- Email: [email protected]
Distributed State Estimation for Distribution Network with Phasor Measurement Units Information
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Energyonline Procedia 00 (2018) 000–000 Available onlineatat www.sciencedirect.com Available www.sciencedirect.com Energy Procedia 00 (2018) 000–000
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Energy Procedia 158 Energy Procedia 00(2019) (2017)4129–4134 000–000 www.elsevier.com/locate/procedia
10th International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong Kong, 10th International Conference on Applied Energy China(ICAE2018), 22-25 August 2018, Hong Kong, China
Distributed State Estimation for Distribution Network with Phasor 15th International Symposium on District Heating and Cooling DistributedThe State Estimation for Distribution Network with Phasor Measurement Units Information Measurement Units Information Assessing the feasibility of using the heat demand-outdoor a Ying Chena, Xiangyu Kongaa, Chengsi Yongaa*, Xiyuan Mabb, Li Yubb Ying Chen , Xiangyu , Chengsi Yong *, Xiyuan , Li Yu forecast temperature function forKong a long-term district heatMa demand Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin, China ； a
Electric Power Research Institute of ChinaofSouthern Power Grid, Guangzhou 510080, China Key Laboratory of Smart Grid of Ministry Education, Tianjin University, Tianjin, China ；
ba
a a b c Electric Research Institute of China Power Grid, 510080, ,China I. Andrića,b,c *, Power A. Pina , P. Ferrão , J.Southern Fournier ., B.Guangzhou Lacarrière O. Le Correc b
a
IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal
b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Abstract c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France Abstract As the distribution network structure becomes increasingly complex, this paper proposes a distributed state estimation for As the distribution structure becomesunits increasingly complex, this paper proposes a distributed stateestimation. estimationThis for distribution network network with phasor measurement (PMUs) information to improve the performance of state distribution network with measurement units (PMUs) information the performance of scale state estimation. proposed method takes thephasor PMU installation locations as alternative pointstoofimprove the partition, and takes the of sub-zone,This the Abstract proposed takes the PMU installation as alternative the partition, scale of sub-zone,state the number ofmethod real-time measurement, and the DGlocations configuration positionpoints as the of partition criteria,and andtakes then the conducts distributed number of real-time measurement, and thethe DGroot configuration position as the partition criteria, estimation. During the state estimation, bus voltage and branch current are usedand as then state conducts variablesdistributed to reservestate the District heating networks commonly addressed involtage the as one of the are most effective solutions fortodecreasing the estimation. the stateare estimation, the root busand and branch current used as state variables reserve advantage ofDuring measurement conversion technology, theliterature traditional measurement data and PMU measurement data the are greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat advantage of measurement conversion technology, and the traditional measurement data and PMU measurement data are converted into corresponding currents, which simplifies Jacobian matrix, thereby reducing iterations and improving the sales. Dueinto to corresponding theof changed climate conditions and renovation policies, heatreducing demand in verify the future could decrease, converted currents, whichthe simplifies the Jacobian matrix, thereby andeffectiveness improving the calculation speed state estimation. Finally, IEEEbuilding 69-bus radial distribution network is used iterations to the of prolonging the investment return period. calculation of state estimation. Finally, the IEEE 69-bus radial distribution network is used to verify the effectiveness of the proposedspeed method. The main scope of this paper is to assess the feasibility of using the heat demand – outdoor temperature function for heat demand the proposed method. forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 Copyright © 2018 Elsevier Ltd. All rights reserved. ©buildings 2019 The Authors. Published by Elsevier Ltd. of vary in both construction period andthetypology. weatherofscenarios medium,Conference high) and on three district Copyright ©that 2018 Elsevier Ltd. Allresponsibility rights reserved. International Applied Selection and peer-review under scientificThree committee the 10th (low, This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were th Selection and peer-review under responsibility of the scientific committee of the 10 International Conference on Applied Energy (ICAE2018). Peer-review under responsibility of the scientific committee ofpreviously ICAE2018developed – The 10th International Conference on Applied Energy. compared with results from a dynamic heat demand model, and validated by the authors. Energy (ICAE2018). The results showedstate thatestimation; when onlyPMU weather change is considered, margin ofconversion error could be acceptable for some applications Keywords: Distributed measurement; partition criteria;the measurement (the errorDistributed in annualstate demand was lower than 20% for all weather considered). Keywords: estimation; PMU measurement; partition criteria;scenarios measurement conversion However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the 1.The Introduction decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and 1. Introduction renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the State estimation distribution network is used to modify calculate consistent and reliable state with some real-time coupled scenarios). in Thethe values suggested could be used to thea function parameters for the scenarios considered, and State estimation in the distribution network is used to calculate a consistent and reliable state with some real-time measurement data according to some estimation criteria. With the expansion of distribution network, the increasing improve the accuracy of heat demand estimations.
measurement data according to some estimation criteria. With the expansion of distribution network, the increasing © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Tel.: +86-131-3220-0633
address:author. [email protected] * E-mail Corresponding Tel.: +86-131-3220-0633 Keywords: Heat demand; Forecast; Climate change E-mail address: [email protected] 1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. Selection peer-review under responsibility the scientific 1876-6102and Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the 10th International Conference on Applied Energy (ICAE2018). Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. 10.1016/j.egypro.2019.01.820
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Ying Chen et al. / Energy Procedia 158 (2019) 4129–4134 Ying Chen, Xiangyu Kong , Chengsi Yong, Xiyuan Ma, Li Yu/ Energy Procedia 00 (2018) 000–000
numbers of nodes and their measurement data, the computing scale of state estimation is increasing. The addition of distributed generation (DG) permeability, EVs and energy storage systems (ESS) makes accurate state estimation more difficult [1]. The phasor measurement unit (PMU) is gradually applied to the distribution network, which measures the voltage phasors and the branch current phasors of installed nodes [2-3], making the distribution network measurement data optimized. Therefore, the traditional state estimation method has been difficult to meet the current distribution network requirements for calculation speed and accuracy. Reference [4] decomposes the distribution network according to the geographical location or network topology, which adds the voltage of the DG access points as state variables, and estimates the boundary value of the adjacent sub-region as a pseudo-measurement to estimate the distributed state. Reference [5] partitions the installation point of Advanced Measurement System (AMI) as a boundary node and decouples the network into multiple sub-zones for state estimation to improve the speed of state estimation. However, the partitions in this paper do not consider the impact of DGs on estimation. Reference [6] uses the full measurement configuration as a boundary node for decoupling, but it does not mention which device measures the full measurement data. Reference [7] considers the sub-zone scale and redundancy as the partition standard, but the demarcation point is not clear. Considers combining multi-criteria partition with a hybrid solution algorithm to improve the speed and accuracy of state estimation is studied in [8], but the long period of AMI measurement data leads to a longer period of state estimation for selecting the AMI measurement point as the partition boundary point. The error of state estimation is relatively large while taking DGs as the direct negative load. In [4, 9-10], the influence of the DGs on the state estimation and detail the model of DGs is considered to improve the accuracy of state estimation. According the cases that the PMU has been added to the measurement equipment in the distribution network and the DG has greater volatility, the partition method combining PMU measurement with DGs still lacks research and relevant arguments. Aiming at the deficiencies of existing methods, a distributed state estimation method for distribution network with PMUs in formation was proposed in the paper, which takes the PMU installation location as an alternative point of the partition, and uses the sub-zone scale, the real-time measurement quantity, and the DG configuration position as the partition criteria to perform distributed state estimation of the distribution network. Using the root bus voltage and branch current as state variables, measurement conversion technology converts the traditional measurement data and PMU measurement data into corresponding currents, which can simplify the Jacobian matrix, reduce the number of iterations, and decrease the calculation time of the state estimation. Finally, the 69-bus radial distribution network is used to verify the effectiveness of the proposed method. 2. Partition standard based on PMU measurement There are several types of traditional measurement in distribution networks: (1) Three-phase current magnitude and power flow are measured on some switches of the feeder trunk and branch lines; (2)The root bus is equipped with three-phase voltage measurement; (3)Some important loads are equipped with real-time power injection measurements. Since advanced functions such as fault diagnosis require measurement data with a uniform time scale, the PMU is gradually installed in the distribution network. Since the PMUs can measure the voltage phasor of installed buses and the current phasor of connection branches, this paper proposes to take the PMU installation locations as alternative points, and takes the scale of sub-zone, the number of real-time measurement and the DG configuration position into account to partition the distribution network into different sub-zones, so that the speed and accuracy of the three-phase unbalanced state estimation can be improved. 2.1. Decouple the distribution network using the PMU installation location In this paper, the PMU installation buses are used as candidate partition points, and the PMU installation bus B is split into two buses B1 and B2, as shown in Fig. 1. The voltage phasors of B1 and B2 are the same, in which case the network is divided into two sub-zones of A1 and A2. And the root buses and border buses of each sub-zone are both PMU nodes.
Ying Chen et al. / Energy Procedia 158 (2019) 4129–4134 Ying Chen, Xiangyu Kong , Chengsi Yong, Xiyuan Ma, Li Yu/ Energy Procedia 00 (2018) 000–000
P N1
B
A1 N2
4131 3
A2 N1
B1
N2
B2
Fig. 1. PMU bus splitting Combined with the static equivalent method of the power system, for the sub-zone A1, the sub-zone A2 is an external system. Therefore, each downstream branch connected to the bus B can be equivalent to the injection power to replace the sub-zone A2. The equivalent injection power is: *
s PB ' jQB ' U B I injection I B , Ni i 1
(1)
where PB ' , QB ' are the equivalent injection power of the bus B; U B is the voltage phasor of the bus B; I injection is the equivalent current phasor of power injection of bus B; I B , Ni is the current of the downstream branch connected to the bus B; S is the number of downstream branches connected to the bus B. For the sub-zone A2, the upstream network connected to bus B can be equivalent to the injection power instead of sub-zone A1. Therefore, sub-zones A1 and A2 can be decoupled to perform state estimation respectively. Voltage amplitudes and phase angles of the reference buses in each sub-zone are known to avoid hierarchical boundary condition exchanges and overall phase angle update, which can achieve parallel state estimation of distribution networks to improve calculation speed and accuracy. 2.2. Network partition standard Since the calculation time of the distributed state estimation is determined by the largest scale of sub-zones, the network is divided into sub-zones with similar topological scales. Defining the metric for the network topology scale is f1. Few real-time measurements in the distribution network and the combination of traditional distribution network measurements and PMU measurements cannot make the distribution network completely observable. To balance the real-time measurement number of each sub-zone, defining the metric for determining the measurement number of each sub-zone is f2. Due to the fluctuation of DGs output power, the DGs’ prediction accuracy is lower than that of traditional load. To make DGs not concentrated in one sub-zone, defining the metric for the number of DGs in the sub-zones is f3. There are competing or conflicting relationships among the three objective functions of the scale of sub-zone f1, the number of real-time measurement f2 and the DG configuration position f3. This paper converts the multiobjective function optimization into a single objective function optimization problem. The integrated objective function is as follows: min f w1 f1 w2 f 2 w3 f 3 (2) 1 . The where w1 , w2 and w3 are the weights of the objective function, w1 0 , w2 0 , w3 0 , and w1 w2 w3 closer the value of f1 is to 1, the higher the overall calculation efficiency is. The closer the value of f2 is to 1, the higher the balance of the measurement configuration between sub-areas. The closer the value of f3 is 1, the more balanced the number of DGs between sub-zones. And they can be calculated as follows: max n1 , n2 , , nN max 1 ,2 , , N max 1 , 2 , , N f1 , f2 , f3 (3) min n1 , n2 , , nN min 1 ,2 , , N min 1 , 2 , , N where N is the number of sub-zones; ni is the number of buses in each subzone; i mi xi , mi is the number of measurements in the sub-zone i, and xi is the number of state variables in the subzone i; i is the number of DGs in sub-zone i.
Ying Chen et al. / Energy Procedia 158 (2019) 4129–4134 Ying Chen, Xiangyu Kong , Chengsi Yong, Xiyuan Ma, Li Yu/ Energy Procedia 00 (2018) 000–000
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3. Distributed state estimation based on PMU measurement 3.1. Equivalent current measurement conversion The current phasor measured by the PMUs can be expressed as follows: I ijm, r I ij cos ij (4) m I I sin , ij x ij ij where Iij and ij are the current amplitude and phase angle of branch i-j; I ijm, r and I ijm, x are the real and imaginary parts of the equivalent branch current respectively. The amplitude of the branch current can be described by the following nonlinear equation:
I
I ijm, r 2 I ijm, x 2
(5)
The power flow of the branch i-j can be converted into the corresponding branch current through the relationship with the voltage of bus i, and the bus power injection is similar to the branch power flow. The solution formula can be described as:
Pij ei Qij fi Pij fi Qij ei Pe Pi fi Qi ei i i Qi f i (6) ， I ijm, x ， I im,r ， I im,x 2 2 ei fi ei 2 fi 2 ei 2 fi 2 ei 2 fi 2 where Pij and Qij are the power flow of the branch i-j; the voltage of the bus i can be obtained by backward substitution; Pi and Qi are the active and reactive injection power of the bus i respectively; I im,r and I im, x are the real and imaginary parts of the equivalent injected current respectively. In this paper, the root bus voltage and branch current are selected as state variables, so that the voltage phasors of the remaining buses except the root bus can be expressed as follows: r x (7) ei jfi vroot jvroot Rk jX k ikr jikx I ijm, r
k
where is the path between the bus i and the root bus; Rk and X k are the resistance and reactance of branch k r x and vroot are the real part and the imaginary part of the root bus voltage respectively. The respectively; vroot elements in the obtained Jacobian matrix are constant, and retain the advantages of measurement conversion. 3.2. Weighted least squares method based equivalent Current Through the above measurement conversion, the objective function of the state estimation is converted into the following form:
min J
ms
I
mc 2 2 m m ij , ri ri ij , r ij , xi xi ij , x i 1 j 1
wi
h (I ) I
h (I
) w j I mj hcj ( I ij , r , I ij , x )
2
(8)
where ms is the number of power measurements and current phasor measurements; mc is the number of current amplitude measurements and w is the weights of measurements. The form of the iterated equation can be obtained as: (9) x k G1 x k H T x k W z h x k k k 1 k k k T th ; x and x are the state variables obtained by the k and the (k+1)th where G x H x WH x iteration respectively. The solution steps of the distributed state estimation method for the distribution network based on PMU measurement proposed in this paper are shown in Fig. 2.
Ying Chen et al. / Energy Procedia 158 (2019) 4129–4134 Ying Chen, Xiangyu Kong , Chengsi Yong, Xiyuan Ma, Li Yu/ Energy Procedia 00 (2018) 000–000
4133 5
Start Partition standard based on PMU measurement
DG
Power flow measurement Current magnitude measurement Injection power measurement
59 60 61 6263 64 65 6667 6869
Decouple the distribution network
40 41
Distributed state estimation
57 58
DG
DG
0 1 2 3 4 5 6 7 8 9 10 11 12 1314 15 1617 18 19 20 2122 23 24 25 26 27 Sub-zone 1
Sub-zone N
Sub-zone 2
3637 38 39 Measurement conversion
Measurement conversion
WLS
WLS
...
Measurement conversion
55 56 42 43 44 4546 47 48 49 50 51 52 53 54
28 2930 31 3233 34 35
WLS
DG
DG
Fig. 3. Wiring diagram of IEEE-69 distribution network Output
Fig. 2. Schematic diagram of algorithm
4. Case studies The example used in this paper is referred to [11]. In the simulation, the power flow calculation result is a true value, while the measurement data is formed by superimposing the corresponding random measurement error which obeys normal distribution based on the power flow results of the test system. For the traditional measurements, the standard deviation of the power measurement is 0.02, while the standard deviation of the current amplitude measurement is 0.01. For the PMU measurements, the standard deviation of the amplitude measurement is 0.002, and the standard deviation of the phase angle measurement is 0.005. The standard deviation of the pseudomeasurement of the load is 0.02, and the power factor is kept constant. In addition, the reference value of the power is 1MVA, while the reference value of the line voltage is 12.66kV of the root bus voltage. The main wiring is shown in Fig. 3 and PMU installation location are bus 3, 9, 20 respectively. This paper chooses w1=0.5, w2=0.3 and w3=0.2 based on experience and actual operation. The position, power and deviation of the DG are shown in Table 1, and the power factor is taken as 0.9[8]. Table 1. Specifications of DG units. Bus
Type
16 23 31 49 64
PV WT WT WT WT
Active power /kW Phase A Phase B 40 50 30 30 35 35 50 50 15 15
Phase C 60 30 35 50 15
Measurement deviation/%
Whether the measurements are configured
0.5 0.5 40.0 0.5 0.5
Yes Yes No Yes Yes
The partition scheme of the 69-bus distribution network and the corresponding objective function values are shown in Table 2. Table 2. Partition scheme and objective function value. Partition number 2 3 4 5 6
Objective function value 1.315 2.51 2.245 2.245 1.9
It can be seen from the table that when the number of partitions is 2, the objective function value is the smallest in the improved 69-bus distribution network, so that the partition scheme at this time is the optimal partitioning scheme. Besides, due to the distribution of real-time measurements and DGs, the objective function value is the
Ying Chen et al. / Energy Procedia 158 (2019) 4129–4134 Ying Chen, Xiangyu Kong , Chengsi Yong, Xiyuan Ma, Li Yu/ Energy Procedia 00 (2018) 000–000
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largest when the number of partitions is 3. On this basis, the distributed state estimation is performed and the final estimation results are compared with that of the method in literature [12] with no partition. The comparison results are shown in Table 3. Table 3. Results comparison of two algorithms. Method The proposed method Method in [12]
Average estimation error Real part of branch current 1.146 1.244
Imaginary part of branch current 1.361 1.457
Calculation time/s 0.2154 0.3527
It can be seen from the table 3 that the proposed method has advantage in the average estimation error and calculation time. In this partition scheme, the 69-bus network is decomposed into two decoupled sub-zones with similar scales, and high degree of balance between the number of real-time measurements and DGs, which can both ensure the accuracy of the state estimation results and reducing the calculation time. 5. Conclusions This paper proposes a distributed state estimation method for distribution network based on PMU for the increase of DG permeability and gradual application of PMU to distribution network. Considering the three dimensions of the scale of sub-zone, the number of real-time measurement and the DG configuration position, the distribution network is partitioned, and the advantages of measurement conversion are preserved in the distributed state estimation process, so that the accuracy of state estimation in each sub-zone can be ensured and the overall calculation efficiency can be improved. Acknowledgements This work was supported by the Project Supported by the National Key Research and Development Program of China (2017YFB0902900, 2017YFB0902902). References Wu Zaijun, Xu Junjun, Yu Xinghuo, et al. Review of State Estimation Technology of Active Distribution Network [J]. Automation of Electric Power Systems, 2017, 41(13): 182-191. [2] Pau M, Pegoraro P A, Sulis S. Efficient Branch-Current-Based Distribution System State Estimation Including Synchronized Measurements [J]. IEEE Transactions on Instrumentation & Measurement, 2013, 62(9):2419-2429. [3] Pau M, Pegoraro P A, Sulis S. Branch current state estimator for distribution system based on synchronized measurements[C]// IEEE International Workshop on Applied Measurements for Power Systems. IEEE, 2012: 1-6. [4] Wei Zhinong, Chen Sheng, Sun Guoqiang, et al. Distributed Three-phase State Estimation for Active Distribution Network Integrated with Different Types of Distributed Generators[J]. Automation of Electric Power Systems, 2015, 39(9):68-74. [5] HOU Yushen, BAI Xuefeng, GUO Zhizhong. Layered method for distribution system state estimation and pseudo measurement calculation considering AMI [J]. Proceedings of the CSU-EPSA, 2014，26 (8) :71-76. [6] Huang Wei, Pang Lin, Cao Bin, et al. Parallel and distribution computing for an area-decoupled state estimation method for distribution systems [J]. Power Syetem Protection and Control, 2014, 42(15): 45-51. [7] Liu Keyan, Sheng Wanxing, HE Kaiyuan, et al. Distributed state estimation of complex active distribution network based on Lagrange relaxation technique[J]. Power System Protection and Control, 2017, 45(15):125-132. [8] Ma Jian, Tang Wei, Xu Sheng, et al. State estimation of active distribution network based on multi-criteria partition and WLS-PDIPM algorithm [J]. Automation of Electric Power Systems, 2016, 40(12):28-36. [9] Ju yuntao, Lin yi, Wang jing, et al. Multi-phase distribution state estimation considering detailed models of distributed generators [J]. Power System Protection and Control, 2016, 44(23):147-152. [10] Wang Shao, Jiang Zhuohan, Zhu Jiangfeng, et al. State estimation of distribution network involving distributed generation [J]. Power System Protection and Control, 2013(13):82-87. [11] Ju Y, Wu W, Zhang B. A new method for distribution state estimation accommodating current measurements[J]. Proceedings of the Csee, 2011, 31(19): 82-89. [12] Baran M E, Arthur W, Kelley A W. A branch-current-based state estimation method for distribution systems [J]. IEEE Trans on Power Syetems, 1995, 10(1): 483-491. [1]
ScienceDirect ScienceDirect
Energyonline Procedia 00 (2018) 000–000 Available onlineatat www.sciencedirect.com Available www.sciencedirect.com Energy Procedia 00 (2018) 000–000
ScienceDirect ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Energy Procedia 158 Energy Procedia 00(2019) (2017)4129–4134 000–000 www.elsevier.com/locate/procedia
10th International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong Kong, 10th International Conference on Applied Energy China(ICAE2018), 22-25 August 2018, Hong Kong, China
Distributed State Estimation for Distribution Network with Phasor 15th International Symposium on District Heating and Cooling DistributedThe State Estimation for Distribution Network with Phasor Measurement Units Information Measurement Units Information Assessing the feasibility of using the heat demand-outdoor a Ying Chena, Xiangyu Kongaa, Chengsi Yongaa*, Xiyuan Mabb, Li Yubb Ying Chen , Xiangyu , Chengsi Yong *, Xiyuan , Li Yu forecast temperature function forKong a long-term district heatMa demand Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin, China ； a
Electric Power Research Institute of ChinaofSouthern Power Grid, Guangzhou 510080, China Key Laboratory of Smart Grid of Ministry Education, Tianjin University, Tianjin, China ；
ba
a a b c Electric Research Institute of China Power Grid, 510080, ,China I. Andrića,b,c *, Power A. Pina , P. Ferrão , J.Southern Fournier ., B.Guangzhou Lacarrière O. Le Correc b
a
IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal
b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Abstract c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France Abstract As the distribution network structure becomes increasingly complex, this paper proposes a distributed state estimation for As the distribution structure becomesunits increasingly complex, this paper proposes a distributed stateestimation. estimationThis for distribution network network with phasor measurement (PMUs) information to improve the performance of state distribution network with measurement units (PMUs) information the performance of scale state estimation. proposed method takes thephasor PMU installation locations as alternative pointstoofimprove the partition, and takes the of sub-zone,This the Abstract proposed takes the PMU installation as alternative the partition, scale of sub-zone,state the number ofmethod real-time measurement, and the DGlocations configuration positionpoints as the of partition criteria,and andtakes then the conducts distributed number of real-time measurement, and thethe DGroot configuration position as the partition criteria, estimation. During the state estimation, bus voltage and branch current are usedand as then state conducts variablesdistributed to reservestate the District heating networks commonly addressed involtage the as one of the are most effective solutions fortodecreasing the estimation. the stateare estimation, the root busand and branch current used as state variables reserve advantage ofDuring measurement conversion technology, theliterature traditional measurement data and PMU measurement data the are greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat advantage of measurement conversion technology, and the traditional measurement data and PMU measurement data are converted into corresponding currents, which simplifies Jacobian matrix, thereby reducing iterations and improving the sales. Dueinto to corresponding theof changed climate conditions and renovation policies, heatreducing demand in verify the future could decrease, converted currents, whichthe simplifies the Jacobian matrix, thereby andeffectiveness improving the calculation speed state estimation. Finally, IEEEbuilding 69-bus radial distribution network is used iterations to the of prolonging the investment return period. calculation of state estimation. Finally, the IEEE 69-bus radial distribution network is used to verify the effectiveness of the proposedspeed method. The main scope of this paper is to assess the feasibility of using the heat demand – outdoor temperature function for heat demand the proposed method. forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 Copyright © 2018 Elsevier Ltd. All rights reserved. ©buildings 2019 The Authors. Published by Elsevier Ltd. of vary in both construction period andthetypology. weatherofscenarios medium,Conference high) and on three district Copyright ©that 2018 Elsevier Ltd. Allresponsibility rights reserved. International Applied Selection and peer-review under scientificThree committee the 10th (low, This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were th Selection and peer-review under responsibility of the scientific committee of the 10 International Conference on Applied Energy (ICAE2018). Peer-review under responsibility of the scientific committee ofpreviously ICAE2018developed – The 10th International Conference on Applied Energy. compared with results from a dynamic heat demand model, and validated by the authors. Energy (ICAE2018). The results showedstate thatestimation; when onlyPMU weather change is considered, margin ofconversion error could be acceptable for some applications Keywords: Distributed measurement; partition criteria;the measurement (the errorDistributed in annualstate demand was lower than 20% for all weather considered). Keywords: estimation; PMU measurement; partition criteria;scenarios measurement conversion However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the 1.The Introduction decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and 1. Introduction renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the State estimation distribution network is used to modify calculate consistent and reliable state with some real-time coupled scenarios). in Thethe values suggested could be used to thea function parameters for the scenarios considered, and State estimation in the distribution network is used to calculate a consistent and reliable state with some real-time measurement data according to some estimation criteria. With the expansion of distribution network, the increasing improve the accuracy of heat demand estimations.
measurement data according to some estimation criteria. With the expansion of distribution network, the increasing © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Tel.: +86-131-3220-0633
address:author. [email protected] * E-mail Corresponding Tel.: +86-131-3220-0633 Keywords: Heat demand; Forecast; Climate change E-mail address: [email protected] 1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. Selection peer-review under responsibility the scientific 1876-6102and Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the 10th International Conference on Applied Energy (ICAE2018). Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. 10.1016/j.egypro.2019.01.820
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Ying Chen et al. / Energy Procedia 158 (2019) 4129–4134 Ying Chen, Xiangyu Kong , Chengsi Yong, Xiyuan Ma, Li Yu/ Energy Procedia 00 (2018) 000–000
numbers of nodes and their measurement data, the computing scale of state estimation is increasing. The addition of distributed generation (DG) permeability, EVs and energy storage systems (ESS) makes accurate state estimation more difficult [1]. The phasor measurement unit (PMU) is gradually applied to the distribution network, which measures the voltage phasors and the branch current phasors of installed nodes [2-3], making the distribution network measurement data optimized. Therefore, the traditional state estimation method has been difficult to meet the current distribution network requirements for calculation speed and accuracy. Reference [4] decomposes the distribution network according to the geographical location or network topology, which adds the voltage of the DG access points as state variables, and estimates the boundary value of the adjacent sub-region as a pseudo-measurement to estimate the distributed state. Reference [5] partitions the installation point of Advanced Measurement System (AMI) as a boundary node and decouples the network into multiple sub-zones for state estimation to improve the speed of state estimation. However, the partitions in this paper do not consider the impact of DGs on estimation. Reference [6] uses the full measurement configuration as a boundary node for decoupling, but it does not mention which device measures the full measurement data. Reference [7] considers the sub-zone scale and redundancy as the partition standard, but the demarcation point is not clear. Considers combining multi-criteria partition with a hybrid solution algorithm to improve the speed and accuracy of state estimation is studied in [8], but the long period of AMI measurement data leads to a longer period of state estimation for selecting the AMI measurement point as the partition boundary point. The error of state estimation is relatively large while taking DGs as the direct negative load. In [4, 9-10], the influence of the DGs on the state estimation and detail the model of DGs is considered to improve the accuracy of state estimation. According the cases that the PMU has been added to the measurement equipment in the distribution network and the DG has greater volatility, the partition method combining PMU measurement with DGs still lacks research and relevant arguments. Aiming at the deficiencies of existing methods, a distributed state estimation method for distribution network with PMUs in formation was proposed in the paper, which takes the PMU installation location as an alternative point of the partition, and uses the sub-zone scale, the real-time measurement quantity, and the DG configuration position as the partition criteria to perform distributed state estimation of the distribution network. Using the root bus voltage and branch current as state variables, measurement conversion technology converts the traditional measurement data and PMU measurement data into corresponding currents, which can simplify the Jacobian matrix, reduce the number of iterations, and decrease the calculation time of the state estimation. Finally, the 69-bus radial distribution network is used to verify the effectiveness of the proposed method. 2. Partition standard based on PMU measurement There are several types of traditional measurement in distribution networks: (1) Three-phase current magnitude and power flow are measured on some switches of the feeder trunk and branch lines; (2)The root bus is equipped with three-phase voltage measurement; (3)Some important loads are equipped with real-time power injection measurements. Since advanced functions such as fault diagnosis require measurement data with a uniform time scale, the PMU is gradually installed in the distribution network. Since the PMUs can measure the voltage phasor of installed buses and the current phasor of connection branches, this paper proposes to take the PMU installation locations as alternative points, and takes the scale of sub-zone, the number of real-time measurement and the DG configuration position into account to partition the distribution network into different sub-zones, so that the speed and accuracy of the three-phase unbalanced state estimation can be improved. 2.1. Decouple the distribution network using the PMU installation location In this paper, the PMU installation buses are used as candidate partition points, and the PMU installation bus B is split into two buses B1 and B2, as shown in Fig. 1. The voltage phasors of B1 and B2 are the same, in which case the network is divided into two sub-zones of A1 and A2. And the root buses and border buses of each sub-zone are both PMU nodes.
Ying Chen et al. / Energy Procedia 158 (2019) 4129–4134 Ying Chen, Xiangyu Kong , Chengsi Yong, Xiyuan Ma, Li Yu/ Energy Procedia 00 (2018) 000–000
P N1
B
A1 N2
4131 3
A2 N1
B1
N2
B2
Fig. 1. PMU bus splitting Combined with the static equivalent method of the power system, for the sub-zone A1, the sub-zone A2 is an external system. Therefore, each downstream branch connected to the bus B can be equivalent to the injection power to replace the sub-zone A2. The equivalent injection power is: *
s PB ' jQB ' U B I injection I B , Ni i 1
(1)
where PB ' , QB ' are the equivalent injection power of the bus B; U B is the voltage phasor of the bus B; I injection is the equivalent current phasor of power injection of bus B; I B , Ni is the current of the downstream branch connected to the bus B; S is the number of downstream branches connected to the bus B. For the sub-zone A2, the upstream network connected to bus B can be equivalent to the injection power instead of sub-zone A1. Therefore, sub-zones A1 and A2 can be decoupled to perform state estimation respectively. Voltage amplitudes and phase angles of the reference buses in each sub-zone are known to avoid hierarchical boundary condition exchanges and overall phase angle update, which can achieve parallel state estimation of distribution networks to improve calculation speed and accuracy. 2.2. Network partition standard Since the calculation time of the distributed state estimation is determined by the largest scale of sub-zones, the network is divided into sub-zones with similar topological scales. Defining the metric for the network topology scale is f1. Few real-time measurements in the distribution network and the combination of traditional distribution network measurements and PMU measurements cannot make the distribution network completely observable. To balance the real-time measurement number of each sub-zone, defining the metric for determining the measurement number of each sub-zone is f2. Due to the fluctuation of DGs output power, the DGs’ prediction accuracy is lower than that of traditional load. To make DGs not concentrated in one sub-zone, defining the metric for the number of DGs in the sub-zones is f3. There are competing or conflicting relationships among the three objective functions of the scale of sub-zone f1, the number of real-time measurement f2 and the DG configuration position f3. This paper converts the multiobjective function optimization into a single objective function optimization problem. The integrated objective function is as follows: min f w1 f1 w2 f 2 w3 f 3 (2) 1 . The where w1 , w2 and w3 are the weights of the objective function, w1 0 , w2 0 , w3 0 , and w1 w2 w3 closer the value of f1 is to 1, the higher the overall calculation efficiency is. The closer the value of f2 is to 1, the higher the balance of the measurement configuration between sub-areas. The closer the value of f3 is 1, the more balanced the number of DGs between sub-zones. And they can be calculated as follows: max n1 , n2 , , nN max 1 ,2 , , N max 1 , 2 , , N f1 , f2 , f3 (3) min n1 , n2 , , nN min 1 ,2 , , N min 1 , 2 , , N where N is the number of sub-zones; ni is the number of buses in each subzone; i mi xi , mi is the number of measurements in the sub-zone i, and xi is the number of state variables in the subzone i; i is the number of DGs in sub-zone i.
Ying Chen et al. / Energy Procedia 158 (2019) 4129–4134 Ying Chen, Xiangyu Kong , Chengsi Yong, Xiyuan Ma, Li Yu/ Energy Procedia 00 (2018) 000–000
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3. Distributed state estimation based on PMU measurement 3.1. Equivalent current measurement conversion The current phasor measured by the PMUs can be expressed as follows: I ijm, r I ij cos ij (4) m I I sin , ij x ij ij where Iij and ij are the current amplitude and phase angle of branch i-j; I ijm, r and I ijm, x are the real and imaginary parts of the equivalent branch current respectively. The amplitude of the branch current can be described by the following nonlinear equation:
I
I ijm, r 2 I ijm, x 2
(5)
The power flow of the branch i-j can be converted into the corresponding branch current through the relationship with the voltage of bus i, and the bus power injection is similar to the branch power flow. The solution formula can be described as:
Pij ei Qij fi Pij fi Qij ei Pe Pi fi Qi ei i i Qi f i (6) ， I ijm, x ， I im,r ， I im,x 2 2 ei fi ei 2 fi 2 ei 2 fi 2 ei 2 fi 2 where Pij and Qij are the power flow of the branch i-j; the voltage of the bus i can be obtained by backward substitution; Pi and Qi are the active and reactive injection power of the bus i respectively; I im,r and I im, x are the real and imaginary parts of the equivalent injected current respectively. In this paper, the root bus voltage and branch current are selected as state variables, so that the voltage phasors of the remaining buses except the root bus can be expressed as follows: r x (7) ei jfi vroot jvroot Rk jX k ikr jikx I ijm, r
k
where is the path between the bus i and the root bus; Rk and X k are the resistance and reactance of branch k r x and vroot are the real part and the imaginary part of the root bus voltage respectively. The respectively; vroot elements in the obtained Jacobian matrix are constant, and retain the advantages of measurement conversion. 3.2. Weighted least squares method based equivalent Current Through the above measurement conversion, the objective function of the state estimation is converted into the following form:
min J
ms
I
mc 2 2 m m ij , ri ri ij , r ij , xi xi ij , x i 1 j 1
wi
h (I ) I
h (I
) w j I mj hcj ( I ij , r , I ij , x )
2
(8)
where ms is the number of power measurements and current phasor measurements; mc is the number of current amplitude measurements and w is the weights of measurements. The form of the iterated equation can be obtained as: (9) x k G1 x k H T x k W z h x k k k 1 k k k T th ; x and x are the state variables obtained by the k and the (k+1)th where G x H x WH x iteration respectively. The solution steps of the distributed state estimation method for the distribution network based on PMU measurement proposed in this paper are shown in Fig. 2.
Ying Chen et al. / Energy Procedia 158 (2019) 4129–4134 Ying Chen, Xiangyu Kong , Chengsi Yong, Xiyuan Ma, Li Yu/ Energy Procedia 00 (2018) 000–000
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Start Partition standard based on PMU measurement
DG
Power flow measurement Current magnitude measurement Injection power measurement
59 60 61 6263 64 65 6667 6869
Decouple the distribution network
40 41
Distributed state estimation
57 58
DG
DG
0 1 2 3 4 5 6 7 8 9 10 11 12 1314 15 1617 18 19 20 2122 23 24 25 26 27 Sub-zone 1
Sub-zone N
Sub-zone 2
3637 38 39 Measurement conversion
Measurement conversion
WLS
WLS
...
Measurement conversion
55 56 42 43 44 4546 47 48 49 50 51 52 53 54
28 2930 31 3233 34 35
WLS
DG
DG
Fig. 3. Wiring diagram of IEEE-69 distribution network Output
Fig. 2. Schematic diagram of algorithm
4. Case studies The example used in this paper is referred to [11]. In the simulation, the power flow calculation result is a true value, while the measurement data is formed by superimposing the corresponding random measurement error which obeys normal distribution based on the power flow results of the test system. For the traditional measurements, the standard deviation of the power measurement is 0.02, while the standard deviation of the current amplitude measurement is 0.01. For the PMU measurements, the standard deviation of the amplitude measurement is 0.002, and the standard deviation of the phase angle measurement is 0.005. The standard deviation of the pseudomeasurement of the load is 0.02, and the power factor is kept constant. In addition, the reference value of the power is 1MVA, while the reference value of the line voltage is 12.66kV of the root bus voltage. The main wiring is shown in Fig. 3 and PMU installation location are bus 3, 9, 20 respectively. This paper chooses w1=0.5, w2=0.3 and w3=0.2 based on experience and actual operation. The position, power and deviation of the DG are shown in Table 1, and the power factor is taken as 0.9[8]. Table 1. Specifications of DG units. Bus
Type
16 23 31 49 64
PV WT WT WT WT
Active power /kW Phase A Phase B 40 50 30 30 35 35 50 50 15 15
Phase C 60 30 35 50 15
Measurement deviation/%
Whether the measurements are configured
0.5 0.5 40.0 0.5 0.5
Yes Yes No Yes Yes
The partition scheme of the 69-bus distribution network and the corresponding objective function values are shown in Table 2. Table 2. Partition scheme and objective function value. Partition number 2 3 4 5 6
Objective function value 1.315 2.51 2.245 2.245 1.9
It can be seen from the table that when the number of partitions is 2, the objective function value is the smallest in the improved 69-bus distribution network, so that the partition scheme at this time is the optimal partitioning scheme. Besides, due to the distribution of real-time measurements and DGs, the objective function value is the
Ying Chen et al. / Energy Procedia 158 (2019) 4129–4134 Ying Chen, Xiangyu Kong , Chengsi Yong, Xiyuan Ma, Li Yu/ Energy Procedia 00 (2018) 000–000
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largest when the number of partitions is 3. On this basis, the distributed state estimation is performed and the final estimation results are compared with that of the method in literature [12] with no partition. The comparison results are shown in Table 3. Table 3. Results comparison of two algorithms. Method The proposed method Method in [12]
Average estimation error Real part of branch current 1.146 1.244
Imaginary part of branch current 1.361 1.457
Calculation time/s 0.2154 0.3527
It can be seen from the table 3 that the proposed method has advantage in the average estimation error and calculation time. In this partition scheme, the 69-bus network is decomposed into two decoupled sub-zones with similar scales, and high degree of balance between the number of real-time measurements and DGs, which can both ensure the accuracy of the state estimation results and reducing the calculation time. 5. Conclusions This paper proposes a distributed state estimation method for distribution network based on PMU for the increase of DG permeability and gradual application of PMU to distribution network. Considering the three dimensions of the scale of sub-zone, the number of real-time measurement and the DG configuration position, the distribution network is partitioned, and the advantages of measurement conversion are preserved in the distributed state estimation process, so that the accuracy of state estimation in each sub-zone can be ensured and the overall calculation efficiency can be improved. Acknowledgements This work was supported by the Project Supported by the National Key Research and Development Program of China (2017YFB0902900, 2017YFB0902902). References Wu Zaijun, Xu Junjun, Yu Xinghuo, et al. Review of State Estimation Technology of Active Distribution Network [J]. Automation of Electric Power Systems, 2017, 41(13): 182-191. [2] Pau M, Pegoraro P A, Sulis S. Efficient Branch-Current-Based Distribution System State Estimation Including Synchronized Measurements [J]. IEEE Transactions on Instrumentation & Measurement, 2013, 62(9):2419-2429. [3] Pau M, Pegoraro P A, Sulis S. Branch current state estimator for distribution system based on synchronized measurements[C]// IEEE International Workshop on Applied Measurements for Power Systems. IEEE, 2012: 1-6. [4] Wei Zhinong, Chen Sheng, Sun Guoqiang, et al. Distributed Three-phase State Estimation for Active Distribution Network Integrated with Different Types of Distributed Generators[J]. Automation of Electric Power Systems, 2015, 39(9):68-74. [5] HOU Yushen, BAI Xuefeng, GUO Zhizhong. Layered method for distribution system state estimation and pseudo measurement calculation considering AMI [J]. Proceedings of the CSU-EPSA, 2014，26 (8) :71-76. [6] Huang Wei, Pang Lin, Cao Bin, et al. Parallel and distribution computing for an area-decoupled state estimation method for distribution systems [J]. Power Syetem Protection and Control, 2014, 42(15): 45-51. [7] Liu Keyan, Sheng Wanxing, HE Kaiyuan, et al. Distributed state estimation of complex active distribution network based on Lagrange relaxation technique[J]. Power System Protection and Control, 2017, 45(15):125-132. [8] Ma Jian, Tang Wei, Xu Sheng, et al. State estimation of active distribution network based on multi-criteria partition and WLS-PDIPM algorithm [J]. Automation of Electric Power Systems, 2016, 40(12):28-36. [9] Ju yuntao, Lin yi, Wang jing, et al. Multi-phase distribution state estimation considering detailed models of distributed generators [J]. Power System Protection and Control, 2016, 44(23):147-152. [10] Wang Shao, Jiang Zhuohan, Zhu Jiangfeng, et al. State estimation of distribution network involving distributed generation [J]. Power System Protection and Control, 2013(13):82-87. [11] Ju Y, Wu W, Zhang B. A new method for distribution state estimation accommodating current measurements[J]. Proceedings of the Csee, 2011, 31(19): 82-89. [12] Baran M E, Arthur W, Kelley A W. A branch-current-based state estimation method for distribution systems [J]. IEEE Trans on Power Syetems, 1995, 10(1): 483-491. [1]