WRP Based Energy Efficient Multiple Mobile Sink Path Selection in WSN

Transcription

1 WRP Based Energy Efficient Multiple Mobile Sink Path Selection in WSN Ann Mary Francis 1, Jinto Mathew 2 1 M.Tech Scholar, Mar Baselios Institute of Technology and Science, Nellimattom, India 2 Assistant Professor ECE, Mar Baselios Institute of Technology and Science, Nellimattom, India Abstract Researchers concerned with networks, in these days use a mobile sink as it help to reduce the energy consumption of nodes and also prevent the formation of energy holes in wireless sensor networks (WSNs). However, the benefits of mobile sinks are dependent on the path taken by the sink, especially in delaysensitive applications, as all forwarded data must be collected within a given time bound. In this paper, a new approach is proposed to address this issue by forming a hybrid moving pattern in which a mobile sink node only visits nodes designated as rendezvous points (RPs), instead of all nodes. Other nodes that are not designated as RPs forward their sensed data to their nearest RPs through multihopping. Computing an optimal tour that visits all these RPs within a given application delay limit is a fundamental problem. To address this issue, a heuristic called weighted rendezvous planning is proposed in which a weight is assigned to each sensor node based on its hop distance from the tour and number of data packets it forwards to closest RP.The simulation results are shown to demonstrate that WRP enables mobile sink to collect all forwarded data within a given time-limit while reducing the energy expenditure of sensor nodes. Index Terms Power factor correction (PFC), Compact fluorescent lamp (CFL), Discontinuous conduction mode (DCM), Displacement power factor (DPF), distortion factor (DF), total harmonic distortion. nodes that are closer to the sink ruins faster than the farther ones that may have more than 80% of their initial energy [13]. This problem results in depletion of energy in nonuniform manner, which leads to network separation due to energy holes formation[14],[15].fig. 1 shows this situation. Due to this, the sink becomes detached from other nodes and impairs the WSN.Thus, energy consumption balancing of sensor nodes to prevent formation of energy holes is a major issue in WSNs. W I. INTRODUCTION IRELESS sensor networks (WSNs) are dense networks of large number of small, low-cost sensor nodes that collect and forward environmental data. They have got a widerange of applications, such as in military operations [1] [3], environment monitoring [4], [5], agriculture [6], [7], home automation [8], smart transportation [9], [10], and health [11]. Each sensor node can collect and process data from other nodes and finally forward the sensed data back to one or more sink nodes which act as data collector via their wireless transceiver in a multihop manner. In addition, sensor nodes run with the help of a battery, and once it runs out of battery, it may be difficult or impractical to replace, given the number of sensor nodes and deployed environment. These limitations led to designing of energy-efficient algorithms for wireless sensor networks [12]. Unlike singlehop,in multihop communications, nodes which are located closer to the sink tend to become crowded as they forward the data from farther nodes. Thus the battery of sensor Fig. 1. Nodes closer to the sink depletes their energy faster To solve this, previous works such as [15] and [16] used mobile sinks. These mobile sinks move and collect data directly from sensor nodes and help sensor nodes to save energy by avoiding the multihop communications of nodes. Fig. 2 shows a mobile sink performing data collection in a WSN.The squares denote the feasible sites from which mobile sink will collect data. Mobile sink s current position determines the data forwarding path from sensor node to the sink. Mobile sink may change its location over time and sensor nodes need to dynamically plan some data forwarding

2 paths to each feasible sites. As shown by [15],lifetime of sensor nodes can be increased by a mobile sink that travels along the periphery of a sensor field network.eventually,forwarding tree will include a different set of sensor nodes as sink changes its position over time and hence will help in balancing the energy consumption of nodes[17]-[21]. In this paper, in order to solve this problem, we proposed a heuristic method called weighted rendezvous planning (WRP), for determining mobile-sink node s tour. In WRP, sensor nodes which are located in congested area and have more hop count from the computed are given more priority. This will help in reducing non-uniform depletion of energy. Fig. 2. Mobile sink performing data collection in a WSN.A source node sends data to feasible sites. Real-time requirement of data produced by nodes determines the traveling path of a mobile sink. Residual energy of sensor nodes [23]-[27] decides the feasible sites and respective sojourn time of mobile sink. In general, movement of a mobile sink is governed by restrictions such as maximum number of feasible sites [28], maximum distance between them and the minimum sojourn time or the upper limit on load time. Major problem with WSNs employing a mobile sink is to decide how the mobile sink collects the sensed data. One method is to receive sensed data by visiting each sensor node directly and collect data [29].This leads to traveling salesman problem (TSP) [30] that finds the shortest tour which visits all sensor nodes. But if the number of nodes increases, this problem may become impractical since the final tour length may exceed the delay limit of applications. To solve this, researchers bound the tour length by proposing the use of rendezvous points (RPs) [31], [32]. This requires a subset of sensor nodes to be designated as RPs, and the rest non-rp nodes forward their data to these RP nodes. For the set of these RPs, then a tour is computed which is shown in Fig. 3.This leads to a problem called rendezvous design in which selected RPs should be such that it can minimize energy consumption of multihop communications while adhering to the required packet delivery bound. Another problem is that the selected RPs should cause uniform energy expenditure of sensor nodes that maximize lifetime of networks. Fig. 3. Hybrid movement pattern for a mobile sink node. Thus, this paper can be summarized as: We need to find a set of RPs that are visited by a mobile sink. Its objective is to reduce multihop transmissions from sensor nodes to RPs thereby minimizing the energy consumption. This also ensures that resulting tour does not exceed the required application deadline by limiting the number of RPs. We propose WRP, which is a method to determine the travelling path of mobile sink that minimizes the sensor node s energy consumption.wrp works by assigning a weight to each sensor node depending on its number of data packets and hop count from the tour.wrp selects sensor nodes with highest weight as RP. We prove that selecting sensor nodes with highest weight as RP minimizes the energy consumption; as compared with other sensor nodes. II. LITERATURE REVIEW Existing methods on using a mobile sink in WSNs can be grouped into two categories: 1) direct, where a mobile sink visits each sensor node and collects data via a single hop; and 2) rendezvous, where a mobile sink only visits nodes designated as RPs. The main goal of protocols in category 1 is to minimize data collection delays, whereas those in category

3 2 aim to find a subset of RPs that minimize energy consumption while adhering to the delay bound provided by an application [17].In the following, we review the challenges faced by these protocols. A. Direct Initial studies used a mobile sink that visits sensor nodes randomly and transport collected data back to a fixed sink node. An example is the use of animals as mobile- sink nodes to assist in data collection from sensor nodes scattered on a large farm [16]. To reduce the latency of visiting each sensor node randomly, researchers have proposed TSP-based data collection methods. In essence, the problem is reduced to finding the shortest traveling path that visits each sensor node. For example, TSP with neighborhood involves finding the shortest traveling tour for a mobile-sink node that passes through the communication range of all sensor nodes. Another TSP-based algorithm [35] called label-covering considers a WSN as a complete graph. For each edge, it calculates a cost and associates a label set. The cost of an edge is the Euclidean distance between nodes, whereas the label set contains sensor nodes whose transmission range intersects with the given edge. The label-covering algorithm selects the minimum number of edges where their associated label set covers all sensor nodes. B. Rendezvous The problem with collecting data directly from sensor nodes is that it becomes impractical when there are a large number of sensor nodes. Visiting each sensor node increases the mobile sink s traveling path length and results in sensor nodes experiencing buffer overflow due to data collection delays. To address this problem, researchers have proposed a rendezvousbased model, in which a mobile sink only visits a subset of sensor nodes called RPs. The sensor nodes outside the mobile sink path send their data via multihop communications to this RPs.Studies deploying this approach can be classified according to the mobile sink s trajectory, i.e., whether it moves along a fixed path or its path is unconstrained by any external factors. 1) Fixed: Here path of the mobile sink is fixed, and sensor nodes are randomly deployed near the sink s traveling path. Sensor nodes that are inside a mobile sink s communication range play the role of RPs and collect data from other sensor nodes. An example application is a traffic management system where mobile sinks are public buses that roam a city to collect data from sensor nodes placed on buildings. In these approaches, the length of the traveling path is not dependent on the buffer size of sensor nodes or application deadline. Hence, the buffer of RPs may overflow or packets may expire before they are collected by the sink. Xing et al [33] proposed RD-FT, where the movement of a mobile sink is governed by application deadline. They also consider obstacles that restrict the movement of a mobile sink along a predefined path. The objective is to find a set of RPs on the fixed path such that the length of data forwarding paths from sensor nodes to RPs is minimized and that the traveling time between RPs is limited to the required packet delivery time. 2) Unconstrained : In RD-FT WSN with a static sink node and a mobile element (ME) is assumed to collect data from RPs. Moreover, RPs perform data aggregation. An algorithm called RD-VT is proposed with the objective of identifying traveling path that is shorter in duration than the packet delivery time. The algorithm first constructs a Steiner minimum tree (SMT) rooted at the sink node. RD-VT then starts from the sink s position and traverses the SMT in preorder until the shortest distance between visited nodes is equal to the require packet delivery time. Since, in an SMT, a Steiner point may be a physical position and does not correspond to the position of a sensor node, RD-VT replaces these virtual RPs with the closest sensor nodes. A major limitation of RD-VT is that traversing the SMT in preorder leads to the selection of RPs that in turn results in long data forwarding paths to sensor nodes located in different parts of the SMT. As a result, RD-VT causes nodes to have an unbalanced data forwarding load and energy consumption. Xing et al. [31] propose rendezvous planning with a constrained ME path (RP-CP). Similar to RD-VT, the authors consider a WSN with a fixed sink node and a ME. The RP-CP first constructs a routing tree that is rooted at the sink node and connects all sensor nodes. Then, each edge of the routing tree is assigned a weight that corresponds to the number of nodes that use that edge to forward their data to the sink node. The ME is restricted to moving only on the edges of the tree. To construct the ME s traveling path, RP-CP first sorts all edges according to their weight. It then selects the edges with the highest weight until the length of the selected edges becomes equal or less than the required packet delivery time. The problem with RP-CP is that the traveling path of the ME is restricted to routing tree edges. This also means that the ME will visit the sensor nodes on the selected edges twice. Xing et al, propose an improvement to RP-CP, which is called the RP-UG algorithm. Initially a geometric tree, which is rooted at the fixed sink node, is constructed, and all edges on the tree are split into multiple short intervals, which are denoted as Lo. All points that join two edges with length Lo are considered RP candidates. RP-UG starts from the sink s position and, in each step, adds the RP that minimizes the distance of sensor nodes from selected RPs and also results in the shortest traveling tour between RPs. RP-UG uses a TSP solver to calculate the tour length. To finalize the tour, RP-UG replaces virtual RPs with the closest sensor nodes and marks them as RPs. RP-UG does not balance the energy consumption rate of sensor nodes, which has a significant impact on network lifetime. Specifically, the network lifetime is determined by the sensor node with the highest energy consumption rate, e.g., n, assuming all nodes have the same initial energy level. In this regard, RP-UG does not aim to minimize the energy consumption rate of node n. In addition, when using RP-UG with a small Lo value, the number of RPs increases significantly, and the complexity of RP-UG grows exponentially. The algorithm uses TSP solver N

4 times in each iteration, where N is the number of RPs. Hence, RP-UG has a running time complexity of O(N2 O(TSP)). In CB algorithm [32] a binary search procedure is used to select RPs. It works as for example consider a network with ten nodes where maximum allowed tour length is 90 m. In the first iteration, using binary search CB selects five random cluster heads. Other nodes then establish a path to their closest cluster head in terms of hop count. After the clusters are determined CB starts from the sink node s position and selects one node from each cluster as an RP, which is the closest node to the set of selected RPs. Now if the final tour has length larger than 90 m, CB will reduce the number of clusters. But the final tour calculated does not pass through dense parts of the network consisting of nodes with a larger number of neighbors. This problem causes long data forwarding paths from sensor nodes to the RPs and non uniform energy depletion, which reduces the lifetime of the WSN. III. METHODOLOGY In order to alleviate the energy holes problem, a mobile sink can collect sensed data directly from sensor nodes, and thereby, help sensor nodes save energy that otherwise would be consumed in multihop communications. Considering the required delivery time of sensed data, visiting all sensor nodes may exceed the required delivery time of collected data packets. In WSNs with a large number of sensor nodes and limited delivery time for data packets, the time to visit all sensor nodes may exceed the required packet delivery time. Therefore, in order to meet packets delivery time, a mobile sink was programmed to visit only a set of sensor nodes called Rendezvous Points (RPs).Each RP is similar to a static sink, where senor nodes forward their sensed data to the closest RP which is then collected by a mobile sink. Selecting a set of RPs such that the travel time between them does not exceed the required data packet delivery and also uniformly balances sensor nodes energy consumption rates is a well-known mobile sink path selection problem. The main challenge is to identify the most suitable Rendezvous Points (RPs) for a mobile sink in order to minimize the energy consumed by sensor nodes during multihop communication while meeting a given packet delivery bound. The problem is NP-hard. A heuristic algorithm called Weighted Rendezvous Planning (WRP) is then proposed to determine mobile sink s trajectory and the set of RPs that optimize the energy consumption of sensor nodes. WRP assigns a weight to each sensor node corresponding to its hop distance from the tour and the number of data packets that it forwards to the closest RP A. Problem Formulation To mitigate energy holes in WSNs mobile sink was proposed. In this method, an autonomous mobile sink travels within a network area and collects data directly from each sensor node. Using this approach, sensor nodes no longer forward data to a base station. However, in a network with a large number of sensor nodes and strict delay tolerance such as like precision agriculture, visiting all sensor nodes violates the required packet delivery time. To meet the delay bound constraint, RPs have been proposed by researchers in order to limit a mobile sink s tour length. In this approach, a subset of sensor nodes are selected as RPs and non-rp sensor nodes forward their data to selected RPs. The mobile sink only visits RPs and collect buffered data from them. Selecting the most suitable RPs that minimizes the energy consumption and meeting a given packet delivery bound is the main problem. In addition, selecting the set of RPs that result in uniform energy expenditure amongst sensor nodes in order to maximize network lifetime is a secondary problem. B. Assumptions The proposed solution makes the following assumptions: 1) The communication time between the sink and sensor nodes is negligible, as compared with the sink node s traveling time. 2) Each RP node has sufficient storage to buffer all sensed data. 3) The sojourn time of the mobile sink at each RP is sufficient to drain all stored data. 4) The mobile sink is aware of the location of each RP. 5) All nodes are connected, and there are no isolated sensor nodes. 6) Sensor nodes have a fixed data transmission range. 7) Each sensor node produces one data packet with the length of b bits in time interval D. C. Notation We model a WSN as G (V, E), where V is the set of homogeneous sensor nodes, and E is the set of edges between nodes in V. If sensor node i send b bits to node j, its energy consumption is: E TX(i, j) = b(α1 + α2 d γ i,j) Where d i, j is the physical distance between sensor node i and j, and α1 is the energy consumption factor indicating the power per bit incurred by the transmitting circuit. The expression α2d γ i,j indicates the energy consumption of the amplifier per bit, where α2 is the energy consumption factor of the amplifier circuit. Here, γ is the path-loss exponent, which usually ranges between 2 and 4, depending on the environment. Path loss is the power density reduction of the electromagnetic wave when it propagates through the air. Moreover, the power consumption incurred by node i to receive b bits from node j is: E RX(i, j) = b β Where β is a factor that represents the energy consumption per bit of the receiving circuit. As sensor nodes generate the same

5 size data packets and have fixed data transmission range, E TX and E RX do not depend on distance between nodes and are identical for all sensor nodes. The mobile-sink node moves with a constant speed v. Hence, the maximum length of the traveled path l is: l max = D v A mobile-sink node starts its movement from a node m 0 V and before time D returns to its starting point. Each sensor node sends its generated data packets to the closest RP through multihop transmissions. We define a function called H(i,M) that returns the closest RP in terms of hop count to the sensor node i, where M is the set of RPs. Specifically H (i, M) = {h i, mj m k M,h i, mj h i, mk } Where h i,j is the hop distance between nodes i and j. For each RP m i, our algorithm constructs a data forwarding tree T mi comprising of the closest sensor nodes to said RP. The number of data packets NFD(i) that sensor node i forwards to the closest RP m i in each time interval D is equal to its own generated data packet plus the number of its children in the data forwarding tree T mi. Specifically, NFD(i) = C(i, T mj) +1 where C(i, T mj ) is a function that returns the number of children that node i has in the data forwarding tree rooted at its corresponding RP m j. W i = NFD(i) H(i,M) Based on the above equation, sensor nodes that are one hop away from an RP and have one data packet buffered get the minimum weight. Hence, sensor nodes that are farther away from the selected RPs or has more than one packet in their buffer have a higher priority of being recruited as an RP. From the previous equation of energy incurred and consumption, the energy consumption is proportional to the hop count between source and destination nodes, and the number of forwarded data packets. Hence, visiting the highest weighted node will reduce the number of multihop transmissions and thereby minimizes the energy consumption. In addition, as dense areas give rise to congestion points due to the higher number of nodes, energy holes are more likely to occur in these areas. Hence, a mobile sink that preferentially visits these areas will prevent energy holes from forming in a WSN. WRP works in the following manner: It takes as input G(V,E), and it outputs a set of RPs. WRP first adds the fixed sink node as the first RP. Then, it adds the highest weighted sensor node. After that, WRP calls TSP( ) to calculate the cost of the tour. If the tour length is less than the required length lmax, the selected node remains as an RP. Otherwise, it is removed from the tour. After a sensor node is added as an RP, WRP removes those RPs from the tour that no longer receives any data packets from sensor nodes. This is because adding a sensor node to the tour may reduce the number of data packets directed to these RPs. All sensor nodes will be added to the tour when the required tour length for a mobile sink is bigger than the time to visit all sensor nodes. In our project we have used multiple mobile sink to reduce the traffic congestion. D. Delay-Aware Energy-Efficient Traveling Path The objective is to find a tour M = m 0,m 1,m 2,..., m n,m 0, where m i V, such that 1) the tour M is not longer than l max, and 2) the energy consumption for sending sensed data from sensor nodes to the tour M, as defined by (ETX + ERX) i V H(i,M), is minimized within time interval D. DEETP is NPhard by a reduction from TSP. The travelling salesman problem (TSP) asks the following question: Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city. It is an NP-hard problem in combinatorial optimization, important in operations research and theoretical computer science. E. Weighted Rendezvous Planning WRP preferentially designates sensor nodes with the highest weight as a RP. The weight of sensor node i (W i) is the product of the number of packets that it forwards NFD(i) and its hop distance from the closest RP on the tour H(i,M):

6 uniform energy consumption and mitigates the energy-hole problem. This is the key advantage of WRP over previous existing algorithms.we have used multiple mobile sinks in WSN to reduce traffic congestion. IV. SIMULATION RESULTS The proposed method has been simulated using NS- 2 tool. The simulation result of the proposed method is given in Fig. 5. As mentioned before, WRP is a hybrid moving pattern in which mobile sink stops and collects data from nodes designated as rendezvous points (RPs), as opposed to all other nodes. Sensor nodes that are not designated as RPs forward their data to the nearest RPs via multihopping.highest weighed nodes are designated as RPs.After calculating weight based on hop distance and data packets forwarded,congested nodes which are closer to sink will be selected as RP.This will help to reduce non-uniform energy depletion. We have used multiple mobile sinks to reduce the traffic congestion and in turn reduce energy consumption. Fig. 4. Example of WRP operating in a WSN of ten nodes The above figure shows an example of how WRP finds a traveling tour for a mobile sink. The maximum tour length is lmax = 90 m. WRP starts from the sink node and adds it to the tour, i.e.,m = [Sink]. Then, an SPT rooted at the sink node is constructed [see Fig. 4(a)]. In the first iteration, WRP adds node 10 to the tour because it has the highest weight, yielding M = [Sink, 10]. As Fig. 4(b) shows, the tour length of M is smaller than the required tour length (56 < 90), meaning node 10 stays in the final tour. In the second iteration, WRP recalculates the weight of sensor nodes because node 10 is now part of the tour. In this iteration, WRP selects node 6 as the next RP, which has the highest weight. As Fig. 4(c) shows, the tour length of M = [Sink, 10, 6] is larger than the required tour length (119 > 90). Consequently, WRP removes node 6 from the tour M = [Sink, 10]. In the third iteration, the weight of sensor nodes will not change because node 6 is not selected as an RP but it stays marked and will not be selected. WRP selects node 8 because it has the highest weight and is not marked [see Fig. 4(d)]. The TSP function returns 76 m for M = [Sink, 10, 8], which is less than 90 m. Therefore, node 8 is added to the tour. The process continues, yielding a final tour of M = [Sink, 8, 7, 10, 9] with a tour length of 81 m, which is less than the required tour length [see Fig. 4(e)]. As shown in Fig. 4, the final tour computed by WRP always includes sensor nodes that have more data packets to forward than other nodes as RPs. This ensures FIG.5.SIMULATION RESULT As given in the above figure we have grouped the entire network into three smaller sub networks and assigned a mobile sink to each sub network.in this manner we have reduced traffic congestion in the network along with reducing the nonuniform energy depletion of WSN.Each mobile sink collect data from corresponding RP

7 V. CONCLUSION In this paper, we have presented WRP, which is a novel algorithm for controlling the movement of a mobile sink in a WSN.WRP assigns weight to each sensor node based on number of packets it forwards and its hop distance and selects highest weighted sensor node as RP.In other words, WRP selects the set of RPs such that the energy expenditure of sensor nodes is minimized and uniform to prevent the formation of energy holes while ensuring sensed data are collected on time. Unlike other methods, in WRP the sensor nodes with more connections to other nodes and placed farther from the computed tour in terms of hop count are given a higher priority. Giving priority to these sensor nodes help to mitigate the energy-hole problem. Along with this we have used multiple mobile sink which help to reduce traffic congestion. Fig.6(a) Average energy consumption level The above graph shows performance level of WRP between packet size (x-axis) and average energy consumption level (yaxis). Fig.6(b) Throughput The above graph shows performance level of WRP between time interval (x-axis) and throughput (y-axis) which shows the efficiency of our method. REFERENCES [1] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, Wireless sensor networks: A survey, Comput. Netw., vol. 38, no. 4, pp , Mar [2] S. Diamond and M. Ceruti, Application of wireless sensor network to military information integration, in Proc. 5th IEEE Int. Conf. Ind. Vienna, Austria, Jun. 2007, vol. 1, pp [3] M.C. Ghanem, K.Al-Haddad and G. RoBoost Converter With Unity Power Factor, IEEE Transactions on Power Electronics, pp , [4] Mohammad Mahdavi, HoseinFarzanehfard, Zero-Current-Transition Bridgeless PFC Without Extra Voltage and Current Stress, IEEE Transactions on Industrial Electronics, vol. 56, no. 7, pp , July [5] Kuthadi, Venu Madhav, Rajalakshmi Selvaraj, and T. Marwala. "An Efficient web services framework for secure Data collection in Wireless sensor Network." British Journal of Science 12.1 (2015): [6] Woo-Young Choi and Joo-SeungYoo, A Bridgeless Single-Stage Half- Bridge AC/DC Converter, IEEE Transactions on Power Electronics, vol. 26, no. 12, pp , December [7] Hsien-Yi Tsai, Tsun-Hsiao Hsia, and Dan Chen, A Family of Zero- Voltage-Transition Bridgeless Power-Factor-Correction circuits with a zerocurrent switching auxiliary switch, IEEE Transactions on Industrial Electronics, vol. 58, no. 5, pp , May [8] Laszlo Huber, Yungtaek Jang and Milan M. Jovanovic, Performance Evaluation of Bridgeless PFC Boost Rectifiers, IEEE Transactions on Power Electronics, vol. 23, no.3, pp , May [9] W. Wei, L. Hongpeng, J. Shigong, and X. Dianguo, A novel bridgelessbuck-boost PFC converter, in Proc. IEEE Power Electron. Spec. Conf.,2008, pp [10] Yungtaek Jang, Milan M Jovanovic Bridgeless High power factor Buck converter, IEEE Trans. Power Electron., vol. 26, no. 2, pp , Feb [11] Kuthadi, V. Madhav, R. Selvaraj, and C. Rajendra. "A Study Of Security Challenges In Wireless Sensor Networks." Journal of Theoretical and applied information technology 20.1 (2009): [12] M. Mahdavi and H. Farzanehfard, Bridgeless SEPIC PFC rectifier withreduced components and conduction losses, IEEE Trans. Ind. Electron.,vol. 58, no. 9, pp , Sep [13] Sebastian, J., Cobos, J.A., Lopera, J.M., and Uceda, J.: The determination of boundaries between continuous and discontinuous conduction mode in PWM DC-to-DC converters used as power factor preregulators, IEEE Trans. Power Electron., 1995, 10, (5) [14] CnndA. Sabzali, E. H. Ismail, M. Al-Saffar, and A. Fardoun, New bridgelessdcm sepic and Cuk PFC rectifiers with low conduction and switchinglosses, IEEE Trans. Ind. Appl., vol. 47, no. 2, pp , Mar./Apr