A novel seamless control algorithm for a single-stage photovoltaic interface employing DC bus signaling

Electrical Power and Energy Systems 113 (2019) 90–103

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

A novel seamless control algorithm for a single-stage photovoltaic interface employing DC bus signaling

T

Ahmad Malkawia, , Luiz Lopesb ⁎

a b

Department of Mechatronics Engineering, University of Jordan, Amman, Jordan Department of Electrical and Computer, Concordia University, Montreal, Quebec, Canada

ARTICLE INFO

ABSTRACT

Keywords: DC nanogrid DC bus signaling Droop control Maximum Power Point Tracking

DC bus signaling (DBS) is frequently employed for coordinating the operation of Distributed Energy Resources (DERs) in DC micro and nanogrids, in a decentralized way. The V vs. I curve of Renewable Energy Sources (RESs), such as solar photovoltaic (PV), usually includes a droop, a Maximum Power Point Tracking (MPPT) and a current limiting segment/mode. However, the reference current for the interface (I) cannot be determined solely based on the DC bus voltage (V). Variations of the solar irradiance change the DC bus voltage values on the V vs. I curve where transitions from one mode to another occur. This is an issue for single-stage power interfaces that, without the intermediate DC bus of two-stage interfaces, cannot employ conventional search-type MPPT algorithms. This paper presents a novel control scheme in which a non-search-type MPPT algorithm that does not rely on measurements of the solar irradiance is employed. It allows a smooth transition for the reference current of the interface as the mode of operation, on the V vs. I curve, changes due to variations in the solar irradiance and DC bus voltage. The performance of the proposed scheme is demonstrated experimentally for a stand-alone DC nanogrid based on DBS for the PV source operating by itself and along with an energy storage unit. Load and solar irradiance variations are considered in the experiments.

1. Introduction DC is an interesting alternative to AC distribution in residential and office nanogrids that employ Renewable Energy Sources (RESs) and electrical storage units because most of them present DC characteristics. Besides, many of the modern AC electronic loads are “DC compatible” having an AC-DC converter to create an intermediate DC bus. DC distribution does not require frequency and phase control, as AC distribution, what facilitates the control strategies of distributed energy resources (DERs). In addition, the power electronic interfaces tend to present lower cost and volume while a higher efficiency and reliability [1–6]. The conventional methods to control power and current in a DC nanogrid are based on a centralized controller, which requires information from each component of the system [7]. It employs a communication network and a complex supervisory control structure. If communication fails, the system is disabled, thus resulting in a system with relatively low reliability [7–9]. Alternatively, the nanogrid can be controlled with a hierarchical structure in a de-centralized way, where the DER interfaces operate with a good degree of autonomy [1,10–13]. In general, the hierarchical control consists of three levels. The primary

⁎

controller for DERs and loads capable of demand side management (DSM) is based on locally measured quantities. These define the power injected/absorbed into/from the DC bus based on DC bus signaling (DBS) [11,12,14,15]. In such a case, the magnitude of the DC bus voltage, which carries information about the system’s load level, is allowed to vary within a narrow range. Higher load levels and/or low injected power by renewable energy sources (RESs) imply a lower DC bus voltage [16]. In DBS, the power injected/absorbed by each interface depends on its V vs. I (or V vs. P) curve and locally measured quantities. By defining the shapes and values of the V vs. I curves, one can define how each interface will react to varying load and power generation conditions. The secondary level of the hierarchical control is to ensure that the electrical levels in the system are within the acceptable value. Finally, the tertiary control level manages the power flow in the DC nanogrid, for a more economical operation of the system [10,17]. The parameters of the V vs. I curve can be modified by the secondary and tertiary control levels using a low bandwidth communication channel. A distributed control strategy based on DBS is usually used to control a nanogrid [11,12,18]. A supervisory control is used for a seamless transition in [19,20], which needs a communication link between the DERs

Corresponding author. E-mail addresses: [email protected] (A. Malkawi), [email protected] (L. Lopes).

https://doi.org/10.1016/j.ijepes.2019.05.037 Received 29 May 2018; Received in revised form 24 March 2019; Accepted 14 May 2019 Available online 21 May 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.

Electrical Power and Energy Systems 113 (2019) 90–103

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Nomenclature DBS DER PV MPP

CV CPS SoC RES CCM SAS

DC Bus Signaling Distributed Energy Resource Photovoltaic Maximum Power Point

that is not available in the de-centralized control. The V vs. I curves of RESs, such as solar photovoltaic (PV), usually consist of a droop, a maximum power point tracking (MPPT) and a current limit segment. The primary control logic of the interface should allow a smooth transition from one segment to another. This is relatively simple to accomplish with two-stage DC-DC converters with an intermediate energy storage element [1,19]. The first stage runs an MPPT algorithm while the second controls the current injected into the DC bus (I) as a function of the DC grid voltage (V), as per the V vs. I curve of the interface. If the power injected into the DC bus is less than that drawn from the PV panel with MPPT, the intermediate DC bus voltage increases. As this voltage reaches, say, 110% of the rated DC bus voltage value, the MPPT logic is disabled in the first stage, until the intermediate DC bus voltage drops to, say, 90% of the rated value. Conventional search MPPT methods, such as perturb and observe (P& O), can be used since the intermediate energy storage element provides a good degree of decoupling between the continuously varied PV power and the power injected into the DC grid. However, when a single-stage converter is used, the power drawn from the PV panel corresponds to that injected into the DC grid, which does not necessarily correspond to the current that should be injected according to the V vs I curve. This imposes constraints on the type of MPPT algorithm that can be used. In [20], a scheme for multiple single-stage PV interfaces operating with DBS and presenting smooth switching between constant voltage (CV) mode, not droop, and MPPT is presented. Each unit presents parallel CV and MPPT loops. The impact of DC bus voltage variations on the output signal of the CV loop PI controller is clear, but there is no discussion on the MPPT logic and how it should affect the output signal of the MPPT loop PI controller. Besides, the important current limit mode, and transition, is not discussed. A similar approach is used in [21], where the search-type P&O MPPT method is employed. The performance of the scheme is verified by means of simulation only, and it is hard to estimate the speed of response of the system since the waveforms cover a time range of several seconds. The relevance of smooth transitions between droop and MPPT was also discussed in

Constant Voltage Constant Power Source State-of-Charge Renewable Energy Source Continuous Conduction Mode Solar Array Simulator

[17], but experimental results were conducted with a constant power source (CPS) emulating the PV interface. The option of running the MPPT logic periodically, say every 1 s, and then comparing the magnitudes of the modulating signals from parallel loops is not considered in this discussion since it should lead to a slower dynamic response. This paper presents a novel control strategy for single-stage PV interfaces operating with DBS and three modes of operation: Droop, MPPT and current limit. The reference current for the interface (I) cannot be determined solely based on the DC bus voltage (V). Variations of the solar irradiance change the DC bus voltage values on the V vs. I curve where transitions from one mode to another occur. A non-search type MPPT algorithm is proposed as a means to achieve smooth and seamless variations of the reference current, as the operating point in the V vs. I curve changes from one mode of operation to another, due to DC bus voltage and solar irradiance variations. This paper is organized as follows. The V vs. I curves for DERs operating with DBS are briefly discussed in Section 2. The main control loop for the DERs are presented in Section 3. The proposed control algorithms for the PV and storage units are described in Section 4 and 5, respectively. The experimental set-up developed for testing the proposed algorithms is introduced in Section 6. Extensive experimental tests are discussed in Section 7 while the Conclusions are presented in Section 8. 2. The V VS. I curves of DERs in a DC nanogrid The DC nanogrid considered in this work is a unipolar single-bus system, as shown in Fig. 1. It consists, without loss of generality, of a RES, a storage unit and a variable load. The impedances between DERs and load(s) are assumed negligible. The nanogrid is controlled in a decentralized way with a hierarchical structure based on DBS. In such a case, the current injected by a DER (IDC) varies with the locally measured grid voltage (VDC) according to a particular V vs. I curve. This usually consists of various segments including droop, maximum power point tracking (MPPT) and current limiting. For droop control, the injected current is given by:

Fig. 1. Unipolar DC nanogrid with one RES (PV), one storage unit and a variable load. 91

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Fig. 2. V vs. I curves of the storage and of the solar (PV) interfaces.

IDC = (VNL

VDC )

1 Rd

bus voltage further drops to 0.95 pu, and for rated solar irradiance, the solar interface operates in the current limit mode. For lower solar irradiances, the transition from droop to MPPT mode occurs at a higher value of VDC while the MPPT to current limit occurs for a lower value of VDC, as shown by the dashed line in Fig. 2. Concerning the storage interface, its threshold voltage (VNL_B) is usually selected as 1 pu, the rated voltage of the DC nanogrid. It can be adjusted by using optimal microgrid control strategies [22]. The storage means, typically a battery, is charged (IDC_B < 0) when VDC > VNL_B and it is discharged, into the DC nanogrid, otherwise. It operates in the droop region for a DC bus voltage (VDC) between 1.025 and 0.975 pu. By making the rated power of the storage system equal to the rated power of the RES, the former will be able to draw rated PV power at the no-load condition. In such a case, the droop factor of the storage interface (RdB) will be the same as that of the RES (RdS). However, the RES and the storage unit will not operate together in the drop mode since their droop regions are defined for different DC bus voltage ranges. For DC bus voltages above 1.025 pu, the storage interface absorbs its rated current (IBc) and for voltages below 0.975 pu, it injects rated current, if its state-of-charge (SoC) is within acceptable values. If not, the injected/ absorbed current should be decreased. A summary table with the DC bus voltage ranges and the corresponding modes of operation of the PV and storage interfaces are shown below, for the PV interface operating by itself and along with the storage unit (see Tables 1 and 2). Neglecting the voltage drops between the DER interfaces and the equivalent system load, the DC bus voltage (VDC) of a nanogrid operating with DBS and multiple DERs can be determined from:

(1)

where VNL is the threshold or no-load voltage and the slope of the V vs. I curve is given by:

Rd =

VDC IDC

(2)

RESs such as solar PV are expected to operate with MPPT in cases of high power demand by the load or when one can charge the storage unit(s). Finally, there should be a current limit mode to prevent the interface from injecting/absorbing more power than either the source or storage means allow, as well as for the converter to protect itself against over-currents. Fig. 2 shows the sketch of two typical V vs. I curves for the storage unit (with droop and current limit) and the RES (with droop, MPPT and current limit). The voltage levels are defined in a per unit (pu) basis. They correspond to the values proposed in [1] for a DC nanogrid with a rated voltage of 380 V. The DC nanogrid operates with a voltage regulation of about ± 5%, giving an operating DC bus voltage range between 1.05 and 0.95 pu. The threshold voltage for the droop segment of the RES (VNL_S) is set at the maximum DC nanogrid voltage: 1.05 pu. The RES operates in droop mode, increasing the injected current as VDC decreases, up to the point where it reaches its maximum power capacity. Then, its V vs. I curve changes to an MPPT mode, where the injected current increases less than in the droop region, for a given decrease in the DC bus voltage. In the case shown in Fig. 2, and considering rated solar irradiance, the solar interface changes to the MPPT mode when the DC bus voltage drops to 1.025 pu. When the DC Table 1 DC bus voltage ranges and modes of operation of the PV and storage interfaces. DC bus voltage ranges (pu)

1.05 ≥ VDC ≥ 1.025 1.025 > VDC ≥ 0.975 0.975 > VDC ≥ 0.95 VDC < 0.95

PV interface only

PV and storage interfaces

PV

Storage

PV

Storage

Droop MPPT MPPT Current limit

OFF OFF OFF OFF

Droop MPPT MPPT Current limit

Current limit Droop Droops Current limit

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For the design of the controller of the inductor current loop, a transfer function for boost type DC-DC converters is needed. This has been presented in the literature [23,24] and is given by

Table 2 Basic parameters of the PV and storage interfaces used in the experimental setup. Parameter

PV interface

Storage interface

No-load voltage (V vs. I curve) Droop slope Current limit Rated input voltage Switching frequency Input filter

50.5 V

48 V

Rds = 0.289 Ω ISc = 4.68 A 29 V 20 kHz LPV = 100 μH and C1 = 470 μH CDC1 = 750 μH KPI = 0.0114, τ = 171 µs, TP = 37 µs

RdB = 0.289 Ω IBc = 4.32 A 24 V 20 kHz LB = 100 μH and C2 = 470 μH CDC2 = 750 μH KPI = 0.0114, τ = 171 µs, TP = 37 µs

Output filter PI controller (Type 2)

G=

IDC _i

(3)

i=1

where IDC_i are computed according to the V vs. I curves of the n DERs. This allows the calculation of the value of VDC. With this value, one can then calculate the individual contributions of the DERs, in terms of injected currents, from their V vs. I curves.

=

CVDC s + 2IDC L

LCs 2 + R s + (1

D )2

(5)

4. Control scheme for the solar interface As mentioned in Section 2, the solar interface will be controlled with a V vs. I curve that includes a droop, an MPPT and a current limit mode. This Section describes the MPPT algorithm considered in this work and then an approach for determining the reference inductor current in the three modes, as the solar irradiance and the DC nanogrid voltage vary.

3. Control scheme for the RES and storage units The conventional power electronics topologies for the interfaces of the DC power sources and storage units usually employed in DC nanogrids are shown in Fig. 1. The actual power source and storage units are located in the input of the power interfaces along with a boost inductor. The converters usually operate in continuous conduction mode (CCM) and low current ripple. Conversely, the output current, that is injected into the DC nanogrid, tends to present a larger ripple, thus requiring a larger filter capacitor (CDC1 > C1.). Although the V vs. I curves of the RES and storage interfaces have been defined for the DC nanogrid voltage (VDC) and injected current (IDC), it is more convenient to control the average (DC) value of the boost inductor current (IL), in the PV/battery side, which presents a small ripple. In order to convert the reference current value in the DC bus voltage side (IDC), obtained from the V vs. I curve, into one for the boost inductor (IL), one can use the power balance equation with a typical converter efficiency (η):

4.1. The Maximum Power Point Tracking (MPPT) algorithm The MPPT algorithm used in this work is based on the assumption of linearity between the PV current at the maximum power point (MPP), IPV(n) = IMP, and the maximum power, Pm(n) = PMP, for all solar irradiance levels (6). The proportionality coefficient (Kp), as shown in (7), varies with the PV panel temperature (T) but can be adjusted using the hill-climbing method. Theoretical and experimental verification of these relations have been presented in [25,26]. The actual power drawn from the PV panel at any given time, P(n), is given by (8).

(4)

IL Vin = IDC VDC

d (s )

where C is the DC bus voltage capacitor and R is the equivalent load resistance. In such a case, an appropriately designed PI controller should suffice to provide zero error in steady state with a good dynamic response. The details and design procedure for the interface and control loops are presented in Section 6. The schematic diagram of the current control loop of the RES and storage units are shown in Fig. 3. They are similar but the value of the reference inductor current (ILr) will change with the type of V vs. I curve of the interfaces. An approach to determine this value, while transitioning from one mode to the next, as a result of DC nanogrid voltage and solar irradiance variations, is discussed in the following Sub-Sections.

n

ILoad =

iL (s )

Pm (n) = Kp IPV (n)

(6)

KP = KPo + T

(7)

P (n) = VPV (n) IPV (n)

(8)

Fig. 4 shows the P vs. IPV curve of the solar panel for rated solar

where Vin is the voltage of the PV source or storage unit.

Fig. 3. Control schemes of the solar and storage interfaces with their V vs. I curves and current control loop. 93

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This can be done according to (10), where gain Ksc is usually selected as the ratio between the current at the MPP at rated solar irradiance (IPV_MP) and the short-circuit current of the PV panel at rated solar irradiance (IPV_SC) [25,26]. If the difference between P and Pm is less than a small value, the MPPT algorithm can keep the value of IL constant, thus avoiding continuous variations around the MPP.

ILm = P (n)/Kp

(9)

ILm = Ksc IPV (n)

(10)

4.2. Transitioning from one mode of operation to another As shown in the previous Sub-Section, the inductor reference current for operation in the MPPT mode is computed based only on the PV panel conditions as a function of the solar irradiance. It is assumed that the DC nanogrid voltage (VDC) entices the solar interface to operate in this mode. However, as VDC varies, the operation of the solar interface might need to change to either droop or current limit mode. In such cases, the value of the reference injected current (IDC) is dictated by the V vs. I curve of the solar interface. The reference inductor current (ILr) for operation in those modes can be calculated by reflecting the reference injected current (IDC) to the PV/battery side (IL) using (4). One challenge is to determine which reference current to use, as the values of the solar irradiance and VDC vary. The options according to the mode of operation are: IDC_d, in the droop mode, IDC_m, in the MPPT mode and IDC_c, in the current limit mode. Fig. 5 shows the V vs. I curve of the solar interface from Fig. 2 with some additional information. In solid lines, the reference injected currents that should be selected as the value of VDC varies. The dashed lines show candidate values of reference currents, which were not selected in those VDC segments. As an example, considering a VDC slightly lower than VNL, the value of IDC in the droop mode (IDC_d), calculated from (1) and shown as a solid line, is lower than the values one would get for the MPPT (IDC_m) and current limit (IDC_c) modes, in dashed lines. While the value of IDC_c is known, that of IDC_m, which is expected to vary with the solar irradiance, is not. Besides, the value of VDC at the transition from the droop to the MPPT

Fig. 4. Logic for the non-search type MPPT algorithm based on the variable P vs. I and fixed Pm vs. I curves.

irradiance (8), in red, and the Pm vs. IPV curve (6), in green. The latter curve depicts the values of IPV required to operate at the Maximum Power Point (MPP) for all solar irradiance levels. For rated solar irradiance, IPV at the MPP (IPV_MP) corresponds to the point of intersection of these two curves, which corresponds to the rated maximum power of the solar panel (PMAX). As the solar irradiance decreases, the point of intersection of curves (6), green straight line, and (8), red curve whose magnitude varies with the solar irradiance, will occur at lower values of IPV. By comparing these two curves, one can identify two regions. In Region I, for a given value of IPV, P, obtained from (8), is larger than Pm, obtained from (6). This occurs for IPV smaller than IPV_MP. In Region II, P is smaller than Pm, what occurs for IPV larger than IPV_MP. At Region I, the inductor current should be increased by the MPPT algorithm to drive the operating point towards the MPP. This is done using (9) and is shown in Fig. 4, for a few consecutive iterations. Conversely, in Region II, the inductor current should be decreased by the MPPT algorithm.

Fig. 5. Solar V vs. I curve in droop, MPPT and current limit modes. 94

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mode changes with the solar irradiance, which is unknown, increasing as the solar irradiance decreases. An algorithm to select the reference inductor current for the solar interface operating in droop, MPPT and current limit, for varying solar irradiance and DC grid voltages is proposed in this paper. It is shown in the flowchart of Fig. 6. The first step is to sense the values of the DC grid voltage (VDC) and the PV current and voltage (IPV and VPV). Operation of the PV panel with IPV > IPV_MP is not desirable because of the resulting low values of VPV and potentially exceeding the voltage gain limits of the boost converter. Therefore, the algorithm first verifies whether the system operates in Region II, where P < Pm. In such a case, the reference inductor current (ILr) should be reduced until operation is shifted to Region I. That is where the system is expected to operate for all three modes. When P > Pm, the algorithm computes a candidate value for the next cycle of the reference inductor current according to the MPPT algorithm (ILm). This should have a higher value than the actual IPV, according to (9). ILm is then compared to the candidate reference value from the droop mode (ILd). This is a function of VDC and is computed from IDC using the droop Eq. (1), then reflected to the PV side of the boost converter using (4). The lowest of the two values is called ILmin

and is selected for a final comparison with the candidate current limit value, reflected to the PV side of the boost converter (ILc), using (4). As shown in Fig. 5 for low values of VDC, the value of IDC in the current limit mode (IDC_c) can become lower than the candidate currents in the droop mode (IDC_m) and MPPT mode (IDC_d), and should be selected by the algorithm. That is why for low values of VDC in Fig. 5, the candidate curve for IDC_c is represented by a solid line with the not selected ones, IDC_d and IDC_m, are shown in dashed lines. To illustrate the proposed algorithm, let us consider the case where the solar irradiance is high, the sensed values of VDC is high and that of IPV is low. In such a case, due to a high VDC and according to Fig. 5, the solar interface should operate in the droop mode, supplying less power than maximum possible at the MPP. The first decision block should result in “Yes”, meaning that the system operates in Region I, (IPV < IPV_MP), of Fig. 4. A high value is calculated for ILm from (9). Next, a candidate reference current in the droop region, ILd, is computed from (1), using the sensed value of VDC, and then (4). Then, in the following decision block, with ILd < ILm, ILd is selected and then compared to the large ILc. Finally, being the smallest value of them all, ILd is used as the reference current for the next cycle. The smooth transition of the reference current to another mode, say MPPT, can be justified as follows. If the solar irradiance decreases significantly, IPV should not change much because of the inductor while VPV should decrease, leading to a small(er) value of P and consequently a smaller value of ILm, from (9). This is achieved without any “search” for the MPP. With ILm smaller than ILd and ILc, the operation of the system changes smoothly to the MPPT mode where ILm is adjusted as described in Fig. 4, until it reaches IPV_mp, the current that leads to the maximum PV power for that solar irradiance. The smooth transition of the reference current from the droop to the MPPT mode, as a result of a decrease in VDC, the DC bus voltage, is more intuitive. According to (1) and (4), this will make ILd increase, becoming larger than ILm. Thus, the reference inductor current will change from ILd to ILm with a similar value. 5. Control scheme for the storage interface As mentioned in Section 2, a storage unit usually operates in two modes: Droop and current limit. However, its state-of-charge (SoC) must be kept within certain limits and plays a role in the current values of its V vs. I curve, as discussed below. A number of methods to estimate the battery’s SoC has been presented in the literature, such as in [27]. 5.1. Transition from one mode of operation to another The control algorithm of the battery interface is similar to that of the solar interface. It does not have an MPPT mode, but depending on the state-of-charge (SoC) of the battery, the interface should prevent its further discharge or charge. In the proposed algorithm, first one computes the value of the inductor reference current according to the droop curve (ILd) based on the values of the grid voltage (VDC) and the battery no-load voltage (VNL_b). If ILd is positive, one checks whether the SoC is smaller than, say 20%, when the reference current (ILr) should be equal to zero to prevent any further battery discharge. Otherwise, ILr should be the smallest between ILd and the reference inductor current based on the current limit (ILc), as for the solar interface. On the other hand, when ILd is negative and the SoC is high, say 95%, ILr should be equal to zero to prevent any further battery charge. Otherwise, ILr should be the largest between ILd and ILc, both negative values. The flowchart of the control algorithm for the battery interface is shown in Fig. 7. 6. Experimental set-up The DC nanogrid shown in Fig. 1 was built in the laboratory for verifying the performance of the proposed control strategies. Fig. 8 shows a picture of the experimental setup. Its rated voltage is 48 V, and the DC bus voltage should be kept between 45.5 V and 50.5 V in the

Fig. 6. Proposed algorithm to calculate the reference current for the PV interface with smooth transition between modes of operation. 95

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Fig. 7. Algorithm to calculate the reference current for the battery interface considering the SoC.

Fig. 8. Picture of the experimental setup.

normal operation range (∼ ± 5%). A Solar Array Simulator (SAS) from Agilent (E4350B) was used as the PV source. At rated solar irradiance, it has a maximum PV power of 213 W at 7.35 A and 29 V. Thus, the value of Kp was selected as 29 and the temperature effects were neglected in

the experimental results with the SAS. The storage unit is based on a 165F Maxwell supercapacitor. A three-phase Semikron inverter was employed to realize the power electronic interfaces, with one leg of the three-phase inverter used for 96

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each DER. The 1500 µF capacitor at the DC bus of the inverter corresponds to the main filter at the DC bus of the nanogrid. The converters switch at 20 kHz. An LC filter (100 µH and 470 µF) is connected between two phases of the three-phase inverter and the storage and the source elements, to create the classical Class C DC-DC converter. The overall power electronics interface is illustrated in Fig. 9. The control schemes of the RES and storage unit are implemented in a single dSPACE DS-1103. Concerning the parameters of the V vs. I curves, the no-load voltages of the solar and storage interfaces are VNL_S = 50.5 V and VNL_B = 48 V, respectively. For the definition of the main current values of the solar interface (ISm and ISc), it is assumed that the converter is ideal and that the impact of the ohmic losses can be represented by a decrease of the solar irradiance, and power produced by the PV source, on the V vs. I curve of the solar interface. At rated solar irradiance, an ideal solar interface should inject rated PV power (213 W) at VDC = 49.2 V (∼1.025 pu) and ISm = 4.32 A. From there, one can compute the droop slope as Rds = 0.289 Ω. The current limit mode will be activated for rated solar irradiance when the interface injects rated power for VDC = 45.5 V (∼0.95 pu), that is ISc = 4.68 A. Considering the storage unit, its rated current is such that it can absorb all PV power for rated solar irradiance in case of no-load. Therefore, IBc = ISm = 4.32 A and RdB = 0.289 Ω. The current control loop of both DERs employ a PI type-III compensator. They were designed for the same plant with a transfer function shown in (5) and for a crossover frequency of fx = 2 kHz (10% of the switching frequency) and phase margin of PM = 80°. The key system parameters for the ideal power electronics interface are taken as: VDC = 48 V, IDC = 4.44 A, R = 10.8 Ω, L = 100 µH, C = 1500 µF, and D = 0.4. Where R is selected for the maximum load that could be supplied by the solar interface and D is the duty cycle for operation with MPPT at rated solar irradiance (VPV = 29 V) and a DC nanogrid voltage of VDC = 48 V. The resulting PI controller parameters are KPI = 0.0114, τ = 171 µs and TP = 37 µs. The time-step used in the dSPACE system was 20 μs. A summary table with the basic parameters from the experimental set-up are presented below.

current, and consequently the mode of operation of the DER power interfaces, in a seamless and smooth fashion. Two configurations will be tested: The solar interface operating by itself and then, along with the storage unit. The mode of operation of the DER(s) of the nanogrid shall change as a result of load and solar irradiance variations. The resistive load bank used in this experiment consists of 8 parallel switchable resistors of 40 Ω. 7.1. Solar interface operating by itself The solar interface is controlled with the V vs. I curve depicted in Fig. 2, using the control algorithm described in Section 4 and the power interface and PI controller discussed in Section 6. The first experiment concerns the behavior of the system for the solar interface operating with rated solar irradiance. The power demanded by the load is increased by switching in equal resistors of 40 Ω. The following waveforms are presented in Figs. 10–12, for various load variations: The DC nanogrid voltage (VDC), the current of the PV panel (IL_PV), the load current (IDC in Fig. 9) and other waveforms that show the action of the proposed control algorithm. In Fig. 10, the load changes from R1 = 39.53 Ω to R2 = 19.5 Ω at t = 0.1 s. The steady-state values of VDC for both load conditions, 50.13 V and 49.77 V, correspond to the droop region. However, during transient conditions, VDC decreased below 49.2 V, which concerns the MPPT region. The dynamic response of the system is relatively slow because the value of the injected current cannot increase much as VDC decreases in the MPPT mode. The execution of the proposed control algorithm can be verified in the bottom screen of Fig. 10. Initially ILd < ILm but as VDC decreases, ILd increases, exceeding the value of ILm. This sets a control flag to “high” what indicates operation in the MPPT mode for a short time. This can be confirmed by observing that the waveform IL_PV, in the second screen from the top, follows ILd when the control flag is “low” and follows ILm when the control flag is “high”, as expected from the control algorithm in Fig. 6. In Fig. 11, the load changes from R1 = 13 Ω to R2 = 9.8 Ω at t = 0.1 s. The steady-state values of VDC for both load conditions, 49.4 V and 43.2 V, correspond to the droop and MPPT modes, respectively. This can be asserted by observing the value of the control flag and by comparing the values of ILd and ILm. As in the previous case, the waveform IL_PV follows ILd when the control flag is “low” and follows ILm

7. Experimental tests and results The main objective of the experimental tests is to verify whether the proposed techniques are effective in terms of changing the reference

Fig. 9. Schematic diagram of the experimental power electronics interface. 97

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Fig. 10. Waveforms of the DC nanogrid with the solar interface operating by itself for a varying load impedance: DC bus voltage; solar inductor current; load current; control algorithm waveforms. Always in the droop mode.

Fig. 11. Waveforms of the DC nanogrid with the solar interface operating by itself for a varying load impedance: DC bus voltage; solar inductor current; load current; control algorithm waveforms. Mode changed from droop to maximum power.

when the control flag is “high”, The final value of IDC is 4.39 A, which is slightly higher than ISm (4.32 A), defined as the minimum current for the MPPT mode at rated solar irradiance. For the final load condition and operation in the MPPT mode, the value of VDC is lower than 45.6 V (0.95 pu), which is the minimum value for VDC in the MPPT mode for rated solar irradiance and a loss-less converter shown in Fig. 2. This can

be justified by modeling the converter losses as a decrease of the solar irradiance, what is represented by the dashed curve in Fig. 2. Lastly, in Fig. 12, the load changes from R1 = 9.8 Ω to R2 = 7.8 Ω at t = 0.1 s. The steady-state values of VDC for both loads, 43.2 V and 37.8 V, correspond to the MPPT and current limit modes, respectively. It should be noted that these values are lower than those expected 98

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Fig. 12. Waveforms of the DC nanogrid with the solar interface operating by itself for a varying load impedance: DC bus voltage; solar inductor current; load current; control algorithm waveforms. Mode changed from maximum power to current limit.

considering an ideal power electronics converter, shown in Fig. 2. As in the previous case, this reduction can be visualized by considering a V vs. I curve for an ideal power converter but at a lower solar irradiance. The injected current value at the current limit mode is 4.72, very close to ISc (4.68 A). The mode of operation is confirmed based on the value of the control flag and by comparing the values of ILm and ILc. As

expected, the value of VDC varies more for smaller IDC variations in the MPPT and current limit modes, than in the droop mode, which presents a small slope. Next, the performance of the system for the variation of the solar irradiance with a constant load is considered. First, in Fig. 13, for a load of R = 13 Ω and rated solar irradiance (PPV_M = 213 W) leading to a

Fig. 13. Waveforms of the DC nanogrid with the solar interface operating by itself with a constant load impedance and variable solar irradiance: DC bus voltage; solar inductor current; load current; control algorithm waveforms. Solar irradiance changed from 100% to 90%. 99

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VDC = 49.4 V. This value is higher than VDC = 49.2 V (1.025 pu), which was defined as the lowest DC bus voltage in the droop mode for rated solar irradiance and ideal power electronics converter. At t = 0.1 s, the solar irradiance is decreased to 90% (PPV_M = 192 W). As a result, the power injected into the DC bus decreases, decreasing the DC bus voltage. As shown in the bottom screen of Fig. 13, a decreasing VDC causes ILd to increase, based on (1) and (4), making ILm the smallest of all the candidate reference currents. Therefore, the transition from the droop to the MPPT mode, with a smooth transition of the reference current value from ILd to ILm takes place. The control flag changes from low to high (MPPT). In the MPPT mode, VDC = 47.7 V, above VDC = 45.5 V (0.95 pu), which was defined as the lowest voltage in the MPPT mode. Fig. 14, depicts the case of solar irradiance variation when the solar interface is already operating in the MPPT mode. This is achieved with a lower load resistance, R = 9.8 Ω, and the solar irradiance decreasing from 100% to 90% at t = 0.1 s. The value of VDC decreases from 43.2 V to 41 V. These are lower than VDC = 45.5 V (∼0.95 pu), which was defined for rated solar irradiance and ideal converter. As shown in Fig. 2, a decrease in the solar irradiance leads to a change in the V vs. I curve of the solar interface in the MPPT region, from the solid to the dashed line, and a lower DC bus voltage for a constant load. Regarding the mode of operation, one can see in the screen at the bottom, that the value of ILm is the smallest of all, keeping the control flag at high, as expected for continuous operation in the MPPT mode.

mode, absorbing power under light-load conditions, (VDC > VNL_B = 48 V) and supplying otherwise. As a result, the DC bus voltage should vary between 49.2 V (1.025 pu) and 46.8 V (0.0975 pu), if the power losses in the power electronics converters were negligible. Two types of results are presented in this Section. First, one shows the V vs. I curves of the of the solar and storage interfaces, as well as of the DC nanogrid, along with markers at operating points obtained with various load resistances. This is to demonstrate that the proposed control scheme yields steady-state operating conditions as define by the V vs. I curves. Second, waveforms of the key quantities in the DC nanogrid are presented showing how they vary dynamically as a result of step load variations. Fig. 15 shows, on the left, the V vs. I curve of the DC nanogrid, for varying load impedances. This is obtained with the V vs. I curves of the solar (blue line) and storage (red line) interfaces, on the right. The markers on the plots depict the experimental operating points for the following DC nanogrid loads (in Ω): ∞, 39.5, 19.5, 13, 9.8, 7.8, 6.6, 5.6 and 4.9. The markers representing the experimentally obtained operating points are very close to the theoretical V vs. I curves of the solar and storage interfaces, as well as of the DC nanogrid. It should be noted that with the three-phase converter used in this experiment, it was not possible to sense exclusively the values of IDC_PV and IDC_B shown in Fig. 1. Finally, it is worth mentioning that for the lowest load impedance, the solar interface operates in the MPPT mode and the storage unit in the current limit mode. The dynamic response of the DC nanogrid operating with the solar and storage interfaces employing the proposed control algorithms is shown next. The solar irradiance is kept constant at rated value (PPV_M = 213 W). In Fig. 16, one can see the variation of key waveforms of the DC nanogrid operating under light load conditions. At t = 0.1 s, the load resistance changes from R1 = 39.5 Ω to R2 = 19.5 Ω, increasing the current it draws from the DC nanogrid (IDC, bottom

7.2. Solar and storage interfaces operating together In the second set of experiments, the solar and the storage interfaces operate together. With the parameters defined in the previous Sections and for rated solar irradiance, the solar interface should operate in the MPPT mode, from no-load to full DC nanogrid load (∼2 PPV_M = 426 W). The storage interface should operate in the droop

Fig. 14. Waveforms of the DC nanogrid with the solar interface operating by itself with a constant load impedance and variable solar irradiance: DC bus voltage; solar inductor current; load current; control algorithm waveforms. the Solar irrafiance changed from 90% to 80%.

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Fig. 15. Solar and storage interfaces operating together: (a) Theoretical and measured DC bus voltage and load current, (b) theoretical and experimental DC bus voltage and DC currents from solar and storage interfaces.

screen). As a result, on the top screen, the DC bus voltage decreases from 48.7 V to 48.4 V. Just below, the current of the solar interface (IL_PV) changes very little since it operates in the MPPT mode. Conversely, the current of the storage interface (IL_B) operating in the droop mode, changes much more, decreasing the amount of power it absorbs as the DC bus voltage decreases. In Fig. 17, one can see the variation of key waveforms of the DC nanogrid operating under heavy load conditions. At t = 0.1 s, the load resistance changes from R1 = 5.6 Ω to R2 = 4.9 Ω and the DC bus voltage decreases from 46.9 V to 43.6 V, as shown in the top screen. Just below, the current of the solar interface changes very little, still operating in the MPPT mode. On the other hand, the current in the storage interface changes much more. Initially

it operates in the droop region supplying power to meet the load demand. As the load demand increases, it provides even more current/ power until it enters the current limit mode, as dictated by its V vs. I curve, for a low DC bus voltage. It should be noted that all steady state operating points seen in these screens for VDC, IL_PV, IL_B, and IDC are represented by a marker in Fig. 15. 8. Conclusions This paper has presented a novel control algorithm for a single-stage photovoltaic (PV) interface of a DC micro or nanogrid that employs DC bus signaling (DBS). Its key feature is a seamless transition of the

Fig. 16. Waveforms of the DC nanogrid with the solar and storage interfaces operating together with a varying load impedance: DC bus voltage; solar inductor current; storage inductor current; load current.

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Fig. 17. Waveforms of the DC nanogrid with the solar and storage interfaces operating together with a varying load impedance: DC bus voltage; solar inductor current; storage inductor current; load current.

reference current signal for the interface considering DBS control modes that are based on DC grid side parameters (droop and current limiting) and on source side parameters: Maximum power point tracking (MPPT). In such a case, search type MPPT algorithms are hard to use due to the absence of an energy storage element, usually found in the intermediate DC bus of two-stage interfaces, that decouples input and output power flows until a final decision is made. This paper proposes a solution based on a non-search type MPPT algorithm and a logic for selecting which reference current signal should be used as the mode of operation changes between droop, MPPT and current limit considering both solar irradiance and DC bus voltage variations. The performance of the algorithm is verified experimentally for an autonomous DC nanogrid. First, tests with a “PV only” system are conducted, for load demand and solar irradiance variations that lead to all sorts of transitions between modes of operation. In all cases, the logic provides a reference current to the solar interface with smooth transitions between the three candidate reference currents: Droop, MPPT and current limit. The algorithm is also tested in a “PV plus storage” system where the PV operates mostly in the MPPT mode while the storage unit operates in the droop and current limiting modes, supplying and absorbing power.

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