 on May 9 Beijing time (Universal Time (UT) + 8) [33]. Another event occurred between 14:00 on October 13 and 17:00 on October 14 Beijing time when the geomagnetic activity reached the levels of medium and light magnetic storms for 9 h and 12 h, respectively. The Kp indices of the two events are shown in Fig. 3. The geomagnetic data recorded by the Meridian Project in China include the north–south (H), east–west (D), and vertical (Z) components. The GMDs were analyzed using all three geomagnetic components from 00:00 to 24:00 UT on May 8 and from 00:00 to 24:00 UT on October 13, as shown in Fig. 4(a) and (b), respectively. The data were obtained at Shisanling Geomagnetic Observatory, Beijing, China (40.3° N, 116.2° E). In general, the GIC through a power grid significantly depends on the rate of change of the H-component of the geomagnetic variation. This is evident in Fig. 4(a) and (b). It is seen in Fig. 4(a) that the Hcomponent rapidly changed between 00:00 and 24:00 UT on May 8. Meanwhile, on October 13, the H-component decreased slowly to its
(10)
When the reactive power Q3L at X′3 is neglected, we have
Q0 = Qb
(13)
where all of the variables on the right side are known on the basis of measurements, and | · | represents the modulus. Since the neutral point voltage U0 is stable when the reactive power compensation is determined, the fluctuations in I3̇ can be neglected. Thus, the excitation current fluctuations in the presence of a GIC can be identified by measuring I1̇ and I2̇ . Both (9) and (14) can be used to recognize the response of a power system due to a GMD from PMU measurements. However, the excitation reactive power (Qm) is affected by two factors: low-voltage side reactive power (Q3L) and the flux leakage reactive powers (Q′1, Q′2, and Q′3). That is to say a transformer is also a source of reactive power because it absorbs or consumes reactive power on the flux leakage. The excitation current (Im) is only affected by the low-voltage side current (I3). In China, the 3-winding 500 kV transformers are usually connected to reactive power compensation devices on the low-voltage sides, which results in only small fluctuations of I3. Therefore Eq. (14) may be more suitable to recognize the impact of GIC on a system.
The equivalent circuit of a three-winding transformer is shown in Fig. 2, where the reactive power consumption of the transformer includes two parts: the excitation reactive power Qm in the excitation branch and the flux leakage reactive power generated by the load currents flowing in the leakage reactances. A PMU measures the reactive power separately on the high- and mid-voltage sides. The total reactive power consumption of the transformer can be expressed as
Q0 = Q1 − Q2L = Qb + Q3L
∑ U1 ∑ U2
The excitation current Iṁ and load current I3̇ on the low-voltage side are reactive power currents. Their phases can be deemed consistent or have a difference of 180°; thus, the amplitude of the sum of Iṁ and I3̇ on the low-voltage side is equal to the sum of their amplitudes. The response variable Iex can be defined and calculated as follows:
3.1. Reactive power response of a transformer to GIC
Qm + Q1′ + Q2′ + Q3′ = Q1 − Q2L − Q3L ⏟ Qb
(12)
where Iṁ is the excitation current; I1̇ , I2̇ , and I3̇ are the currents on the high-, mid-, and low-voltage sides, respectively; I1̇ and I2̇ can be obtained by PMUs; and k12 and k13 are the transformer ratios of the high- and mid- voltage sides and the high- and low- voltage sides, respectively, and can be calculated as follows:
(11)
When the load current on the low-voltage side is stable, Q3L can be treated as a constant. Moreover, the reactive power change due to the leakage inductances X′1 and X′2 can be neglected when the load current on the mid-voltage side varies only slightly. Then, the fluctuations in Q0 reflect the changes in Qm, which indicates that the transformer reactive power consumption in the presence of a GIC can be recognized through PMU measurements of Q1 and Q2L. If the Q0 and GIC waveforms are similar, the changes in Q0 can be regarded as the response of the reactive power to the GIC. It is noted that in general, if the load current has large fluctuations, the reactive power on the low-voltage side cannot be ignored. In this condition, the magnitude of the change in Qb is not the only parameter determined by the GIC. 3.2. Excitation current response of a transformer to a GIC The analysis above indicates that (9) has a strict constraint when it is used to recognize the effects of a GIC because the reactive power of a 934
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Fig. 3. Kp indices of two magnetic storms (UT).
Fig. 5. Wiring diagram of a 500-kV power grid in Shanxi province.
the power grid responses to GMDs. The 500-kV network containing Yangquan Substation is shown in Fig. 5, and was used to calculate the GIC at that Substation. Here, the typical parameters of the 500 kV transformers of Yangquan Substation are provided in Table 1. To calculate the geoelectric field from the geomagnetic data, a onedimensional (1D) layered earth conductivity model was established according to the geological structure and electromagnetic sounding data in [22,33]. The conductivities at different depths in Yangquan City are listed in Table 2. The GIC in a power grid is greatly affected by factors such as the grid topology and network parameters [34]. When the power grid topology and parameters are defined, the GIC amplitude mainly depends on dH/dt. After analyzing the geomagnetic data in Fig. 4, we calculated the geoelectric field and GIC at Yangquan Substation using the geomagnetic data acquired from 02:00 to 07:00 UT on May 8 and from 16:00 to 20:00 UT on October 13. These results are shown in Fig. 6. 5. Recognizing power system responses to GMDs from PMU measurements According to the analysis introduced above, the GIC flowing through a power grid will result in a response that can be identified in PMU measurements. The GICs calculated at Yangquan Substation during the two aforementioned magnetic storms were employed in this study to confirm the power system response to each GMD.
Fig. 4. Variations in the geomagnetic components during two magnetic storms (a) from 00:00 to 24:00 UT on May 8, 2016 and (b) from 00:00 to 24:00 UT on October 13, 2016.
5.1. Reactive power response to a GMD lowest point from 06:00 to 16:00 UT, as shown in Fig. 4(b). Eq. (9) provides a method of recognizing the reactive power response by performing calculations using PMU measurements, based on which the reactive power consumed by a transformer during each of the
4.2. GIC calculation based on geomagnetic data The PMU data were obtained at Yangquan 500 kV Substation (37.97° N, 113.63° E), which serves as the connection between the Hebei and Shanxi power grids, and is approximately 300 km away from the Shisanling Geomagenetic Observatory. To verify the power system response to a GMD, the GIC impacts should be recorded. However, GIC monitoring data are not available for that substation because GIC monitors are not widely applied in the power grids in China. Since a numerical method for calculating the GIC based on geomagnetic data has been developed [8–12], the calculated GICs can be used to verify
Table 1 Typical parameters of the 500 kV transformers in Yangquan Substation.
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Parameters
Value
Core construction Voltage ratings Power ratings Impedance percent Winding connections
3-single-phase-three leg 525 kV/230 kV/36 kV 1000 MVA/1000 MVA/300 MVA 15.7 (H-M), 60.3 (H-L), 40 (M-L) Yyn0d11
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Table 2 Layered-earth conductivity structure in Yangquan City. Depth (km)
Conductivity (S/m)
0–31 31–41.51 41.51–47.34 47.34–68.96 > 68.96
0.0670 0.0021 0.1653 0.0001 0.1269
Fig. 7. Comparison of the currents on the high- and mid-voltage sides at Yangquan Substation during the GMDs on (a) May 8, 2016, and (b) October 13, 2016.
Fig. 6. Calculated geoelectric fields and GICs at Yangquan Substation during the GMDs on (a) May 8, 2016, and (b) October 13, 2016.
aforementioned magnetic storms was calculated. In the calculations, the influence of the load current on the reactive power must be taken into account. The currents measured by the PMUs on the high- and midvoltage sides are presented separately in Fig. 7. In Fig. 7(a), which depicts the currents measured during the magnetic storm on May 8, the current on the high-voltage side is quite different from that on the mid-voltage side, demonstrating the load current fluctuation during the geomagnetic storm. In Fig. 7(b), which depicts the currents during the magnetic storm on October 13, the currents on the high- and mid-voltage sides are almost the same, which demonstrates that the load current experienced little fluctuation in that case. It should be noted that the electricity load was heavy during the magnetic storm on May 8 from 10:00 to 17:00 Beijing time and light during the magnetic storm on October 14 from 00:00 to 04:00 Beijing time. Kazerooni et al. [35] PMU data to validate a geomagnetic disturbance model, which makes a good reference. Based on the knowledge that an approximate linear relationship exists between the reactive power and the GIC for a single-phase transformer [15,35], we performed regression analysis to verify the Q0 response to each GIC and obtained the results shown in Fig. 8. As Fig. 6 (b) shows, there is a large difference in the GIC effect on the grid prior to and around 19:00. Thus,
Fig. 8. Results of a regression analysis between the reactive power and the GIC for the GMDs occurring on (a) May 8, 2016 and (b) October 13, 2016.
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Table 3 Correlations between the calculated GICs and Q0. Date
Variable 1
Variable 2
Statistic
R
Sig.
May 8
∼ IGIC ∼ IGIC
∼ Q0 ∼ Q0
Pearson
0.768
0.00
Pearson
0.833
0.00
October 13
a model comprising two segmented and piecewise linear regression analysis was considered more suitable for the verification, as shown in Fig. 8(b). Next, a Pearson correlation analysis was applied to the two variables after removing the mean value of each:
∼ ⎧ Q0 = Q0 − Q¯ 0 ∼ ⎨ IGIC = IGIC − I¯GIC ⎩
(15)
Then, the correlation coefficient of the two variables is
Rge =
∼ ∼ 〈Q0, IGIC 〉 ∼ ∼ ||Q0 || ||IGIC ||
(16)
The correlation results for the two geomagnetic storms are presented in Table 3. According to Table 3, the correlation coefficients of the variables during the magnetic storms on May 8 and October 13 are 0.768 and 0.833, respectively, and the results pass the significance test, which illustrates a strong correlation between Q0 and the GIC. Thus, the reactive powers measured by the PMUs are responses to the GICs. It is mentioned that the response is affected by the load current in that the correlation coefficient for the event on May 8 is less than that for the event on October 13. To illustrate the relation between the GIC and Q0 more clearly, they are both depicted in Fig. 9 using a double coordinate system, where the GIC and Q0 peaks appear at almost the same times during the magnetic storms. The measured reactive power and GIC agree well during the two magnetic storms; thus, the response of a power system to a geomagnetic storm can be described using the reactive power. Obvious differences between Q0 and GIC can also be seen in Fig. 9. One reason for that is the uncertainties in the calculated GIC which come partly from spatially varying earth conductivity and partly from spatially varying magnetic field variation; another possible reason is the reactive power loss of a transformer can be influenced by the variation of the load. For example, the shift of Q loss in Fig. 9(a) around 4:00 is caused by the reactor connected to the tertiary winding which was put into use during that time.
Fig. 9. Comparison of the transformer reactive power and calculated GIC at Yangquan Substation during the GMDs on (a) May 8, 2016 and (b) October 13, 2016. All of the measurements in this figure were obtained by removing the mean values from the original data.
principle, the projection of the vector x onto the vector y can be described as
||→ xL || = ||→ x ||·cosθ x ||·R = ||→ xy
=
〈→ x ,→ y〉 ||→ y ||
(18)
Thus, the projection coefficient is defined as
||→ x || Km = →L || y ||
5.2. Excitation current response to a GMD
(19)
In the same coordinate system, the two vectors can be represented as According to (11), the transformer excitation current could also be employed to analyze responses to GMDs using PMU measurements. To verify the excitation current responses, the mean values of the relevant variables are examined first, i.e.,
∼ ⎧ Iex = Iex − I¯ex ∼ ⎨ IGIC = IGIC − I¯GIC ⎩
→ → ⎧ xL = Km· x → ⎨ y ⎩
(20)
As shown in Fig. 10, the peaks in the excitation current and GIC waveforms agree well during each magnetic storm, which illustrates that the excitation current can also be used to describe the power system responses to GMDs.
(17)
where IGIC is the absolute value of GIC, I¯ex and I¯GIC are the mean value of Iex and IGIC, respectively. Considering that the relation between the excitation current and the GIC is approximately a piecewise linear function rather than a linear function, a linear correlation analysis is not suitable for these variables. Thus, the method of waveform comparison was employed to analyze the relation between them. Verification could be performed by analyzing the peak times. The waveforms of I¯GIC and I¯ex during the two magnetic storms are shown separately in Fig. 10. To show two vectors of the same length clearly in a single figure, the projection coefficient was introduced. On the basis of the projection
6. Analysis and discussion With the rapid development of power systems, the status of power system operations are becoming increasingly complex, making safety and stability more critical issues. However, effective power system control remains a major problem. To study the effects of GMDs on power grids, the actual responses of power grids need to be recognized. In this study, the response at Yangquan Substation, as represented by PMU measurements, was taken as a practical example, and the calculated GICs were employed for response verification. Since the response 937
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On the contrary, the excitation current alone can be utilized as the response quantity since its fluctuations mainly depend on the GIC. In practical dispatching, the fluctuations in the electrical quantities attract more attention than GICs. Therefore, the excitation current is a suitable response quantity, even though the correlation between the excitation current and the GIC cannot be calculated owing to the nonlinearity of the excitation current. In terms of power grid security and stability, risk assessment is becoming increasingly important, particularly with regards to the effects of natural disasters. In previous research, some efforts have been made to perform risk assessment on the basis of GIC calculations. However, it is difficult to employ GIC calculations throughout a power grid and even more difficult to perform GIC calculations in real time. It is also necessary to develop a more precise GIC calculation model in future work because the GIC accuracy is important when studying the mechanisms which impact power grid electrical equipment. 7. Conclusion The actual power grid responses during two geomagnetic storms were investigated in this study. Response quantities obtainable through PMU measurements were verified using GIC calculations. On the basis of comparisons of the response quantities and calculated GICs, the following conclusions can be drawn: (1) The waveforms of the reactive power and excitation current response quantities both agree with the GICs, which demonstrates that power grids experience responses during GMDs. (2) The excitation current is the most suitable quantity for assessing power grid responses to geomagnetic storms. Moreover, the correlation results indicate that not all reactive power fluctuations are caused by GMDs. (3) The two practical examples analyzed in this study demonstrate that a power grid can experience a response even during a small geomagnetic event. Thus, PMU measurements can be employed to assess the risks of future geomagnetic storm impacts on power grids.
Fig. 10. Comparison between the excitation current and calculated GIC at Yangquan Substation during the GMDs on (a) May 8, 2016 with Km = 0.145 and (b) October 13, 2016 with Km = 0.30. All of the measurements in this figure were obtained by removing the mean values from the original data.
quantities, i.e., Q0 and Iex, both agreed well with the GICs, we consider them to represent the actual dynamic power system responses to the GMDs. In the waveform results in Figs. 9 and 10, both Q0 and Iex calculated from the PMU measurements display obvious responses during the two investigated geomagnetic storms. However, the reactive power alone cannot be employed as the response quantity since it is sensitive to the load current. In general, the load current exhibits significant randomness; thus, when the reactive power is used to analyze the power grid response to a GMD, it is also necessary to analyze the correlation between the measured reactive power and the calculated GIC to ensure that the reactive power fluctuations are mainly caused by the GIC. Furthermore, our results show that GIC calculations should be necessary in future power systems.
The responses represented by PMU measurements in this paper can provide data indicating the actual state of a power grid flexibly and in real time and the robustness of the grid. In future work, power grid risk prediction will be realized by employing PMU measurements together with geomagnetic data. Acknowledgment The authors would like to thank the geomagnetic network of the Meridian Project of China for the geomagnetic data (http://www.sepc. ac.cn/), and the North China Branch of the National Power Dispatching & Control Center for the PMU data.
Appendix A Since the PMUs in a power system measure the fundamental components under normal operation, we show below that the fundamental component of excitation current increases under the influence of GIC. The excitation current i(t) without the effects of the GIC can be expressed as
i (t ) = inm (t ) = Is sin ωt
(1)
When the GIC appears, the excitation current can be represented as
i (t ) = inm (t ) + IGIC + ia (t ),
(2)
where
ia (t ) =
{
(Ks − 1) Is (sin ω t − 1 + K dc ), 0
θ<ω t<π−θ (3)
Within θ < ωt < π-θ, applying Fourier analysis to (3), we obtain the DC component Iad, fundamental component ia1, and harmonic component iah 938
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of ia(t), as follows:
Iad =
A0 2
(4)
ia1 = A1 cos ω t + B1 sin ω t
(5)
iah = An cos n ω t + Bn sin n ω t
(6)
where An and Bn are undetermined coefficients, which can be solved by (3) and Fourier equations.
A0 =
1 π
A1 =
1 π
∫θ
B1 =
1 π
∫θ
∫θ
π−θ
π−θ
π−θ
C1 sin x + C2 dx =
2C1 C cos θ + 2 (π − 2θ) π π
(7)
(C1 sin x + C2) cos x dx = 0 (C1 sin x + C2) sin x dx =
(8)
C1 C (π − 2θ + sin 2θ) + 2 2 cos θ 2π π
(9)
In (7)–(9),
ωt = x C1 = (Ks − 1) Is ⎨ ⎩C2 = (Ks − 1) Is (K dc − 1) ⎧
In order to prove that the fundamental component of excitation current is increased under the influence of GIC, we simply need to prove that ia1 is increased.
ia1 = ⎛ ⎝
Ks − 1 π 1 ⎞ ⎡ − θ − sin 2θ⎤ Is sin ωt . π ⎠⎣ 2 2 ⎦
(10)
Obviously, Ks > 1, sin ωt > 0. Let,
g (θ) =
π 1 − θ − sin 2θ 2 2
Consider the situation at 0 < IGIC < Is, and the offset angle at 0 < θ < π/2 (The same is true of other cases.), we have,
π g ⎛ ⎞ = 0, g ′ (θ) = −cos 2θ − 1 < 0 ⎝2⎠ which explains that for any θ ∈ [0, π/2], g (θ) > g
( ) = 0. Thus, the fundamental component of excitation current is increased. π 2
Space Weather 2014;12(1):76–91. [14] Marti L, Rezaei-Zare A, Narang A. Simulation of transformer hotspot heating due to geomagnetically induced currents. IEEE Trans Power Del 2013;28(1):320–7. [15] Marti L, Berge J, Varma RK. Determination of geomagnetically induced current flow in a transformer from reactive power absorption. IEEE Trans Power Del 2013;28(3):1280–8. [16] Overbye TJ, Hutchins TR, Shetye K, Weber J, Dahman S. Integration of geomagnetic disturbance modeling into the power flow: a methodology for large-scale system studies. In: North American Power Symp. (NAPS), Champaign, USA, pp. 1–7. [17] Demiray T, Beccuti G, Andersson G. Risk assessment of the impact of geomagnetic disturbances on the transmission grid in Switzerland. In: 2013 IEEE Power & Energy Society General Meeting (PES), Vancouver, BC; 2013. p. 1–5. [18] Gaunt CT, Coetzee G. Transformer failures in regions incorrectly considered to have low GIC-risk. 2007 IEEE Lausanne Power Tech 2007:807–12. [19] Marshall RA, Gorniak H, Van Der Walt T, et al. Observations of geomagnetically induced currents in the Australian power network. Space Weather 2013;11(1):6–16. [20] Liu CM, Liu LG, Pirjola RJ. Geomagnetically induced currents in the high-voltage power grid in China. IEEE Trans Power Del 2009;24(4):2368–74. [21] Guo S-X, Liu L-G, Pirjola RJ, Wang K-R, Dong B. Impact of EHV power system on geomagnetically induced currents in UHV power system. IEEE Trans Power Del 2015;30(5):2163–70. [22] Liu C, Wang X, Wang H, Zhao H. Quantitative influence of coast effect on geomgnetically induced currents in power grid; a case study. J Space Weather Space Clim 2018;8, [Article A60, 21, December 2018]. [23] Brahma S, Kavasseri R, Cao H, Chaudhuri NR, Alexopoulos T, Cui Y. Real-time identification of dynamic events in power systems using PMU data, and potential applications models, promises, and challenges. IEEE Trans Power Del 2017;32(1):294–301. [24] Pignati M, Zanni L, Romano P, Cherkaoui R, Paolone M. Fault detection and faulted line identification in active distribution networks using synchrophasors-based realtime state estimation. IEEE Trans Power Del 2017;32(1):381–92. [25] Castillo MRM, London JBA. Off-line detection, identification and correction of branch parameter errors using SCADA and synchronized phasor measurements. In: 2014 IEEE PES Transmission & Distribution Conference and Exposition-Latin America (PES T&D-LA). pp. 1–5. [26] Basu C, Padmanaban M, Guillon S, de Montigny M, Kamwa I. Combining multiple sources of information for situational awareness of geomagnetic disturbances. In: Proc. IEEE Power Energy Society General Meeting, Denver, CO, USA, July 2015.
References [1] Albertson VD, Thorson JM, Clayton RE, Tripathy SC. Solar-induced-currents in power systems: cause and effects. IEEE Trans Power App Syst 1973;PAS92(2):471–7. [2] Molinski TS. Why utilities respect geomagnetically induced currents. J Atmos SolTerr Phys 2002;64(16):1765–78. [3] Kappenman JG. Geomagnetic storms and their impact on power systems. IEEE Power Eng Rev 1996;16(5):5–8. [4] Bolduc L. GIC observations and studies in the Hydro-Quebec power system. J Atmos Sol-Terr Phys 64(16);2002:1793–802. [5] Wik M, Viljanen A, Pirjola RJ, Pulkkinen A, Wintoft P, Lundstedt H. Calculation of geomagnetically induced currents in the 400 kV Power grid in southern Sweden. Space Weather 2008;6(7):11. [6] Vakhnina VV, Shapovalov VA, Kuznetsov VN, Kretov DA. The influence of geomagnetic storms on thermal processes in the tank of a power transformer. IEEE Trans Power Del 2015;30(4):1702–7. [7] Faxvog FR, Fuchs G, Jensen W, Wojtczak D, Marz MB, Dahman SR. HV power transformer Neutral Blocking Device (NBD) operating experience in Wisconsin. MIPSYCON Conference November 7, 2017. [8] Boteler DH, Pirjola RJ. Modelling geomagnetically induced currents produced by realistic and uniform electric fields. IEEE Trans Power Del 1998;13(4):1303–8. [9] Pirjola RJ. Geomagnetically induced currents as ground effects of space weather. In: Cuesta HJM, editor, Space Science, InTech, 2012, Ch. 2, pp. 27–44. [Online] Available: < http://www.intechopen.com/books/space-science/geomagneticallyinduced-currents-as-ground-effects-of-space-weather > . [10] Viljanen A, Pirjola RJ, Wik M, Ádám A, Prácser E, Sakharov Y, et al. Continental scale modelling of geomagnetically induced currents. Space Weather Space Climate 2012;2(1):A17–28. [11] Horton R, Boteler D, Overbye TJ, Pirjola RJ, Dugan RC. A test case for the calculation of geomagnetically induced currents. IEEE Trans Power Del 2012;27(4):2368–73. [12] Viljanen A, Pirjola RJ, Prácser E, Ahmadzai S, Singh V. Geomagnetically induced currents in Europe: characteristics based on a local power grid model. Space Weather 2013;11(10):575–84. [13] Fiori RAD, Boteler DH, Gillies DM. Assessment of GIC risk due to geomagnetic sudden commencements and identification of the current systems responsible.
939
Electrical Power and Energy Systems 113 (2019) 932–940
J. Chen, et al.
China. [32] Kamwa I, Beland J, Trudel G, Grondin R, Lafond C, McNabb D. Wide-area monitoring and control at Hydro-Quebec: past, present and future. In: 2006 IEEE Power Engineering Society General Meeting, Montreal, Que, Canada. [33] Zhang JJ, Wang C, Tang BB. Modeling geomagnetically induced electric field and currents by combining a global MHD model with a local one-dimensional method. Space Weather 2012;10:S05005. [34] Zheng K, Boteler D, Pirjola RJ, Liu LG, Becker R, Marti L, et al. Effects of system characteristics on geomagnetically induced currents. IEEE Trans Power Del 2014;29(2):890–8. [35] Kazerooni M, Hutchins T, Overbye T, Zhu H. Use of PMU data for geomagnetic disturbance model validation. North American Synchrophasor Initiative; 2015.
p. 1–5. [27] Kamwa I, Beland J, Trudel G, Grondin R, Lafond C, McNabb D. Wide-area monitoring and control at Hydro-Quebec: past, present and future. In: 2006 IEEE Power Engineering Society General Meeting, Montreal, Que., Canada, June 2006, p. 1–12. [28] Birchfield AB, Gegner KM, Xu T, Shetye KS, Overbye TJ. Statistical considerations in the creation of realistic synthetic power grids for geomagnetic disturbance studies. IEEE Trans Power Syst 2017;32(2):1502–10. [29] Walling R, Khan A. Exciting current characteristics of transformers under GICs. IEEE Trans Power Del 1991;6(4):1707–14. [30] Rezaei-Zare Afshin. Behavior of single-phase transformers under geomagnetically induced current conditions. IEEE Trans Power Del 2014;29(2):916–25. [31] Yao J, Liu M, Li C, Li Q. Harmonics and reactive power of power transformers with DC bias. In: 2010 Asia-Pacific Power and Energy Engineering Conf., Chengdu,
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