1. Introduction
A DC microgrid (DCMG) is a promising solution for integrating renewable resources at a low scale [
1] and powering electric vehicles, spacecraft, ships, submarines, and telecommunication systems [
2,
3,
4]. Most distributed energy resources (DER) and energy storage devices are inherently DC, therein the importance of DCMGs in modern systems [
5,
6]. Another important factor is the increasing use of DC-loads in residential and commercial areas [
7]. These loads include lighting systems, computers, servers, data centers, battery chargers, and variable speed drives for heating, ventilation, and air conditioning. Electric vehicles and their charging stations are also DC-loads that may be integrated into a DCMG [
8].
A DCMG can operate standalone, or exchange power with the AC distribution system [
9]. Regardless of the operation mode, it must operate with high efficiency, stability, and safety standards. Therefore, a specialized control must be designed to achieve these standards. Several control objectives are achievable: voltage regulation, power control, load sharing, loss reduction, energy management, and cost minimization [
10]. A hierarchical scheme of three levels is typically adopted to achieve one or several of these objectives [
11]. The primary control stabilizes the system at a given operating point, while the secondary control brings the system to the nominal voltage, and the tertiary control achieves economic dispatch. The primary control is decentralized using a droop in power electronic converter [
12]. The secondary controller can be centralized, distributed, or decentralized according to its communication links. Generally, centralized and distributed controls require some communication infrastructure [
13]. Tertiary control is usually an optimization algorithm that minimizes costs or power loss [
14].
Nowadays, model predictive control (MPC) is a popular control strategy, especially in power electronics [
15]. MPC uses a mathematical model to predict the system’s future behavior in a predefined horizon and select the optima actuation by minimizing a cost function at each sampling step [
16]. MPC has outstanding advantages such as fast transient response, flexibility, easy implementation of multiple objectives, and control restrictions for linear and non-linear systems [
17,
18]. A significant advantage of MPC is that the predicted system outputs may reduce the measurements simplifying the hardware in the implementation stage. Meanwhile, the main disadvantage is the computational complexity when the prediction horizon is high [
19].
According to the mathematical model and communication infrastructure, MPC can be centralized, distributed, or decentralized. Distributed and decentralized approaches are helpful to reduce the computational effort [
19]. Decentralized controls regulate the voltage at the point of common coupling (PCC) in a scalable and reliable way without communications with other DER [
20]. The inclusion of the power converter model in the MPC formulation allows for replacing inner loops and droop control. A decentralized MPC is a suitable solution for the constant power load instability problem [
21]. In contrast to decentralized approaches, distributed methods require some communication links. Distributed-MPC requires local measurements and predicted information from its neighbors [
22]. MPC execution results in a suboptimal solution in decentralized and distributed strategies since only partial information is available. Instead, an optimal solution can be obtained when all the information is available, as it happens in centralized MPC (CMPC) [
23].
There are few publications about CMPC in DCMG. Some works present CMPC controllers that act at the top level of the hierarchical control structure, not requiring a DCMG electrical circuit. For example, the optimal operation of some interconnected microgrids is studied in [
23,
24], while a CMPC that determines optimal load profiles for electric vehicles is presented in [
25]. In the literature, MPC is usually limited to the control of only one DER [
26]. In these applications, the control takes into account the model of the power converters that regulate the power exchange between microgrid components. Higher DERs, loads, and the number of storage elements increase the mathematical model complexity. The computational effort reduction is a huge challenge in CMPC.
In the proposed controller in this paper, the high computational effort of predictive controllers is approached in two ways. The first one consists of the mathematical model simplification that is used in the prediction. In the model, a microgrid admittance matrix is used, which is reduced only to those nodes where variable power is injected or absorbed. The other way to reduce computation time is to use a one-step prediction horizon. Regarding the control strategy, this work proposes a CMPC to replace the primary and secondary control of the hierarchical control architecture by a single control strategy. This feature is a novelty since the typical case is to use independent controllers: a droop control on the primary level and a typical control of the secondary level [
27]. Additionally, the dynamic model of the DCMG allows to control both voltage and power, prioritizing the variable to control by adjusting a weighting factor.
An additional feature of this work is the validation of the controller on a hardware-in-the-loop (HIL) platform. Usually, the results of the controller’s performance at primary and secondary levels in DCMGs are presented only at simulation level. HIL experimentation has been positioned as a significant step in the controllers design for complex systems prior to their implementation in test systems [
28]. A HIL tool is used to emulate the proposed DCMG. Several versatile buck–boost converters are used as an interface to transfer power at the supply and power consumption nodes, which increases the power access and control capability in this DCMG. The versatile buck–boost converter has been presented for different applications, such as fuel cell hybrid power [
29,
30], automotive traction applications [
31], and is proposed as a power electronic building block in [
32].
The motivation for this research is the potential that DC microgrids have in integrating renewable energies and the increase in loads that demand energy directly in DC. The scientific community’s interest in the study of DC microgrids and the application number is also increasing. This work proposes a new control strategy for DCMG. The main contributions of this paper are as follows:
A mathematical model simplification for the microgrid is developed in which the admittance matrix is reduced, decreasing the computational effort.
A single control strategy is developed based on CMPC, which is specialized in replacing the primary and secondary control of the hierarchical control architecture, allowing control of both voltage and power.
Finally, the use of the same power electronics converter for the interface between the supply and power consumption node is proposed; this technology is the versatile buck–boost converter (VBCC). The VBBC is characterized by high efficiency; variables are easily controllable and can support uni- or bi-directional power flow without hardware modifications. These features make the VBBC suitable for the application.
This paper is organized as follows:
Section 2 presents the DCMG model and the controller design. The test model description is presented in
Section 3. After, experimental results are shown in
Section 4, followed by conclusions in
Section 5.
4. Results
The proposed controller has been validated using hardware-in-the-loop (HIL). HIL tools have become very popular in the controller design and validation stages. HIL can emulate parts of the test system such as controllers, power converters, or the power systems where the converters are integrated [
38]. This reason makes HIL tools especially useful in microgrid applications. The experimental setup based on HIL is shown in
Figure 8.
The experimental results show the evolution of the voltages, currents, and powers in the nodes of the reduced DCMG (nodes 3, 5, and 7) from a null initial condition to a steady-state condition. The reference voltage remains fixed at 48 V, and the power references change from an initial to a final one dataset defined as Test1 and Test2, which are listed in
Table 4. It is essential to mention that the sign convention used for current and power is a positive sign for sources and a negative sign for loads. Moreover, the sampling period (
) is
s.
Additionally, the proposed MPC controller performance is compared with the average voltage control.
4.1. Model Predictive Control
The weighting factor
must be conveniently defined to apply the proposed control law (Equation (
13)).
allows the controller to prioritize between voltage or power tracking.
Figure 9a,b show the root mean square error (RMSE) of voltage and power tracking as a function of the factor
. The power references in
Figure 9a,b are, respectively, the sets Test1 and Test2, while the DC-bus voltage reference is 48 V in both cases.
Figure 9a,b show that
, which minimizes the power RMSE for Test1 and Test2, are
and
, while
minimizes the voltage tracking.
4.2. Average Voltage Control (AVC)
The average voltage, operating in conjunction with a droop control, is proposed to compare the predictive controller. The average voltage is a distributed secondary technique of the hierarchical control scheme. Droop control is a classic control at the primary level. It is a proportional controller, so it operates with a steady-state error. The droop control response is modified by the AVC technique to reduce the steady-state error. Each converter measures its voltage and then communicates it with the other converters to modify this gain. Thus, every converter, or most of them, will have the measured voltage of its neighbors. Then, using the global average of these voltages, each converter computes its control signal, modifying the droop gain. Finally, the globally average voltage of the converters will follow the bus voltage reference. The block diagram of the joint operation of both techniques is shown in
Figure 10. The controller parameters are:
and
.
4.3. Results and Comparison
Experimental results are shown in
Figure 11,
Figure 12,
Figure 13,
Figure 14 and
Figure 15. The first test evaluates the controller performance to a power reference change.
Figure 11 and
Figure 12 show results from CMPC and AVC, respectively. In both cases, the nodes’ voltage, current and power responses are shown for a reference change from dataset Test1 to Test2. The average results are shown in
Table 5,
Table 6 and
Table 7. Waveforms in
Figure 11 and
Figure 12 depict that both controllers exhibit similar behavior in steady-state. The average powers obtained by the controllers for each reference, which are listed in
Table 7, show that the CMPC performs a better power tracking. This observation is based on the errors (RMSE) listed in
Table 7, where it can be seen that the maximum errors of the CMPC and the AVC control are
and
, respectively. Regarding the transient responses, the CMPC exhibits a shorter settling time, while the AVC shows a higher overshoot in conjunction with a high-frequency oscillatory component. In addition, the waveforms obtained by applying CMPC present a uniform ripple, while the responses of AVC present a non-uniform ripple and high noise content.
The next test shows a comparison between the proposed CMPC and the AVC. This test achieves the power references defined by the dataset of Test1, starting from null initial conditions. The start-up voltage, current and power responses in nodes 3, 5, and 7 are shown in
Figure 13 for CMPC, and
Figure 14 for AVC.
Figure 13c shows how the proposed CMPC rapidly follows the given power references without overshoot, while the AVC presents a damped response and a longer settling time, as shown in
Figure 14c. The settling time of the CMPC and AVC are 4 ms and 60 ms, respectively.
In general, the good dynamic response of the proposed CMPC is validated both at start-up and the reference change. The controller reaches the reference without overshoot and in a minimum time in both cases. On the other hand, the AVC controller presents a damped behavior in transitions. This behavior depends on the internal PI controller-tuning of the AVC. Then, adjusting the PI constants can achieve a balance between settling time and overshoot.
The controller performance in nodes 3, 5, and 7 was shown in the previous results, where VBBCs act to stabilize the microgrid according to the proposed predictive controller. In addition, there are constant power loads connected to nodes 2 and 8, where there are also VBBC that regulate the power regardless of the microgrid operation conditions. Thus, the sudden power change that occurs at
s is detected by the converters connected at nodes 2 and 8 to continue supplying the load with constant power. The current waveforms supplied by the converters to the load at nodes 2 and 8 during the sudden power change are shown in
Figure 15. The timebase in
Figure 15a,b are 100 ms/div and 10 ms/div, respectively. These figures show load current results before and after the sudden change that occur in
s. It can be noticed how each converter detects this change and stabilizes the constant power load current.