The minimum inductor size required to achieve the required output voltage Vout for an input voltage of Vin is given by Equation 2, and the inductor ripple current ∆Il is given by Equation 3.
In Equation 3, ∆Il is the inductor ripple current and f is the switching frequency of the converter. The minimum size of the output capacitor required to achieve the ripple voltage of ∆Vout is given by Equation 4.
A boost converter has a non-linear relation between the duty cycle and output voltage due to the non-linear characteristics of the inductor. When an inductor changes, the voltage drops across it decreased exponentially and current through it increases exponentially. The inductor current and voltage have an exponential relation with charging time. The exponential charging characteristics of a boost converter can be seen from Equations 5 and 6.
It can be seen from Equations 5 and 6 that the charging time of the inductor is exponentially related to the inductor voltage and inductor current. The output voltage of a boost converter is directly proportional to the voltage dropped across the inductor. For a fixed operating frequency, the duty cycle and output voltage are also going to be related exponentially. This also creates non-linearity between the output voltage and PWM duty cycle in a boost converter.
A bidirectional buck-boost converter is a DC/DC converter that allows the power to flow in both directions. The converter acts as boost converter when the operated no forward mode and the converter will act on buck mode when operated on reverse power flow mode. As it can be seen from figure 3 that the bidirectional boost converter consists of two MOSFETs. When operating on boost mode Q2 is supplied with the PWM and Q1 is only turned on when Q2 is turned off. When Q2 is turned on inductor l1 charges. When Q2 turns off Q1 is turned on and charged inductor discharges through Q1 to the capacitor C2. This process keeps on repeating while the converter is operating on boost, forward power flow mode. When the converter is operated on buck backward power flow mode Q1 acts as a high-speed switch to control the power and Q2 acts as freewheeling MOSFET when Q1 is turned off. Q1 and Q2 are supplied with PWM signals inverted to each other.
When operating on boost mode, the inductor size required for the given converter to generate the required output voltage for the given input voltage is given by equation 8. Similarly, the inductor ripple current is given by equation 8. The minimum capacitor size required on output is given by equation 9. When the converter is operated on buck mode inductor size required is given by equation 13. The inductor for the bidirectional buck-boost converter was selected using equation (7) and equation (8). The inductor satisfies the minimum requirement criteria of both equation (2) and equation (8).
Similarly, equation 9 shows how a capacitor should be chosen for the input of the converter. The minimum value of the input capacitor should be greater than the value given by equation 9 where Iin is minimum
Converter 1 and converter 2 are boost converters and converter 3 is a buck-boost converter. Converter 1 and 2 operate in current regulation mode and converter 3 operate in voltage regulation mode. PI controller is used for current and voltage regulation. Logic level MOSFET were used in this setup. To drive the MOSFETs on the converters IR2110 MOSFET driver was used. PI-based feedback controller for boost converter is as shown in Figure 4 and Figure 5. The control parameters are given in table 6 for the converters used in this project. The PWM resolution used in the project was of 12 bits. Similarly, the resolution of the ADCs used in the feedback systems was also 12 bits. The sampling frequency of ADCs were maintained around 1khz for all converters and gate driving frequency was kept at 31khz for all converters.
Figure 4: PI voltage regulation controller for Buck-boost converter
Figure 5: PI current regulation controller for boost converter
6. Coordination strategy
In renewable energy-based microgrids, there is constant fluctuation in power generation. Because of which the supply capacity of the generator continuously varies. So, there is a need for a central control system that coordinates the power flow between distributed generators. In the developed system storage system acts as a grid forming generator and the rest act as grid supporting generators. The storage system is connected to a buck-boost converter which connects to the bus. Solar generators are connected to the grid with the help of boost converters. These converters normally work in MPPT mode and push the maximum possible current to the bus and also help reduce strain on the grid forming converter. In this way storage system contributes the least possible power while maintaining bus voltage. If the generation is more than demand then the grid voltage will rise above the required level. To bring down the grid voltage back to the required level, the grid forming converter will operate on buck mode and draw a controlled amount of power from the grid to maintain constant bus voltage. The power drawn from the grid will either be used to charge the battery or directed to dump load. Buck-boost converter will help maintain constant bus voltage by drawing power from the bus, however, this mode of operation will put unnecessary strain on the Boost converters on the generator's side. If the power is being dumped to dump load then the SCADA system will be notified about this condition and SCADA will instruct one of the generators to change their mode of operation to controlled current source mode and reduce the power contribution by the same amount which is being drawn by dump load, which will reduce strain on the MOSFETs’ of the converter. This operation will be reversed if there is a power deficiency in the grid. In this system grid forming and current regulation mode-based converters will use PI controller and MPPT converters use Petrov and observe algorithm. Following is the grid coordination strategy proposed in this research.
In case of any load or generation change event grid forming converter is responsible for maintaining grid voltage. Normally all generators run in MPPT Mode and storage systems on grid forming mode. In this mode of operation two conditions are possible, either the generation is higher or lower than demand. If the generation is higher than demand and the battery is not fully charged excess generation is used to charge the battery, but if the battery is already fully charged the excess power goes to dump load. In this condition, both MPPT converter and Grid forming converters are bearing unnecessary strain, so to reduce strain on the converters SCADA calculates excess power being generated and commands the MPPT converter to act as current source converter and reduce power by the required amount, reducing strain on both Grid supporting and forming converters. After this, if generation is lesser than the demand while grid forming converter is contributing more than 10% of the demand then generation side converters will again go to MPPT mode. In the proposed system, SCADA has a communication time delay of up to 5 seconds. So transient stability of the grid is maintained by grid forming converter due to communication delay in SCADA. However, converters in doing so bear unnecessary strain on themselves. So, SCADA mitigates unnecessary strain in the converters by coordinating the power contribution of the converters in the grid because of which converters run optimally in a steady-state condition.
Generation monitoring and control is one of the main functions of the SCADA system. On the generation side, two solar generators of 150 watts and 50 watts are used. Each of the generators is connected to boost converters. The boost converters convert the generation voltage to a steady bus voltage of 48 volts. The power rating of each converter is 150 watts. Similarly, battery storage is also connected to the bus with a buck-boost converter. The power contribution of these systems to the grid is monitored and controlled by the SCADA system. Here boost converter connected to the battery works as a grid forming converter. The main function of this converter is to maintain a steady grid voltage at 48 volts. If the battery system is in discharging state all other converters will act as current source converters and try to inject as much current to the grid, while storage is in charge of maintaining grid voltage. If the generators are generating and injecting enough power into the grid to sustain the grid by themselves then one of the generators will be given the task to act as a grid forming converter after that battery will go to charging mode and act as a load. Similarly, if the second grid forming controller goes to zero power contribution condition, then the last converter will go to voltage regulation mode and maintain the grid. In this way, one of the converters will work as a voltage source and the rest will act as a current source converter. to perform this experimental setup was developed as shown in Figure 51. Figure 52 shows the responce of the system during load fluctuations.
To connect the multiple generators to the grid there is a need for a control system that tells how much power to draw from each generator, which generator should act in grid forming, and the grid following configuration. The stability of the grid in the proposed system will be maintained by the grid forming converter and power coordination in the grid will be done by the SCADA system. when load or generation changes occur in the grid, a grid-forming converter will draw or push the power from or to the grid depending upon the need. If a grid forming converter is pushing power to the grid, then SCADA will check if the power drawn from the generators can be increased. If yes then the SCADA will instruct the generator to increase power contribution which will cause the reduction in power contribution of the grid forming converter (Storage system) as shown in Figure 56.
Similarly, if there is a sudden decrease in load in the system the grid forming converter will draw power from the grid and direct it to dump load. In this condition, the three is excess power in the grid which is causing unnecessary strain on both grid-forming and generation side converter. in this case, SCADA will instruct generation side converters to reduce power contribution by the necessary amount. The response generation side and in this case is as shown in Figure 57.