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Maiden application of SSA‐optimised CC‐TID controller for load frequency control of power systems

2018; Institution of Engineering and Technology; Volume: 13; Issue: 7 Linguagem: Inglês

10.1049/iet-gtd.2018.6100

1751-8695

Dipayan Guha, Provas Kumar Roy, Subrata Banerjee,

Power System Optimization and Stability

IET Generation, Transmission & DistributionVolume 13, Issue 7 p. 1110-1120 Research ArticleFree Access Maiden application of SSA-optimised CC-TID controller for load frequency control of power systems Dipayan Guha, Corresponding Author Dipayan Guha dipayan@mnnit.ac.in orcid.org/0000-0002-2603-6955 Electrical Engineering Department, Motilal Nehru National Institute of Technology, Allahabad, IndiaSearch for more papers by this authorProvas Kumar Roy, Provas Kumar Roy Electrical Engineering Department, Kalyani Government Engineering College, Kalyani, West Bengal, IndiaSearch for more papers by this authorSubrata Banerjee, Subrata Banerjee Electrical Engineering Department, National Institute of Technology, Durgapur, West Bengal, IndiaSearch for more papers by this author Dipayan Guha, Corresponding Author Dipayan Guha dipayan@mnnit.ac.in orcid.org/0000-0002-2603-6955 Electrical Engineering Department, Motilal Nehru National Institute of Technology, Allahabad, IndiaSearch for more papers by this authorProvas Kumar Roy, Provas Kumar Roy Electrical Engineering Department, Kalyani Government Engineering College, Kalyani, West Bengal, IndiaSearch for more papers by this authorSubrata Banerjee, Subrata Banerjee Electrical Engineering Department, National Institute of Technology, Durgapur, West Bengal, IndiaSearch for more papers by this author First published: 27 March 2019 https://doi.org/10.1049/iet-gtd.2018.6100Citations: 32AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This study describes a maiden application of salp swarm algorithm (SSA) optimised cascade tilt–integral–derivative controller (CC-TID) for frequency and tie-line power control of interconnected power systems (IPSs). The proposed controller includes both the merit of the cascade control algorithm and fractional-order calculus. In the proposed CC-TID controller, TID controller is used as a slave controller and a proportional–integral (PI) controller served the role of master controller. To elucidate the effectiveness, the designed controller has employed to, initially, two-area IPS followed by four-area IPS. SSA is used to pursue the optimum settings of the CC-TID controller via the minimisation of area control error. Performances of CC-TID controller is obtained and compared with I-, PI-, PI–derivative-, cascade PI–PD, and TID controllers. Simulation results, apparently, show that SSA: CC-TID controller exhibits superior performance compared with other controllers described above. Moreover, the performance of SSA is evaluated and compared with differential evolution and flower pollination algorithm in terms of convergence profile, power density, and statistical results. Finally, time-varying step load perturbation and random load perturbation are applied to confirm the robust behaviour of SSA: CC-TID controller. 1 Introduction The control of area frequency and maintaining zero steady-state error of tie-line power against continuous load fluctuation are extensively crucial for the stable and safe operation of the modern interconnected power system (IPS). During the significant disturbance in the areas, the primary controller is found to be incompatible to suppress the frequency and tie-line power oscillation because of the sluggishness of speed governor dynamics. Load frequency control (LFC) is recognised as an indispensable process for balancing the megawatt (MW) power production and load demand to uphold the frequency and scheduled tie-line power at steady-state levels [1]. LFC aims to regulate the MW power output of synchronous generators in the line of randomly changing load demand. The critical features of LFC are (i) to nullify the error in frequency, (ii) to keep the steady flow of power through transmission lines, and (iii) to maintain synchronisation between the connected generators [2]. Hitherto, several works were discussed in the literature for design, analysis, and synthesis of LFC issue. The study of real-time LFC is accomplished with the use of proportional–integral (PI) controllers or its variant owing to its numerous amenities. In [3], the focus has been given to the design of an intelligent PI controller for a two-area non-reheat thermal power system. Nanda et al. [4] studied the dynamics of a two-area hydrothermal power system utilising I and PI controllers. A robust decentralised PI controller for frequency monitoring with time delay is presented in [5]. The dynamic performance of a three-area IPS employing PI–derivative (PID) controller has been pointed out in [6]. Guha et al. [7] proposed a PID plus double derivative (DD) controller to stabilise frequency and tie-line power responses of a four-area IPS. The results obtained with PID + DD controller is compared with the results of PID controller to describe the superiority of PID + DD controller. Although a considerable improvement is achieved with these controllers, the performance of I/PI/PID controllers highly deteriorates with the increase of the complexities of the power system such as large load fluctuation, boiler dynamics, the presence of various non-linearities etc. Additionally, the conventional controller can start to take remedial action against random perturbation only after the sufficient deviation of controlled output from the reference input level. The plant must sense the disturbance before the controller initiates any control action. One of the possible ways of solving this problem is by using a feed-forward controller. However, the problem associated with the feed-forward controller is that it requires direct measurement of disturbances and model of power system must be known before to calculate the suitable controlled output. Cascade controller can be used as an alternative to alleviate the performance of the closed-loop system by employing secondary measurement and secondary feedback arrangement. Dash et al. [8] have studied the LFC issue of an interconnected four-area power system using a coordinated PI–PD controller. The benefits of using cascade controllers over single-loop controllers have been documented in [9]. A 2-degree-of-freedom cascade controller is discussed in [10] for LFC of a three-area power system. The practicabilities of the fuzzy logic controller (FLC) and artificial neural network (ANN) have also been identified in this area for improving system stability [11, 12]. A hybrid neuro-fuzzy controller for LFC of a four-area power system is studied in [13]. However, in the design of FLC, no specific mathematical background has been specified for selecting the rule base, membership functions, defuzzification, scaling factor etc. An inappropriate choice may affect the stability of the system. Contrariwise, more training data set is needed for the supervised learning of ANN. Again, the number of layers and neurons in layers increases with the increase of power system order [14]. Recently, considerable attention to the betterment of the conventional controller performance has been identified by the inclusion of fractional-order (FO) calculus. In FO controller, the power of D and I terms is non-integer. Taher et al. [15] have practised FOPID controller for LFC analysis of IPS. The improvement of frequency and tie-line profile of IPSs with FOPID controller is illustrated in [16, 17]. In [18], FOID controller is designed and applied for LFC analysis. In these previous references, only two- and three-area power systems have been investigated. Tilt–ID (TID) controller, proposed by Lurie [19], is another variant of PID controller that houses both the merits of FO calculus and PID controller. In TID, unlike conventional PID controller, the integer power of proportional block is replaced with a tilted factor of . This resulting model provides a close approximation of an optimal feedback controller for attaining proper set-point tracking and better disturbance rejection ability. In [20], a TID controller with filter is realised and applied for LFC study. The competence of TID controller was established over PID controller by transient analysis. However, the superiority of TID controller was verified only for two- and three-area interconnected systems. Besides these, several other intelligent controllers such as predictive control algorithm [21], internal model control [22], reinforcement learning [23], sliding mode controller [24], H∞ controller [25] etc. have been successfully implemented in the power systems to deal with LFC issue. Modern power systems demand high intelligence and accurate selection of controller gains for better frequency and tie-line power stabilisation against load perturbation. The conventional tuning methods are found to be ineffective to explore the best and optimum values of controller settings due to uncertainties and non-linearities associated with the system. Furthermore, classical tuning algorithms are suffering from local optima entrapment, require derivative of the search space, and poor solution accuracy. Hence, utilisation of various evolutionary algorithms for the fine-tuning of controller gains has been identified as a keen research topic in the recent past and may consider as an I part of LFC study. Genetic algorithm (GA) has been applied to tune I-controller gains for studying the closed-loop performances of a three-area power system [26]. The premature convergence of the GA reduces its efficiency and searchability [27]. Bacterial foraging optimisation (BFO) was derived in [27] to optimise LFC parameters of a three-area thermal power system. The performance of BFO, in the chemotaxis process, is highly reliant on the random search direction matrix that may introduce a time lag in attaining the global solution. Biogeography-based optimisation has been utilised in [28, 29] for optimisation of controller parameters. Guha et al. [30] have recently applied symbiotic organism search algorithm for the optimal solution of the LFC problem. The study was confined to a two-area multi-source IPS. Close reviews in this area further unfolds the effective use of imperialist competitive algorithm [15], firefly algorithm [18], differential search algorithm [14], differential evolution (DE) [20], flower pollination algorithm (FPA) [8], grey wolf optimisation [31], teaching learning-based optimisation [24, 31], and JAYA [31]. The participation of tidal power generation in LFC has been reviewed in [32]. The controller parameters were optimised by quasi-oppositional harmony search algorithm (QOHSA). Reviewers are, incessantly, working toward the exploration of modern optimisation tools for improving the performances of available algorithms and/or finding efficient solutions for a broad class of unsolved problems. According to 'no-free-lunch' theory, no optimisation scheme is well-defined for all optimisation problems. Thus, identification and application of novel algorithms to solve LFC problem are always imperative [31]. Salp swarm algorithm (SSA) is a recent addition in this endeavour, contributed by Mirjalili et al. [33]. The SSA imitates the swarming behaviour of salp during navigating and foraging in the ocean. It is noted from the literature that maximum of the previous research in this domain is associated with isolated [2], two- [3, 4, 14, 20] and/or three-area [2, 6, 10, 12, 26, 31] IPSs. Less care had given to the assessment of system dynamics for four- [7, 8, 13] and/or five-area power systems. Surprisingly, in the line of merits, TID controller with cascade control structure has not been attempted for LFC study. In this paper, an attempt has been taken to develop and applied an optimised cascade TID (CC-TID) controller to deal with the LFC issue of large IPSs. The motivations for studying large-scale power system are as follows: (i) A large-scale power system provides technological, economical, and environmental benefits such as the pooling of large power production units, sharing of spinning reserve, and utilisation of renewable power sources considering ecological limitations such as nuclear power plant in selected areas, hydropower from distant regions, solar energy from desert areas, and coordination of large offshore wind farms. (ii) The liberalisation in the power company confirms more interconnections of power systems to enrich the power sharing amongst the regions or countries. (iii) Transmit of cheaper energy over long distances to the load centres. (iv) The flexibility of building power plants and increase the reliability of the power system. (v) The optimised operation of power stations reduces losses. To design a CC-TID controller, TID, and PI controllers are used as slave and master controllers, respectively. SSA is used for optimising CC-TID controller gain parameters to achieve better dynamic stability of the IPS. The notable contributions of the current study are summarised below: (i) This work demonstrates a realisable model of LFC for balancing power generation and load demand. Modelling of two IPS followed by a hybrid power system has been presented to perform this paper. (ii) The controlling superiority and feasibility of CC-TID controller have been established over I-, PI-, PID-, cascade PI–PD, and TID controller. (iii) Application of SSA has been elucidated for exploring optimum CC-TID controller gains. (iv) The performance of SSA is verified over DE and FPA concerning convergence mobility, power density function, and minimum fitness value. (v) To affirm the efficacy and robust performance of CC-TID controller, time-varying step load perturbation (TVSLP) and random load perturbation (RLP) are projected to IPS. (vi) The effectiveness of the designed CC-TID controller is also validated by taking system non-linearities. The rest of this paper is documented as follows. The modelling of IPS to perform this analysis is described in Section 2 following a detailed discussion on the CC-TID controller. The SSA is briefly discussed in Section 3 with design constraints. Dynamic results and comparative study are deployed in Section 4. Section 5 provides the concluding remarks of the present paper. 2 Model and methodology 2.1 System under study Two different test systems have been considered to establish the practicability of CC-TID controller. The small-signal stability of the test systems has been assessed following appropriate load perturbations. Initially, a two-area non-reheat thermal power plant has been examined, and afterwards the study is forwarded to a four-area power system. Fig. 1a depicts the transfer function (TF) model of test system-1 for LFC study [20]. Each area of test system-1 has the capacity of 2000 MW with a maximum loading of 1000 MW. In Fig. 1a, are the time constants of a speed governor, steam turbine, and power system, in order; is the gain of the power system; R is a governor speed regulation parameter; is the synchronising coefficient; are load disturbance and tie-line power error, respectively; are frequency errors of areas 1 and 2, in order. The nominal values of system parameters are appended in Table 1. The calculation of damping and inertia constants are shown in Appendix. The dynamic behaviour of test system-1 is examined against 10 and 20% SLP in areas 1 and 2, in order. Owing to the page limitation, TF model of a two-area power system is only discussed under this heading. However, the schematic model of a four-area power system is shown in Fig. 1b. Fig. 1Open in figure viewerPowerPoint Models of test systems(a) TF model of two-area non-reheat thermal power plant (test system-1), (b) Schematic representation of a four-area power system, (c) Structure of cascade controller, (d) TID controller with a derivative filter Table 1. Nominal values of test system-1 and test system-2 parameters [8, 20] Parameter value Parameter value Parameter value 0.08 s 0.3 s 20 s 120 Hz/pu MW 0.545 pu 10 s R 2.4 Hz/pu MW 0.5 B 0.425 pu MW/Hz 2.2 Cascade TID controller Cascade controllers generally realised in multi-loop control systems for good set-point tracking and better disturbance rejection. Unlike conventional controller, the cascade controller has two loops called 'primary or inner or slave' loop and 'outer or secondary or master' loop. The inner loop responds much faster than the outer loop such that disturbance appears in the process can be diminished before it propagates to the other sections of the process. In [18], the merits of the cascade controller over the single-loop controller are available. Fig. 1c illustrates a block diagram of the control system with a cascade controller. The controlled output of the closed-loop system is calculated using the equation below: (1)In (1), and are the reference and disturbance inputs to the plant, respectively, and are the TF of master and slave controllers, respectively. A TID controller has a similar structure of PID controller, except the proportional gain is replaced by a block of a TF , where is called 'tilt parameter' and chosen in between [20]. This structure referred to 'tilt controller' [19]. It alludes in the literature that the tilt controller is more efficient to show better output as compared with PID controller [19]. The purpose of applying for tilt compensation in LFC loop is to provide improved feedback loop compensation, so that best and optimal response can derive. It further helps to keep the stability of the system under external and/or internal perturbations. Fig. 1d illustrates a general layout of TID controller. The TF of TID controller is given in (2) (2)In (2), are ID gains, in order; N is the low-pass filter cut-off frequency. To perform an LFC analysis of the concerned test systems, the authors have developed a CC-TID controller. In the proposed model of CC-TID controller, TID controller is used in the inner loop, while PI controller acts as a master controller. 3 Salp swarm algorithm SSA is a currently introduced population-based optimisation algorithm motivated by the swarming behaviour of salp (salp chain) in the deep oceans. The salp populations segregated as leader and followers to derive the model of salp chain [33]. The location of salps is expressed in the d-dim search space, where d is the number of problem-specific optimised parameters. In SSA, the current position of leader salp (first salp in the chain) has changed with respect to food location by using the equation below: (3)where is the location of leader salp in the j th-dim; is the food location in the j th-dim; are upper and lower limits of the j th-control variables, respectively. In SSA, food location is considered as an optimum global point and salp chain is a search agent that approaches to food location. The variable balances between exploration and exploitation phases using the equation below [33]: (4)where l and L are present and the highest generation numbers, in order. The positions of following salps in the chain are updated by using the equation below [33]: (5)In (5), is the location of the k th follower salp in the j th-dim; t is the time; and and are initial and final velocities of salp. Since in the optimisation process time is treated as generation count, hence (5) can express as (taking ) (6)Fig. 2 shows a general flowchart of SSA. The advantages of SSA are discussed as follows: (i) It saves the best salp position as a food location; hence, it will remain in the solution even if the entire solutions deteriorate. (ii) SSA has only one control parameter , which is adaptively reduced during generations. (iii) It has a straightforward algorithmic structure and simple to realise. The performance index is a qualitative measure of the system behaviour and accordingly chosen, so that emphasis is given to the required specifications. A quantitative measure of the performance indices is needed for automatic parameter optimisation of the control system. The proposed LFC study is formulated as a constraint optimisation problem subjected to CC-TID controller parameter bounds. The gain parameters of the CC-TID controller are selected via the minimisation of I time absolute error (ITAE)-based area control error (ACE) function due to its high acceptability [34]. To guarantee a fair comparison, the same objective function as defined in [20] has been considered and described in the equation below: (7)where i is the number of control areas; is the frequency bias constant; is the frequency error of the i th- control area; indicates the tie-line power error among i th- and j th- control areas; and are two extreme limits of PID-controller gains; and are the minimum and maximum values of tilt parameter, in order; and are the minimum and maximum levels of filter cut-off frequency, respectively. To guarantee a fair comparison with the results of state of art, the PID- and PI-controller gains are optimised within [20] for test system-1 and [8] for test system-2. The range for tilt parameter is considered as 2 and 10 [20] for both the test systems. The derivative filter gain is selected in the range of . Fig. 2Open in figure viewerPowerPoint General flowchart of SSA 4 Results and discussion In this section, a close review of the dynamic responses of IPSs has been performed to confirm the efficacy and supremacy of the proposed SSA-tuned CC-TID controller. To carry out this study, the Simulink diagram of test systems are derived in the MATLAB/Simulink domain, while the codes of SSA are separately written in. m-file. To perform this optimisation, 50 population size and 100 iteration counts are chosen. The simulations were executed on an Intel Core i3 processor with 4 GB random access memory of 2.4 GHz frequency and MATLAB 2010 environment. Owing to the fuzziness of evolutionary algorithms, 20 trials were made before selecting the final solutions. The plot of global minima offered by CC-TID controller after 20 runs is shown in Fig. 3a. To describe the supremacy of CC-TID controller, the global minima calculated with TID- and PID controller are portrayed in Fig. 3a for the same test system. It is obtainable from Fig. 3a that SSA:CC-TID controller provides the best solution compared with SSA:TID and SSA:PID controllers. Furthermore, the solution obtained with SSA:CC-TID controller remains in the vicinity of global minima. The same observation is also made for SSA:TID and SSA:PID controllers. Thus, the robustness of the SSA is believed. The convergence profile of SSA under the action of CC-TID controller is shown in Fig. 4. It is remarkable from this graph that the initial guess of the search agents is also close to each other, and thereby confirming the consistency of SSA in searching the global optimum point for the defined problem. The performance of the controller and SSA is assessed considering convergence rate, lowest minimum ACE value, distribution rate, and minimum transient performance characteristics. Fig. 3Open in figure viewerPowerPoint SSA(a) Plot of optimal value with number of runs for test system-1, (b) Convergence characteristic with different controllers for test system-1, (c) Convergence profile for test system-2 Fig. 4Open in figure viewerPowerPoint Convergence characteristic of SSA under the action of CC-TID controller for test system-1 4.1 Transient performance of test system-1 Similar to [20], the dynamics of test system-1 as available in Fig. 1a is assessed against 10 and 20% SLPs in areas 1 and 2, in order. To handle these perturbations, PID, TID, and CC-TID controllers are designed separately and included in the LFC loop. The gain parameters of the controller are selected employing SSA through the minimisation of (7). To show efficacy, the closed-loop responses obtained with the CC-TID controller are compared with that of TID and PID controllers. The optimised gains of CC-TID controller are tabulated in Table 2 along with PID and TID controller gains. Fig. 3b illustrates the convergence characteristic of SSA under the actions of PID, TID, and CC-TID controllers. Table 2. Optimised controller parameters of test system-1 GA:PID [20] PSO:PID [20] DE:PID [20] DE:TIDF [20] SSA:PID SSA:TID SSA:CC-TID Slave Master Boldface shows best value. Fig. 3b depicts that CC-TID controller converges smoothly and speedily to the global optimum point than PID and TID controllers. Time-domain performances of test system-1 correspond to best controller gains as reported in Table 2 are obtained and compared in Fig. 5. The transient characteristics such as peak overshoot (OS), undershoot (US), and settling time (ST) of system oscillations are computed and provided in Table 3. From Table 3 and Fig. 5, it is noteworthy that SSA-optimised CC-TID controller is superior concerning ST, system oscillations, and magnitude of the oscillations. The STs of , , and are decreased by 39.55, 26.5, and 8.31%, respectively, compared with the results given in [20]. Hence, it may conclude that SSA:CC-TID controller outperforms SSA:TID, SSA:PID, and the controllers discussed in [20]. However, the peak USs of frequency and tie-line power oscillation is more with SSA:CC-TID controller in comparison with DE:tilt-integral-derivative with filer (TIDF) controller, which is justifiable because the simultaneous improvement of ST and US/OS is not possible. Again to show tuning competency of SSA, the results are compared with GA [20], DE [20], and particle swarm optimisation (PSO) [20]. It is apparent from Table 2 that SSA provides the least minimum fitness value than that of GA [20], PSO [20], and DE [20]. This shows that SSA is best for tuning the controller parameters than GA, DE, and PSO. Since SSA:CC-TID controller provides the best output compared with other controllers, hence the remaining of the work is performed with SSA:CC-TID controller. Fig. 5Open in figure viewerPowerPoint Transient behaviour of test system-1(a) frequency deviation of area-1, (b) frequency deviation of area-2, (c) tie-line power deviation, (d) control output of area-2 Table 3. Transient specifications of test system-1 Parameters GA:PID [20] PSO:PID [20] DE:PID [20] DE:TIDF [20] SSA:PID SSA:TID SSA:CC-TID ST US (×10−2) ST US (×10−2) ST US (×10−2) ST US (×10−2) OS ST US ( × 10−2) OS ST US ( × 10−2) OS ST US ( × 10−2) 6.93 8.74 5.30 8.58 3.58 7.80 2.20 6.98 0.0165 1.73 12.64 0.0041 1.52 11.65 0.0087 1.33 11.66 6.74 5.22 6.41 4.36 4.85 3.92 3.47 3.18 0 3.06 7.50 0 2.59 6.71 0 2.55 6.71 4.87 2.01 5.03 1.57 4.20 1.53 3.01 1.23 0 3.30 2.57 0 2.63 2.30 0 2.56 2.31 Boldfaces show best value. 4.2 Transient performance of test system-2 A four unequal area reheat thermal power plant with a capacity of area 1:2000 MW, area 2:4000 MW, area 3:8000 MW, and area 4:16,000 MW has been investigated to appraise the performance of CC-TID controller. The controlled areas of test system-2 are comprised of a single stage reheat turbine with generation rate constraint of 3%/min. The general layout of test system-2 is displayed in Fig. 1b. The Simulink diagram of test system-2 is obtainable from [8]. The gain parameters of CC-TID controllers are concurrently tuned through SSA. After tuning, the controller settings are offered in Table 4. For showing the supremacy of the designed CC-TID controller, test system-2 is further studied with TID- and FPA-optimised I-, PI-, PID-, and PI–PD controllers [8]. The gain parameters of TID controller are computed by using SSA and displayed in Table 4. A step load increase of 1% is provided to area 1 for investigating the dynamic behaviour of test system-2. Fig. 3c depicts the convergence profile of the proposed SSA under the actions of CC-TID and TID controllers. From Fig. 3c, it is remarkable that SSA smoothly converges to the global optimum point and least minimum ITAE value is acquired by CC-TID controller. It is also observed in Fig. 3 that SSA requires 70–80 generations to attain the optimum global value that upholds the selection of generation number 100 for the present study. Dynamic responses correspond to SSA:CC-TID, SSA:TID, FPA:I, FPA:PI, FPA:PID, and FPA:PI–PD are obtained and compared in Fig. 6. The transient characteristics such as rising time (RT), peak time (PT), OS, US, and ST are computed from Fig. 6 and presented in Table 5. It is revealed in Fig. 6 that FPA:PID controller exhibits sluggish time responses with high US. Furthermore, FPA:I, FPA:PI, and SSA:TID controllers produce oscillatory outputs with more ST. Contrariwise, SSA:CC-TID controller adds good damping to the system oscillation and quickly restores the system stability. It is noteworthy from Table 5 that SSA:CC-TID controller provides least OS, US, and fast ST as compared with the controllers marked in Table 5. Thus, SSA:CC-TID proves to be efficient for test system-2 and may realise in the real-time practise. Table 4. Optimised controller gains of test system-2 Controllers Control areas Slave TID controller Master PI controller J kp ki N n kp1 ki1 CC-TID area 1 0.3664 0.8853 0.2344 18.2175 2.5476 0.9572 0.9884 0.0281 area -2 0.9672 0.1283 0.1256 8.4589 2.1258 0.0126 0.0167 area 3 0.1542 0.8761 0.1641 5.1897 2.8257 0.8105 0.8765 area 4 0.7646