Distribution system security region: definition, model and security assessment

Transcription

1 Published in IET Generation, Transmission & Distribution Received on 3rd November 2011 Revised on 5th June 2012 ISSN Distribution system security region: definition, model and security assessment J. Xiao 1 W. Gu 1 C. Wang 1 F. Li 2 1 Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin , People s Republic of China 2 University of Tennessee, Knoxville, TN, USA xiaojun@tju.edu.cn Abstract: The region-based method has been successfully applied in transmission systems. This study proposes the definition, model and applications of security region for distribution systems. With the ongoing smart grid initiatives, a large amount of real-time network information will be available. This is the motivation of an accurate calculation of the security boundary. First, this study presents the concepts of distribution system security region (DSSR); and discusses N 2 1 contingency scenarios for both substation transformers and feeders. Second, distribution system security boundary is modelled in the Euclidean space as several intersected hyperplanes. Furthermore, DSSR for substation transformer contingency is modelled as the space surrounded by the security boundaries and the set of all operating points that ensure the distribution system N 2 1 security. Third, distance from an operating point to a security boundary is formulated and a new index is also presented for security evaluation. The proposed DSSR-based security assessment method provides a new approach for future smart distribution system operation. Finally, the results from a real distribution system have demonstrated the effectiveness of the proposed concepts and methods; and the geometric characteristics of DSSR are also illustrated by means of two-dimensional visualisation of the test system. 1 Introduction Security is one of the most important concerns for distribution system operation and planning. This paper presents a new approach of security assessment, which is called distribution system security region (DSSR). The concept of security region originates from power transmission systems. Security of a transmission system is considered to be an instantaneous, time-varying condition that is a function of the robustness of the system relative to imminent disturbances [1]. The security region is the set of all the operating points that is subject to security conditions. Typically, the steady-state security region is defined as the set of injections space for which, on one hand the power flows can be balanced and there is no equipment overload or violations on nodal voltages, and on the other hand the system can maintain small-disturbance stability [2, 3]. In transmission systems, the research on security region has made substantial achievements [4 6]. Yu has developed the theory of security region and defined a practical region model for industrial applications [7, 8]. The region method is a general method, which has convincing advantages over the point-wise method [9]. The region can give systematic and global information about the feasible operation region. It can be calculated offline and applied on-line to determine whether an operating point is secure by judging whether the current injection lies inside a considered security region. Moreover we may know the relative location of a point in the security region, which is very useful for operators to decide how many generations or loads can be increased in each direction of injection space and which direction is suitable for security control. The region method has provided a new theoretic tool to implement the Dy Liacco s security framework [10, 11]. In contrast, the security region method has never been applied in distribution area. In distribution control centres, the loading levels of distribution feeders and substation transformers are visualised on the operators computers. Operators judge system security according to the N 2 1 guideline, which is widely applied in distribution operation and planning [12, 13]. That is, Loading rate greater than 0.5 (or 0.65 when considering transformer overloading factor 1.3) in a substation with two transformers are usually considered too high to meet the N 2 1 security guideline. However, the result of this paper has shown that this traditional secure loading level for substation transformers is conservative. Traditional researches are focused on case by case N 2 1 simulation test and service restoration when fault happens within feeders [14, 15]. In a typical restoration operation, the service to the upstream of a faulted feeder section will be restored after opening the first switchable component upstream to the faulted section, and the service to the downstream will be restored through back feed via closing a normally open switch. However, this load transfer is now confined to feeder N 2 1 test, whether the feeders are automated or not. When a fault happens to a substation transformer, load will be only transferred to other IET Gener. Transm. Distrib., 2012, Vol. 6, Iss. 10, pp

2 transformers in the same substation, while load could be also transferred to other substations through feeders with tie-lines or tie-switches. The reason that the load transfer through feeders is not performed is that most of current 10 or 20 kv feeders are not fully automated and the switch operations need much longer time. So, loading of substation transformers satisfying N 2 1 security standard is low; and in other words, the related assets are far from being fully utilised. Smart Grid will upgrade the distribution systems to fully information-based systems. A large amount of real-time information of network can be obtained through new sensors and communication; and remotely-controlled switching equipment will be widely used. All of these can make the future distribution system work more efficiently and smartly [16]. Thus, load can be transferred or dispatched among different substations swiftly and freely, which will result in a higher load factor within the security constraints. This draws the attention of an accurate calculation of the security boundary. The research in this paper is based on this motivation and challenge in order to improve system security and efficiency of assets under smart distribution grids. Total supply capability (TSC) is a newly proposed concept which is defined as the capability that a system can supply the load when the N 2 1 security for distribution systems is considered [17, 18]. TSC is a concept similar to TTC in transmission systems [19]. In[17], it is demonstrated that some TSC results can be used as security boundary for distribution systems. Available supply capability is also defined in [17], which is closely related to the security assessment. Based on the previous TSC research and the region methodology, this paper proposes the concept of DSSR, its mathematical formulation, and a case study to illustrate the new region-based distribution security assessment and control approach. 2 Definition for DSSR 2.1 Definition of DSSR The DSSR in this paper is based on the N 2 1 guideline for distribution systems. If a distribution system is N 2 1 secure, it means that any fault in the primary feeders or substation transformers will lead to a service interruption of the faulted section only and the service will be restored through back feed via closing a normally open switch. The DSSR is defined as the set of all operating points that make the distribution system N 2 1 secure, taking into account the capacities of substation transformers, network topology, network capacity and operational constraints. An operating point in a transmission system is the current power injections of nodes. The operating point for a distribution system is the set of substation transformers load and the set of feeder load. The reason to use the load of substation transformer and feeder to describe the operating point is the uniqueness of distribution systems. In a transmission system, information of almost every node can be observed on-line by the SCADA/EMS. Based on the observed information, the system operator can analyse the security of the transmission system. In contrast, the node amount is huge in a typical distribution system such that only loads of feeders and substation transformers are usually observed by the distribution system operator. N 2 1 security of feeder or transformer can be calculated based on the information. 2.2 DSSR contingency scenarios for transformers and feeders The proposed DSSR concept is based on contingency scenarios. Substation transformer and feeder contingency are two main types of scenarios considered in security analysis. DSSR for transformer contingency is noted as DSSR t, whereas DSSR for feeder contingency is noted as DSSR f. In general, the entire DSSR is composed of DSSR t and DSSR f. In this paper, only DSSR for transformer contingency is formulated. The reason that we chose DSSR t is to highlight the most typical factors in finding security boundary of distribution systems. This is explained in detail as follows. Although faults are more likely to occur on feeders than transformers, the fault of transformer is more critical and of higher impact. The key of security region is to find the limit of a given system, which is a matching problem including two aspects. One is the match of substations and their load, which means the system should have sufficient substation capacity and reasonable network structure to match the load. The other is the match of feeders and their load, which means the system should have sufficient feeder capacity and reasonable network structure to match the load. According to the planning and construction guideline, the capacity of a substation transformer is always smaller than the sum of capacity of all the feeders that connected with it. The total load that makes all feeders N 2 1 secure is too much to pass the transformer N 2 1 security check. The key point of DSSR is the security boundary, which is to find how much load the network can serve securely. Thus, in most cases, the N 2 1 security boundary is limited by the capacity of transformers rather than that of feeders. So transformer N 2 1 is the first choice for DSSR research. Furthermore, in the DSSR for transformer N 2 1 security, the feeder N 2 1 security is also taken into account implicitly for the feeders involved in load transfer. The information of load transfer path consists of both feeder topology and conductor capacity. When load is transferred through some feeders to transformers in other substations, these feeders should be assured N 2 1 security first in their feeder contingency test. In conclusion, DSSR for transformer contingency is more typical to illustrate the proposed DSSR concept. Thus, this formulation of DSSR is based on transformer fault scenario in this paper; and the formulation method can also be applied in the case of feeder fault. In the following sections, the note DSSR stands for DSSR t for simplicity. 3 DSSR model for substation transformer contingency The concepts of the link and load transfer are introduced briefly before the modelling of DSSR. In a distribution system, a transformer can be connected with a transformer in the same substation or a transformer in another substation through feeders with tie lines or tie switches. The interconnection between transformers is designated as a link [17]. The security of a distribution system is enhanced by these links. In a typical transformer N 2 1 case, that is, the fault occurs at transformer i, the load of transformer i can be transferred to other transformers (e.g. the load can be transferred to transformers within the substation through bus tie switches and transformers in other substations through switches between feeders). When there are several tie lines between two transformers, they are combined as 1030 IET Gener. Transm. Distrib., 2012, Vol. 6, Iss. 10, pp & The Institution of Engineering and Technology 2012

3 one link. After this transfer, all the transformers cannot be overloaded. The transfer is also constrained by the capacity of links. Therefore the load of all transformers should be under a series of constraints, and the model of DSSR can be expressed as W P i min(kr j P j, RL i,j ) j[v (i) 1 V DSSR = + min(r j P j, RL i, j )( i) j[v (i) 2 where W is the operating point corresponding to P 1, P 2,..., P n. The operating point for DSSR t is the set of load of studied substation transformers, expressed as W ¼ (P 1, P 2,..., P n ) T. W is a vector in the Euclidean space, where P i is the load of substation transformer i. R i ¼ rated capacity of transformer i; P i ¼ load of transformer i; k is the overload factor of transformers allowed for a short time, assuming all transformers have the same k value; RL i,j is the transfer capacity of the link between transformer i and transformer j; V (i) 1 is the set of transformers that have a link to transformer i within the local substation and; V (i) 2 = set of transformers that have a link to transformer i in other substations. To simplify the calculation the model of DSSR, the overload factor k is considered to be 1 in this paper, thus the model of DSSR can be simplified as B 1 P 1 min(r j P j, RL 1,j ) j[lu 1 j=1 B 2 P 2 min(r j P j, RL 2,j ) V DSSR = B i = j[lu i j= B n P n min(r j P j, RL n,j ) j[lu n j=n where LU i is short for the link unit [17] i, which is the set consisting of transformer i and all transformers that have links with transformer i. The B i in inequality (2) shows transformer i should pass N 2 1 test, which means that if fault occurs to transformer i, the load of transformer i can be transferred to other transformers with no overloaded transformer. Each inequality in (2) is a security boundary for operating points in distribution system, and the number i boundary is expressed as B i here. It can be seen from (2) that there are n boundaries if there are n transformers in the distribution system. In addition, the space surrounded by these boundaries is the distribution system DSSR. What is more, B i is a piecewise linear function, which means each piece of the inequality is a hyperplane in the Euclidean space. In fact, if there are s transformers linked with transformer i, the security boundary B i will consist of 2 S hyperplanes. It should be pointed out that the voltage drop is not taken into consideration in the model of DSSR. Since in urban areas feeders are usually short in length, the most critical problem is not voltage drop but overloading under contingencies. In rural areas where feeders are longer, the voltage may drop too much if the feeder supplies too much loads. Although power flow is accurate for calculating the voltage drop, it is overcomplicated to be included in the current DSSR model and likely unnecessary from the standpoint of security-based planning. A more simple but (1) (2) acceptable approach is to set limits of the transferred load for feeder links according to their length to guarantee voltage drop at a reasonable level. Regarding the losses, the network losses within the distribution feeders are considered since the load here is observed at the distribution substation. Also, the losses will change if the network topology changes, when we consider different configurations for restoration after a hypothetical contingency event. However, this will give a small change of system losses, which can be reasonably ignored. Further, a DG can be regarded as a negative load in the model, which is included in the load of the substation transformer by adding loads of all the nodes connected with the transformer. 3.1 Relationship between DSSR and TSC DSSR shows the secure region of operating points. In a distribution system, the efficiency is another concern apart from the security. In [17], TSC is defined as the capability that a system can supply the load when an expanded concept of the N 2 1 security for distribution systems is considered. It also shows that at the most efficient operating point of the distribution system when the load is equal or close to TSC, the facilities in the distribution system are usually fully utilised. In this paper, it is further introduced that TSC is a very special operating point on the boundary of DSSR. It is obvious that the TSC is included in DSSR and because the operating points that makes TSC should be N 2 1 secure because of the constraint model. The TSC operating point is on the boundary of DSSR because the system cannot take more load than TSC before it is insecure. As TSC is the most efficient operating point of the distribution system with the most balanced load [17], TSC operating point should be used as an objective in the planning process of the distribution system. 4 DSSR-based security assessment 4.1 Location calculation of operating points in DSSR DSSR shows the secure region of operating points in a distribution system. By means of DSSR, the assessment of security of distribution systems can be very efficient, which is based on the locations of operating points in DSSR. The location of an operating point in DSSR is expressed as the distance from the operating point to all the security boundaries. The distance from the operating point W to the security B i (i ¼ 1, 2,..., n) can be calculated and expressed as L i = min(r j P j, RL i, j ) P i (3) j[lui j=i where L i shows the distance from the operating point W to the security B i. When L i is positive, the operating point satisfies the security constraint i, or the operating point is inside the security boundary i. The greater the positive distance, the securer the operating point is, the value of L i shows the surplus capacity of transformer i, which means the load of transformer i can be increased by L i MVA. Otherwise, if L i is negative, the operating point doses not satisfy the security constraint i, or the operating point is outside the IET Gener. Transm. Distrib., 2012, Vol. 6, Iss. 10, pp

4 security boundary i. Also, the greater the negative distance is, the more insecure the operating point is. The value of L i shows the lacked capacity of transformer i, which means that the load of the distribution system will lose L i MVA at least if fault occurs to transformer i. To summary, L i shows the distance from the operating point to one security boundary expressed by distance in power (MVA). The distance is also a security margin for the current state of the distribution system, which provides important information in security assessment. Based on L i, a comprehensive security assessment index named DSSR distance, noted as D is defined, which can describe the security situation of the distribution system with one value, D is formulated as D = n i=1 n i=1 L i /n ( L i 0) min(l i,0)/n ( i, s.t.l i, 0) when D is positive, the operating point is secure, the greater D, the securer operating point, Otherwise, when D is negative, the operating point is insecure, the greater D, the securer operating point. D not only shows whether the distribution system is secure or not, but also indicates the value of the security of operating point. It can describe the security of a distribution system briefly, which can be used as a decision-making index in security assessment for distribution systems. 4.2 DSSR-based approach against N 2 1 test The national electric code in China has enforced the N 2 1 security criterion for all new and upgraded urban distribution systems. Therefore in the traditional planning process, utility engineers should suppose all the transformers in the distribution system is possible to be faulted, and would test the distribution system security if a fault occurs at each transformer one by one. If the system is large enough and consists of a large number of transformers, the amount of calculation may increase significantly. The DSSR makes the N 2 1 security analysis of the distribution system much more efficient. If the topology and configuration of the system is fixed, the DSSR of the (4) system is fixed as well, regardless whether the tie switch is closed or open and how the operating point changes. Once the DSSR of the system is calculated, security assessment can be accomplished very fast by calculating the distances between operating point location and the DSSR boundaries. Further, the DSSR calculation is CPU time-saving, because it can calculate the load transfer after each of the transformer is faulted at the same time. Apart from the calculation speed, the DSSR not only shows the operating point is secure or not, but also indicates the location of the operating point in DSSR. 5 Case study 5.1 Overview of the test system In this section, the evaluation method of the DSSR concept is tested on a real distribution system with eight transformers in four substations (Fig. 1). The data of the test system are shown in Tables 1 and 2. Both the overload factor (k ¼ 1) and the conductor name is based on the national electrical code in China. 5.2 DSSR of the test system and its geometric characteristics Based on (2), DSSR of the test system can be P 1 min(40 P 2, 40) + min(63 P 5,7.8) +min(63 P 7,6.0) P 2 min(40 P 1, 40) + min(63 P 6,8.7) P 3 min(40 P 4, 40) + min(63 P 5,11.3) P 4 min(40 P 3, 40) + min(63 P 8,11.3) P 5 min(40 P 1,7.8) + min(40 P 3,11.3) +min(63 P 6, 63) P 6 min(40 P 2,8.7) + min(63 P 5, 63) P 7 min(40 P 1,6.0) + min(63 P 8, 63) P 8 min(40 P 4,11.3) + min(63 P 7, 63) It can be seen that the DSSR of the test system is surrounded by eight security boundaries, which are named from B 1 to B 8, respectively. Each B i is a piecewise linear function, which means each security boundary consists of several pieces of hyperplanes. For example, as transformer T2 is linked with two transformers (T1 and T6), B 2 consists of 2 2 ¼ 4 pieces (5) Fig. 1 Test distribution system with eight transformers 1032 IET Gener. Transm. Distrib., 2012, Vol. 6, Iss. 10, pp & The Institution of Engineering and Technology 2012

5 Table 1 Substation data of the network Substation Transformer Voltage, kv/kv Capacity, MVA S1 T1 35/ T2 35/ S2 T3 35/ T4 35/ S3 T5 110/ T6 110/ S4 T7 110/ T8 110/ Table 2 Conductors and capacities of the tie lines in the study case Link Conductor Capacity, MVA 1 5 JKLV JKLYJ JKLYJ JKLYJ JKLYJ of hyperplanes, the four hyperplanes can be expressed as P P 1 P 6 (P 1 0, P ) P P 6 (P 1 0, P ) (6) P P 1 (P 1 0, P ) P (P 1 0, P ) To visualise the location of operating points in this DSSR, the dimension of the DSSR is reduced to 2. Take operating point W 1 ¼ (32, 16, 16, 24, 50.4, 25.2, 18.9, 44.1) as an example, we choose transformers T2 and T6 to observe in this paper, Thus, substitute (P 1 ¼ 32, P 3 ¼ 16, P 4 ¼ 24, P 5 ¼ 50.4, P 7 ¼ 18.9, P 8 ¼ 44.1) into formula (5), then the following 2D DSSR is obtained, in which only load of T2 and T6 are adjustable. { P 2 min(63 P 6,8.7) 8 0 P 6 min(40 P 2,8.7) (7) (8) The 2D DSSR and the corresponding security boundaries are shown in Fig. 2. In Fig. 2, the 2D DSSR at W 1 is the rectangle AOEI, which is formed by boundaries (7) and (8). Boundaries (7) and (8) Fig. 2 Security boundary and shape of the 2D DSSR at W 1 can be divided into two parts, respectively: (7) for AB and BC, (8) for EF and FG. AB and EF are constrained by value of RL 2,6, the capacity of the link between transformer T2 and T6, BC and GF are limited by N 2 1 security constraint for T2 and T6, which means no transformer should be overloaded after the load transfer in N 2 1 case. CD and HG indicate that the load cannot exceed the rated capacity of transformer. What is more, the shape of the DSSR is also influenced by load of other transformers, which cannot be observed in the 2D DSSR. Thus, if the capacity of links and load of the other transformers that is not observed in the 2D DSSR change, the shape of the 2D DSSR will change as well: as the capacity of links increases the shape of the 2D DSSR can be pentagon with three right angles and then triangle. The pentagon-dssr and the triangle-dssr are shown in Fig Security assessment of operating points The location of a given operating point in DSSR can be obtained through formula (3), and the security index DSSR distance D can be obtained through (4) Secure operating point: When all transformers are half loaded, the operating point of the system is W 2 ¼ (20, 20, 20, 20, 31.5, 31.5, 31.5, 31.5) T, Table 3 shows the distance from W 2 to all the boundaries. It can be seen form Table 3 that the operating point W 2 is secure and the distances from it to the security boundaries are large enough. The D of operating point W 2 is MVA, which is also large enough Insecure operating point and security control: If the operating point of the distribution system is given by W 3 ¼ (32, 32, 32, 32, 50.4, 50.4, 50.4, 50.4) T, which means loading rate of all transformers are all 0.8. The location of W 3 is shown in Table 4. It can be seen from Table 4 that the operating point W 3 is outside all the security boundaries. For example, as L 7 is MVA, the system should lose 31.8 MVA load when fault occurs at transformer T7. The D of W 3 in the system is MVA, which is too low, so the system is overloaded too much. If the operating point is W 1 ¼ (32, 16, 16, 24, 50.4, 25.2, 18.9, 44.1) T, the location of W 1 is shown in Table 5. It can be seen from Table 5 that the operating point W 1 is outside the boundary B 6, which means LU 6 is overloaded and distribution system will lose 3.9 MVA at least if fault occurs to transformer T6. The D of W 1 in this system is , which is close to 0, so the system is overload, but not much. The location of W 1 is shown in Fig. 3. The location of operating point W 1 can be easily observed in Fig. 4. It can be seen that W 1 is outside one security boundary. The load of transformer T6 should be decreased by 3.9 MVA at least to make the system N 2 1 secure. For example, the operating point W 1 can be adjusted to operating point W 1 (P 2 ¼ 16, P 6 ¼ 18) through the short dashed arrows shown in Fig. 4. Further, the most efficient operating point for P 2 and P 6 at W 1 can also be obtained, which is (P 2 ¼ 16.7, P 6 ¼ 21.3). This efficient point has shown the optimal control scheme for the current operating point. In this scenario, only load of T2 and T6 can be adjusted. Hence, after load of T6 is cut to from 25.2 to 21.3 MVA, the load of T2 can be increased from 16 to 16.7 MVA at most, when the system is still within the DSSR security boundary. IET Gener. Transm. Distrib., 2012, Vol. 6, Iss. 10, pp

6 Fig. 3 Pentagon-2D-DSSR and triangle-2d-dssr Table 3 Distance from W 2 to all the boundaries Table 6 Distance from W TSC to DSSR boundaries L i, MVA L i, MVA Table 4 Distance from W 3 to all the boundaries The corresponding operating point is L i,mva Table 5 Distance from W 1 to all the boundaries L i, MVA W TSC = (24.36, 24.36, 25.64, 25.64, , , , ) The location of W TSC is shown in Table 6. It can be seen from Table 6 that distance to B 2, B 3, B 4, B 6, B 7 are all 0, which means TSC point is on these boundaries. However, distance to B 1, B 5, B 8 are not 0. D of W TSC is 2.6 MVA, which indicates that operating point W TSC is just secure. In theory, TSC point is the best operating point of the system, which is useful in both operational optimisation and planning. If the load of all the transformers can be controlled, the system should be optimised close to this operating point. 6 Conclusions Fig. 4 Location of operating point W 1 in the 2D DSSR Additionally, there are many 2D DSSR figures to visualise DSSR at one operating point; and W 2 and W 3 cannot be shown in the same 2D DSSR figure at W TSC point: Use the method in [17] to calculate the TSC of the system, which is MVA MVA. Also, the corresponding load rates of all transformers are T TSC = (0.609, 0.609, 0.641, 0.641, 0.569, 0.569, 0.548, 0.548) This paper proposes new concepts of security region for distribution systems. The region-based method is a new approach in security analysis of power systems and has been successfully applied in transmission system. This paper applies the region-based method for future smart distribution system. First, the operating point for a distribution system is defined as the set of load of studied substation transformers, which is a vector in the Euclidean space. Second, the security boundary of the distribution system is modelled as several intersected hyperplanes in the Euclidean space. The DSSR model for substation transformer contingency is then proposed as the space that is surrounded by these security boundaries, which is also the set of all operating points that each ensures the distribution system N 2 1 secure. Based on the DSSR concept and model, a new region-based method for security assessment is presented. Finally, results from a real distribution system have demonstrated the effectiveness of the proposed DSSR. The geometric characteristics of DSSR are also discussed by means of a 2D visualisation at an operating point. It has shown that the DSSR boundary is a piecewise linear function and the 2D shapes of DSSR include rectangle, pentagon and triangle. Moreover, 1034 IET Gener. Transm. Distrib., 2012, Vol. 6, Iss. 10, pp & The Institution of Engineering and Technology 2012

7 DSSR-based security assessment and control for the test system is also illustrated. The proposed DSSR can be used in both operation and planning of distribution systems; and the DSSR-based security assessment method is a new approach for future smart distribution system operation. It is also needed to point out that the DSSR model in this paper is only the first step for the DSSR theory. The present DSSR model can replace the transformer N 2 1 test in the distribution system, but not feeder N 2 1 test. The formulation approach in this paper is also applicable for feeder N 2 1. In addition, more works are needed to fully consider the positions of loads, the effect of integration of DGs and voltage constraints. Further, the control method in the case study is for illustrative purposes; and additional works are needed in the further research such as an optimisation method to select transformers to adjust their load. 7 Acknowledgments This work was supported by the National Basic Research Program of China (973 Program, no. 2010CB234608) and National Natural Science Foundation of China (no ). 8 References 1 Wu, F.F., Tsai, Y.K., Yu, Y.X.: Probabilistic steady-state and dynamic security assessment, IEEE Trans. Power Syst., 1988, 3, (1), pp Yu, Y.: Security region of bulk power system. Proc. Power Conf on Power System Technology, 2002, vol. 1, pp Liu, C.-C., Wu, F.F.: Steady-state voltage stability regions of power systems. Proc. 23rd Conf. on Decision and Control, 1984, vol. 23, (1), pp Liu, C.-C.: A new method for the construction of maximal steady-state security regions of power systems, IEEE Trans. Power Syst., 1986, 1, (4), pp Zhu, J.Z.: Optimal power system steady-state security regions with fuzzy constraints, IEEE Trans. CAS, 2002, 2, pp Wu, F.F., Kumagai, : Steady-state security regions of power systems, IEEE Trans. Circuits Syst., 1982, 11, pp Yu, L., Jizhong, Z.: Study on N and N 1 steady-state security regions. Proc. CSEE, 1993, vol. 2, pp (in Chinese) 8 Fei, W., Yixin, Y.: Power system thermal security region based on wide area measurement system. Proc. CSEE, 2011, vol. 10, pp (in Chinese) 9 Yixin, Y.: Methodology of security region and practical results, J. Tianjin Univ., 2003, 9, pp (in Chinese) 10 Dy Liacco, T.E.: The adaptive reliability control system, IEEE Trans. Power Appar. Syst., 1967, PAS-86, pp Dy Liacco, T.E.: Real-time computer control of power systems, Proc. IEEE, 1974, 62, pp State Grid Co. of China: Guidelines of urban power network planning, in China, 2006 (in Chinese) 13 Lakervi, E., Holmes, E.J.: Electricity distribution network design stevenage (Peregrinus, UK, 1995) 14 Miu, K.N., Chiang, H.-D.: Service restoration for unbalanced radial distribution systems with varying loads: solution algorithm, IEEE Power Summer Meet., 1999, 1, pp Toune, S., Fudo, H., Genji, T., Fukuyama, Y., Nakanishi, Y.: Comparative study of modern heuristic algorithms to service restoration in distribution systems, IEEE Trans. Power Deliv., 2002, 17, pp Lu, J., Xie, D.: Research on smart grid in China. Transmission and Distribution Conf. and Exposition: Asia and Pacific, Xiao, J., Li, F., Gu, W., et al.: Total supply capability (TSC) and associated indices for distribution planning: definition, model, calculation and applications, IET Gener., Transm. Distrib., 2011, 5, (8), pp Fengzhang, L., Chengshan, W., Jun, X., et al.: Rapid evaluation method for power supply capability of urban distribution system based on N 2 1 contingency analysis of main-transformers, Int. J. Electr. Power Energy Syst., 2010, 32, (10), pp Transmission Transfer Capability Task Force: Available transfer capability definitions and determination. North American Electricity Reliability Council, Princeton, NJ, June 1996 IET Gener. Transm. Distrib., 2012, Vol. 6, Iss. 10, pp