DC/DC converter specifications in simulation.

## Abstract

This paper presents a new energy management control technique for PV-Battery system used in DC microgrids. The proposed control technique is performed based on a droop control algorithm that maintains DC-bus voltage in a desirable and required range adaptively. Tightly Regulating the bus voltage In the islanded mode of operation is very challenging. However, the proposed control method by introducing a nonlinear droop profile with four adaptive parameters shows its superiority. Adaptive parameters determined by the non-linear optimal algorithms. Tightly regulating the DC bus voltage during extensive changes in demand loads/sources within a DC Micro Grid is the responsibility of the adaptive parameters. Stability of the proposed method in the whole system for a very broad range of operating conditions are proved. Simulation results along with the experimental results verify the feasibility of the proposed approach while demonstrate its superior performance compared to the conventional control method.

### Keywords

- Adaptive Droop Control
- PV-Battery Systems
- DC Micro-grid Systems
- Nonlinear Optimization
- Renewable energy

## 1. Introduction

** T**he main interfaces utilized in microgrids (MGs) for Renewable Energy Sources (RESs) and Energy Storage Systems (ESSs) are power electronic converters [1, 2]. MGs’ reliable operation depends on these power electronic converters [3, 4, 5, 6]. Specifically, power converters’ control systems which introduced recently, can make MG systems more reliable for future mainstream power generation.

The AC power system are more common due to its advantages for long distance power transmission (i.e., transformers can be used to adjust optimal voltage levels). Thus, the development of micro-grid technology has been mostly confined to AC micro-grids [4, 5]. However, as the number of local micro-grids increase the need for long distance power transmission will significantly decline. Therefore, local DC micro-grids can potentially be more efficient due to the fact that many loads require DC power (e.g., electronic loads, LED lighting systems, electric vehicle charging, etc.). In addition, most renewable energy systems and energy storage systems are either inherently DC (batteries, solar panels) or incorporate a DC stage (inverter connected wind turbines) [6]. Since the number of DC sources and loads will inevitably increase in the future, the need for a DC MGs will also increase. The reason is that the need for PV cells and ESSs is increasing. The advantages of the DC MGs over the AC MGs are summarized as follows [7, 8]:

DC MGs are more efficient and the natural fits for DC sources and loads.

Most of the existing challenges in AC MGs are due to reactive power flow, power quality, and frequency regulation, which do not exist in the DC MGs.

In terms of transmission efficiency (loss associated with the reactive current is eliminated) and power supply reliability (more reliability overall because of fewer components), DC MGs have a superior performance in comparison to AC MGs [8].

Thus, DC microgrids seem to be a natural framework for future power delivery [9].

In DC MGs, regulating the common DC-bus voltage is the main control task. To gain this goal, two different methods have been proposed in the literature [10, 11, 12, 13, 14], autonomous droop-based control schemes and non-autonomous centralized controllers (that are based on communication links). Droop-based methods are widely used due to their simplicity and reliability (centralized methods can not be relied upon due to their dependency on the communication links) [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]. However, the existing and conventional droop-based methods cannot propose an optimal performance in terms of reliability and efficiency exclusively in the islanded mode of operation. In addition, existing droop controllers usually result in large voltage variations at the DC bus during transients in the islanded mode. Large voltage fluctuations may jeopardize the system reliability and damage power electronic converters in MGs [3, 4]. However, the proper performance of linear or conventional droop controllers with a constant droop gain is reduced in light and full load conditions. This is due to a trade-off between voltage deviation and current sharing. In terms of current sharing accuracy and stabilization of Constant Power Loads (CPLs), high droop gains are preferable [11]. In term of voltage regulation low droop gains are desirable. Due to this trade-off between current sharing and voltage deviation, constant droop gains can not guarantee high performance, and it would be a big challenge. Figure 1 shows this trade-off in the conventional droop control in a simplified DC MG’s with two DC sources. It shows that constant droop gain can not be a precise and comprehensive method in both light and full load conditions [11].

To address this issue, different methods have been proposed in the literature to maintain a high level of reliability [5, 6]. A fuzzy logic strategy for energy balancing is proposed in [12]. This method is based on utilizing the virtual resistances which are calculated based on the

Three nonlinear droop control methods are proposed in [17, 18, 19]. In [17], it is claimed that the effect of sensor calibration errors and cable resistances is minimized, while it improves voltage regulation and load sharing compared to linear droop control techniques. This method adaptively adjusts the droop gains based on three novel high-order polynomial droop equations. The three methods are proposed in this research are High-Droop Gain (HDG), Polynomial Droop Curve (PDC), and Polynomial Droop Curve With Voltage Compensation (PDCVC), which are shown in Figure 2. However, the chosen droop gain value in the HDG method exhibits poor current sharing near the operating point. On the other hand, the PDC method could improve load sharing near the operating point, but shows an unexpected performance in voltage regulation under heavy-loading condition. In the PDCVC method, both current sharing and voltage regulation are improved except near no-load conditions. Two important factors were not considered in this paper, the impact of output impedance on the stability of the whole DC MG and the impact of droop control on the efficiency of system. Later in [18], a split droop controller is investigated, which droop gain can be calculated based on voltage error measurement. This strategy calculates several different slopes for each load conditions to reduce the current sharing and voltage deviation errors, which shows this task well implemented. However, differences between droop slopes create switching modes, which will be abrupt. The sudden changes in output resistance of the power converters may lead to undesired transients and oscillations. In [19], the performance of the different second order droop expressions namely parabola and ellipse droop as nonlinear droop control methods are evaluated and compared with the linear droop. The parabola and ellipse droop equations showed a good performance in both load sharing and voltage regulation but a weak performance with negative current [16]. A nonlinear programmable droop method for a low-voltage DC MG is proposed in [20] considering the effects of line resistances and the state of charge of the batteries in the power- sharing process. This method has been able to reduce the impacts of sensor and cable errors at heavy load. It also reduces the voltage variation while load sharing is still guaranteed. However this method does not have a good performance, when the converter output current is negative. Moreover, under light-loading conditions, the values of droop gain lead to creating poor load sharing [20].

In this paper a novel control system has been proposed to improve the reliability and efficiency of DC micro-grids operating in the islanded mode. Figure 3 shows the block diagram of the DC MG considered in this paper. Two energy storage systems along with two solar energy harvesting systems are connected to the DC bus to feed 4 kW DC loads. The focus of this paper is on small scale DC micro-grids for residential applications, which means the line impedance can be negligible [14, 19]. The main contribution to this article is that the proposed control system allows RESs to operate at their maximum power point whenever it’s possible. The main advantage of the proposed control system is that the MG can optimally utilize energy storage system in conjunction with renewable energy systems. Additionally, the proposed control system can maintain tight regulation of the DC bus voltage within a predefined range. Unlike the aforementioned nonlinear methods, the presented method has a precise performance in negative current (when the output power is absorbed by the battery) which is similar to the positive current (when the battery converter injects power to the MG). The calculations of the droop gain in the proposed method are independent of the measured output current. Therefore, this method immunizes the proposed control system from current ripples and sensor errors in comparison to the methods with high order polynomial droop methods. This method has an ability to change the droop gain smoothly from light load to full load conditions, without switching modes resulting in no abrupt in the control system. Voltage deviation and current sharing improved in this method in comparison to other nonlinear and conventional droop control, and it will be shown and explain in the following section. This method has been implemented and analyzed in the Micro-Grid systems due to this fact, the most difficult tasks and challenges have occurred in the MG system, not in the grid- connected system. In the grid-connected system the bus voltage is constant with less complexity and less non-ideal elements or parameters. Various power flow scenarios have been analyzed to verify the performance of the MG.

This paper is organized as follows. The proposed control system and various operating scenarios are described in Section 2, respectively. Moreover, two subsections called the definition and ranges of the adaptive parameter are added in Section 2. In Section 3, the optimal selection of the the adaptive parameters is presented. The stability analysis performed in Section 4. Finally the simulation and experimental results are presented in Section 5.

## 2. Proposed Control System

In order to describe the performance of the proposed control system in all operation modes, a scenario will be discussed. Energy devices and systems in which the solar system and battery are connected to the grid/load through power converters have four operating modes which are listed as follows:

Grid-connected mode: When the system is connected to the grid, in order to transmit the maximum power, the power converter connected to the solar cells performs maximum power point tracking (MPPT). During this mode, the battery’s state of charge should be controlled so that when the system is disconnected from the grid and turns into an island system, the battery has enough energy to supply the island system. Therefore, in accordance with the battery’s state of charge, the battery is charged or discharged, which are two modes of operation.

Island mode: In this mode, the power converter connected to the solar cells still performs MPPT. During this mode of operation, the DC-bus voltage should be kept constant (within the range of 10%) by the power converter; whereas, in grid-connected mode, the voltage of DC-bus is relatively constant for various conditions. Therefore, to achieve power-sharing and load voltage regulation, the battery connected power converter is controlled with the droop control method. For instance, if the load voltage decreases, battery is discharged to transmit more power; and when the load voltage increases, power is transmitted back to the battery and charges it.

Special case of island mode: If the battery is fully charged/discharged during the island mode, the power-sharing and output voltage regulation are achieved by the solar connected power system. Hence the power system evades MPPT and is controlled with the droop control method.

In the islanded mode of operation, one of the main problems with the existing droop-based controller is that the MG components are not utilized in an efficient manner [30, 31]. For example, in several scenarios, to keep the stability of the system, renewable energy sources must deviate from their maximum PowerPoint [30, 31]. The main contribution of this method shows the presented control system allows RESs to operate at their maximum power point whenever it can be possible. Figure 4 shows the general block diagram of the proposed control systems for the solar energy harvesting system and the energy storage system (ESS) in the DC MG. The solar control system consists of one MPPT control and one adaptive droop control, which are separated from each other by a state modifier. The structure of the solar control system will be discussed in the next paragraph. After that, the battery control system will be discussed in details as the main proposed control method. The battery control system consists of a supervisory adaptive droop control to manage energy through the DC MG system. The optimal utilization is performed through incorporating the adaptive charge/discharge terms to the control system of the ESS. These terms implement a nonlinear adaptive droop profile for the ESS in order to perform a tighter voltage regulation. Moreover, due to working in a high level of power (More than 100 W), all the analysis are preferred in continues conduction modes, because working in discontinuous conduction mode in high-level power comes with high peak current and power loss, which it is not desired.

According to Figure 5, the schematic of the solar controller along with its boost converter is illustrated. The outer control loop of the solar energy harvesting system consists of two blocks: the MPPT controller that ensures maximum power is extracted from the solar module, and the adaptive DC-bus voltage controller. The switching between these two control algorithms is preformed by the state modifier block as follows:

where

The block diagram of the ESS is discussed according to the Figure 4. In this figure, the presented control method offers four modes of operations: charging mode, discharging mode, fast charging mode, and fast discharging mode while the conventional droop control method offers only, charging mode and discharging mode. Using the two extra modes, the control system is able to offer voltage regulation, while improving the reliability of the system. The outer loop produces a reference value for the inner current control loop. The outer loop is optimized droop controller that incorporates two extra modes (i.e., fast charge, and fast discharge) into the control system. These modes are incorporated through two nonlinear functions,

Control systems based on optimization methods can be the proper solutions in determining the critical and unknown parameters of the MG systems [28, 29]. According to Figure 3, the optimal droop controller produces the reference value for the output current of the ESS. This current is given by:

The reference current includes three terms. The first term is produced by the DC-bus voltage droop controller given by:

where

### 2.1 Adaptive parameters definition

The other two terms,

where

Figure 6 shows the way to calculate the current reference based on the DC-bus voltage for the Battery or ESS. This figure shows, the proposed controller provides two extra modes (i.e., fast charge and fast discharge), when the DC-bus voltage is lower than

### 2.2 Adaptive parameters range

In order to achieve a stable and reliable system, the limitation on the numerical domain of Eq. (2) should be considered. The aforementioned limitation is set to meet the requirements of the implemented control system. The considered limitation, which is defined according to voltage regulation range, resources power rating, and load demanded power, will be discussed in detail as follows. In the Table 1 all the implemented components and variables are listed. The natural Logarithm domain and charge/discharge rate limitations of the implemented batteries, specified the values of

Symbols | Parameters | Values |
---|---|---|

Nominal Output Power for Battery#1 converter | 1 kW | |

Nominal Output Power for Battery#2 converter | 1 kW | |

Nominal Output Power for PV#1 converter | 1 kW | |

Nominal Output Power for PV#2 converter | 1 kW | |

Switching Frequency | 100 kHz | |

Nominal DC MG Voltage | 190 V DC | |

Battery Bank Voltage | 80 V DC | |

PV Bank Voltage | 80 V DC | |

Battery input Inductor | 150 | |

PV input Inductor | 330 | |

Output Capacitor | 200 |

The upper range of

Finally the upper and lower range of

In the implemented control system, the proposed range of the DC-bus voltage is considered to be

and

Therefor, the upper and lower range of

The main advantages of the profile proposed in Figure 5 are twofold. It provides a much better dynamical result for the ESS to utilize the available energy optimally. It also provides a small margin in the range of DC-bus voltage or its variations. Thus, it gives a chance for the converters to operates more optimally. The proper voltage deviation and desired power-sharing can be achieved by this method adaptively and autonomously, without any switching modes which lead to the harsh transients. Figure 8 shows the flowchart of the control system for ESS. This figure shows how various modes of operation get activated by the DC-bus voltage. The (

## 3. Optimal droop control parameters

In this section, the procedure to determine the optimal values of the parameters for the proposed optimal droop controller is described. The objective is to find appropriate values for four parameters:

The proposed algorithm is based on sequential quadratic programming (SQP) [33], which is an iterative method for nonlinear optimizations. It can handle any degree of non-linearity, including non-linearity in the constraints [32]. Figure 10 shows the block diagram of the energy storage system with the proposed control system with the all details. This diagram shows the nonlinear optimization block with its inputs and outputs. Figure 11 shows that the SQP algorithm calculates the optimal values for the adaptive parameters. The proposed controller uses these values to generate the nonlinear functions

The optimization variables are defined as:

where

The general form of the objective function is defined as:

where

Having two modes of operation (charge and discharge modes) and more than one optimization variable, the need for the cost function to optimize more than one variable simultaneously, will be increased. The cost functions for this optimization problem are defined as:

Discharging mode:

Charging mode:

The total cost function is defined as the weighted sum of the aforementioned functions given by:

where

The

Case 1:

Case 2:

Case 3:

According to (25) and (26), two operating cases have been considered for the discharge mode based on

## 4. Stability analysis

In this section, the stability analysis of the proposed control method is performed. The proposed optimal droop control system utilizes profiles with linear and nonlinear parts. When the system operates in the linear part (i.e., conventional droop profile), the stability analysis is straight forward. However, nonlinear methods (e.g. the Lyapunov stability theory) must be used to analyze the stability of the nonlinear part (the stability analysis has been carried out only for the islanded mode of operation) [34, 35].

Figure 13 shows the block diagram of the closed-loop control systems and the schematic diagram of the converter. According to Figure 13, the dynamical model of the battery is also considered in the schematic block diagram. According to Figure 13, the state-space model of the ESS is given by [29]:

where,

According to (28), the system dynamics include fast changing current,

According to (28) and Figure 13, the dynamics of the DC/DC converter for the current loop is given by:

In (29),

where

According to Figure 13, the voltage loop includes the nonlinear droop block and the closed loop block of the inner current control loop. It is worthwhile to mention that the voltage loop does not try to render the voltage error zero. Thus, the asymptotic stability is not required and the boundedness of the voltage variables is the only requirement. In order to investigate the boundedness, the energy function for the voltage error signal is defined as:

where

According to (28) the dynamics of the voltage error is given by (due to the fast varying current loop, it is assumed that the inductor current and duty cycle have already reached their final values):

The derivative of the energy function (32) is given by:

due to the fact that

## 5. Simulation and experimental results

Simulation and experimental results are presented in this section. In Tables 1 and 2 the specifications of the DC/DC converter used in the experimental prototype and simulations software are given in.

Symbols | Parameters | Values |
---|---|---|

Nominal Output Power for Battery#1 converter | 500 W | |

Nominal Output Power for Battery#2 converter | 250 W | |

Nominal Output Power for PV converter | 500 W | |

Switching Frequency | 100 kHz | |

Nominal DC MG Voltage | 190 V DC | |

Battery Bank Voltage | 80 V DC | |

PV Bank Voltage | 80 V DC | |

Battery input Inductor | 150 | |

PV input Inductor | 330 | |

Output Capacitor | 200 |

The DC MG configuration is shown in Figure 3 which implemented to obtain the simulation results. The concept of dropbased control is based on reducing the voltage deviation caused by the change in MG load. Therefore, to simulate voltage deviation, two types of step change are applied in MG Load. The performance of the proposed control system is compared with the conventional drop-down method in reducing the MG voltage deviation. All the simulation results are implemented with

Figure 20 and 21 show the DC-bus voltage variations for different values of

A small-scale DC micro-grid set-up has been implemented to evaluate the performance of the proposed method. The implemented experimental setup includes three boost converters in the power conditioning systems for the two energy storage (battery1 = 500 W and battery#1 = 250 W) and solar systems (PV panel = 500 W) with variation of DC loads. The specifications of the implemented converters are given in Table 2. Figure 22 shows the experimental prototype of the bidirectional DC/DC converters, solar, battery#1, and battery#2 converters. The implemented converters use three separate phases for optimal performance (each phase changes phase 120 degrees to reduce the current wave). Figure 23 shows a test prototype including two battery converters, a PV converter, a PV simulator, a battery simulator and a DC load to evaluate the proposed control system in the case of practical situation. For cost and safety reasons, experiments are performed at reduced power scale (1/2). All test results are based on a nominal voltage of

Figure 24 shows the high frequency wave forms of the implemented boost converter. Figure 25 shows the performance of the PI controller in tracking the reference value of the output current. The proposed method is validated under light and heavy load changing conditions with

Load step change | Method | Batteries SOC value | Voltage deviation | Voltage deviation improvement* | Compensated load current | |
---|---|---|---|---|---|---|

Battery #1 | Battery #2 | |||||

Reference to Light Load (500 W to 50 W) | Conventional | NA (80%) | 17 V | NA (0%) | 0.9A | 0.42A |

Proposed | 80% | 7 V | 58% | 1.2A | 0.65A | |

Reference to Full Load (500 W to 1100 W) | Conventional | NA (80%) | 20 V | NA (0%) | 1.1A | 0.55A |

80% | 6 V | 71% | 1.8A | 0.93A | ||

Proposed | 60% | 11 V | 45% | 1.5A | 0.75A | |

40% | 14 V | 31% | 1.3A | 0.65A |

### 5.1 From reference to light load of SoC = 80 %

Figure 26 illustrates the performance of the conventional droop control when the load is changing from reference value to the light load (from 500 W to 50 W). The minimum voltage devotion in the conventional method is

### 5.2 From reference to full load of SoC = 80 %

Figure 28 presented the conventional droop control performance when the load changes from reference value to the full load (from

### 5.3 From reference to full load of SoC = 80 % , 60 % , and 40 %

Figures 29–31 illustrated the proposed control system performance in maintaining the DC voltage at three values of

Figure 32 shows the efficiency curve of the battery converter in the full range of output power variation from zero to full load. The rated power of the battery converter is 500 W as mentioned in Table 2. It should be mentioned that the proposed control system is a supervisory control system that control the flow of power between the converter and the DC grid by providing power references of the converter controller. Therefore, the proposed control system does not have any effect on the efficiency level of the converters and there are no extra losses caused by the proposed method. Moreover, the proposed method affects the control system only in transients and in steady-state operation, the control system is not affected by the proposed method.

## 6. Conclusion

In this chapter, a new adaptive droop control technique for the Battery or ESS has been proposed in the islanded mode. The proposed method provides a very tight DC-bus voltage regulation, while charge/discharge control task of the battery system is performed. In this control scheme, two extra operation modes (i.e., fast charge and fast discharge) has been proposed, which can offer an optimal performance for the DC MG. Thus, the extra power generated by the renewable energy sources can effectively charge the battery so fast. In case of voltage dropping, the battery is fast discharged, which can keep the desired DC-bus voltage range. In addition, a nonlinear optimization method has been introduced to determine the adaptive parameters in the optimal droop controller. Experimental and simulation results have validated the superior performance of the presented controller in comparison with the conventional controller.