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Automatic Learning of Fine Operating Rules for Online Power System Security Control Hongbin Sun, Senior Member, IEEE, Feng Zhao, Student Member, IEEE, Hao Wang, Kang Wang, Weiyong Jiang, Qinglai Guo, Senior Member, IEEE, Boming Zhang, Fellow, IEEE, and Louis Wehenkel
Abstract— Fine operating rules for security control and an automatic system for their online discovery were developed to adapt to the development of smart grids. The automatic system uses the real-time system state to determine critical flowgates, and then a continuation power flow-based security analysis is used to compute the initial transfer capability of critical flowgates. Next, the system applies the Monte Carlo simulations to expected shortterm operating condition changes, feature selection, and a linear least squares fitting of the fine operating rules. The proposed system was validated both on an academic test system and on a provincial power system in China. The results indicated that the derived rules provide accuracy and good interpretability and are suitable for real-time power system security control. The use of high-performance computing systems enables these fine operating rules to be refreshed online every 15 min. Index Terms— Automatic learning, critical flowgate, knowledge discovery, online security analysis, smart grid, total transfer capability.
I. I NTRODUCTION
W
ITH the simultaneous increase in power demand and in intermittent power generation, power systems are operating with security margins that are more and more brittle. Indeed, as for the rapid development of smart grids, greater uncertainty, time–space complexity, and variability in the operating conditions of power systems have made it more difficult to grasp and anticipate their security features. It is thus becoming increasingly difficult to determine both safe and accurate operating rules using offline analyses. Indeed, rules determined offline are often too conservative under normal operating conditions and, at the same time, not relevant under extreme operating conditions not anticipated in the offline context. This situation greatly increases the challenges Manuscript received October 25, 2013; revised September 6, 2014 and January 5, 2015; accepted January 5, 2015. Date of publication February 9, 2015; date of current version July 15, 2016. This work was supported in part by the Foundation for Innovative Research Groups through the National Natural Science Foundation of China under Grant 51321005, in part by the National Science Fund for Distinguished Young Scholars under Grant 51025725, and in part by the National Key Basic Research Program (973 Program) of China under Grant 2013CB228203. H. Sun, F. Zhao, H. Wang, K. Wang, W. Jiang, Q. Guo, and B. Zhang are with the State Key Laboratory of Power Systems, Department of Electrical Engineering, Tsinghua University, Beijing 100084, China (e-mail:
[email protected];
[email protected];
[email protected];
[email protected];
[email protected];
[email protected];
[email protected]). L. Wehenkel is with the Department of Electrical Engineering and Computer Science, University of Liège, Liège 4000, Belgium (e-mail:
[email protected]). Digital Object Identifier 10.1109/TNNLS.2015.2390621
associated with real-time operation of power systems and leads to greater security risks [1]. Automatic learning is an effective method to account for physical phenomena that cannot be modeled analytically or that require computationally intensive or repetitive computations [2]. Automatic learning method has been widely applied to power system security analysis and control. There are many reports about the automatic learning method applied to security analysis of power systems [3]–[15], [18], especially to the dynamic security analysis [4], [10]–[15], [18]; at the same time, automatic learning has also been applied to power system control scheme and decision making [16], [17]. A large number of simulation data is the basis of the automatic learning method [3], [4], [8]; however, as for the development of PMUs and smart grids, the real-time Phasor Measurement Unit (PMU) measurements are also used in automatic learning method for power system security analysis [11], [12]. Compared with other methods, automatic learning has the potential to yield better computational efficiency and interpretability [3]. To obtain effective automatic learning results, a large sample database is necessary, and so the Monte Carlo simulation is typically employed [3], [4], [8]. Knowledge discovery methods, which lie at the heart of automatic learning, such as decision trees (DTs) [3], [5], [7], [8], [11], [12], [16], artificial neural networks (ANNs) [4], [6], and k nearest neighbor methods (k-NNs) [7] are commonly used. ANNs exhibit high accuracy but are difficult to interpret and validate by human experts, and ANN training is orders of magnitudes slower than DT training. The k-NN method is quite sensitive to the type of distance used and is not scalable to high dimensions [7]. Because of their accuracy and excellent computational efficiency and interpretability, DTs have been used in practice [8], [11]–[13], [16], [19]–[22]. Some real-life applications of automatic learning for security control exist. For example, the Hydro-Québec system uses automatic learning to improve the calculation of the stability limits of transmission corridors [3], [23]–[25], and automatic learning is used for dynamic security assessment in the French EHV system [3], [8], [19], [26]. These real-world applications confirm the feasibility of applying automatic learning to actual power system problems and suggest a pathway toward the use of automatic learning for power system security analysis. In general industrial practice, operating rules are designed offline to appraise system security domains
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Fig. 2. Fig. 1.
Offline determination of security limits.
and enable real-time operation. In particular, total transfer capabilities (TTCs) of critical flowgates are widely used, and several studies have been reported on the automatic refreshing of TTCs online [27]–[32]. However, these online-computed TTCs are typically based on critical flowgates determined offline and are not always relevant under online conditions, especially when large-scale intermittent power sources inject production into the power grid. The automatic operator, described in [2], can feature modern energy control centers with high-level information, intelligence, integration, and automation, as proposed in [33]. Based on [2] and [33], the concept of fine operating rules was proposed in [34] and further investigated in [35]–[37]. Fine operating rules model the influence of relevant power system features and are determined based on the online operating condition. Fine operating rules are thus flexible and potentially more suitable for real-time power system operation than conventional offline-constructed rules. In this paper, we developed and validated a complete framework for automatic online learning of fine operating rules. The paper is organized as follows. Section II describes the concept of fine operating rules, and the framework for their automatic learning is outlined in Section III. Section IV presents the key technologies of the proposed system, and two case studies are examined in Section V. Section VI draws the conclusion and suggests further research directions. II. C ONCEPT OF F INE O PERATING RULES A. Offline Determination of Security Limits In current power system practice, operating rules are determined offline, and they are typically formulated as TTCs over critical flowgates. This offline discovery process, shown in Fig. 1, begins with the choice of critical flowgates, typical operating conditions, contingencies, and increasing direction of generation/load by power system experts. Then security limits are computed based on repeated security analyses. Finally, the operating rules are checked in the energy management system (EMS) based on the supervisory control and data acquisition (SCADA) data. Once determined, these limits typically will be used as operating rules for long time periods (e.g., several months or a year).
Online determination of the fine operating rules.
The main shortcomings of the offline approach are summarized as follows. 1) Offline Determination of Operating Rules: Offline operating rules are determined using a large number of tedious calculations, based on typical flowgates and operating conditions selected offline by power system experts. Significant time and work are required for the analysis, and the quality of the rules strongly depends on the experience of power system experts. 2) Form and Content of Offline Operating Rules: Many power system security features are difficult to account for in offline operating rules. As a result, offline rules often correspond to only one feature per rule, such as a TTC of one offline-selected critical flowgate. Other important factors are implicitly accounted for by choosing worst case scenarios and imposing large safety margins on computed limits. 3) Online Application: Because the workload associated with offline discovery of operating rules is huge, once discovered, the offline operating rules are used for long time periods, such as several months or a year. Offline operating rules are thus often too conservative under normal operating conditions and, at the same time, insufficiently secure under extreme operating conditions. B. Online Determination of Fine Operating Rules To circumvent the above shortcomings, we developed the online concept of fine operating rules. A fine operating rule is a linear model that relates a TTC over a given flowgate to variations in operating conditions around the current operating state. The rules are determined automatically online, as sketched in Fig. 2. First, critical flowgates, power system contingency sets, and the increasing direction of generation and load are automatically determined based on online operating conditions. Then, the fine operating rules, one for each critical flowgate, are constructed using automatic learning from online security analyses. The EMS dispatcher then uses the fine operating rules based on the SCADA data. Compared with offline operating rules, fine operating rules have the following advantages. 1) Online Determination of Fine Operating Rules: Fine operating rules are based on online operating conditions and on critical flowgates adapted to
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Fig. 3. Architecture of the system for the online discovery of fine operating rules.
those conditions. In addition, fine operating rules can be periodically tuned by high-performance computing systems; they may be refreshed at every cycle of the online security analysis process, e.g., every 15–30 min. 2) Form and Content of Fine Operating Rules: Because they are discovered automatically through online automatic learning, fine operating rules may consider more power system security features, namely, not only the TTCs of critical flowgates but also their sensitivity with respect to other relevant variables that characterize the system state. 3) Online Application of Fine Operating Rules: Fine operating rules may be applied until the completion of the next security analysis cycle according to system condition changes and anticipated states, thereby allowing the operator to rapidly adjust TTCs according to the variations in operating conditions and to determine security control decisions if needed. III. A RCHITECTURE OF THE AUTOMATIC O NLINE D ISCOVERY S YSTEM OF F INE O PERATING RULES The architecture of the proposed online automatic learning system for the fine operating rules is shown in Fig. 3. First, the online operating conditions are obtained from the EMS, and a critical flowgate base is formed using the critical flowgates automatic learning method. The critical flowgate base comprises the critical flowgates of the power system, generation and load zones of each critical flowgate, the increasing direction of generation and load of each critical flowgate, and a contingency set for each critical flowgate. Next, numerous nearby operating states are analyzed by the Monte Carlo simulation to yield a sample database. Each sample contains a randomly chosen operating condition in a certain deviation range of the online operating condition and the TTC calculated as operating rules for each flowgate in the randomly chosen operating condition. Then, based on the sample database, a pivotal security feature base is formed for each critical flowgate. The pivotal
security feature base is a subset of variables that characterize the power system state and significantly influence the TTC of the considered critical flowgate. It is obtained using a heuristic regress feature selection (HRFS) method proposed in this paper. After this step, the fine operating rules are learned for each critical flowgate and its corresponding subset of pivotal security features using the linear least squares fitting method. The fine operating rule of a critical flowgate comprises both the base case TTC of this flowgate and its sensitivities with respect to its pivotal security features. Finally, the rule base is exploited by the dispatcher or by an EMS computer to facilitate real-time control of the power system. Key modules of the system, including online critical flowgate automatic learning, simulation of numerous samples, feature selection, and knowledge discovery, are calculated on high-performance computers. IV. K EY T ECHNOLOGIES A. Automatic Learning of Critical Flowgates The critical flowgates of the online operating conditions were discovered automatically. They were obtained in three filtering steps: 1) initial flowgate determination; 2) selection of transfer flowgates from the initial flowgates; and 3) identification of critical flowgates among the transfer flowgates. 1) Electrically close buses were grouped into zones, and only the tie lines between these zones were then considered when defining the initial flowgates in terms of minimal cut sets. To define the zones, the electrical distance between buses i and j were defined by [38] Di j = |Z ii + Z j j − 2Z i j |
(1)
where Di j is the electrical distance between the buses i and j ; Z is the reactance matrix of the power grid; and Z ii , Z j j , and Z i j are the elements of the impedance matrix. The electrical zones were formed through a heuristic clustering method, starting from the initial geographical zones of the power system and then iteratively changing the zone number of each boundary substation of each zone until all zone numbers of all the substations in the boundaries were reasonable. The zone number of a boundary substation m was considered reasonable only when the following [37] was satisfied: ⎧ ⎫ ⎨1 ⎬ 1 Dim < min D j m , l ∈ S (2) ⎩ nl ⎭ nk − 1 i∈k,i =m
j ∈l
where k is the zone number of substation m, S is the set of all zones that are connected with substation m, l is a zone connected with substation m, n k is the number of substations in zone k, and nl is the number of substations in zone l. 2) The line outage distribution factors (LODFs) [38] of each pair of lines in each initial flowgate were then
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calculated, and an initial flowgate S was considered as a transfer flowgate only if the following was satisfied: min{Dl1 −l2 , (l1 , l2 ∈ S)} > Dmin
(3)
where Dl1−l2 is the LODF of lines l1 and l2 , which are two transmission lines in the initial flowgate S, and Dmin is the threshold value of the LODF; the bigger Dmin is set, the more significantly transmission lines in a transfer flowgate influence each other. In this paper, Dmin is set to 0.1, which means that when one transmission line in a transfer flowgate breaks out, every other transmission line in the transfer flowgate will receive at least 10% of the power flow on the transmission line. 3) The security margin of each transfer flowgate was calculated, and a transfer flowgate S was considered as a critical flowgate only if the following was satisfied: Ms = 1 − Ps /PsTTC < Mmin
(4)
where Ms is the security margin of the transfer flowgate S, Ps is the active power on transfer flowgate S, PsTTC is the TTC of the transfer flowgate S (see the next section), and Mmin is a threshold value of the security margin. If Mmin is set smaller, the active power on a critical flowgate will be nearer to TTC of the critical flowgate. In this paper, Mmin is set to 30%, which means that security margin of a critical flowgate calculated according to (4) should be η, then f is added to S and deleted from F. 3) Backward Replacement: j denotes the size of the set S obtained at step II and S si denotes the set when the feature si is deleted from S. Specify i = j and then repeat the following steps until i = 0: select the feature f from F to minimize RC (S\si ∪ f ), and if RC (S\si ∪ f ) < RC (S), then f is added to S and deleted from F, while si is added to F and deleted from S. Then, specify i = i − 1. 2) Supervised Learning Method: As the fine operating rules proposed in this paper are used in a small range of power system operating conditions, we use the linear model to show the relationship between the pivotal features and TTC of the critical flowgate. The relationship between the pivotal features and TTC of the critical flowgate in an academic test power system and a real-world power system are shown in Figs. 5 and 6. In Figs. 5 and 6, z-axis represents the TTC of the critical flowgate, and x-axis and y-axis represent the first two pivotal features, which are the terminal voltage of a generator and active power of a load in the academic test power system and two active generations in the real-world power system. Each blue spot in the two figures represents an operating condition of the power system. As the first two pivotal features in Fig. 5 are the terminal voltage of a generator and active power of a load, respectively,
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the unit of pivotal feature 1 is represented in kilovolts and the unit of pivotal feature 2 is represented in megawatts. In addition, as the first two pivotal features in Fig. 6 are both active powers of a generator, the units of pivotal feature 1 and 2 are both represented in megawatts. Based on Figs. 5 and 6, we can find that there is a linear relationship between the first two pivotal features and TTC of the critical flowgate in both the academic test power system and the real-world power system. Therefore, we can express the relationship between target output PTTC and the selected set of pivotal features S using a linear model, just like the sensitivity widely used in a power system [38]. The relationship between the target output PTTC and the selected set of pivotal features S was approximated using linear regression as follows: PTTC = b1 x 1 + b2 x 2 + L + bm x m
Academic four-generator two-zone test system. TABLE I
L INE L ENGTHS IN THE F OUR -G ENERATOR T WO -Z ONE T EST S YSTEM
TABLE II BASE C ASE A CTIVE G ENERATION AND T ERMINAL V OLTAGE OF THE G ENERATORS IN THE F OUR -G ENERATOR T WO -Z ONE T EST S YSTEM
(9)
where x 1, x 2 , . . . , x m are the selected pivotal features. The regression coefficients b1 , b2 , . . . , bm are determined by least squares fitting over the learning sample. The TTC of a critical flowgate was thus estimated according to the following: PTTC = PTTC0 + PTTC
Fig. 7.
TABLE III A CTIVE AND R EACTIVE L OADS IN THE F OUR -G ENERATOR T WO -Z ONE T EST S YSTEM
(10)
where PTTC is calculated according to (9), and PTTC0 is the initial operating rule on the critical flowgate, namely, the TTC of the critical flowgate in the base-case online operating condition. Therefore, in this paper, we obtain a sample of the measurements taken from an online power system operational condition, and then based on the sample obtained online, we generate a large number of samples through the Monte Carlo simulation method, and at last the fine operational rules are updated based on the sample obtained online and the samples generated through the Monte Carlo simulation method. Therefore, we can say that the fine operational rules are updated online based on each sample of the measurements taken from the grid and the whole process can finish in 15 min, meeting the requirement of the power system online application. V. C ASE S TUDIES The proposed system was applied to academic test systems and to a real-world provincial system in China to evaluate the computational efficiency, accuracy, and physical meaning of the results. The tests were done on a computer with an Intel core i7 CPU (3.07 GHz), 6 G of memory, and a 1-T hard disk, and the multithreading technique was employed to improve the sample simulation calculation efficiency. The per-unit system with a base power S B of 100 MVA was employed in the following two case studies. The results were obtained using the power system analysis software package developed by the China Electric Power Research Institute, which is widely used in Chinese power systems. A. Academic Four-Generator Two-Zone Test System The academic test system [39] is shown in Fig. 7; it was divided into two geographical zones, as shown by the dotted line in the figure.
TABLE IV AVERAGE D ISTANCES B ETWEEN E ACH B OUNDARY N ODE AND E ACH Z ONE IN THE F OUR -G ENERATOR T WO -Z ONE T EST S YSTEM
Each area has two units with a nominal voltage of 20 kV. Each step-up transformer has an impedance of 0 + j 0.15 per unit on a 900-MVA, 20/230-kV base, with an off-nominal ratio of 1.0. The transmission system nominal voltage is 230 kV. The line lengths are listed in Table I. The parameters of the lines in per unit on a 100-MVA, 230-kV base are r = 0.0001 p.u./km, x L = 0.001 p.u./km, bC = 0.00175 p.u./km. The assumed base-case online operating condition of the test system is shown in Tables II and III. The electrical distances between each pair of nodes of the test system were calculated according to (1). The average distances between each boundary node, i.e., nodes 3 and 8 in the test system, and each geographical zone of the test system were also calculated. The results are shown in Table IV. As indicated in Table IV, the zone numbers of node 3 and 8, which were the boundary nodes, were both reasonable. Thus, the electrical zones of the test system used in our simulations were the same as in the geographical zones, and the initial flowgate S was composed of lines 1 and 2 connecting these two zones. The LODFs between lines 1 and 2 were calculated as follows: D1−2 = D2−1 = 1 > Dmin . Thus, S was chosen as a transfer flowgate. The active power on S was PS = 4.41 p.u.
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and the TTC of S was PSTTC = 5.18 p.u. Thus, according to (4), the security margin of S was M S = 14.9% < Mmin and S was a critical flowgate. The Monte Carlo samples were obtained using the method described in Section IV-C. Active and reactive loads were chosen as the adjustable uncontrollable variables D, and the active generation and terminal voltages of each generator were chosen as the adjustable control variables u. The adjustable variables were sampled independently with uniform distributions in the 90%–110% interval for the active generations and active/reactive loads and in the 98.5%–101.5% interval for the generator terminal voltages. The topology was maintained constant, and the active power balance was ensured by distributing the load/generation mismatch proportionally over all generators based on the capacity of each generator. Among the 1 000 samples generated, 200 were retained as a test set to test the average error, maximum error, and minimum error of the fine operating rules. The average error of the fine operating rule was computed according to (11) and the maximum and minimum errors of fine operating rule were computed according to (12) n | PˆiTTC − PiTTC | PiTTC i=1 | PˆiTTC − PiTTC | , i = 1, 2, . . . , n error = max PiTTC | PˆiTTC − PiTTC | error = min , i = 1, 2, . . . , n PiTTC
error =
(11)
(12)
where i is the number of samples in the test set; PiTTC is the TTC of the critical flowgate in sample i , which was calculated by the continuation power flow-based online security analysis method described in Section IV-B; and PˆiTTC is the estimated TTC of the critical flowgate in sample i , which was calculated by the fine operating rule. The relationship between the number of samples in the learning set and the average error as well as the maximum error of the fine operating rule is shown in Fig. 8. As shown in Fig. 8, when the number of samples in the learning set is more than 500, the average error and maximum error of the fine operating rule both come down to a stable value. Therefore, in this paper case, 800 samples were retained as a learning set to obtain the fine operating rule. The input features were selected as follows: PG1 ∼PG4 , which were deviations between the active generation of each generator and that of the online operating condition; U1 ∼U10 , which were deviations between the voltage of each node and that of the online operating condition; and P 1 ∼P 2 , which were deviations between the total active generation of each electrical zone and that of the online operating condition. The deviation between the TTC of the critical flowgate and that of the base-case online operating condition was selected as the output target of the rule. U2 , P 2 , and U6 were the pivotal features selected from the input features by the HRFS method, η = 0.1%, proposed in Section IV-D. The linear least squares fitting method proposed in the same was employed to determine the
Fig. 8. Relationship between the number of samples in the learning set and the average error and maximum error of the fine operating rule in the academic system.
regression formula for the TTC PTTC = PTTC0 + 10.38U2 + 0.126P 2 − 6.74U6 (13) where PTTC0 = 5.18 p.u. is the TTC of the critical flowgate in the base-case online operating condition. Equation (13) thus represents the fine operating rule of the four-generator twozone test system determined by the proposed method. The explanation of (13) is as follows: as the generation and load increased, the dynamic security risk was first exposed, which restricted the TTC of the critical flowgate. Thus, improving the dynamic stability of the test system was helpful for increasing the TTC. Increasing the voltage of node 2 improved the dynamic stability of generators in zone one, which is the exporting zone. Increasing the total active generation of zone two decreased the total active generation of zone one, which consequently improved the dynamic stability of generators in zone one. Because induction motors in the dynamic simulation represented 70% of the loads, decreasing the voltage of node 6 reduced the voltage level of zone two, leading to a decrease in the total load in zone two (which is the load zone) in the transient process, which also improved the dynamic stability of the test system. The residuals of (13) are calculated using the test set and they satisfy the Gaussian distribution based on the Lilliefors test. The average value is −0.0686 MW (−0.000686 p.u.) and the standard deviation is 2.6027 MW, while the 95% confidence interval of the average value is [−0.1409 MW, 0.0037 MW] and the 95% confidence interval of the standard deviation is [2.5570 MW, 2.6593 MW]. Compared with PTTC that is about 5.18 p.u. in (13), the bias can be negligible in engineering. The histogram in Fig. 9 seems to indicate that the residuals are normally distributed. The maximum and minimum errors of (13) were 2.46% and 0.0027%, respectively, while the average error of (13) was 0.29%. In (13), PTTC0 is the result of the online refreshing TTC method [27]–[32]. The average error of the initial operating rule PTTC0 evaluated according to the following was 1.59%: errorinit =
n |PTTC0 − PiTTC | . PiTTC i=1
(14)
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TABLE V C OMPUTING T IMES ON THE F OUR -G ENERATOR T WO -Z ONE T EST S YSTEM
Fig. 9. Residual probability density distribution figures of the fine operating rule in the academic system.
Fig. 10. Relationship between the feature selection accuracy standard η and the average test set error of the fine operating rule of the academic system. Fig. 11.
Hence, compared with the online refreshing TTC method, we thus observed that the use of the learned rule (13) decreased the error by 82% (from 1.59% to 0.29%), and the learned rule (13) can give out the information to improve the TTC. The relationship between the feature selection accuracy standard η and the average error of the obtained fine operating rule is shown in Fig. 10. As η decreased from 5% to 0.001%, additional features were selected, and the average error of the fine operating rule was reduced from 1.59% (the average error of the initial operating rule when no feature was yet selected) to approximately 0.10%. As the feature selection accuracy standard η changes continuously, the number of pivotal features will change discretely, and only when the number of pivotal features changes, the fine operating rule changes and the error of fine operating rule changes. Therefore, in Fig. 10, each plateau means the same number of pivotal features and the same error of the fine operating rule in the corresponding range of η. The curve shown in the inset of Fig. 10, which corresponds to the very small values of η, indicates slight overfitting at very low values of η, which is a well-known phenomenon in automatic learning. At η = 0.1% [at the fine operating rule defined by (13), the results represent a compromise between accuracy and interpretability. The CPU times for the different computational steps are given in Table V; the fine operating rule was determined in less than 7 min.
Geographical area of the Henan province power system in China.
B. Provincial Power System in China The maximum load operating condition of the Henan province power system in China on October 26, 2010 was selected for the second study case. The system is interconnected with the Hubei province power system with four 500-kV synchronous interconnections and with a dc interconnection to the Shaanxi power system. The peak load is approximately 40 GW. In Fig. 11, the twelve geographical areas of the system are shown. The derived model includes the generation and transmission system up to 500-kV buses. The total number of substations is 354, and there are 635 transmission lines, 188 generators, 355 substations, and 615 transformers. The electrical zones of the provincial power system formed using the method proposed in Section IV-A are shown in Fig. 12. In the figure, each single line between two electrical zones indicates several transmission lines. The dotted lines in Fig. 12 are the four transfer flowgates discovered using the proposed method. The compositions and security margins of the four transfer flowgates are shown in Table VI. Only the security margin of transfer flowgate 1 (in bold in Table VI) was smaller than Mmin ; thus, transfer flowgate 1 was the sole critical flowgate of this system. As shown in more detail in Fig. 13, this critical flowgate is composed of six lines.
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Electrical zones of a provincial power system in China.
TABLE VI C OMPOSITIONS AND S ECURITY M ARGINS OF T RANSFER F LOWGATES IN A
P ROVINCIAL P OWER S YSTEM IN C HINA
Fig. 14. Relationship between the number of samples in the learning set and the average error and maximum error of the fine operating rule in the provincial power system in China.
As shown in Fig. 14, when the number of samples in the learning set is more than 800, the average error and maximum error of fine operating rule both come down to a stable value. Therefore, in this paper case, 1600 samples were retained as a learning set to obtain the fine operating rule. The candidate input features were chosen as follows: PGi represented the active generation deviations of each power station and Ui indicated the voltage magnitude deviations at each node. The deviation between the TTC of the critical flowgate and that of the base-case online operating condition was again selected as the target output. In the present case, PG3 , PG2 , PG4 , PG5 , and PG6 were the pivotal features identified using the HRFS method with η = 0.1%. The least squares fitted rule was as follows: PTTC = PTTC0 + 0.827P3 + 0.650P2 + 0.534P4 + 0.519P5 + 0.562P6
Fig. 13.
Critical flowgate of the provincial power system in China.
The Monte Carlo samples were obtained using the method described in Section IV-C, with active and reactive loads as the uncontrollable variables D and active generation and terminal voltage of each generator as the control variables u. The values were sampled independently, with uniform distributions in the 80%–120% interval for the active generations and active/reactive loads and in the 95%–105% interval for the generator terminal voltages. The system topology was maintained constant, and the active power balance mismatch was distributed uniformly over all the generators. Among the 2000 samples generated, 1600 were used as a learning set, and 400 were retained as a test set for accuracy assessment. Among the 2000 samples generated, 400 were retained as a test set for accuracy assessment. The average error and maximum error of the fine operating rule were computed according to (11) and (12). The relationship between the number of samples in the learning set and the average error as well as the maximum error of fine operating rule is shown in Fig. 14.
(15)
where PTTC0 = 14.13 p.u. and is the TTC of the critical flowgate in the base-case online operating condition. The explanation of (15) is as follows: As the generation and load increases, static security risk of the provincial power system was exposed, which restricted the TTC of the critical flowgate. In the online operating condition, active power on the flowgate was not evenly distributed among its six lines, thereby causing the line on which there was a heavy active power flow to reach its transfer limit faster when the generation and load increased in the worst direction. Adjusting the active generation of each power station to distribute the active power flow more evenly over the six lines was beneficial for increasing the TTC of the critical flowgate. Line 1, which is in the north, carries a heavy active power flow, whereas lines 2–6, which are in the south, are less heavily loaded. Thus, increasing the active generation at power stations 5 and 6 in the north of zone five (the load zone) and power stations 2, 3 and 4 in the south of zone six (the generation zone) can enable more even distribution of the active power flow over the six lines. The residuals of (15) are calculated using the test set. Similarly, the Lilliefors test is used to test the residuals and they satisfy the Gaussian distribution. Likewise, the average value, the standard deviation and the confidence interval should
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TABLE VII C OMPUTING T IMES ON THE P ROVINCIAL P OWER S YSTEM OF C HINA
Fig. 15. Residual probability density distribution figures of the fine operating rule in the Henan province power system in China.
Fig. 16. Relationship between the feature selection accuracy standard η and the average error of the fine operating rule in the provincial power system in China.
be calculated. The average value is 0.5918 MW (0.005918 p.u.) and the standard deviation is 22.1782 MW, while the 95% confidence interval of the average value is [−0.4961 MW, 1.6797 MW] and the 95% confidence interval of the standard deviation is [21.4353 MW, 22.9748 MW]. Compared with P TTC0 , which is about 14.13 p.u. in (15), the bias can be negligible in engineering again. The histogram in Fig. 15 seems to indicate the residuals are normally distributed. The maximum and minimum errors of (15), as computed by (12), were 5.11% and 0.0041%, respectively, while the average error of (15), as computed by (11), was 1.32%. Similarly, in (15), PTTC0 is the result of the online refreshing TTC method [27]–[32]. The average error of the initial operating rule PTTC0 , evaluated according to (14), was 3.59%. Therefore, compared with the online refreshing TTC method, we thus observed that that use of the learned rule (15) decreased the error by 63% (from 3.59% to 1.32%), and also that the learned rule (15) can give out the information to improve the TTC. The influence of the feature selection parameter η on the average error of the fine operating rule of the critical flowgate is shown in Fig. 16. As the feature selection accuracy η varied from 10% to 0.0003%, the average error decreased from 3.59% (the average error of the initial operating rule when no feature was yet selected) to approximately 0.66%. Again, a slight over-fitting was observed at very small values of η. As the
feature selection accuracy standard η changes continuously, the number of pivotal features will change discretely, and only when the number of pivotal features changes, the fine operating rule changes and the error of fine operating rule changes. Therefore, in Fig. 16, each plateau means the same number of pivotal features and the same error of the fine operating rule in the corresponding range of η. For this larger system, using the threshold η = 0.1% may be suboptimal with respect to accuracy because smaller values of η would allow significant reductions in the average error. However, a tradeoff must be struck between average error and interpretability; further reduction in the threshold value would also require using more pivotal features, which would consequently reduce the interpretability. The CPU times are shown in Table VII; approximately 11 min were needed to refresh the fine operating rules. If more than one critical flowgate in the online operating condition exist, a parallel computing technique using several high-performance computers can be employed to simulate a large number of samples and ensure that the fine operating rules can be refreshed in 15 min or less, thereby meeting the requirement for the online use. This case study indicates that application of the fine operating rule to the provincial power system in China leads to both accuracy and a very good interpretability. This fine operating rule can provide not only the TTC of the critical flowgate but also the pivotal security features and methods to increase the TTC. VI. C ONCLUSION The fine operating rule concept was introduced in this paper to adapt to the development of smart grids, and a comprehensive framework for its online automatic learning was proposed and validated in two case studies. The first case study was an academic system of small size that thus lent itself to easily reproducible results; the second case study was a realworld provincial power station subsystem in China. The results demonstrated the feasibility of refreshing the fine operating rules every 15 min in a real-world system, and they suggest that these rules are both interpretable and sufficiently accurate for the practical real-time security control in power system. The principal functions and technologies of the various modules in the proposed system are: 1) the automatic learning of critical flowgates; 2) the online calculation of the TTCs of critical flowgates; 3) the simulation of numerous samples via the Monte Carlo sampling; and 4) a knowledge discovery toolbox combining the feature selection and supervised learning. The entire procedure may be applied to large-scale systems using high-performance computing systems and trivial parallelization pathways. While the proposed framework has been demonstrated to be suitable for real-life implementation in its current version,
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future improvements may be achieved by taking advantage of any further progress in power system modeling and simulation, large-scale optimization techniques, and supervised learning. As for the increase of the penetration of the stochastic renewable generation in the smart grid, the time-varying property of the critical flowgate and the fine operational rule will be more and more significant. Therefore, to ensure the security operating of smart grid, the evolution of the critical flowgates and fine operational rules should be researched based on the research framework of this paper, which is a further research content and direction of this paper. At the same time, in the smart grid environment, we will consider the synchronized PMU measurements with high accuracy and speed as the input features based on the research framework of this paper, which is another further research content and direction of this paper. R EFERENCES [1] P. Panciatici, G. Bareux, and L. Wehenkel, “Operating in the fog: Security management under uncertainty,” IEEE Power Energy Mag., vol. 10, no. 5, pp. 40–49, Sep./Oct. 2012. [2] T. E. Dy-Liacco, “Enhancing power system security control,” IEEE Comput. Appl. Power, vol. 10, no. 3, pp. 38–41, Jul. 1997. [3] L. Wehenkel, “Machine learning approaches to power-system security assessment,” IEEE Expert, vol. 12, no. 5, pp. 60–72, Sep./Oct. 1997. [4] E. M. Voumvoulakis and N. D. Hatziargyriou, “A particle swarm optimization method for power system dynamic security control,” IEEE Trans. Power Syst., vol. 25, no. 2, pp. 1032–1041, May 2010. [5] X. Boyen and L. Wehenkel, “Automatic induction of fuzzy decision trees and its application to power system security assessment,” Fuzzy Sets Syst., vol. 102, no. 1, pp. 3–19, 1999. [6] M. T. Schilling, J. C. S. Souza, A. P. Alves da Silva, and M. B. Do Coutto Filho, “Power systems reliability evaluation using neural networks,” Int. J. Eng. Intell. Syst. Elect. Eng. Commun., vol. 9, no. 4, pp. 219–226, 2001. [7] I. Houben, L. Wehenkel, and M. Pavella, “Coupling of K-NN with decision trees for power system transient stability assessment,” in Proc. 4th IEEE Conf. Control Appl., Albany, NY, USA, Sep. 1995, pp. 825–832. [8] L. Wehenkel, “Emergency control and its strategies,” in Proc. 13th Power Syst. Comput. Conf., Trondheim, Norway, Jun. 1999, pp. 35–48. [9] Y. Jiang and Z.-P. Jiang, “Robust adaptive dynamic programming with an application to power systems,” IEEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 7, pp. 1150–1156, May 2013. [10] A. B. R. Kumar, V. Brandwajn, A. Ipakchi, and R. Adapa, “Integrated framework for dynamic security analysis,” IEEE Trans. Power Syst., vol. 13, no. 3, pp. 816–821, Aug. 1998. [11] M. He, J. Zhang, and V. Vittal, “Robust online dynamic security assessment using adaptive ensemble decision-tree learning,” IEEE Trans. Power Syst., vol. 28, no. 4, pp. 4089–4098, Nov. 2013. [12] K. Sun, S. Likhate, V. Vittal, V. S. Kolluri, and S. Mandal, “An online dynamic security assessment scheme using phasor measurements and decision trees,” IEEE Trans. Power Syst., vol. 22, no. 4, pp. 1935–1943, Nov. 2007. [13] C. Zheng, V. Malbasa, and M. Kezunovic, “Regression tree for stability margin prediction using synchrophasor measurements,” IEEE Trans. Power Syst., vol. 28, no. 2, pp. 1978–1987, May 2013. [14] I. Kamwa, S. R. Samantaray, and G. Joos, “Development of rule-based classifiers for rapid stability assessment of wide-area post-disturbance records,” IEEE Trans. Power Syst., vol. 24, no. 1, pp. 258–270, Feb. 2009. [15] Y. Xu, Z. Y. Dong, J. H. Zhao, P. Zhang, and K. P. Wong, “A reliable intelligent system for real-time dynamic security assessment of power systems,” IEEE Trans. Power Syst., vol. 27, no. 3, pp. 1253–1263, Aug. 2012. [16] C. Liu et al., “A systematic approach for dynamic security assessment and the corresponding preventive control scheme based on decision trees,” IEEE Trans. Power Syst., vol. 29, no. 2, pp. 717–730, Mar. 2014.
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Hongbin Sun (M’00–SM’12) received the double B.S. degrees and the Ph.D. degree from Tsinghua University, Beijing, China, in 1992 and 1997, respectively. He is currently the Changjiang Chair Professor with Tsinghua University, an Assistant Director of the State Key Laboratory of Power Systems in China, a fellow of the Institution of Engineering and Technology, and a Senior Member of the Chinese Society of Electrical Engineering. His current research interests include power system operation and control, and information theory applied to power systems.
Weiyong Jiang received the Ph.D. degree from the Department of Electrical and Electronics Engineering, Tsinghua University, Beijing, China, in 2008. He joined Beijing Wanglian HVDC Technology Company, Ltd., Beijing, in 2008, where he has been involved in research and development on highvoltage, direct current systems.
Qinglai Guo (M’09–SM’14) was born in Jilin, China, in 1979. He received the B.S. degree from the Department of Electrical Engineering, Tsinghua University, Beijing, China, in 2000, and the Ph.D. degree from Tsinghua University, in 2005. He is currently an Associate Professor with Tsinghua University. His current research interests include the energy management system advanced applications, in particular, the automatic voltage control and vehicle-to-grid.
Feng Zhao (S’13) received the bachelor’s degree in electrical engineering from Tsinghua University, Beijing, China, in 2009, and the Ph.D. degree from the Department of Electrical and Electronics Engineering, Tsinghua University, in 2014. He is currently an Engineer with the State Grid Corporation of China, Beijing. His current research interests include extraction of fine operating rules in power systems and power system smart scheduling.
Boming Zhang (M’94–SM’95–F’10) received the Ph.D. degree in electrical engineering from Tsinghua University, Beijing, China, in 1985. He was appointed as a Lecturer, an Associate Professor, and a Full Professor with the Department of Electrical Engineering, Tsinghua University, in 1985, 1990, and 1993, respectively. His current research interests include power system analysis and control, in particular, on advanced applications of electric power control centers.
Hao Wang received the B.Sc. degree in thermal engineering from Tsinghua University, Beijing, China, in 2004, and the master’s degree from the Department of Electrical and Electronics Engineering, Tsinghua University, in 2006. He is currently an Engineer with Google, Beijing. His current research interests include data mining, pattern recognition, information theory, and their applications in power systems.
Louis Wehenkel received the Electrical Engineering and Ph.D. degrees from the University of Liège, Liège, Belgium, in 1986 and 1990, respectively. He is currently a Full Professor of Electrical Engineering and Computer Science with the University of Liège. His current research interests include stochastic methods for systems and modeling, optimization, machine learning and data mining, with applications in complex systems, in particular, large-scale power systems planning, operation and control, industrial process control, bioinformatics,
Kang Wang received the B.Sc. degree in electrical engineering from Tsinghua University, Beijing, China, in 2007, and the master’s degree from the Department of Electrical and Electronics Engineering, Tsinghua University, in 2010. He is currently an Engineer with the State Grid Corporation of China, Beijing. His current research interests include data mining, decision trees, and their applications in power systems. and computer vision.
