DC-link Voltage Control Using Battery-side Controller in a Hybrid System

. This work aims to model the PV-Battery hybrid system as well as design a controller used to stabilize the voltage at the DC-link for the load. It is intended to make the voltage between the battery and PV system stable, or it can be said that the voltage at the load becomes stable. The input system used is battery current and PV current is considered as a disturbance because of its characteristics that cannot be controlled when generating maximum power. Therefore, a full order state feedback controller with integrator is designed to reduce the steady state error. In addition, an algorithm is needed to estimate the PV current and at the same time reduce sensor utilization. This work utilizes Disturbance Observer to estimate these parameters as well as disturbance rejection. To verify the proposed system, there are three scenarios. The first scenario tests the system with constant PV load and current. The second scenario tests the system with varying PV current, and finally tests the system with varying load and current. From the scenarios, the system performed well with output voltage RMSE values equal to 0.003 in the first scenario, 0.4 in the second scenario, and 0.481 in the third scenario.


Introduction
Photovoltaic (PV) technology is one of the breakthroughs in the field of renewable energy whose development is quite significant.Climate change due to the use of fossil-powered plants is one of the reasons for the use of this technology to replace conventional technology.There has been a lot of research developed to improve the performance of PV systems, especially in the electrical devices.
It is undeniable that MPPT is a remarkable breakthrough to improve the efficiency of PV systems.However, this condition creates an open problem where the output voltage of the plant cannot be stabilized at a certain nominal value.In other words, the output power cannot match the load requirements.So that systems utilizing PV require additional components such as batteries to store its energy rather than directly delivering it to the load.Batteries are generally used for off-grid or islanded-grid PV systems.
Research [20] developed a power management strategy for PV/Battery by utilizing multiloop control and multi-segment adaptive droop control.The strategy successfully stabilizes the DC-link voltage when islanding conditions with inconstant load.To increase the reliability of PV Inverters can be done by utilizing batteries with system control strategies such as in research [21].However, the work does not discuss in detail the control algorithm used in the system.In contrast to this work, research [22] also utilizes PV-Battery in a hybrid manner by connecting the PV-Battery with a converter that is assembled in series.Since the system output is expected to be in AC form, PQ decoupling control and reactive power distribution methods are proposed to improve the reliability of the system.In addition, the utilization of droop control in the battery converter is also used to participate in regulating the grid voltage and frequency.The converter and controller topologies used are also able to reduce the communication load required on the PV system.
Based on the studies conducted, PV-battery hybrid technology can improve the reliability and performance of PV systems.This work focuses on the output voltage stability of the hybrid system.Unlike previous studies that applied the proposed system to AC networks, this study ignores this and focuses more on the stability of the system output (DC voltage).The contributions of this work include: • Modeling an integrated hybrid PV-battery system.
• Stabilize the system output by controlling the battery current with a simple structure.The problem statement is explained in more detail in the next sub-section.This is followed by system modelling to represent the dynamic state of the hybrid system.

Problem Statement and System Model
Voltage stability in the DC-link of a hybrid system is a necessity.Fluctuations in the DC-link can cause damage to the load.Therefore, a controller is needed that can ensure its stability.A simple under-test hybrid system is shown in Fig. 1.There are two main power-generating components, namely PV and battery.There are also two power converters that convert power from source to DC-link.With this condition, there are electrical resources that are only able to flow one-way power only, namely PV and resources that can flow two-way power, namely batteries.When the battery is charging, the current flows from the DC-link to the battery.Thus, the voltage on the DC-link will decrease.Conversely, if the battery is in discharging condition, the voltage on the DC-link will increase.Figure 2 is the modelling of the system in the form of an electrical circuit.In this case, the position of the battery is close to the load.To simplify the modelling, this study provides the following assumptions: Assumption 1: The resistance and inductance values between the battery and the load can be ignored.This is because the distance between the load and the battery is made as close as possible so that the value of   and   is very small.
Referring to Kirchhoff's law of voltage and current, the differential equations of the model can be written as in equations ( 1) to (3).
If the system objective is to stabilize the output voltage,   , then the battery system output current,   , can be taken as the system input.While the PV current,   , is considered as a disturbance.The detailed controller design is described in the next sub-section.

Controller Design
The mathematical model shown in equation ( 1) to equation ( 3) is a linear system model with disturbances.If it is defined that the capacitor voltage,   , is the output, the battery current,   , is the input, and   is the disturbance to the system, then the state space form of the system can be written in equations ( 4) and (5).
=  (5) where If the system parameters are shown in Table 1, it can be seen that the system poles are located at  1 = −3.2• 10 2 ,  2 = −5.16• 10 3 + 6.5 • 10 4 , and the last pole is located at  3 = −5.16• 10 3 − 6.5 • 10 4 .Thus, the system is stable.To make it easier when designing the controller, the parameter    is defined as a reference signal with a constant value.So that in steady state the system output voltage must be equal to the reference, or it can be written,   =    .If the error signal, , is the difference between the reference signal and the output voltage, then under steady state conditions,   =    −   ≈ 0. Furthermore, the influence of disturbances generated by   can be ignored.So, a full state feedback controller can be selected to force   ≈ 0. A simple full state feedback block diagram for the tracking case is shown in Fig. 3.There are three gains,  1−3 , whose values need to be known to make the system conform to the specifications.To simplify the design, the design is based on Assumption 2 as follows, Assumption 2: The disturbance parameter,   , is assumed to be 0 at steady state.Assumption 3: The load value,   , is assumed to be constant.

Disturbance Observer
Based on Fig. 2, it is known that the battery (left part) and PV (right part) systems are different systems.If it is assumed that they are far enough apart, then to transmit PV current data,   , to the battery controller requires sensors and transmitters.This can be constrained by noise or voltage drop when sending data.For this reason, a PV current estimation mechanism is needed.Several studies have successfully estimated Extended State Observer disturbances, including [25,26].However, this research utilizes the Disturbance Observer (DO) because it is simpler.The DO is generally shown in equation ( 7) [27].
where  is the gain matrix of DO with  = [ 1  2  2 ].Thus,   can be estimated.
The closed loop characteristics of equation ( 7) are determined by the eigenvalue of the matrix − � .Figure 3 is the overall block diagram of the proposed system.

Simulation and Result
This research utilizes MATLAB/Simulink software to verify the controller that has been designed.The computer specifications used are Intel Core i5-8250U CPU @1.6GHz Processor, 8 GB RAM, and 500 GB SSD M.2 PCIe read/write 3000MB/s.In addition, the controller gain parameters are shown in Table 2.There are three test scenarios to prove that the proposed controller effectively stabilizes the voltage on the DC-link.The scenarios are as follows: 1. Scenario  4. With constant PV loading and current, the voltage at the load can achieve a steady state error close to 0. In addition, the resulting rise time is also less than 0.001s.More specifically, the estimated   can reach the actual value of less than 2 × 10 −4 .In scenario 2, the system is loaded with   = 3.3.The   profile is shown in Fig. 5. (b).Based on the results, the estimated PV current is very close to the actual PV current.However, there is a difference during ramp conditions.This is because the algorithm works by utilizing error.However, when   returns to constant, the estimated value is equal to the actual value.When the   condition changes, the controller is still able to maintain the   value with less than 5% fluctuation.This shows that the system is robust to disturbances.When the DO is different from the actual, it has a direct impact on the controller output.When   is ramped up or down, the system output voltage response has a steady state error.As with DO, the controller designed is error-based, so the steady state error will be close to 0 when   / = 0.The last scenario calls for varying values of both   and   .At this stage the   profile is the same as in scenario 2. The   is changed based on equation (8).The system response in this test is shown in Fig. 6.Based on Fig. (a), there is an undershoot that occurs at seconds 0.003s and 0.008s.This is due to a change in the value of the load.However, the   response remains stable at its nominal value.Interestingly, this load change has no effect on the response of the   estimation which is still able to follow the actual value.
The verification details of each scenario in this work are represented in the form of RMSE in Table 3.The data is calculated when the system is in steady state.In other words, the RMSE is calculated at 0.001<t<0.01.In scenarios 1, 2, and 3, the RMSE of   is quite low, less than 1.Similarly, the RMSE of   is much smaller for each scenario.In scenarios 2 and 3, the RMSE value increases dramatically when compared to scenario 1.This is due to changes in the disturbance value and the load.The RMSE calculation in this work uses a very short time span, which is less than 0.001 s.Similarly, the simulation used for verification.Thus, although changes in load and system disturbances cause a decrease in system response performance, the ability of the system to correct the condition and return   to its nominal voltage in a very short time shows that the designed controller produces a good response.

Conclusion
A hybrid system with a combination of PV and battery has been modelled and obtained a stable linear system of order three.This work is focused on how to stabilize the voltage at the DC-link using the battery current under both charge and discharge conditions.Thus, the PV current which in fact cannot be controlled because it is assumed to use MPPT becomes a disturbance in the system.The proposed controller is a full order state feedback with an integrator added.In addition, a DO is also added to estimate the PV current.The estimation results are then used for compensation which is added directly to the input signal.There are three scenarios of system testing.From the three scenarios, changes in load and disturbance values cause the RMSE value to increase significantly.However, each scenario produces a good response characterized by RMSE less than 1.In addition, a short simulation time of 0.01s and a system rise time of less than 0.002s shows that the system can overcome disturbances with a very short time.
Although the test results show a good response, under conditions of ramp signal changes in PV current, the estimation results lag.Therefore, this case still requires an algorithm that can reduce the steady state error under these conditions.In addition, the concept of direct injection of PV current estimation results into the input signal basically cannot directly affect the system.This is due to the presence of line currents.Therefore, further research also requires an algorithm that can directly accommodate PV current estimation to directly affect the system as a disturbance rejection.

Fig. 3 .
Fig. 3. System Under Test with Detailed Controller

Table 1 .
System Parameters

Table 2 .
Controller Parameters 1: The load,   and PV current are constant,   .2. Scenario 2: The load,   , is constant and the PV current,   , is changing.3. Scenario 3: Both parameters are variable.All three tests use the same sampling time of 1 and a test time range of 0-0.01s.The first test is by giving   = 1 and   = 3.3.The test results are shown in Fig.

Table 3 .
System responses in scenario 2; (a) voltage output,   ; (b) estimated PV current,   , and actual PV current, ̃  .RMSE of   and   in All of Scenarios