Implementation of Non-Isolated Zeta-KY Triple Port Converter for Renewable Energy Applications

Abstract

This paper proposes a three-port Zeta-KY dc-dc converter which is fed with hybrid sources like photovoltaic (PV) cells and batteries. The converter proposed here is a multi-input single-output (MISO) structure which harnesses the benefits of Zeta and KY converters. The combination of these converters is highly advantageous since the Zeta converter provides lesser output voltage ripples with high gain and the KY converter topology suits well for withstanding load transients. The KY converter used in this research work is subjected to a topological change to facilitate bidirectional power flow. The bidirectional flow is essential to save the excess power in PV source in batteries during low load conditions. This novel multiport topology with bidirectional facility is first of its kind and has not been discussed earlier in the research arena. In the proposed work, two control algorithms are developed and deployed: the first one ensures the maximum power extraction from the PV and the second one maintains constant dc bus voltage and manages bidirectional power flow. MATLAB Simulink and hardware prototype of the proposed system has been realized for a 72 V dc bus and a 500 W electric vehicular drive. The simulation and experimental results reveal that the proposed system is viable for medium power electric shuttle applications. The proposed system is subjected to various test cases and it is observed that the source and load intermittencies are catered very well by the proposed three port Zeta-KY converter. The developed multiport converter is feasible for renewable energy applications.

1. Introduction

Power generation through distributed sources like photovoltaic, wind energy conversion systems, fuel cells are fast emerging. These alternative energy sources can be part of a distributed power generation (DPG) system. The major challenge that DPG faces is the non-continuous power output due to the intermittent behavior of the renewable sources. For example, the PV system power output changes with respect to solar irradiation level and temperature profile throughout the day. Likewise, the wind energy conversion system (WECS) output changes with respect to the wind velocity. To maximize the available power at output, the power converter control unit embodies a specialized algorithm called maximum power point tracker (MPPT). Its use in a micro grid or nano grid adds complexity to the energy conversion process by requiring dedicated individual control circuit in each renewable energy source. Moreover, the MPPTs are only mandated for operating the PV system to its peak power and as such voltage regulation at the output is not possible. Therefore, the research on proposing multiport converters with optimal switching topology and control algorithm has attracted significant attention in the research forum.

Voltage multiplier cells and coupled inductors were employed in renewable energy systems with isolated structure [1]. Again, an isolated structure with impedance source dc-dc converter was proposed with a greater number of passive components [2]. However, the converter was bulky with isolation transformer and had a higher number of capacitors in the input side. A converter was designed in [3] by Onar et al. for power management of battery and ultra-capacitor energy storage system was integrated although this could not be used for longer period. The discharge rate was larger than the usual batteries. With these drawbacks of the ultra-capacitors they are not mostly preferable. A high frequency dual bridge series resonant dc-dc converter was designed by Xiaodong Li et al. [4] in which an isolated section was provided for conversion process. These converters stated in [1,2,3,4] had drawbacks such as possession of dc link ultra-capacitors and integrated magnetic structures which adds up to the complexity in control schemes. Later on, the dc converters were designed to be sourced from multiple renewable energy sources called as multi input multiple converters. These drawbacks of isolation transformers were eliminated in other studies [5,6] and efficient power conversion is obtained but with a greater number of conversion topologies. An isolated three level dc power conversion was proposed by Dusmez et al. [7] that was cost effective, but the number of components used was more and had different levels of power conversion. In addition, in [8,9], the cascaded H bridge structures were proposed for multiple energy sources, but the power conversion process involved multiple dc links in their converters and increased the overall volume of the dc converter. In other proposed research works [1,2,3,4,5,6,7,8,9], multiple energy sources were fed to dc-dc converters either to feed dc or ac loads as shown in Figure 1a.

The dc-dc converters were developed from the basic buck, boost or buck boost converters that employed dc link voltages and isolation transformers. The converters employed multiple converters for multiple energy sources. Few converters from the above cited research works also employed a greater number of components and complex control topologies for the power conversion. For eliminating these drawbacks that incurred in multi input multiple converters, the dc-dc converters named multiport converters (MPC) emerged into the scenario of dc power conversion. These multiport converters employed a single converter with multiple inputs and multiple outputs depending on the sources and load. These types of converters are in devoid of dc links and the number of components employed in the converter is also lesser compared to the multi input multiple converters. MPCs employed buck, boost, buck-boost converters and recently Sepic, Zeta, and Cuk and KY converters were utilized.

Khaligh et al. proposed [10] a multi input bidirectional boost multiport converter for power harvesting by a three-port system. Multiport dc-dc converters (shown in Figure 1b) were designed for renewable energy systems [11,12,13] to demonstrate high performance gain, but had separate controllers. A single multiport converter with different controllers would make the circuitry more complex. Hence, a common controller was configured in [14,15] for special dc-dc converters such as Cuk, Zeta and Sepic. A Sepic and a Zeta converter were integrated with a boost converter supplied from renewable input source as discussed in [16,17], respectively. A new multiport topology was designed by Falcones et al. [18] wherein a quad active converter bridge was implemented with a solid-state transformer (SST), but again this circuit employed a greater number of active devices. Other research works proposed in the literatures [19,20,21,22] also evaluated the performance of Cuk, Sepic and Zeta converters when used in multiport converters. A boost and a Zeta converter were integrated for multiple sources to develop a multiport converter [23]. This circuit was analyzed and compared with the basic multiport converters and the Zeta converter showed better voltage gain and low output voltage ripples. Fei Wang et al. [24] proposed a Zeta converter that was fed from a PV source to feed a four-phase switched reluctance motor. This MPC was developed based on series of voltage balance techniques. This circuit proved to show unequal voltages which may not be suitable for variable loads. In the other multiport converter, which combined a Zeta and a Landsman converter [25], the efficiency was higher, but the circuit had varied control circuits. The Zeta converters integrated in [26,27] as multiport were isolated using transformers to obtain a high voltage gain for the distributed power generation. In making the best use of the features of the Zeta converter, a suitable dc converter should be combined with it, in order to configure a multiport structure.

Hence, in search of finding a dc converter that is compatible with the Zeta converter, the KY converter features high voltage gain, good load transient response and low output voltage ripples. The literature study inferred that Hwu and Yau [28] proposed the KY converter, analyzed and derived few other configurations for further analysis [29]. Later on, the KY converter was modified in [30,31], to improve the voltage gain but the coupled inductors caused the circuit bulky and lead to noise disturbances in the converter. KY converter was made to operate a boost converter by integrating it with a buck converter [32] and could be applied only for synchronously rectified buck converter. This issue was overcome by integrating KY with an efficient buck boost converter [33] that could be applied for industrial purposes. Ying Zhang et al. [34] integrated a high-performance KY converter to appreciate the transient response of the converter. In all the converters proposed in other works [30,31,32,33,34], either the converter was isolated using transformers or use of coupled inductors to improve its performance. The drawback of using coupled inductors in KY converter was that it would lead to leakage inductance losses and thereby reducing the efficiency of the converter. Therefore, the coupled inductors might be neglected in the KY converters. The designing topologies of the Zeta converter with renewable energy sources were further discussed in the literature [35,36,37,38].

From the published research work based on the multiport converters using buck, boost, buck-boost, Sepic, Zeta, Cuk and KY converters, it is clear that the Cuk converter gives lesser output voltage ripples, but the output is inverted. The Sepic converter provides a discontinuous output current. The Zeta and KY converters showed higher voltage gain with a continuous output current with lesser ripples in their output voltage. The KY converters possess faster transient responses. The multiport converters are designed based on the characteristics of individual converters employed. However, some converters lose their individual characteristics when integrated and may not satisfy the design need. Hence, Zeta and KY converters were suitably selected and integrated to combine maximum number of features for greater efficiency. Though many multiport converters are reported in literature, the integration of Zeta and KY has not been implemented so far. Based on the advantages of the Zeta and KY converters inferred, they are best suited for integrating into a multiport converter to achieve high voltage gain with lesser output voltage ripples. Hence, a triple port Zeta-KY converter has been proposed in this paper for renewable energy applications.

2. Proposed Non-Isolated Zeta-KY Converter

2.1. Structure of Zeta-KY Converter

The proposed triple-port non-isolated Zeta KY converter is an integrated structure of a Zeta and a KY converter. The block diagram is shown in Figure 2. The circuit is fed with two inputs, one for the Zeta structure and other for the KY structure.

The common elements of the conventional Zeta and KY converters are grouped to form a single output. The proposed converter with a novel structure has not been explored earlier. Thus, a dual input single output (DISO) structure has been designed for eliminating the use of isolation transformers. Since the Zeta and KY converters were integrated, the proposed triple port converter features the characteristics of both the structures. This proposed converter provides less output ripple voltage with high voltage gain and improved load transient response. The presented converter comprises three MOSFET switches S₁, S₂ and S₃, three diodes D₁, D₂ and D_3, three inductors L₁, L₂ and L₃ and three capacitors C₁, C₂ and C₃. L₁ and L₂ are individual coupled inductors and L₃ is a filter inductor. The converter is designed to be operated in continuous conduction mode.

It is necessary to measure voltages or currents when feedback controllers are employed. In this proposed work, the actual output voltage of the controller was taken from the output, compared with a reference voltage and an error voltage signal was generated. This error signal was then fed to the controller.

Some assumptions are considered for the performance of steady state analysis: (1) The semiconductor devices are considered as ideal. (2) The parasitic parameters are neglected. (3) The voltage across the capacitors is assumed to be constant. For the purpose of analysis in steady state, the semiconductor devices were considered as ideal. An ideal switch has zero resistance and zero voltage drop in ON state and infinite resistance and zero current in OFF state. Hence, the power loss should be zero in both ON and OFF states even though practically it is not the case.

2.2. Modes of Operation of the Zeta-KY Converter

The Zeta-KY converter can be operated in unidirectional and bidirectional topologies. When both sources are from renewable energy sources or from regulated voltage sources, the converter operates in unidirectional topology. The power flow is from source to the load. When one source is renewable and other source is a battery storage system, the converter operates in bidirectional topology. The power may flow from the load to the source in order to charge the battery.

2.2.1. Topology 1: Unidirectional Converter

In this topology, both input sources were realized as dc voltage sources and the circuit were operated in different modes. Here, the power flow was from source to load. The duty cycles were fed appropriately to the switches so as to meet the load demand. The circuit diagram of the triple port Zeta-KY converter is shown in Figure 3. The conventional Zeta and KY converters are ported together and a modified triple port Zeta-KY dc-dc converter has been designed and developed. The parallel input parallel output (PIPO) architecture of multi porting was adopted. A multiport converter is basically designed by either connecting two or more converters in series or in parallel. It depends on the number of inputs and the number of loads connected to the multiport converter. In the proposed topology, two converters namely Zeta and KY converters were integrated in parallel, and the common elements were shared by both converters. By doing so, an inductor and a capacitor were eliminated from the basic configuration, hence reducing the size of the multiport converter.

The violet arrow referred to the feedback signal taken from the output voltage of the multiport converter and compared with a reference voltage set in the controller. This was a measure of voltage for unidirectional topology.

The operation of the converter is implicit through key waveforms for Topology 1 as shown in Figure 4. The variations of voltage and current through components in the MPC under different operating modes are depicted. The converter was operated in a continuous conduction mode (CCM). The inductors L₁ and L₂, capacitor C₁ along with the switch S₁ belonged to the Zeta part of the circuit. The switches S₂ and S₃, capacitor C₂ and diodes D₂ and D₃ belonged to the KY part of the circuit. The diodes D₂ and D₃ were provided to avoid reversal of current towards the source V₂. The diode D₁ was provided for the purpose of freewheeling. The inductor L₀ and capacitor C₀ were filtering elements common for both the Zeta and KY converters. Both converters shared a common load. The operation of the converter has been explained through different modes.

(i)

Mode 1 (S₁ is ON and S₂, S₃ are OFF): In this mode, the switch S₁ is turned on and switches S₂ and S₃ were turned off. Both the sources V₁ and V₂ were supplying the multiport converter. The inductors L₁ and L₂ were charged to the value of input voltage V₁. The current through L₁ increased linearly to a value V₁/L₁. The capacitor C₁ was charged equal to V_o, which was the output voltage of the converter. Diode D₁ was reverse biased and diodes D₂ and D₃ were forward biased.

The converter was analyzed in a steady state condition and the corresponding equations have been obtained.

$${\mathrm{V}}_{\mathrm{L}2}={\mathrm{V}}_2-{ \mathrm{V}}_{\mathrm{LO}}+{\mathrm{V}}_{\mathrm{C}1}+{ \mathrm{V}}_{\mathrm{L}1}$$

(1)

$${ \mathrm{V}}_{\mathrm{LO}}={\mathrm{V}}_2-{ \mathrm{V}}_{\mathrm{CO}}$$

(2)

$${\mathrm{i}}_{\mathrm{L}1}={\mathrm{i}}_1-{\mathrm{i}}_{\mathrm{Ci}}$$

(3)

(ii)

Mode 2 (S₂ is ON and S₁, S₃ are OFF): In Mode 2, the switch S₂ was turned on and switches S₁ and S₃ were turned off. V₁ was therefore not supplying the circuit. The source V₂ supplied the load through D₂ and D₃. The inductor L₁ discharged its magnetic energy and reduced the voltage across it. The positive voltage of V₂ turned on switch S₂ and the input current flowed through S₂, capacitor C₂ and to load through L₀. Capacitor C₂ discharged. In addition, L₂ then discharged to a value equal to the output voltage.

$${\mathrm{V}}_{\mathrm{L}2}={\mathrm{V}}_2-{ \mathrm{V}}_{ \mathrm{C}2}-{ \mathrm{V}}_{\mathrm{LO}}+{\mathrm{V}}_{\mathrm{C}1}+{ \mathrm{V}}_{\mathrm{L}1}$$

(4)

$${\mathrm{V}}_{\mathrm{LO}}=-{\mathrm{V}}_2-{ \mathrm{V}}_{\mathrm{CO}}-{\mathrm{V}}_{\mathrm{C}2}$$

(5)

$${\mathrm{i}}_{\mathrm{LO}}={\mathrm{i}}_{\mathrm{L}2}+{ \mathrm{i}}_{\mathrm{CO} }+{\mathrm{i}}_{\mathrm{O} }$$

(6)

(iii)

Mode 3 (S₃ is ON and S₁, S₂ are OFF): The switches S₁ and S₂ were turned off in this mode. Switch S₃ was turned on. C₂ started charging and the voltage across it was equal to V₂. The source V₂ supplied the load through C₂ and L_O.

$${ \mathrm{V}}_{\mathrm{L}2}={\mathrm{V}}_2-{ \mathrm{V}}_{\mathrm{LO}}+{\mathrm{V}}_{\mathrm{C}1}+{ \mathrm{V}}_{\mathrm{L}1}$$

(7)

$${\mathrm{V}}_{\mathrm{LO}}={\mathrm{V}}_{\mathrm{C}2}-{ \mathrm{V}}_{\mathrm{CO}}$$

(8)

$${\mathrm{i}}_{\mathrm{C}2}={\mathrm{i}}_2-{ \mathrm{i}}_{\mathrm{LO}}$$

(9)

The circuit diagrams under different operating modes in unidirectional topology configurations are shown in Figure 5.

(iv)

Mode 4 (S₁, S₂, S₃ are OFF): This is the mode in which all the switches were open. The current i₂ flowed through the inductor L₀. The diode D₁ freewheels through the inductor L₂ when there is no source voltage. The energy stored in the inductors dissipated when all switches are turned off. Thus, in turn diode D₁ was forward biases_.

$${\mathrm{V}}_{\mathrm{L}2}={\mathrm{V}}_2-{ \mathrm{V}}_{\mathrm{LO}}+{\mathrm{V}}_{\mathrm{C}1}+{ \mathrm{V}}_{\mathrm{L}1}$$

(10)

$${\mathrm{V}}_{\mathrm{LO}}={\mathrm{V}}_2-{\mathrm{V}}_{\mathrm{CO}}$$

(11)

$${\mathrm{i}}_2={\mathrm{i}}_{\mathrm{LO}}$$

(12)

2.2.2. Topology 2: Bidirectional Mode

Renewable energy applications have now become very vital in the field of energy generation. Of the whole of the renewable energy sources, solar energy is the most readily and easily available source for utilization. Hence, to effectively make use of the solar energy, the proposed multiport converter has been integrated with PV module. This triple port dc-dc converter was operated with one source as PV and other source as battery. Since the battery was used, a bidirectional power flow was possible in this topology.

The circuit was constructed in such a way that a renewable source such as PV fed the load through the Zeta converter. The other source was a battery that connected the load through the KY converter. Both the sources shared a common load, thus acting as a dual input single ended output (DISO) converter. The PV output voltage depended on the irradiance of the solar energy. The maximum power point tracking (MPPT) algorithm was implemented in the controller connected to the PV panel. The MPPT—fractional open circuit voltage was the principle of tracking maximum available power from the PV module, by operating with the maximum efficient voltage. The MPPT algorithm was applied to the circuit based on the design specifications of the PV. The circuit diagram for the bidirectional topology is shown in Figure 6. The violet arrow was again the measure of the output voltage which was fed back to the controller for bidirectional topology.

The diodes D₂ and D₃ connected in the circuit of Topology 1 (unidirectional) were eliminated in the circuit of Topology 2 (bidirectional). This was implemented to provide a bidirectional power flow i.e., the power flow from the battery source to the load and from the load to the battery for charging the battery. The bidirectional power flow was implemented in this topology to charge the battery through the KY converter itself. Switch S₄ was connected in such a way that it was suitably turned on to allow power flow from the load to the source. CCM of operation was also performed in this topology. The operation of the MPC is explained in Figure 7 through variations in the power of PV panel (P_PV), battery (P_battery) and load (P_LOAD).

(i)

Case 1—presence of high irradiation (P_PV > P_LOAD)_: The PV panel fed the load through the Zeta converter. Switch S₁ was turned on. In this case, the converter operated as single input single output (SISO) converter. The excess power that was not consumed by the load was utilized for charging the battery through turning on switch S₄ from the load bus. The converter acts in bidirectional mode as shown in Figure 7a. Hence, energy conservation is carried out in this case.

(ii)

Case 2—presence of moderate irradiation (P_PV < P_LOAD): When the PV was not able to completely meet the load demand, the battery energy storage system supported it through the KY converter. Now, switches S₁, S₂, S₃ were turned on sequentially. In this case, the converter operated as dual input single output (DISO) converter as shown in Figure 7b.

(iii)

Case 3—absence of irradiation (P_PV = 0): The battery fed the load through the KY converter. Switches S₂ and S₃ were turned on as in Figure 7c and the converter operated as single input, single output (SISO) converter.

Figure 7. (a) Case 1: P_PV > P_LOAD; (b) Case 2: P_PV < P_LOAD; (c) Case 3: P_PV = 0 (when there is no irradiation).

Figure 7. (a) Case 1: P_PV > P_LOAD; (b) Case 2: P_PV < P_LOAD; (c) Case 3: P_PV = 0 (when there is no irradiation).

Therefore, the converter fed with PV and Battery as the input sources, acted in both unidirectional and bidirectional modes and the feature of the proposed modified triple port converter was that the converter might be operated in SISO and DISO modes according to the load demand by making the optimum use of power. Energy management was carried out well in the proposed multiport converter. The attributes of the novel combination of Zeta and KY converter has been explicitly brought out well.

The PV panel output varies in accordance with irradiance. The MPPT control algorithm (Appendix A.4) is implemented in the MPC to maintain a constant output voltage from maximum power point tracking. PI Controller is used to control the switches in the multiport converter. The MOSFET switches S₁, S₂, S₃ and S₄ are operated with a switching frequency of 25 kHz. The actual output voltage of the converter is fed to the controller and is actuated in the PI controller. Thus, a closed loop controller is implemented in the converter. The operating mode of the converter is decided according to the load. The transfer function of the converter plant is determined for PV mode and battery mode.

The proposed multiport converter has two input sources, V1 (PV) and V2 (battery). When S1 is open, the first input source V1 will not be able to feed the load. However, the second source V2 will be supplying the load. By suitably turning on the switches S2, S3 and S4, it is possible to feed the load power continuously, even if S1 is off. This is the advantage of the proposed topology in which if one of the sources is not supplying the load, the other source will supply the load.

3. Analysis and Design of the Proposed Zeta-Ky Converter

The proposed DISO converter has been analyzed to obtain the design values of the components used in the MPC. From the steady state equations obtained from different operating modes of the converter, several current and voltage equations have been acquired.

3.1. Output Voltage of the MPC

The output voltage equation is derived by applying volt-sec balance on the inductance L₂ used in the multiport converter. Combining Equations (1), (4), (7), and (10), the average voltage across the inductor ${\mathrm{L}}_2$ is:

$$\begin{array}{c}\Delta {\mathrm{V}}_{\mathrm{L}2}=\left({\mathrm{V}}_2-{\mathrm{V}}_{\mathrm{L}0}+{\mathrm{V}}_{\mathrm{C}1}+{\mathrm{V}}_{\mathrm{L}1}\right){\mathsf{\delta }}_1+\left({\mathrm{V}}_2-{\mathrm{V}}_{\mathrm{C}2}-{\mathrm{V}}_{\mathrm{L}0}+{\mathrm{V}}_{\mathrm{C}1}+{\mathrm{V}}_{\mathrm{L}1}\right){\mathsf{\delta }}_2+\left({\mathrm{V}}_2-{\mathrm{V}}_{\mathrm{L}0}+{\mathrm{V}}_{\mathrm{C}1}+{\mathrm{V}}_{\mathrm{L}1}\right){\mathsf{\delta }}_3\\ \hspace{1em}\hspace{1em}\hspace{1em} +\left({\mathrm{V}}_2-{\mathrm{V}}_{\mathrm{L}0}+{\mathrm{V}}_{\mathrm{C}1}+{\mathrm{V}}_{\mathrm{L}1}\right)\left(1-{\mathsf{\delta }}_1-{\mathsf{\delta }}_2-{\mathsf{\delta }}_3\right)=0\hfill \end{array}$$

(13)

where ${\mathsf{\delta }}_1,{\mathsf{\delta }}_2,{\mathsf{\delta }}_3$ are duty cycles for switches ${\mathrm{S}}_1,{ \mathrm{S}}_2{ \mathrm{and} \mathrm{S}}_3.$ V₁ and V₂ are the input voltage sources. V_C1 and V_C2 are the voltages at C₁ and C_2, respectively.V_L1, V_L2 and V_LO are the voltages across inductors L₁, L₂ and L_O, respectively.

Solving the above equations, the output voltage of the three-port converter is given by:

$${\mathrm{V}}_{\mathrm{o}}=\frac{{\mathrm{V}}_1{\mathsf{\delta }}_1+{ \mathrm{V}}_2(2{\mathsf{\delta }}_2+{\mathsf{\delta }}_3)}{{\mathsf{\delta }}_3}$$

(14)

3.2. Power Devices Voltage

The voltage at switches and diodes are obtained by applying Kirchhoff’s voltage law, (KVL) to the multiport converter when operated at different modes.

$${\mathrm{V}}_{\mathrm{S}1}={\mathrm{V}}_1-{\mathrm{V}}_0={\mathrm{V}}_1\left[1-\frac{{\mathsf{\delta }}_1}{{\mathsf{\delta }}_3}\right]-{\mathrm{V}}_2\left[1-\frac{2{\mathsf{\delta }}_2}{{\mathsf{\delta }}_3}\right]$$

(15)

$${\mathrm{V}}_{\mathrm{S}2}={\mathrm{V}}_{\mathrm{S}3}={\mathrm{V}}_{\mathrm{C}2}-{\mathrm{V}}_2=\frac{{\mathrm{V}}_0\left(2{\mathsf{\delta }}_1+2{\mathsf{\delta }}_3-1\right)+{\mathrm{V}}_2\left(1-2{\mathsf{\delta }}_1-{\mathsf{\delta }}_3+{\mathsf{\delta }}_2\right)}{{\mathsf{\delta }}_3-{\mathsf{\delta }}_2}$$

(16)

where ${\mathrm{V}}_{\mathrm{S}1},{\mathrm{V}}_{\mathrm{S}2}{ \mathrm{and} \mathrm{V}}_{\mathrm{S}3}$ are the voltage stress across the MOSFET switches ${\mathrm{S}}_1,{ \mathrm{S}}_2{ \mathrm{and} \mathrm{S}}_3$, respectively. Voltage stress across the diodes ${\mathrm{D}}_1,{\mathrm{D}}_2,{\mathrm{D}}_3$ are given by ${\mathrm{V}}_{\mathrm{D}1},{\mathrm{V}}_{\mathrm{D}2}{ \mathrm{and} \mathrm{V}}_{\mathrm{D}3}$ respectively:

$${\mathrm{V}}_{\mathrm{D}1}={\mathrm{V}}_0+{\mathrm{V}}_1=\frac{{\mathrm{V}}_1\left({\mathsf{\delta }}_1+{\mathsf{\delta }}_3\right)+{\mathrm{V}}_2\left(2{\mathsf{\delta }}_2+{\mathsf{\delta }}_3\right)}{{\mathsf{\delta }}_3}$$

(17)

$${\mathrm{V}}_{\mathrm{D}2}={\mathrm{V}}_{\mathrm{D}3}={\mathrm{V}}_2-{\mathrm{V}}_{\mathrm{C}2}=\frac{{\mathrm{V}}_2\left({\mathsf{\delta }}_3-{\mathsf{\delta }}_2+2{\mathsf{\delta }}_1-1\right)+{\mathrm{V}}_0\left(2{\mathsf{\delta }}_1+2{\mathsf{\delta }}_3-1\right)}{{\mathsf{\delta }}_3-{\mathsf{\delta }}_2}$$

(18)

3.3. Inductor Currents

Applying the charge-sec balance technique, the current through the inductors is expressed as:

$${\mathrm{i}}_{\mathrm{L}1}=-\frac{{\mathrm{i}}_1{\mathsf{\delta }}_1}{1-2{\mathsf{\delta }}_1}$$

(19)

$${\mathrm{i}}_{\mathrm{L}2}={\mathrm{i}}_{\mathrm{LO}}+\frac{{\mathrm{i}}_0}{2{\mathsf{\delta }}_{1 }-1 }$$

(20)

$${\mathrm{i}}_{\mathrm{L}0}={\mathrm{i}}_{\mathrm{L}2}-\frac{{\mathrm{i}}_{\mathrm{o}}}{2{\mathsf{\delta }}_1-1}$$

(21)

where ${\mathrm{i}}_{\mathrm{L}1},{\mathrm{i}}_{\mathrm{L}2}{ \mathrm{and} \mathrm{i}}_{\mathrm{L}0}$ are the currents through the inductor ${\mathrm{L}}_1,{ \mathrm{L}}_2{ \mathrm{and} \mathrm{L}}_0$, respectively.

3.4. Voltage and Current Ripples

By employing small ripple approximation techniques, the values of inductors and capacitors have been calculated. Voltage ripple are given by $\Delta {\mathrm{V}}_{\mathrm{C}}$ and current ripples by $\Delta {\mathrm{i}}_{\mathrm{L}}$.

$$\Delta {\mathrm{V}}_{\mathrm{C}1}=\frac{-{\mathrm{i}}_1{ \mathsf{\delta }}_1^2}{2{\mathrm{f}}_{\mathrm{s}}\left(1-2{\mathsf{\delta }}_1\right){ \mathrm{C}}_1}$$

(22)

$$\Delta {\mathrm{V}}_{\mathrm{C}2}=\frac{{\mathrm{i}}_2{ \mathsf{\delta }}_2}{2{\mathrm{f}}_{\mathrm{s}}{ \mathrm{C}}_2}$$

(23)

$$\Delta {\mathrm{V}}_{\mathrm{C}0}=\frac{{\mathrm{i}}_0{ \mathsf{\delta }}_1}{2{\mathrm{f}}_{\mathrm{s}}{ \mathrm{C}}_0}\left[\frac{1}{2{\mathsf{\delta }}_1-1}-1\right]$$

(24)

$$\Delta {\mathrm{i}}_{\mathrm{L}1}=\frac{{\mathrm{V}}_1{ \mathsf{\delta }}_1}{2{\mathrm{f}}_{\mathrm{s}}{ \mathrm{L}}_1}$$

(25)

$$\Delta {\mathrm{i}}_{\mathrm{L}2}=\frac{\left({\mathrm{V}}_2-{ \mathrm{V}}_0\right){\mathsf{\delta }}_2}{2{\mathrm{f}}_{\mathrm{s}}{ \mathrm{L}}_2}$$

(26)

$$\Delta {\mathrm{i}}_{\mathrm{L}0}=\frac{\left({\mathrm{V}}_0-{ \mathrm{V}}_2\right){\mathsf{\delta }}_2}{2{\mathrm{f}}_{\mathrm{s}}{ \mathrm{L}}_0}$$

(27)

3.5. Passive Components Selection

Size calculation for ${\mathrm{L}}_1,{ \mathrm{L}}_2{ \mathrm{and} \mathrm{L}}_0$ is given by:

$${ \mathrm{L}}_1=\frac{{\mathrm{V}}_1{\mathsf{\delta }}_1}{2{\mathrm{f}}_{\mathrm{S}}\Delta {\mathrm{i}}_{\mathrm{L}1}}$$

(28)

$${ \mathrm{L}}_2=\frac{({\mathrm{V}}_2-{\mathrm{V}}_0){\mathsf{\delta }}_2}{2{\mathrm{f}}_{\mathrm{S}}\Delta {\mathrm{i}}_{\mathrm{L}2}}$$

(29)

$${\mathrm{L}}_0=\frac{({\mathrm{V}}_0-{\mathrm{V}}_2){\mathsf{\delta }}_2}{2{\mathrm{f}}_{\mathrm{S}}\Delta {\mathrm{i}}_{\mathrm{L}0}}$$

(30)

where $\Delta { \mathrm{i}}_{\mathrm{L}1 }, \Delta { \mathrm{i}}_{\mathrm{L}2}, \Delta { \mathrm{i}}_{\mathrm{L}0 }$ denote the ripple current for inductors ${\mathrm{L}}_1,{ \mathrm{L}}_2{ \mathrm{and} \mathrm{L}}_0$ and f_s is the switching frequency of the proposed converter. To calculate inductors size, $\Delta {\mathrm{i}}_{\mathrm{Lx}}$ is generally assumed to be in the range of 10% to 20% of full load. Similarly, the capacitors size is chosen according to the maximum ripple voltage allowed at the capacitors. Size calculation for each capacitor is expressed as:

$${\mathrm{C}}_1=\frac{-{\mathrm{i}}_1{\mathsf{\delta }}_1^2}{2{\mathrm{f}}_{\mathrm{s}}\left(1-2{\mathsf{\delta }}_1\right)\Delta {\mathrm{V}}_{\mathrm{C}1}}$$

(31)

$${\mathrm{C}}_2=\frac{{\mathrm{i}}_2{ \mathsf{\delta }}_2}{2{\mathrm{f}}_{\mathrm{s}} \Delta {\mathrm{V}}_{\mathrm{C}2}}$$

(32)

$${\mathrm{C}}_0=\frac{{\mathrm{i}}_0{ \mathsf{\delta }}_1}{2{\mathrm{f}}_{\mathrm{s}}\Delta {\mathrm{V}}_{\mathrm{C}0}}\left[\frac{1}{2{\mathsf{\delta }}_1-1}-1\right]$$

(33)

where $\Delta { \mathrm{V}}_{\mathrm{C}1 }, \Delta {\mathrm{V}}_{\mathrm{C}2}, \Delta { \mathrm{V}}_{\mathrm{C}0 }$ represent the ripple voltage at the capacitor C₁, C₂ and C₃ and i₁, i₂ and i₀ denote the currents related with the PV power source, energy storage battery and load consumption, respectively. The calculated values for inductors L₁, L₂ and L_O are 0.62836 mH, 0.72361 mH and 0.517122 mH, respectively. The calculated values of capacitors C₁, C₂ and C_O are 0.12860 mF, 0.381944 mF and 0.10706 mF, respectively.

The transfer functions of the modified triple port converter have been obtained for PV and battery modes.

The transfer function of the converter during PV mode is shown as below:

$$\frac{{\mathrm{V}}_{\mathrm{o}}\left(\mathrm{S}\right)}{{\mathrm{V}}_{\mathrm{in}}\left(\mathrm{s}\right)}=\frac{4\times {10}^6\left(8^2+{10}^4\right)}{\left({\mathrm{S}}^2+20.1\mathrm{s}+1.208\times {10}^3\right)\left({\mathrm{S}}^2+29.9\mathrm{s}+8.279\times {10}^3\right)}$$

The transfer function of the converter during battery mode is as below.

$$\frac{{\mathrm{V}}_{\mathrm{o}}\left(\mathrm{S}\right)}{{\mathrm{V}}_{\mathrm{in}}\left(\mathrm{s}\right)}=\frac{6.5\times {10}^6}{\left({\mathrm{S}}^2+50\mathrm{s}+5\times {10}^6\right)}$$

The circuit was analyzed, and the parametric values were determined for the proposed modified triple port the Zeta-KY converter.

Table 1. Design specifications for the proposed MPC.

Design Specification	Values	Design Specification	Values
PV Voltage, Vmp	36 V	Duty Cycle	0.67
PV Current, Imp	7.64 A	Inductor Ripple Current	0.76 A
PV, Voc	43.20 V	Minimum Inductor, L1	0.63 mH
PV, Isc	9.17 A	Minimum Inductor, L2	0.72 mH
PV Power (Max)	275 W	Ipeak of Filter Inductor	7.71 A
Battery Voltage	40 V	Output Ripple Voltage	0.07 V
Battery Capacity	550.50 Ah	Output Capacitor, Co	0.11 mF
Output Voltage	72 V	Input Ripple Voltage	0.72 V
Output Current	6.94 A	Input C1 Capacitor, C1	0.13 mF
Output Power	500 W	Ripple Voltage of C1	0.36 V
		Output inductor, Lo	0.52 mH
Switching Frequency	25 kHz	C2 capacitor	0.38 mF

shows the design specifications for the PV and battery sources. The ratings of the components’ input and output voltage ripples were calculated.

4. Results and Discussions

4.1. Simulation Results

The converter was simulated in MATLAB platform using the parameters set depicted in Table 1. The converter is operated in open loop control. The actual output voltages of the MPC are compared with the estimated output voltage.

Table 2. Comparison table for the output voltage with varied duty cycles in unidirectional mode.

SL. NO	V1 = V2 (V)	D1 (%)	D2 (%)	D3 (%)	VOUT (Est) (V)	VOUT (Act) (V)
1	24	25	25	40	69	68.0
2	24	50	10	30	80	79.2
3	24	40	10	40	60	59.0
4	24	30	26	40	66	65.1
5	24	35	15	40	63	62.6

depicts a comparison between the estimated and output voltages obtained by varying duty cycles and constant input voltages.

The source voltages V₁ and V₂ were varied and the output voltage was estimated by maintaining constant duty cycles for the switches. These estimated output voltages were compared with the actual output voltages as shown in

Table 3. Comparison table for the output voltage with fixed duty cycles in unidirectional mode.

SL. NO	D1 = 25% D2 = 25% D3 = 40%		VOUT (Est) (V)	VOUT (Act) (V)
	V1 (V)	V2 (V)
1	6	6	17.25	16.2
2	24	12	42.0	41.3
3	12	24	61.5	61.0
4	24	24	69.0	68.5
5	24	20	60.0	59.1
6	20	24	66.5	65.6
7	12	12	34.5	33.8

. In both tables, the actual voltages obtained from simulation were approximately closer to the estimated output voltages. Thus, the operation of the unidirectional modified triple port Zeta-KY MPC was elucidated, and the calculated and actual output voltages are compared.

Figure 8 shows the gate pulses generated from the controller to turn-on the MOSFET switches S₁, S₂, S₃ and S₄. The pulses are generated by the controller that is continuously tracking the output voltage, comparing it with the reference voltage and thereby generate pulses according to the operating mode. The proportional gain for the PI controller, K_P = 100 and integral gain, K_I = 0.1 have been considered. These values have been obtained by tuning the PI controller in MATLAB.

The PV fed the converter when there is solar irradiance. Applying MPPT controller to the PV panel, 40 V output voltage is constantly maintained, which fed the load through the Zeta converter. This was facilitated by triggering switch S₁. Figure 9 shows the output voltage and current fed from the PV at a constant irradiance. At a particular irradiance, the output current of PV will be constant only. This current will change only when the irradiance will change.

The battery was charged during bidirectional mode through the switch S₄. Figure 10 shows battery state of charge (SOC), with a battery voltage of 45 V and a current of −2 A in bidirectional mode. It should be noted that since the SOC of battery changes, the battery current falls immediately and again increases within a very shorter time.

When the PV source is connected to the Zeta part of the MPC with a load connected to the output, the inductor L₁ is initially charged to a value equal to the input voltage of the PV with 40 V. Later it discharged to −40 V. With the MPC working in continuous conduction mode, the current through the inductor L₁ is continuous as shown in Figure 11.

Figure 12 shows the simulated waveforms of the voltage and current through other inductors L₂, L₀ and C_2. The CCM mode was demonstrated from the waveform shown by the current through the inductor L₀.

For the specified design of the proposed converter, the output voltage and current waveforms obtained through the simulation are shown in Figure 13. A constant output voltage of 70 V was obtained across the 20 Ω resistive load.

4.2. Experimental Results

The simulation results were verified through a real time hardware set up of the converter. The MPPT algorithm (Appendix A.4) was implemented for maintaining constant voltage by tracking maximum power from the PV. The components used in the hardware set up and their calculated individual losses have been listed in

Table 4. Calculation of efficiency of the converter through different losses.

SL. NO	Parameters	Values
1	IRF250-MOSFET Losses (Zeta)	5.47W
2	TST20L200CW Diode Losses	2.92 W
3	PT500R-2000 Inductor Losses	3.53 W
4	IRF250-MOSFET Losses (KY)	5.98 W
5	Overall Losses in the MPC due to MOSFETs, Diodes and Inductors	32.30 W
6	Output Power of Converter	500 W
7	Calculated Efficiency	93.54%

.

The pulses were generated with a Dspace1103 controller with the hardware converter. Figure 14 depicts the real time hardware set up of the proposed triple-port Zeta-KY converter. A load resistor of 50 Ω was connected and the output was verified for different loads.

The dSPACE controller generated pulses to trigger switches S₁, S_2, S_3, S_4. The generated pulses from the controller were observed through the digital storage oscilloscope (DSO). The pulses generated for all MOSFETs shown in Figure 15 are similar to the simulated waveforms of the converter.

The switches were operated at a switching frequency of 25 kHz. The voltage across the inductors L₁ and L₂ are shown in Figure 16a,b, in which the plot is obtained for a scale of 25 V/div. The inductor L₁ charged and discharged to its input voltage from the PV source of 40 V. The voltage across the capacitor C₁ initially charged to a value equal to the input voltage and discharged to maintain a constant output voltage, thus maintaining at −70 V as shown in Figure 16c. Figure 16d shows that capacitor C₂ charged to a voltage equal to the battery voltage of 40 V, since C₂ was connected to the KY part of the MPC in which battery acted as the input source.

The output voltage of the proposed converter was maintained with a constant output voltage of 70 V in the dc grid. The output was observed for a constant load of 20 Ω as shown in Figure 17a. This resistive load of 20 Ω was varied to 30 Ω and the output was observed as shown in Figure 17b. The output voltage was 70 V at 20 Ω load and at 30 Ω, there was a small dip in voltage and the output voltage was maintained constant again at 70 V. This demonstrated that the proposed triple-port converter maintained constant output voltage that could be fed to the dc grid for further applications. Thus, the converter is maintaining the constant output voltage irrespective of load changes. One of the characteristic features of the KY converter was demonstrated here with good load transient response.

The output load resistance was varied from 10 Ω to 50 Ω and hence variable output power was obtained. The calculated efficiency curve has been plotted with respect to output power in Figure 18. The converter showed a maximum of 94% at 500 W. The graph is plotted by varying the resistive load gradually from 10 Ω to 50 Ω in bidirectional mode. At 30 Ω resistance when the PV was delivering 286.8 W, the battery charged itself drawing 104 W power. The total input power fed into the converter was 182.8 W. At this instant, there was a small dip in the calculated efficiency at 162.77 W output power. The complete calculations of power loss and efficiency have been shown in Appendix A.1 and Appendix A.2 respectively.

4.3. Comparative Analysis

The number of components used in the converter plays a vital role in the performance and calculated efficiency of the converter. The stress and the losses encountered on each component is very imperative. Hence, the number of components employed in the proposed triple-port modified Zeta-KY converter was compared with those of the conventional multiport converters. In comparison, the proposed converter had moderately lesser number of components with converters of the same power ratings as shown in Figure 19.

Multiport converters are known for combining one or more converters to optimize the renewable power sources in an effective way. The blend of two or more converters effectively reduces the number of active and passive components thereby increasing the calculated efficiency and minimizing the losses incurred. However, the reduction in number of switches is not the direct indication for reduction in size or cost. In practical cases, reduction of a switch not only reduces appreciable losses, but also the complexity related with the commutation process, design of driver units, etc., is reduced. In this work, two renewable sources or combination of one renewable energy source with battery energy sources enhanced the reduction of a switch and a pair of inductor and capacitor. If hybrid renewable energy sources are to be fed, then ‘n’ port MPC has to be designed in which cascading of ‘n’ dc-dc converters will considerably reduce additional switches and passive elements. Hence, the proposed MPC would be efficient for the rated load feasible for hybrid electric vehicles.

Figure 20 shows a comparison plot for the efficiencies of the conventional and the proposed MPC. The power converters considered for comparison were sampled here with their maximum rated load. The load and the corresponding efficiencies are shown for various multiport converters.

From the plot, it could be inferred that at 500 W of rated power, the proposed converter produced the best calculated efficiency compared to the other reported values at different rated powers. The converter reported in [13] demonstrated efficiencies close to the current converter with similar rated power. Though the calculated efficiency reported in [11] was greater than the proposed converter here, it has the ability of supplying constant power to the load. All the input ports to the converters of [11,13] were fed from external sources. However, in the proposed modified Zeta-KY converter, one of the sources (battery) was charged by the converter itself through bidirectional charging. Furthermore, the control complexity and the inductive components used in these converters of [11,13] were larger. The calculated efficiency went down at higher duty cycles in these converters, but it was not the case in the proposed converter. The converter reported in [17] was also compared as the proposed converter when supplied with PV alone was capable of feeding 275 W load. Compared to the advantages and calculated efficiency of the converters, the proposed novel modified Zeta-KY multiport converter was more advantageous than its close competitors and best suited for the renewable energy applications.

The inductor current wave shapes demonstrated that the converter was operated in CCM. The output voltage, output current, stability and calculated efficiency of the converter shown through simulation and hardware validated that the proposed converter adhered to optimum utilization of PV with minimum losses. With variations in load the converter fed constant dc voltage to the grid, thus enabling for hybrid electric vehicle applications.

In summary, the individual advantages of Zeta and KY converters were completely utilized in the proposed converter with which maximum power was optimized from a renewable energy source such as the PV. In general, the converter proved to be stable in operation. A high calculated efficiency of 94% for the 500 W rated converter was achieved with saving of large amount of energy due to the bidirectional mode employed within the proposed system. When the battery was discharged, it was charged by the PV itself. Furthermore, a separate charging station was not required for the battery. The converter was capable of withstanding varying load transients. Though the PV was intermittent, the converter was capable of feeding constant dc output voltage to the dc grid. This was achieved by suitable controlling schemes implemented in the multiport converter. The converter construction was in devoid of isolation transformers which could be an added advantage. The converter system stability and example of calculated efficiencies at different operating modes are presented in Appendix A.3 and Appendix A.5 respectively.

5. Conclusions

The proposed three-port novel Zeta–KY dc-dc converter topology has been developed for renewable energy applications. This multiport converter has been designed with a PV source and a battery as its essential embodiments in order to make optimum use of renewable energy source, the PV. The converter has been analyzed through steady state analysis and small ripple approximation to determine the design of the components. The suggested system has been simulated in MATLAB Simulink and a real-time hardware has been developed. The validated results show the effectiveness of the Zeta-KY topology where the maximum power delivery of the PV is ensured by the Zeta part and the load bus regulation and bidirectional battery charging-discharging is ensured by the KY part. The converter is capable of feeding a constant voltage to the output dc grid irrespective of load variations. Energy management is conceived well in both unidirectional and bidirectional modes. The proposed converter has reduced the number of components and shows an improved calculated efficiency of 94% when compared to the other conventional converters. Since the Zeta-KY converter has been integrated in the MPC, the output voltage ripple is low and responds well to the load transients. The converter has been designed and developed by optimizing the best use of renewable energy sources. The converter is well suited for medium powered applications such as solar driven charge pumps, PV powered battery driven vehicles, electric vehicular drives, etc. Thus, the proposed multiport converter opens the door further to venture into renewable energy sources and to avail the energy at the fullest.