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Optimal Monitor Placement for Voltage Unbalance Based on Distribution Network State Estimation Zhixuan Liu, Huilian Liao, Member, IEEE, Jovica V. Milanović, Fellow, IEEE, Tingyan Guo, Member, IEEE, Xiaoqing Tang, Member, IEEE
Abstract—This paper develops a methodology for the optimal monitor placement of voltage unbalance, based on a limited number of monitors. As voltage unbalance causes overheating problems in both power system equipments and user devices, it is expected that this long term problem can be fully observed and mitigated if necessary. In this paper, by analyzing the importance of every bus against the monitoring of unbalance or measuring the uncertainty in the network, the best location of monitor with full observability of the network is recommended. Therefore, the financial budget for the installation and maintenance of the monitors can be optimized. The developed methodology, combining the uncertainty of state estimation and optimal monitor placement, is illustrated to provide the level of unbalance for both real-time measurement and long term prediction when some parts of the network are not observable. The study is carried out on a section of the UK distribution network and the results are compared to the actual monitoring data. Index Terms—genetic algorithm, monitor placement, power quality, state estimation, voltage unbalance.
I. INTRODUCTION
S
ECURE and reliable power delivery is intensely expected in the future smart grid with minimum economic cost. Because full observability of the operating status is not achieved in real networks for economic reasons, the optimal monitor placement provides the best solution to a reasonable financial budget for the installation and maintenance cost of the monitors. Apart from the essential viewpoints such as faults and outages, the monitor placement of power quality problems becomes a research hotspot in the recent decade. Voltage unbalance, one of power quality problems, describes the phenomenon that three-phase voltages are of different magnitudes and/or do not show a 120° phase shift between each other [1]. It negatively affects both Distribution Network Operators (DNOs) and customers by causing overheating problems in both power system devices and user applications [2]. At distribution level, regardless of the impact This work was supported by Western Power Distribution. Zhixuan Liu is with the State Grid Fujian Electric Power Research Institute, Fuzhou, 350007, China; Huilian Liao is with the Sheffield Hallam University, S1 1WB, U.K.; Jovica V. Milanović and Xiaoqing Tang are with the University of Manchester, M13 9PL, U.K.; Tingyan Guo is with the National Grid, CV34 6DA, U.K. (e-mail:
[email protected];
[email protected];
[email protected];
[email protected];
[email protected]).
of non-transposed or partially transposed transmission lines due to their short lengths, the main cause of unbalance is asymmetrical loading. Over the past ten years, the growing penetration of single-phase and dual-phase customer applications forms a big challenge to the power system [2]. For example, the charging of an electrical vehicle attracts large power from the power system over an unpredictable period of time and the usage of single-phase distributed generation such as domestic photovoltaic generation at the customer end reduces the load connected to the mains grid. As accepted by worldwide standards, voltage unbalance can be quantified by the “Voltage Unbalance Factor (VUF)”, which is defined as the ratio of negative sequence voltage (V2) and positive sequence voltage (V1). The European standard [3] and the Chinese standards [4][5] establish that 95% of the 10minute average VUFs in one week should not exceed 2% for LV and MV networks, and 1% for HV networks. At any instantaneous moment, it should not exceed 4%. Being a long term power quality problem, monitoring unbalance requires full observability of the network. How to use the minimum number of monitors to derive the highest degree of accuracy of the network status forms the main objective of optimal monitor placement. Currently, there are mature researches on optimal monitor placement for fault location [6], load estimation [7], or other power quality problems such as voltage sags [8][9] and harmonics [10], but there are few papers investigating the general optimization framework for the monitor placement for power quality problems including voltage unbalance [11]. This paper aims to fill this gap. With incomplete monitoring data, Distribution Network State Estimation (DNSE) can provide the values of the whole network [12]. It works out the possible range and distribution of unbalances at all buses with random measuring errors, considering the network topology and parameters of online equipments. Because the number of actual measurements is usually less than the number of required state estimates [13], a three-phase state estimator using a pseudo-measurement is employed in this study to enable the real-time detection and the long-run prediction of unbalance. By using DNSE, the location of the source of unbalance can be detected and the health status of the network can be obtained. This is particularly relevant to DNOs as maintenance and mitigation can be carried out accordingly to avoid penalties due to
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standard requirements or customer contract. The state estimation results also demonstrate the accuracy of different monitor sets. By statistically analyzing the numbers and locations of monitors of different monitor sets, a method for optimal monitor placement can be suggested. This paper firstly introduces the motivation for optimal monitor placement for unbalance and the background of unbalance. Secondly, by using DNSE and the developed method for ranking the importance of buses or evaluating the uncertainty in the network, the accuracies of different monitor sets are discussed and the optimal monitor placement is recommended. Finally, the DNSE results are compared to the data resulting from simulations of actual loading data or actual monitoring data. The simulations are performed using a section of the UK distribution network in Matlab. II. DISTRIBUTION NETWORK STATE ESTIMATION A. Three Phase Load Flow 1) Load Flow Equations In simulation, when calculating state estimation, the results of load flow which may involve the actual monitoring data or may not, will be used. The following measurements are calculated in load flow: net injections of active power ( Pi p ) and reactive power ( Qip ) at bus i of phase p, line impedances matrix (Y=G+jB), voltage magnitudes at bus i of phase p ( Vi p ) and voltage angles between two buses and two phases ( θ ikpm ). The three phase Newton-Raphson method provides results for the required parameters and the active and reactive flows from bus k to bus i are formulated in (1) (2) [14]: Pi p = Vi p Vkm [Gikpm cos(θ ikpm ) + Bikpm sin(θ ikpm )]
(1)
k =1... N m ={a ,b ,c}
Qi
p
= Vi Vkm [Gikpm k =1... N m={a ,b ,c} p
sin(θ ikpm )
−
Bikpm
cos(θ ikpm )]
(2)
By using the Jacobian matrix [15], the derivatives of each variable are calculated with respect to the final values. The final converged values can be derived by iterating the computing process. The three phase voltages can be transformed into three sequence voltages using the Fortescue transformation [15][16] for the assessment of unbalance. 2) Line Model The transmission line in this study (predominantly overhead lines in the studied voltage level) is modelled in three phases in admittance form. The admittance matrix is 3×3 with nonzero off-diagonal elements and is assumed to be constant under all circumstances, ignoring changes of temperature, onload transformer tap change, etc. [14][17]. The admittance matrix of time domain (Yabc) is derived by inverting line impedance matrix (Zabc). Then the admittance matrix in sequence domain (Y012) can be obtained using the Fortescue transformation. 3) Transformer Model The transformer type used in the study is delta-earthed-star,
which blocks zero sequence components. The transformers are assumed to be on-load tap changing transformers with secondary side taps [18]. The transformer admittance matrix is formed considering sequence domain components. B. Three Phase State Estimation The parameters derived from load flow are represented as the state variables x. State estimation aims at the smallest error of the estimated variable to its true value, as defined in (3).
e = z − H(x)
(3)
where z is the vector of measurements, H(x) is a non-linear set of equations formulating the relation between the true state of the power system and the state variable x, and e is the vector between the true state values and the observed state variable values [13]. e~N(0,R), where R is the covariance matrix of the measurement errors (e). The objective function of state estimation is shown in (4).
min[z − H(x)]T R −1[z − H(x)]
(4)
x
The state estimation equations can be solved by using update equations iteratively (5) (6):
x k +1 = x k + (H X R −1H X ) −1 HTX R −1[z − H(xk )]
(5)
∂H(xk ) (6) ∂x where xk is the estimation of the state variables at the kth iteration and H x is the Jacobian matrix. In this study, x is defined as the three phase voltage magnitudes or angles of each bus [14]. Hx =
C. Pseudo Measurements The overall accuracy of existing monitors depends on the installation of monitors, including the accuracy of the monitor itself, the location of the monitor and the coverage of the monitor. The monitors may record some or all of the values: active and reactive power flows (P and Q) at a bus, voltage magnitude and angle (|V| and θv) of a bus, and current magnitude and angle (|I| and θI) flowing through a bus. The monitors are expected to have full observability of the whole network; however some buses may remain unobservable or have some data missing. In simulation, it is essential to define the error rate for state estimation, which benefits the affirmation of the possible range of current unbalance level. In this study, the buses with installed monitors or zero net power injections are assumed to have a very small margin of error [19] – a standard deviation of 0.2% of the mean value [20]. Pseudo measurements are applied to the active and reactive power injections of the remaining buses. The error of pseudo measurements is assumed to have a standard deviation of 7% [21]. D. Correlation between Number of Monitors and Accuracy There are different types of monitors, covering different ranges of parameters that can be measured. Owing to the physical materials and structure, all monitors have inevitable inherent errors in monitoring data. If a monitor is installed in a specific bus, the uncertainty in
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this bus will be reduced and the accuracy will be increased. To assess the accuracy of the used monitor set, a definition is formulated in the paper. For each load flow, 100 state estimations will be carried out to estimate the possible range of VUF variation. “Uncertainty” is defined as the difference between the true VUF (VUFTRUE) derived from the load flow or real monitored data and the mean value of the 100 loops of state estimation (VUFSE-MEAN). It is shown as (7). The value of uncertainty always does not exceed 1%. (7) Uncertainty (%) = VUFSE-MEAN – VUFTRUE III. STUDY NETWORK Fig. 1 shows the 24-bus section of the UK distribution network composed of fourteen 33kV buses (labelled green) and ten 11kV buses (labelled red). This section receives power from a balanced external grid through bus 1, which is the only and balanced power supply for this area. The transmission lines are assumed to be fully transposed and entirely balanced and all transformers are delta earthed-star (Dyn11) winded. Every 11kV bus serves a local load that can be the potential source of unbalance in this study.
Fig. 1. 24-Bus distribution network.
IV. METHODOLOGY A. Ranking of Buses To monitor unbalance, full observability is not sufficiently accurate. Due to the different contributions of every bus to the unbalance, the various network circumstances (power system components and operating conditions) result in different degrees of influence on the monitored data. When monitoring the unbalance, if there are more important buses than others, then monitor installations at these highly-affected buses provide better solutions than installation of monitors at the remaining buses, assuming the same number of meters. When there are monitors in the network already, the optimal monitor placement should take the existing monitors into consideration in order to reduce costs. To rank the buses in the network based on their influence on unbalance, a test of importance of individual buses is carried out in the test network. In this test, every load is set to be the single unbalanced source in the network, in turn. The size of active power and reactive power in one phase of the load is adjusted to generate unbalance as follows: phase b and phase c of the selected asymmetrical load remain unchanged while the active power and reactive power of phase a are
multiplied by a same weighting factor (or scaling factor). As long as the apparent powers of three phases are different, the voltages of three phases in the common coupling point will be unbalanced. When the bus to which the unbalanced load is directly connected achieves 1% VUF, the weighting factor of phase a is recorded. The weighting factors of the 10 loads in the 24-bus network are shown in Table I. If the weighting factors are arranged in descending order, the ranking (from the most important to the least important) is: 15, 23, 17, 20, 24, 21, 22, 19, 16, and 18. TABLE I WEIGHTING FACTORS OF 10 LOAD BUSES Actual Load in Bus Number Scaling Factor Phase A(MW) 15 1.153 8.408 16 1.609 1.917 17 1.397 1.792 18 2.126 1.086 19 1.553 1.516 20 1.423 1.524 21 1.530 0.882 22 1.547 1.706 23 1.170 8.606 24 1.484 1.662
It can be seen from the result that, the ranking of buses does not strictly follow the sequence of the size of load connected to the bus. The ranking of buses is influenced by the sizes of the load connected to the bus, as a large load stimulates a large unbalanced current in the network, as well as by the location of buses [22]. For example, bus 16, 17, 18 and 19 are located in the same area. So any unbalanced source inside this area will have a significant effect on this inter-connected area. When there is a monitor in this area, it facilitates the estimation of unbalance and so the reductions of the uncertainties of all buses in the whole area. It is obvious that the more hazardous buses may also confront fault and other power quality problems such as voltage sag and harmonics. Therefore, the investigation in the ranking may facilitate the observation for overall problems. The ranking of buses can be applied to investigate other power quality problems in similar ways. B. Optimization Using Genetic Algorithm (GA) Genetic Algorithm has been widely employed to perform the heuristic search for the optimal monitor placement to provide solutions to power system problems [9][23]. To monitor unbalance, the aim is to derive minimum uncertainty of the network using a minimum number of monitors. Therefore, for a fixed number of monitors, the objective function is set as (8) to be automatically calculated by GA. The compliance to the standard limitation is considered when deriving the monitoring results of the optimal monitor set, rather than at the objective function. n
min | VUF SE − MEAN −VUFTRUE |
(8)
i =1
The selection of the optimal number of monitors can be made by considering the balance between the desired accuracy and financial cost. The GA optimization via computer
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V. OPTIMAL MONITOR PLACEMENT A. Optimal Monitor Placement Using Ranking For one load flow, 100 state estimations are computed. There are ten load buses in the network, i.e. ten locations for monitoring the sources of unbalance. When considering the number of monitors and taking the cost and accuracy of monitoring into account, usually the monitor set with five monitors is examined as recommended by DNOs. Fig. 2 and Fig. 3 illustrate the results obtained with different monitor sets. Fig. 2 displays the monitored results with monitors at the five most important buses in the ranking. The boxes in the figure denote the inter-quartile ranges of the monitored results, which stand for the possible ranges of VUFs of those buses. With a sufficiently narrow box, an accurate result can be inferred from metering. As seen from the figure, the results of monitored buses can be precisely read while the rest of the buses in the network still remain unidentified. Fig. 3 shows the results with the monitors installed at the five least important buses in the ranking. This set of monitors observes the unbalance in local substations but results in larger fluctuations of VUFs at other buses than the previous set. With the same number of monitors, the sums of all ranges of VUFs of 24 buses are 0.56% and 1.21% for results illustrated in Fig. 2 and Fig. 3, respectively. 3.5
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Fig. 2. State estimation results using the best 5 monitor locations. 3.5
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Fig. 3. State estimation results using the worst 5 monitor locations.
The installations of monitors at more important buses will increase not only the accuracy of monitoring locally, but also the accuracy of estimation at other non-monitored buses. The proposed ranking method facilitates accurate monitoring of unbalance with the same financial cost involved, and it can be
applied to bigger networks but with an increased workload. B. Optimal Monitor Placement Using GA The correlation between the number of monitors and the overall uncertainty defined in (8) is shown in Fig. 4. It is obvious that there is a turning point where the gradient of the curve changes, at the point when the number of monitors is 3. With more than three monitors, the uncertainty decreases almost linearly. When there are 7 monitors, the overall uncertainty for the best location of monitors stays below 1%. However, because the scheduled number of monitors is 5, the research on the 24-bus network will be entirely based on 5 monitors. For this network, the result of GA optimization with five monitors is: bus 15, 23, 17, 20 and 24, which is exactly the same set of buses obtained using previously discussed ranking method based on weighting factors. Therefore, the DNSE results with the suggested set of monitors determined by GA will not be repeatedly demonstrated and discussed. Overall Uncertainty in VUF (%)
programming saves time and labor compared to the manual method. It is suitable for and can be applied to both short term evaluation and long term assessment.
5 4 3 2 1 0
0
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4 6 Number of Monitors
8
10
Fig. 4. Correlation between number of monitors and overall uncertainty for 24-bus network.
VI. SIMULATION USING ACTUAL DATA A. Simulation with Real Loading Data The actual loading data of a month were provided by the DNO. Loadings at every bus were recorded once per half an hour and so there are 1490 time points in total. Because the data were read from the transformers, once a transformer is disconnected, the loading at the downstream bus is marked as zero, although it may be connected to other upstream buses via other transformer paths. By adjusting all the loads according to Table II to create the sources of unbalance, the VUF values for all buses for the whole month is demonstrated in Fig. 5. The peak and bottom of each day can be easily distinguished and it is clear that unbalance at weekends is lower than that of weekdays, as the overall loading decreases and people’s activities change. Fig. 6 uses box plot to illustrate the 1490 values for every bus, which shows that bus 15 and 23 have 52.35% and 4.16% of VUF values larger than 1%, respectively. B. Simulation with Real Monitoring Data As provided by the DNO, the 24-bus distribution network is monitored using the type of monitor which records P, Q, |S|, |V| and |I|. Because the monitor only records magnitudes of voltages and lacks angular information, in the study, the phase shifts between each two phases are set to be equal. The voltage profile is read once every ten minutes and there are 5040 points in total. In the network, all buses have single phase monitoring while only bus 16 and bus 24 are three-phase
5
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Fig. 5. One-month prediction of unbalance using real loading data. 1.5
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Fig. 6. Box plot of one-month prediction of unbalance using real loading data for all buses. 0.8 Bus 16 Bus 24
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Fig. 7. Real one-month monitoring data for bus 16 and 24.
Based on the results of actual loading simulation, DNSE provides the possible ranges for every bus. Fig. 8 shows a oneday simulation using the actual loading data of a weekday. The two blue lines in each sub-figure indicate the estimated VUF range building on the state estimation results and the two red lines in the sub-figures of bus 16 and 24 are the on-site measurements for the same day. It can be seen that the actual levels of unbalance locate within the estimated range with a few exceptions at bus 16. With the development of DNSE, when the monitoring data are not available, the possible level of unbalance can be worked out according to the actual loading data, if reasonable load variation is applied. To increase the accuracy of state estimation, the actual monitoring data should be included in the computation
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Fig. 8. One-day estimation of unbalance based on real loading data, with real monitoring data indicated at bus 16 and 24.
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Phase A B C
process. In reality, in addition to the three-phase monitors at bus 16 and 24, there are three more installed at bus 15, 18 and 23. However, they are not accessible due to technical problems. Considering the readings at these three sites, a new state estimation is calculated by the presence of both actual monitoring data at bus 16 and 24, and the mean values of state estimation results of bus 15, 18 and 24, shown in Fig. 9. The actual monitored values are still shown with red curves whereas the mean values of state estimation results that are plotted using green lines. With five monitored sites, the uncertainties in VUF of the non-monitored individual buses are limited to about 0.2%. Bus 23 VUF(%)Bus 21 VUF(%)Bus 19 VUF(%)Bus 17 VUF(%)Bus 15 VUF(%)
TABLE II UNBALANCE SETTING FOR ALL LOADS Multiplying Factor to Active Power Power Factor 1.1 1 0.95 0.97 0.95 0.95
Bus 15
accessible. The VUFs of available buses are plotted in Fig. 7.
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Fig. 9. One-day estimation of unbalance based on actual loading data and actual monitoring data, assuming accessible monitors are installed at bus 15, 16, 18, 23 and 24.
The similar state estimation result with the five most important monitor locations determined by the methodology developed in this paper is plotted in Fig. 10. The chosen set demonstrates narrower ranges than that of Fig. 9. The overall range of VUFs (the sum of all the ranges at every bus and every measuring point, i.e., the sum of ranges of VUFs at 1490×24 points) is 112.5% in Fig. 9 and it has been reduced to 97.22% if the optimal monitor set is used.
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Fig. 10. One-day estimation of unbalance based on actual loading data and actual monitoring data, assuming accessible monitors are installed at bus 15, 16, 17, 20 and 24.
VII. CONCLUSION The paper presents a methodology for optimal monitor placement. In order to apply the methodology, a distribution network state estimator is developed which enables the prediction of unbalance and the fulfillment of incomplete data, as well as the correlation between monitor placement and resultant accuracy in the measurement. By ranking the importance of buses or investigating the overall uncertainty of the network using GA, the best location of monitors is recommended and better monitoring accuracy can be achieved with the same amount of monitors compared to other locations. This enables not only momentary estimation of level of unbalance, but also a long-run prediction of the system state even when monitoring is unavailable or incomplete. The benefits, in terms of both financial costs and labor force for maintenance, help DNOs to operate better conditions of the power system, carry out easier mitigation of power quality problems, and avoid penalties due to poor power supply to customers according to the contract. By considering the existing monitors in the network, the optimal monitor placement facilitates further planning of monitor installations. VIII. ACKNOWLEDGEMENT The authors would like to thank R. Ferris, N. Johnson, J. Berry, and R. Stanley for their help and guidance. IX. REFERENCES [1] [2] [3] [4] [5] [6]
A. Von Jouanne, B. Banerjee, “Assessment of Voltage Unbalance”, in IEEE Trans. on Power Delivery, vol. 16, No.4, pp.782-790, Oct. 2001. Johan Driesen, Thierry Van Craenenbroeck, Voltage Disturbances, Copper Development Association, 2002. EN 50160: Voltage Characteristics in Public Distribution Systems. European Committee for Electrotechnical Standardization, Nov. 1994. GB/T 15543-2008: Power quality - Three-phase Voltage Unbalance, Chinese National Standard Committee, 2008. DL/T 1375-2014: Technical Guide for Power Quality Assessment Three-phase Voltage Unbalance, National Energy Bureau, 2014. Y. Liao, “Fault location observability analysis and optimal meter placement based on voltage measurements,” Electric Power Systems Research, vol. 79, No. 7, pp. 1062-1068, 2009.
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X. BIOGRAPHIES Zhixuan Liu is a power system engineer with the State Grid Fujian Electric Power Research Institute, Fuzhou, China. Her research direction is weak area detection, operation of power system and power quality. Huilian Liao (M’13) is currently working as a lecturer at Sheffield Hallam University, UK, investigating power quality with respect to voltage sags and unbalance phenomena. Jovica V. Milanović (M’ 95, SM’ 98, F’ 10) is a Professor of electrical power engineering and Director of External Affairs in the School of Electrical and Electronics Engineering at The University of Manchester, UK, Visiting Professor at the University of Novi Sad, Novi Sad, Serbia and Conjoint Professor at the University of Newcastle, Newcastle, Australia. Tingyan Guo (S’11 M’16) is currently a power system engineer with the Network Capability Electricity department of National Grid, UK. Xiaoqing Tang received her PhD degree from the Department of Electronics and Electrical Engineering, Queen’s University of Belfast, UK. She is currently working as a Postdoctoral Research Associate at The University of Manchester, UK.
