1 Introduction

Distributed generation (DG) resources due to their inherent features like feeding local loads and continuous and economical operation have been given a lot of consideration from researchers in recent years. This is very good idea for power system growing in terms of economic, climate mitigation and also power system reliability [1, 2]. For this reason, different structures together with several control algorithms within research area have been proposed so far. Hence, energy storage units such as batteries, capacitors and coils are the essential elements for renewable energy systems [3]. There are some power sources which can be used as the energy resource such as photovoltaic (PV) and superconductor magnetic energy storage system (SMES) that are considered as combined source in this paper. However some papers addressed each one for distributed generation but a hybrid source including both has been not investigated yet in which considered in this work. The SMES is an inductor that can store large amount of electric energy in the form of magnetic flux by flowing DC current through its coil without experiencing losses. SMES systems have attracted the attention of both electric utilities and the military due to their fast response and high efficiency (a charge/discharge efficiency over 95 %) [4]. The most important advantages of SMES devices include high power and energy density with outstanding conversion efficiency, unlimited number of charging and discharging cycles, much longer lifetime compared to the battery storage systems and fast and independent power response in four-quadrants [5, 6]. As a new sample work, in [7] the SMES was used as a single source for distributed generation and a new controlling method was introduced but there was not addressed a hybrid source for DG. On the other hands, photovoltaic system is another energy resource which has been addressed in some researches. As a sample in [8] a PV source system is proposed in a wide area power system and measurement control has been addressed but a hybrid energy source has been not investigated. Maximum power point tracking (MPPT) is a more important factor in the PV systems. The MPPT is based on both irradiance and temperature [9]. Moreover, similarly to SMES, some converters should be used in PV system for its connecting to power grid. Regarding to investigate to energy storage components which can be used as DG power source, a good idea for energy resource is a hybrid source for using in a DG system. Naderi in [10] showed a hybrid distributed generation system using hybrid battery/photovoltaic system. The MPPT was performed and the control of active and reactive powers was investigated according to state of charge (SoC) of battery. Furthermore, in this method there is no reactive power control and bi-level inverter is used. In [11] a hybrid source including a combustion engine and a PV system was used for energy source of a DG system and a control strategy was introduced. In [12], a control strategy influence on the efficiency of a hybrid PV-Battery-Fuel Cell system was investigated for DG system and cost management was considered for control strategy and in [13] a nonlinear control strategy for PV-Fuel cell hybrid source was introduced in which MPPT has been addressed and converter using include of DC/DC and DC/AC was investigated. In [14], another hybrid source with CHP/PV system was investigate for in-house power backup and in [15], modeling and control of hybrid wind/PV/Fuel cell DG system was introduced and relative controllers were designed. Noticing to performed researches in DG area, in addition to storage components, the power electronic converters are other essential equipment which should be considered in DG systems. However DC/DC and DC/AC converters are used in many papers but DC chopper that is a special component is more important for SMES using. This paper presents a new control method for a three-level-bi-directional chopper in a hybrid DG system. In [16], an algorithm was presented base on a new switching method but a high frequency triangular wave was used for switching and high speed switches were considered. In [17] a 4-quadrant chopper was introduced for controlling of capacitors used in a five-level inverter but the SMES coil connecting to the mentioned chopper is not possible. In an old work [18], presents a new, optimized PWM scheme and control approaches for a three-level two-quadrant chopper in a SMES power conditioning system (PCS) but, many switch were used in chopper structure. In [19] a multi-level buck-boost controller was investigated with voltage controller method but it is a voltage feed converter and is not a good choice for SMES application. The hybrid power source for distributed generation needs to optimization algorithms [20, 21] and also power source sizing [2] in which addressed in recent decade. Now in this paper a hybrid DG structure is considered by SMES-PV system and a current feed three-level-bi-directional chopper is introduced with a novel controlling method. The paper is organized in eight sections. In the Sect. 2, considered structure for distributed generation issue using SMES and PV system is presented and the photovoltaic system model with maximum power point tracking is explained in Sect. 3 with presenting of a way for its power controlling through a DC/DC converter. In the Sect. 4, the way of controlling SMES through a chopper is presented and in the Sect. 5, the applied inverter is explained. Designed harmonic filter is illustrated in Sect. 6 and a fuzzy controller for controlling of active and reactive power followed into the power grid is designed in the Sect. 7. Finally, the proposed structure is verified through simulation results.

In general, the advantageous points of this paper in comparison with other available papers could be categorized as follows:

  1. 1.

    Using of SMES/Photovoltaic hybrid system as a distributed generation resource which is offered in this paper as a novel structure.

  2. 2.

    Presenting a novel structure for controlling bi-directional-three-level chopper connected to SMES which was offered by the researcher of this paper for the first time. The mentioned structure, in addition to its quick and accurate control system, provides the ability of direct connection of chopper to SMES.

2 Proposed structure

The proposed structure based on SMES and photovoltaic system which first proposed in this paper, is shown in Fig. 1. The maximum power of photovoltaic system varies according to temperature, so after estimating the power, a DC/DC converter regulates the received power on the maximum value. SMES system is connected to a bi-directional chopper and both DC-link voltage and connected capacitor bank are regulated through chopper switching. With regard to the connection of a three-level inverter to the group consisting of SMES and photovoltaic, it is required that the voltage of capacitors in capacitor bank is controlled equally. The control of the injected active and reactive power into the grid is performed through inverter switching control and the output of the inverter after connecting to a transformer and a filter, is connected to a transformer inside the ground substation of the distribution network.

Fig. 1
figure 1

The introduced structure of distributed generation in this paper based on SMES and photovoltaic

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The control process of the different parts of the system including the DC-link voltage and the output power of photovoltaic system and also active and reactive power flow into the grid and finally, estimating the maximum power of photovoltaic system are performed based on the following steps:

  • The maximum power of photovoltaic (PV) system in a particular temperature and radiation is estimated.

  • The output power of photovoltaic system is controlled around the maximum value by a DC/DC converter

  • DC-link’s voltage just is the capacitor bank voltage is regulated by chopper switching control.

  • Regulation of active and reactive power flow into the grid is performed by inverter switching control. Two open-loop fuzzy controllers regulate both the phase angle of the wave modulation and its modulation index.

3 Photovoltaic system, the accessible power estimation and receiving

A photovoltaic (PV) system is consisted of a number of series/parallel cells as shown in Fig. 2 which in [7, 8], the way of their modeling is explained. In the modeling process of the mentioned system, a current source which its value depends upon solar radiation is used according to Fig. 2 and the voltage and current equations are as (1)–(4). In Fig. 3a the voltage and current curve of a sample PV array with parameters according to Table 1 is shown and in Fig. 3b the maximum power curves in different temperatures and radiations are shown. Moreover, from the resulted curves, the dependence of the array power on the temperature and radiation could be clearly concluded. As it is clear from Fig. 3b, the maximum power of array in each temperature and radiation takes place for a particular conditions and to use the array optimally, it is required that the maximum power point is tracked and is received from photovoltaic system. The curves from Fig. 3 and the parameters from Table 1 are used in the simulation part for future sections of paper. Noticing to mention that from the data of Fig. 3b and Table 1, the tracking of the maximum power point is achievable according to Fig. 4.

$$\begin{aligned}&I_{PH} =[I_{sc} +K_I (T_c -T_{ref} )]\cdot \lambda \end{aligned}$$
(1)
$$\begin{aligned}&I_{RS} =\frac{I_{sc} }{e^{\frac{q\cdot V_{oc} }{N_s\cdot k\cdot A\cdot T_c}}-1}\end{aligned}$$
(2)
$$\begin{aligned}&I_S =I_{RS} \left( \frac{T_c }{T_{ref} }\right) ^3 \cdot e^{\frac{q\cdot E_G\cdot \left( \frac{1}{T_{ref} }-\frac{1}{T_c }\right) }{k\cdot A}}\end{aligned}$$
(3)
$$\begin{aligned}&I=N_P \cdot I_{PH} -N_P \cdot I_s \left[ e^{\frac{q\left( \frac{V}{N_s }+\frac{R_s \cdot I}{N_p }\right) }{k\cdot T_c \cdot A}}-1\right] -\frac{\frac{N_P V}{N_S }+R_s \cdot I}{R_{sh} } \end{aligned}$$
(4)
Fig. 2
figure 2

Photovoltaic system model consisting of series/parallel cells

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Fig. 3
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a The power–voltage curve of a sample photovoltaic system to be used in simulation. b The maximum power of a sample photovoltaic system based on radiation and temperature to be used in simulation

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Fig. 4
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Data table to be used for estimating the maximum power of photovoltaic system

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Table 1 The parameters of a sample photovoltaic package
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With regard to the proposed structure in Fig. 1, it is required that the power is received from the photovoltaic system. For this reason, a DC/DC converter as Fig. 5 is used and for a particular switching frequency, the switching pulse width is determined by a PI-controller. PI-controller determines the constant value to be compared with saw-tooth wave with a particular switching frequency as shown in Fig. 5 and as a result, the power received from photovoltaic system is regulated according to the determined value from data table.

Fig. 5
figure 5

The way of controlling the extracted power from the photovoltaic system

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4 Super conductive magnetic energy storage (SMES), bi-directional-three-level chopper and DC-link voltage control

According to Figs. 1 and 5, SMES and photovoltaic system (PV) together are used as distributed generation resource. In this part, the way by which DC-link voltage is controlled is presented knowing that the DC-link voltage is the common output of bi-directional-three-level chopper and DC/DC converter. The bi-directional-three-level chopper is shown in Fig. 6 and it could be seen from Fig. 6 that the chopper’s input is connected to SMES and its output is connected to the capacitor bank. It is a key note that the SMES coil in which modeled with two lumped components include of an inductance (L\(_{\mathrm{SMES}})\) and also a lump resistance (R\(_{\mathrm{SMES}})\) is a current feed component which cannot be open circuit anyway. As this moment, a proper converter should be used as an interface between the coil and DC link which is the shown chopper in Fig. 6. Now, a relative switching controller should be designed for coil’s current path in charge, discharge and hold modes. The chopper consists of four switch and 16 switching states which 7 states are used according to Table 2 and the input–output relation is based on the mentioned table. The chopper structure with current path in operating modes, have been illustrated by Fig. 7.

Fig. 6
figure 6

Bi-directional-three-level chopper

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Table 2 The seven modes and operation states of the bi-directional-three-level chopper
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Fig. 7
figure 7

The chopper structure and current path in operating modes

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The control operation of the chopper must be in a way that the output voltage of the chopper just is the DC-link voltage of the distributed generation system, is fixed on a desirable value and the voltage of the capacitors is equal and half the DC-link voltage according to relations (5, 6).

$$\begin{aligned} V_{DC} =V_{DC{\text{- }}Ref} \end{aligned}$$
(5)
$$\begin{aligned} V_{c1} =V_{c2} =\frac{V_{DC{\text{- }}Ref} }{2} \end{aligned}$$
(6)

The operation modes of chopper listed in Table 2 are considered, following the change of operation modes, the charging and discharging process between SMES and DC-link capacitors takes place and DC-link voltage would be controlled to achieve the above-mentioned relations. For this reason, the algorithm which is shown as flowchart in Fig. 8 is used which was first proposed by the researcher of this paper. The advantages of this algorithm could be described as its wide area of voltage controllability and quick-responding and desirable dynamic. If f\(_{\mathrm{ch}}\) is considered as chopper switching frequency, a reference wave is used during the switching process and as the rising edge is detected, the operation mode of the chopper is changed in order to apply the control algorithm. The process is shown in Fig. 8.

Fig. 8
figure 8

The flowchart of DC-link voltage control through changing the modes of bi-directional-three-level chopper

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5 Three-level inverter and the connected three-phase transformer

After controlling and fixing the DC-link voltage, it is required that this voltage is transformed into 3ph AC voltage. To achieve this goal, in this paper a cascade three-level inverter and the transformer connected to it, is used as in Fig. 9. The switching algorithm of this inverter is based on carrier and modulation waves, in which two triangular waves as carrier waves and three sinusoidal waves with base frequency as modulation waves determine the inverter switching. The switching hardware and also the switching method are described in Fig. 10 for a sample leg. If modulation waves as (7) are considered, the main component of 3ph wave of inverter’s output would be at the same phase and the same frequency as the modulation waves. The more the frequency of the carrier wave becomes; the better would be the harmonic spectrum of the inverter’s output. In reality, comparing the modulation and carrier waves, the trigger pulses of inverter’s switches are determined in a way that the main component of inverter’s output would be at the same phase and the same frequency as the modulation waves. In such conditions, considering the value equals to 1 for the magnitude of the carrier wave, the coefficient \(0<A<0.85\) is considered for modulation waves. The switching technique of three-level inverter and its control process is described in [22].

$$\begin{aligned} V_{ma}&=A\times Sin( {2\pi f \cdot t+\varphi })\nonumber \\ V_{mb}&=A\times Sin( {2\pi f \cdot t+120+\varphi })\\ V_{mc}&=A\times Sin( {2\pi f \cdot t-120+\varphi })\nonumber \end{aligned}$$
(7)
Fig. 9
figure 9

The structure of three-level inverter used in this paper

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Fig. 10
figure 10

SPWM switching of inverter for leg A as a sample leg

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6 LCL filter

For filtering the inverter’s output voltage, it is required that a low pass harmonic filter is used and a LCL filter can be a good choice which is shown in Fig. 11. In this filter the transfer function and resonance frequency are approximately independent of the load amount. The existing relations for this filter are written as (8)–(10). Where, f\(_{0}\) denotes to cut-off frequency of filter.

$$\begin{aligned} \frac{\text{ V }_{\mathrm{O}} (\text{ S })}{\text{ V }_{\mathrm{i}} (\text{ s })}=\frac{\text{ R }}{\text{ L }_1\cdot \text{ L }_2 \cdot \text{ C }\cdot \text{ S }^3+\text{ L }_1 \cdot \text{ R }\cdot \text{ C }\cdot \text{ S }^2+( {\text{ L }_1 +\text{ L }_2 })\text{ S }+\text{ R }} \end{aligned}$$
(8)
$$\begin{aligned} f_0 =\frac{1}{2\uppi }\times \sqrt{\frac{\text{ L }_1 +\text{ L }_2 }{\text{ L }_1 \cdot \text{ L }_2 \cdot \text{ C }}}\end{aligned}$$
(9)
$$\begin{aligned} f_0 =\frac{1}{2\uppi }\times \sqrt{\frac{3}{2\text{ L }_2 \cdot \text{ C }}} \end{aligned}$$
(10)

Considering \(f_{0}\) and \(f\) as the cut-off and base frequencies, in order to have \(f_{0}=k \cdot f\), the capacitor value is calculated according to (11). Bode diagram of this filter for k = 20, f = 50 Hz for several amounts of load is as Fig. 12 and it could be clearly seen that the transfer function is virtually independent of the load amount.

$$\begin{aligned} C=\frac{3}{8\pi ^2\cdot k^2\cdot f^2\cdot L_2 } \end{aligned}$$
(11)
Fig. 11
figure 11

The single line diagram of LCL filter connected to the inverter’s output

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Fig. 12
figure 12

Bode diagram of the LCL filter for sample values

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The output power from photovoltaic system and the also active and reactive power fellow into the grid must be controllable. To achieve the mentioned goal, two closed-loop fuzzy controllers are used regarding that in controllers, phase angle and the magnitude of modulation waves are regulated and the designed algorithm is shown in Fig. 13. In Table 3 the inputs and outputs of fuzzy controllers are listed. The constants K\(_{\mathrm{e}}\), K\(_{\mathrm{d}}\), K\(_{\mathrm{o}}\) are regulated to reach the better operation of controllers.

Fig. 13
figure 13

The structure of two fuzzy controllers for controlling the transmitted active and reactive power into the grid

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Table 3 The inputs and outputs of closed-loop fuzzy controller for controlling the transmitted active and reactive power
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For designing the phase controller, the membership functions and fuzzy rules are designed according to Figs. 14, 15 and Table 4 in which the signs nvb, nb, nm, ns, z, ps, pm, pb, pvb are described as ‘negative very big’, ‘negative big’, ‘negative medium’, ‘negative small’, ‘zero’, ‘positive small’, ‘positive medium’, ‘positive big’ and ‘positive very big’ in order. In Figs. 12 and 13, vectors are normalized and are between 0 and 1.

Fig. 14
figure 14

The membership functions of fuzzy controllers

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Fig. 15
figure 15

The fuzzy surface of fuzzy controllers

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Table 4 The applied fuzzy rules to the fuzzy controllers of transmitted active and reactive power into the grid
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In Fig. 16 the general block diagram of the system is shown. Inputs and outputs are shown in different subsystems. With regard to this structure, chopper controller controls the capacitors DC-link voltage and two controllers control the injected active and reactive power into the grid. These two controllers are the fuzzy controllers described in the previous part and it should be known that the controlling process takes place by regulating the modulation waves. Chopper controller regulates DC-link voltage by changing the operation mode in every period of the switching period.

Fig. 16
figure 16

The control structure block diagram

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7 Simulation

In order to simulate the structure proposed in Fig. 1 and to demonstrate the efficiency of control algorithm in different subsystems, several simulations are performed in MATLAB Environment. The system parameters are according to Table 5 and the parameters pertaining to photovoltaic system are according to Table 1 and Figs. 3 and 4.

Table 5 The system parameters for simulation
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With regard to system parameters, for initial current of I\(_{0}=1,000\) A in magnetic energy storage element, the SMES capacity is equal to \(W_{SMES} =\frac{1}{2}\cdot L\cdot I^2=1\,MJ\) and the maximum power of photovoltaic system for maximum radiation according to Figs. 3 and 4 is roughly equal to 200 KW. The considered local load is equal to 80 KW. It is known that the received power from photovoltaic system by data table for each temperature and radiation is regulated on the maximum value and as a result if the transmitted power into the grid is more than the power of photovoltaic system, the remainder of power is produced by SMES and the element is discharged. On the other hands, if the transmitted power into the grid is less than the power of photovoltaic system, the element is charged and its current rises. Now the assumption is that the initial current of energy storage inductance is equal to 1,000 A and the temperature is at 30 \(^\circ \)C and the radiation is reached from 100 to 50 % at t = 5 s (even though such change is unlikely in real world). In order to test the fuzzy controllers operation, some changes for transmitted active and reactive power into the grid is considered according to Fig. 17 and simulation results are shown in Figs. 17, 18, 19, 20 and 21 and the results are described.

Fig. 17
figure 17

The way of regulating the transmitted active and reactive power into the grid by fuzzy controllers

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Fig. 18
figure 18

The way of regulating the magnitude and phase of the inverter’s modulation waves for regulating the active and reactive power

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Fig. 19
figure 19

The operation modes of chopper for controlling the DC-link voltage and the voltage across the magnetic energy storage inductance

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Fig. 20
figure 20

The power of photovoltaic system and the modulation waves of the DC/DC converter for regulating the power of photovoltaic system for 1–8 s

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Fig. 21
figure 21

The DC-link voltage, current of the SMES coil and flowed power to power grid for 1–8 s

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In Fig. 17, the reference active and reactive power is changed in each 2 s. As it is clear from the figure, the fuzzy controllers, based on the reference values, follow the transmitted power acceptably. The regulation from fuzzy controllers is performed through regulating both the phase angle and the magnitude of the inverter’s modulation waves as it is shown in Fig. 18. In Fig. 19, in order to demonstrate the operation of the chopper’s controller, the voltage across the energy storage inductance and also the operation modes of the chopper are shown. As it is clear from the figures, the controller performs the DC-link voltage control by changing the operation mode of the chopper for each switching period of the chopper. In Fig. 20, the operation of power controller in photovoltaic system is shown, in which the output of the PI-controller is connected to DC/DC converter and also the power regulation of photovoltaic system on its maximum value is shown. In Fig. 21, as the radiation of the environment is changed, the maximum power of photovoltaic system is changed consequently and as a result, the controller changes the converter switching by changing the output of the PI-controller in a way that the output power from the photovoltaic system is regulated on its reference value acceptably. In middle part of Fig. 21, the simulation results for the current of the SMES, DC-link voltage and the flowed active power into the grid are shown. As it is understood from the middle part of the Fig. 21, whenever the received power from the photovoltaic system exceeds the addition of the local load power and the transmitted power into the grid, the remainder of power flows into the storage element (SMES) through the chopper and the current of the storage element rise which mean the SMES charging. Such condition could be clearly seen during the time from 4 to 6 s. On the opposite side, if the received power from the photovoltaic system falls below the addition of the local load power and the transmitted power into the grid, the remainder of power is produced by the storage element and this process will result in the current fall. Such condition usually takes place after 6 s.

8 Conclusion

In this paper a novel structure for distributed generation system based on the SMES and photovoltaic system together with necessary controllers were introduced. Two fuzzy controllers were used to regulate the transmitted active and reactive power into the grid on the desirable reference value and a PI-controller was used to regulate the extracted power from the photovoltaic system on the maximum value which is determined according to a data table consisting of radiation and temperature. The control of the DC-link voltage was performed by the chopper which is connected to the superconductor and a new control algorithm for the mentioned chopper was presented. The simulation results have verified the efficiency and capabilities of designed control algorithms and introduced structure and led to the accurate operation. The advantages of this paper over the others are as follows:

  • Proposing a new algorithm for controlling the three-level chopper which is connected to the superconductor

  • The accurate and thorough control of the DC-link voltage with fast dynamic

  • The direct connection of superconductor to the chopper without using a filter

  • The composition of superconductor and photovoltaic system as distributed generation resource

  • Having a comprehensive control over system voltage and power.

Some of the above-mentioned advantages are first proposed in this paper. For further research, some ideas such as ‘proposing and comparing the operation of other controllers with active and reactive power fuzzy controllers’ and ‘the more accurate modeling of superconductive elements with non-compressed element’ and ‘targeted regulation of the transmitted active and reactive power into the grid based on the peak hours and local load values’ and also ‘the way of distributed generation system is landing introduced in this paper’ are proposed.