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2016 China International Conference on Electricity Distribution (CICED 2016) Xi’an, 10-13 Aug, 2016 The Bi-level Programming Model of Load Transferring Strategy Based on Topological Units of High-voltage Distribution Network First A. JIN Yong1,3 ,Second B. LIU Junyong1, Third C. LI Hongwei2, Fourth D. ZHANG Xi1 1. College of Electrical Engineering and Information Technology,Sichuan University, 2. College of Electrical Engineering and Information Technology,Southwest Petroleum University, 3. State Gird of China in Chengdu. Abstract—A load transferring strategy for High-voltage distribution network (HVDN) is presented in this paper to mitigate operation congestion in urban power system. A novel bi-level programming model based on topological units (group) is established in this paper instead of traditional intelligent algorithm with 0-1 integer variables. In the upper level, the balance factor is defined to guide the reasonable load allocation of the system, while the load shedding factor is to coordinate the unbalance between transformer capacity and load in emergency; In the lower level, the supply channel matrix is used to execute orders from upper and feedback the results. The simulation using proposed models is verified in simplifying decision space which is very suitable for online analysis. Index Terms—HVDN,Load transfer,PSO, Topological units (group). Fig.1 the topological units Typically, there is at least 1 line reserved for an 110kV substation, as well as large amount of bus bar breakers inside the substation which makes the operation mode of HVDN very complex. A local urban power system can be converted into the schematic diagram with symbol of topological units in Fig 2(a), (b). Fig.2 (a) the topological diagram of HVDN I. I NTRODUCTION WITH the rapid development of urban load in china, the congestion of transmission section and short-term overload risk of transformer is appearing significantly. Load transfer is a nonlinear optimization problem of multi-objective with constraints to get the best optimal performance or index which is always modeled as an 0-1 mixed integer programming solved with intelligent algorithm. Fig.2 (b) the HVDN with topological unit II. THE TOPOLOGICAL ANALYSIS OF HVDN A. The topological unit The definition of topological unit is the cluster of those equipments which is responsible for the load transferring from high voltage to the lower voltage, including the main bus bar, and the transformer as well as the switches or breakers besides. The letter U is used in Fig 1 and the transformer in operation is called available topological unit. B. The topological unit group From Fig2 (b) above, topological units of the 110kV HVDN connecting with each other constitute a group which is supplied by 220kV substations. The 220kV line which is used to supply power to the group is called power supply channel in this paper, such as 11 12 33 ….in Fig3 (b).Accessible matrix A(n×n) is defined to express such connected relationship of n topological units across the network. The meaning of each elements of A is shown as below: 1, at least one pathbetweenU i and U j Aij (1) 0, else Accessible matrix A can be transformed to a new CICED2016 Session x Paper No xxx Page /7 2016 China International Conference on Electricity Distribution (CICED 2016) matrix like (2) where o means all the element is 0 and the matrix Aα, Aγ means the square matrix of and to express connected units of or ,respectively. A A' o o (2) A Acquiring the number of the column in Aα and making a new vector rα of 1 . Each element in rα corresponds to a certain unit. Then the topological unit group can be descibed as, G = Ui | i r (3) An example like Fig3 is demonstrated as follow: Fig.3 the schematic diagram based on topological unit The accessible matrix about Ui and Uj with deliberately disordering the sequence is expressed as, 1 2 3 4 5 6 1 0 1 A 1 1 0 0 1 0 0 0 1 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 (4) 0 1 0 0 0 1 1 1 1 A' 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 1 (5) 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 So it can be concluded that there are 2 topological unit group of G and G which is correspond to r and r in (6). (6) The topological units in G and G is also shown in (7). G {U1 ,U 3 ,U 4 ,U 5 } G {U 2 ,U 6 } (7) Now, it can be concluded that topological unit is the minimum operable unit to adjust the structure of HVDN, and could be used to make appropriate allocation of load among 220kV substations in order to CICED2016 Session x 11 Bus (ij ) n1 1N nN (8) ij Means the possibility weather unit could supply by some sources. ij =1 means unit i could supply by source j, or else ij =0. And Bus.initial can be got with depth searching as a constant matrix as an initial status. The vector Lp is used to present the load of each unit in a group where P(Ui ) is the load of unit Ui. Lp {P(U1 ), P(U 2 ),..., P(U n )} (9) The group load allocation matrix D can be deduced D = L p Rus (10) j D( j ) D 100% (11) III. THE PSO BASED BI-LEVEL MODEL 1 1 A 1 1 r (1,3, 4,5) r (2, 6) C. The supply channel matrix Supply channel matrix is presented in this paper to express the connection relationship of topological unit and power sources (mainly the 220kV substations in HVDN) in case that there is no 220kV/110kV electromagnetic looped network and units without power supply. So the supply channel matrix of n N with n units and N power sources in a certain topological group can be illustrated as (8). Where j means the actual load proportion of power source j, D(j) means the load of supply channel j in the group. Where A , A is respectively shown as, 1 1 A 1 1 achieve the equilibrium of system. D is a vector of 1 N and each element of D means the load supplied by certain power channel in the group. Thus, the load proportion of a group can be calculated as, The transformer of matrix A to A' is shown in (5), 1 5 3 4 2 6 Xi’an, 10-13 Aug, 2016 Paper No xxx A novel bi-level programming model based on PSO is presented in this paper to mitigate transmission congestion and the disequilibrium of system. In the upper level, the balance factor and load shedding factor is used to generate the pre-allocation of the system load; in the lower level, the actual load allocation and the interruptible load is getting closer to those of the upper according to the iteration of the algorithm. jm is the balance factor; hm is the load shedding factor for the topological unit group of Gm ;the dotted circle indicate the total load of topological units before and after shedding respectively; jm is the load proportion of the group Gm (see (11)). The jm is used to guide jm getting closer to jm to balance the load ratio of 220kV substations. A. Programming Strategies in Upper Level The main purpose of upper level is to realize the load Page /7 2016 China International Conference on Electricity Distribution (CICED 2016) Xi’an, 10-13 Aug, 2016 balance of the system and avoid transmission line congestion. Where Pm is the load of Gm before shedding. A.1. the Balance Factor and The Balance Degree To ensure the reliability of power supply, the total Taking Fig.5 as an example, there are 5 power sources shedding load could not be too much. Thus, the in Fig.5, S1 , ... , S5 , 8 power supply channels: 11 , shedding degree H could be defined as the sum of all hm for the whole system: 12 , 21 , 32 , 33 , 42 , 43 , 53 ( jm indicates H hm the power supply channel between power source S j (15) and topological unit group Gm ) and 3 topological units The shedding degree H should be as small as group: , possible. If H is too large, there will be a serious , unbalance between load and power sources, so it is G1 U1 ,U2 ,U3 ,U4 ,U5 ,U6 G2 U8 ,U9 ,U10 ,U11 ,U12 ,U13 G3 U14 ,U15 ,U16 ,U17 ,U18 ,U19 . The balance factor jm can be defined as the expected load proportion from power source S j to the topological units group of Gm through power supply channel jm . And jm should be subjected to, (12) m 1 Where m means the sum of all the balance factors related to the topological units group of Gm . For example, for G1 in Fig.5, 11 21 1 . Then, the load rate of each 220kV substation could be calculated by, ( S j ) P ' j j / Pm ja x ' j factor related to S j ; P of power source S j . To evaluate the load balance results, the balance degree is defined based on the form of 2-norm as, 0 , here 1 ( S j ) is the N mean load rate for all power sources. A.2. The Load Shedding Factor and The Shedding Degree Sometimes (especially for emergency), m (16) 1 0 hm hm max Sij Sij .max Where Sij refers to the apparent power transforming from S i to S j ; j refers to the voltage at 220kV node j ; 1 and 2 are the weights of K and H . B. Programming Strategies in Lower Level By adjusting the structures of topological units inside and outside the substation, the strategies in lower level aim to make load proportion of each topological unit closer to the balance factor. B.1 the close factor and the close degree In order to describe the close degree between the actual distributional percentage of load and the balance factor, the close factor c m can be defined as, cm suitable solutions could not be obtained because some constraints cannot be satisfied at all. Thus, the load shedding factor j min j j max shedding; Pj max refers to the maximum active power 2 F Min(1 K 2 H ) s.t. 1 2 1 indicates the total active power supplied by S j after K ( S j ) 0 A.3. The Upper level Programming Model The goals in upper level are to balance the load of all the substations and to minimize the shedding degree, so the optimized objective function is defined as (16) and the constrains include transmission line capacity, source apparent powers, voltage bounds, shedding degree and shedding factor, the equation (12) and so on. (13) where ( S j ) indicates the load rate of power source S j ; j is the balance necessary to take more investment of equipment. hm is introduced and defined. Load ( m m ) 2 (17) Where cm is the close factor of the topological unit group of Gm , m is the balance factor that related to Gm and m is the actual distributional percentage shedding factor hm (hm hm max ) reflects the shedding for all the power supply channels m that connected load percentage of Gm . to Gm . Those factors can be calculated by (8) ~ (11) After shedding, the load Pm' of Gm is, respectively. Pm' Pm (1 hm ) CICED2016 Session x (14) Paper No xxx The close factor c m reflects the closeness of the actual load distribution in each power supply channel Page /7 2016 China International Conference on Electricity Distribution (CICED 2016) and the expected load distribution with balance factor from the upper level. It can be inferred that the bigger c m , the more different between the actual load distribution and the expected load distribution, and vise versa. Considering the topology constraints of each unit, it is difficult that the distributional percentage of load in each unit to match the balance factor very well. Here, in order to describe the adaptability of balancing plan to the actual structure, the close degree can be defined by summing up all of the close factor, cm (18) It is obvious that the smaller , the stronger the adaptability. Xi’an, 10-13 Aug, 2016 f min(3 4 O ) s .t . N Pi ui u j ( gij cos ij bij sin ij ) (22) j 1 N Qi ui u j ( gij sin ij bij cos ij ) j 1 ui min ui ui max S pq min S pq S pq max 3 4 1 where ui is the node voltage; S pq is the apparent power transforming from S p to S q ; The constraints consists of power flows constraints, apparent power constraints and voltage bound constraints; 3 and 4 indicate the weights of and O . B.2 The shedding vector In upper level, the shedding ratios have been obtained for all topological units. Here, considering difference for any unit in each topological unit, for example, some units have much more important load and less load can be curtailed, the shedding vector is defined as, (19) [ x1 ,..., xn ] C. PSO based solving strategy C.1 the encoding The balance factors and the load shedding factors are adopted to be the variables of PSO, that is Where xi is the shedding load percentage of indicates the number of topological unit groups. Gi , 0 x1 1 ; n is the total number of units in Gi . Then, the actual load of each unit after shedding can be calculated by, Pj' Pj Pi hi Pj x j (20) ni P x j 1 j where ni is the total number of units in Gi ; Pj x j ni P x j 1 j j where j 1, j 1, 2,..., N ' (23) xi indicates the position of particle i ; N ' C.2 The fitness function After determining the particle positions, the fitness function could be built by considering the upper-level’s target F and the lower-level’s target f . F and f j means the shedding load of unit j; xi ( 11 , 12 ,..., 21 , 22 ,..., h1,...hN ') means the can be calculated by formulas (16) and (22). Then, the fitness is defined as, Fobj Min( F f ) (24) The fitness function aims at reflecting the close degree of the upper-level and the lower-level. total shedding load in Gi ; Pi hi means the expected shedding load from shedding factor hi . Pj and Pj' are the active powers of unit i before and after shedding respectively. B.3 Number of switch operations The supply channel matrix Bus can be obtained by enumeration. After iteration, comparing with initial supply channel matrix Bus .initial , the number of switch operations O can be calculated by, O | B us (i, j ) - Bus.initial (i, j ) | 2 (21) B.4 The lower level Programming Model The lower-level programming model should be close to the upper-level’s results with the minimum number of switch operations. The lower-level programming model could be built as, C.3 the steps Firstly, the balance factors and the load shedding factors are solved obtained based on PSO and then the expected load assignments are calculated with (16). Secondly, the feasible supply channel matrixes Bvalid are obtained by enumeration. Then, the close degrees are calculated with (17) and the feasible supply channel matrix with minimum close degree is selected. The F and f are decreased gradually by iterations, and finally the load assignments among every topological unit tend to be a feasible balancing state. The position and velocity of the particles are updated with, vidk 1 vidk c1r1k ( pbestidk xidk ) (25) c2 r2k ( gbestidk xidk ) xidk 1 xidk vidk 1 The process can be divided into 7 steps as follow: CICED2016 Session x Paper No xxx Page /7 (26) 2016 China International Conference on Electricity Distribution (CICED 2016) Step1: Initialize the positions of m particles randomly (the balance factors and the load shedding factors). Step2: Calculate the load pre-distribution in 220kV power grid according to (16). Step3: Enumerate the supply channel matrix of each topological unit, then calculate the close degrees with (18) and choose the topology with the minimum close degree. Step4: Check the results whether it meet the flow constraints. Step5: Calculate the fitness with (24). Step6: Judge whether it meets the quit criteria: if “yes”, quit; if “no”, go to Step7. Step7: Update the particle speed and particle position with (25) and (26), then go to Step2. Fig.4 is the flow chart of proposed method. It is necessary to point out that the Step 3 among all topological units are independent, so the speed can be improved by using distributed parallel computation. Xi’an, 10-13 Aug, 2016 (b) The initial state for 110kVnetwork Fig.5 the structure of a local urban HVDN based on functional unit B. The results The load ratios of the 220kV substation and transmission lines are shown in Tabs. 2 and 3. It can be seen that the load ratio is reasonably unbalanced. Some substations (like S1 , S 2 , S6 ) are heavily over-loaded and some (like S3 , S5 ) are lightly over-loaded. And the over-loaded line S3-S5 extremely exceeds their limits. Using the method discussed above, the results under different load levels are shown without the number limits of switch operations in Fig.6. Tab.2 The initial load ratio of 220kV substations Substations Fig.4 the flow chart of BPSO S1 S2 S3 S4 S5 S6 Load ratio 94.9% 87.5% 30% 47.2% 16.9% 95.2% IV. Numerical test A. the description of test Taking a part of a high voltage distribution network as an example, the topological structure is shown in Fig.5 based on function units. There are more than 44 transfer paths and coupling switches in the system. Six topological unit groups can be formed and the total load of peak period is 830MW. Tab.3 The initial load ratio of 220kV lines Line BS-S1 Load ratio 85% BS-S2 BS-S3 BS-S4 78% 83% 79% S1-S2 64% Line S1-S5 Load ratio 43% S1-S6 87% S4-S6 32% S3-S5 129% S4-S5 23% S6 x61 x64 S5 x15 S1 x45 x35 x12 S2 S4 S3 x01 x04 x02 x03 (a) Below 90% load ratio and without the limit of switch operations BS (a) 220kV network CICED2016 Session x Paper No xxx Page /7 2016 China International Conference on Electricity Distribution (CICED 2016) (b) Below 80% load ratio and without the limit of switch operations Xi’an, 10-13 Aug, 2016 algorithms. 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Pezoa, “Greedy reconfiguration algorithms for medium-voltage distribution networks,” IEEE Transactions on Power Delivery, Jan, 2009, Vol.24(1) :328-337. [1] (c) Below 70% load ratio and without the limit of switch operations Fig.6 the results for different load level control Based on the results from Fig.6, when the load ratio control decreases from 90% to 70%, the balance degree decreases obviously, but the close degree increases somewhat. This reflects that although some of the balancing effects can be obtained, it is much difficult for the lower-level getting much closer to the upper-level in order to balance the whole system. Moreover, when the control is changed from 90% to 80%, the load need not to be curtailed, but the numbers of switch operations increases from 3 to 8. When the load control decreases to below 70%, there are no feasible solutions for no load shedding. It is necessary to curtail load (here 8% curtailed below 70% load ratio) to get a feasible balancing load distribution. From Fig. 6 (a),(b) and (c), it can be seen that the (c) has a better balancing result, but the cost is 8% load shedding. Fig.7 the balancing effects of 220kV lines under different load control The power flows for transmission 220kV lines are shown in Fig.7 where the line S3 S5 is heavily over-loaded in the initial structure, but it will not be over-loaded after the optimal reconfiguration based on the proposed method. Considering the number of switch operations is not too large in actual project, this number limit is added to the fitness function. V. CONCLUSION In this paper, the models of topological units and power supply channels have been introduced based on the topological structures of 220kV and 110kV high voltage distribution networks. On the basis of those models, some strategies for load balance are inferred. And then a 2-level programming optimization method is used to get the feasible and optimal solution. The method can reduce the dimension of the load transferring problem and improve the calculating speed. The strategies and method can apply to the online analysis of the load transferring problem for high voltage distribution networks. The test system proved the validity and the feasibility of the proposed CICED2016 Session x Paper No xxx First A. JI Yong He received B.S. degree in electrical engineering from Sichuan university in China in 2000. His research interests are Distribution system analysis and control, electrical marteking. Second B. LIU Junyong He received his Ph.D. from Brunel University, UK, in 1998. He is a professor in the School of Electrical Engineering and Information, Sichuan University, China. His main research areas of interest are power market, FACTS, power system planning, operation, stability, and computer applications. Third C.LI Hongwei He received M.S. degree in electrical engin eering from Southwest Jiaotong university in China in 2005. His research interests are Distribution system analysis and control, Dis tributed Generation modeling and Control. Page /7