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Transmission Contingency Screening Considering Impacts of Distribution Grids Zhengshuo Li, Student Member, IEEE, Jianhui Wang, Senior Member, IEEE, Hongbin Sun, Senior Member, IEEE, and Qinglai Guo, Senior Member, IEEE Abstract—As traditional transmission contingency screening (TCS) methods neglect impacts of distribution grids, the contingency selection result may not be always satisfactory, especially when distribution networks are more frequently looped in a smart grid. Two new contingency screening methods considering impacts of distribution grids are proposed in this letter. The first one is based on global power flow, and the second only utilizes distribution network equivalencing. Numerical tests show both new methods can give more reliable results than TCS. Index Terms—Contingency analysis, contingency selection, contingency screening, network equivalencing, global power flow.
I. INTRODUCTION
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N order to shorten the computational time of transmission contingency analysis (TCA), contingency screening (CS) is usually used [1], in which only a subset of the credible contingencies is selected to be further checked by full transmission power flow (TPF) to see whether severe operational limit violations will happen. In traditional transmission CS (TCS), distribution is regarded as a constant injecting load into the transmission, so the impacts of distribution power flow (DPF) on transmission after a transmission contingency are neglected. However, with the distribution network more frequently looped and the potential for distributed generation in smart grids, the interaction of transmission and distribution will be much more active [2], neglecting the distribution impacts in the TCS process may lead to unreliable selections, even missing severe contingencies. Therefore, we propose two new CS methods in this letter, both of which consider the impacts of distribution grids to improve the reliability of the contingency selections and screening. II. METHODOLOGY The first CS method (named as CS1) utilizes one iteration of the master-slave-splitting (MSS) solution of global power flow (GPF) [2] to obtain an approximation of the TPF, and then evaluates the security violations. GPF is capable of calculating accurate power flow of both transmission and distribution. CS1 can be carried out as follows. Step 1: Distribution control center (DCC) computes the network equivalent admittance and sends it to the TCC. Manuscript received August 02, 2014; revised October 14, 2014; accepted January 19, 2015. This work was supported in part by the National Key Basic Research Program of China (973 Program) (2013CB228203) and in part by Innovative Research Groups of NSFC (51321005). The work of J. Wang was supported by the U.S. Department of Energy Office of Electricity Delivery and Energy Reliability. Paper no. PESL-00121-2014. Z. Li, H. Sun, and Q. Guo are with the Department of Electrical Engineering, Tsinghua University, Beijing 100084, China (e-mail:
[email protected]). J. Wang is with Argonne National Laboratory, Argonne, IL 60439 USA (e-mail:
[email protected]). Digital Object Identifier 10.1109/TPWRS.2015.2412692
Step 2: Transmission control center (TCC) adds the equivalent admittance into the TPF model and calculates the net nodal loads by excluding the influence of the equivalent from the current boundary bus power [2]. Step 3: For each contingency, TCC computes TPF within a predetermined maximum iteration number and sends the DCC the voltages of the boundary buses that connect with the distribution feeders. Step 4: DCC calculates DPF within a predetermined maximum iteration number and sends the TCC the new values of the boundary bus power. Step 5: TCC computes the new net nodal loads as step 2 and computes the TPF. A security performance index (PI) regarding line overloading and voltage magnitude violations [1] is evaluated. Step 6: Contingencies with larger PIs are selected into a list and checked by full GPF calculations afterwards. The major steps of CS1 are similar to MSS in [2], except that only one iteration1 of the MSS is performed to accelerate calculation. Clearly, composite characteristics of distribution load can be reflected in CS1. Moreover, CS1 can be further accelerated by decreasing the maximum iteration numbers of both TPF and DPF. Our numerical tests show the obtained approximate solution is usually good enough for the CS results. In the second proposed method (named as CS2), only the network equivalent of distribution is considered and added into the transmission 1P1Q method [1]. It is straightforward in the sense that an equivalent of a distribution grid should be able to partly reflect the interactions between the TPF and DPF. Though a network equivalent is not always accurate, especially when loads are notably voltage-sensitive, introducing a network equivalent of distribution in CS2 may still lead to more accurate TPF results than traditional TCS, which will be shown in the numerical tests. CS2 can be carried out as follows. Step 1: DCC computes the network equivalent admittance and sends it to the TCC. Step 2: TCC adds the equivalent admittance into the TPF model and calculates new nodal loads by excluding the influence of the additional equivalent from the current nodal loads. Different from CS1, the new nodal loads are deemed constant in Step 3. Step 3: As for a contingency, TCC performs the 1P1Q method based on the model in step 2. A PI is calculated. Step 4: Contingencies with larger PIs are selected into a list and checked by full GPF calculations afterwards. Since the interactions of the transmission and distribution are reflected in more detail in CS1 and CS2, the proposed methods can be more accurate than traditional TCS, especially when a distribution grid is electrically looped. 1In principle, accuracy of CS1 can be improved by performing more iterations. However, after testing on different scales of systems in [2], one iteration of the MSS is found most effective with acceptable accuracy.
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TABLE I SCREENING RESULTS COMPARISON BETWEEN CS1, CS2, AND TCS
III. CASE STUDIES Two test systems, 30Dr and 30Dl, are used to show the effects of the proposed methods. In both systems, one IEEE 30-bus transmission system is connected with three copies of a 6-feeder distribution grid. The transmission buses connecting distribution feeders are No. 14, 3, 24, 7, 30, 20, 5, 6, 15, 8, 9, 10, 25, 26, 16, 17, 18, and 19. In 30Dr, the distribution grids are all radial; in 30Dl, each distribution grid has two loops which connect Feeders #1 and #4, Feeders #2 and #3. Further details of the distribution can be referred to [2]. For each system, the static characteristics of loads are modeled as [3] if they are considered. A PI is chosen as follows [1, Expression (11.9)]:
where and are both chosen as 5. representing the bus voltage magnitude violation tolerance is set to be 0.075 p.u. [4]. A contingency with a PI larger than 1.0 is selected. The contingency analysis (CA) results given by an exhaustive search using GPF are used as a benchmark. The results of traditional TCS, CS1, and CS2 whose maximum iteration numbers of TPF and DPF are both set to 10 are compared in Table I. Firstly, the results of traditional TCS where the interactions of transmission and distribution are neglected are most unreliable, with the most missed alarms and false alarms. Over 50% of the alarms are missed in 30Dl with looped distribution grids. On the contrary, since the interactions of transmission and distribution are reflected, the results of CS1 and CS2 are both more reliable, for the numbers of the missed alarms are both smaller. With CS1, no alarm is missed for all the cases; while with CS2, only one alarm is missed if notable static load characteristics are present. Meanwhile, the false alarm numbers of both CS1 and CS2 are reduced as well. That indicates the screening accuracy generally follows that , because the interaction of transmission and distribution is considered more and more in detail. The CS computational time and the total CA time including the CS and GPF-based checking are compared in Table II. As shown in Table II, the CS time with CS2 is comparable to that with TCS, and so is the total time except for the case in 30Dl with notable static load characteristics. In that case (marked in bold and underlined), as fewer false alarms are given by CS2, the total time is reduced to about 65% of that with TCS. As for CS1, despite the most reliable selection result, the total time
TABLE II COMPUTATIONAL TIME COMPARISONS BETWEEN CS1, CS2, AND TCS
with CS1 is the longest, as the computation time in the CS1 stage is about 5 times of that of CS2 or TCS. In order to see the time-saving effect of the new CS methods, we additionally tested the total CA time with the two new methods for 118D systems in [2]. Compared to the exhaustive search, the total time is reduced to 15% with CS2 and 40% with CS1, and no missed alarm is produced. In fact, the time-saving effect of our new methods would be more notable when the communication time consumed in GPF calculations is considered. Taking 30D systems as an example, using CS1 and CS2 prior to full GPF-based checking can reduce the total iteration number in GPF by 80% to 90%, so the communication between TCCs and DCCs would also be reduced by about the same ratio. Therefore, using CS1 and CS2 is capable of effectively reducing the practical running time of GPF-based CA. Moreover, the number of the maximum iterations of TPF and DPF in CS1 can be flexibly set to balance the speed and reliability. For example, for 30D systems, if the maximum iteration numbers of TPF and DPF are both set to be 1, the total CA time can be reduced by about 100 ms, but 1 missed alarm is produced; if the maximum iteration numbers of TPF and DPF are both set to be 2, the total CA time can be reduced by about 80 ms but no missed alarm is produced. IV. CONCLUSION In this letter, two new CS methods, CS1 and CS2, are proposed for transmission contingency analysis with more looped distribution systems. Both methods are able to select most severe contingencies, i.e., more reliable than the traditional one. Numerical tests show that CS2 has a shorter overall computational time, while CS1 has a higher accuracy, especially when the loads are notably voltage-sensitive. Both methods may effectively reduce the computational time of the GPF-based exhaustive search, especially for larger systems. REFERENCES [1] A. J. Wood and B. F. Wollenberg, “Power System Security,” in Power Generation, Operation and Control, 2nd ed. New York, NY, USA: Wiley, 1996, pp. 410–450. [2] H. Sun, Q. Guo, B. Zhang, Y. Guo, Z. Li, and J. Wang, “Master-slavesplitting based distributed global power flow method for integrated transmission and distribution analysis,” IEEE Trans. Smart Grid, to be published. [3] H. Sun and B. Zhang, “Distributed power flow calculation for whole networks including transmission and distribution,” in Proc. IEEE Power Energy Soc. Transm. Distrib. Conf. Expo., Chicago, IL, USA, Apr. 21–24, 2008. [4] G. C. Ejebe and B. F. Wollenberg, “Automatic contingency selection,” IEEE Trans. Power App. Syst, vol. PAS-98, no. 1, pp. 97–109, Jan. 1979.
