# DC-Microgrid System Design, Control, and Analysis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Photovoltaic DC Microgrid System

## 3. Simulink Representation of the Complete PV System and the Proposed MPPT Techniques

#### 3.1. Modeling of the Solar PV System

_{d}is

_{B}= Boltzmann’s contact; $q$ = electron charge; I

_{d}= diode current (A); V

_{d}= diode voltage (V); I

_{0}= diode saturation current (A); T = Cell temperature (K); n

_{i}= Diode ideality factor; and N

_{cell}= Number of cells connected in series.

#### 3.2. Modeling and Simulation of the Boost Converter

#### 3.3. Incremental Conductance MPPT

#### 3.4. Perturb and Observe Algorithm

#### 3.5. Practical Swarm Optimisation for MPPT

- Step 1. (Parameter Selection): As far as the planned MPPT algorithm is concerned, the converter’s duty cycle is described as the particle position; the derived output power being considered to operate as the fitness vale assessment function; with each particle’s initial 99 velocity and position being initialized at random and in a consistent distribution within the search space.
- Step 2. (Fitness Evaluation): The fitness value of particle i, is calculated subsequent to the controller issuing the duty cycle directive, symbolizing the location of particle i.
- Step 3. (Update Individual and Global Best Data): pbest, i and gbest positions and values are revised by evaluating the freshly computed fitness values with those obtained previously, plus having pbest, i, and gbest and their resultant positions replaced accordingly.
- Step 4. (Update Individual and Global Best Data): Updating fitness values, gbest (global best fitness values) and pbest (individual best positions), of each particle is achieved by having the fresh computed fitness values with the preceding examples as well as substituting the gbest and pbest equivalent to their positions as needed.
- Step 5. (Update Velocity and Position of Each Particle): By engaging the assessment of all particles, each particle’s positions and velocities in the swarm are updated via engaging PSO equations.
- Step 6. (Convergence Determination): The converge criterion are located either to the optimal solution or reach the maximum number of iterations. If the convergence criterion is met, the process will terminate; otherwise, rerun Steps 2 through to 7.
- Step 7: (Re-initialization): By considering the PSO technique, the convergence technique is either to establish the most favorable solution, or attain the maximum number of iterations. However, the fitness value in PV systems does not remain constant, since it varies respective of the applied load as well as the atmospheric conditions. For that reason, there is the need to reinitialize PSO while a search recommenced for a novel method of identifying the novel MPP upon having the output of the PV module varied.

#### 3.6. PV Simulink Model

#### 3.7. Modeling of Bidirectional Buck-boost Converter

_{S}) and load resistance (R

_{L}). The critical inductance for the boost converter is:

_{o}, inductor ripple current is ∆I

_{L}.

#### 3.8. Bidirectional Buck-Boost Converter Controller

#### 3.9. Modeling of the Inverter and Inverter Controller

#### 3.10. Modeling of the Battery

## 4. Input Irradiance Variation Effect

^{2}, the PV gives the highest power similar to its rating at almost 20 kW. While decreasing the irradiance, the power output of the PV also decreases with time. As described above, in this system the DC grid voltage of 340 V has been used. DC grid voltage and power supplied to DC load obtained in simulation as shown in Figure 20. As the PV array cannot produce less than the grid voltage, the DC-DC boost converter boosts the PV array voltage to 340 V. From the figure, we can see that DC grid voltage is around 340 V and the power supplied to the DC load is around 1000 W though there are fluctuations when the irradiance suddenly drops down or goes up for both the DC grid voltage and power provided to the DC load.

^{2}, the produced power from the PV system is not enough to feed the loads, so the bidirectional converter is working in boost mode to make the battery voltage from 160 V to 340 V, causing the battery to discharge as shown in the Figure 24. When the input irradiance is more than 700 W/m

^{2}the battery works in charging mode, as in the 3 and 4 mins the irradiance is around 790 W/m

^{2}and the battery charges during this period.

## 5. Stability Analysis Investigation

- Set A: Set of the states x within an arbitrary “radius” $\beta $ (in other word, satisfying the inequality p(x) < β, where p(x) has an arbitrary shape)
- Set B: Set of the states x for which an arbitrary $\gamma $ is an upper bound of the Lyapunov function V(x);
- Set C: Set of the states x for which $\dot{V}\left(x\right)$ is negative. It should be noted that this the only set that depends directly on F(x);

- Step 1: “To start the VS iteration, a first estimation of the LF is determined using the linear approximation of (3) in the vicinity of the equilibrium point yielding the following”;$$\dot{x}=A\xb7x$$$${A}^{T}P+PA+Q=0$$The corresponding LF is determined using:$$V={x}^{T}Px$$
- Step 2: “In this step, V(x) is held fixed while $\gamma $ and ${s}_{2}\left(x\right)$ are determined using Equations (15) and (17), using the bisection method to iteratively determine the biggest value of $\gamma \text{}$;”
- Step 3: “In this step, V(x) is held fixed while both $\beta $ and ${s}_{1}\left(x\right)$ are determined using Equation (16). However, Equation (10) is bilinear in $\beta $ and ${s}_{1}\left(x\right)$, bisection is used to obtain ${s}_{1}\left(x\right)$ while keeping $\beta $ fixed”
- Step 4: “In this step $\beta $, $\gamma $, ${s}_{1}\left(x\right)$, and ${s}_{2}\left(x\right)$ are held fixed while V(x) is determined using Equations (14) through (17) and normalized with respect to $\gamma $ to avoid numerical problem”;
- Step 5a: “If the value of $\beta $ converges, the iteration process is stopped; otherwise, the process flow restarts at step 2”;
- Step 5b: “Determine the variation in the shaping function following”$$\Delta p\left(x\right)=p\left(x\right)-V\left(x\right)$$

_{2}> 0, i

_{1}> 0.

_{T}= [x

_{1}, x

_{2}, x

_{3}, x

_{4}] = [i

_{1}, v

_{1}, i

_{2}, v

_{2}] and the system can be rewritten as state space model:

_{1}> 0, x

_{4}> 0

_{1}as zero we get;

_{2}as zero we get;

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 7.**IncCond algorithm relations for Figure 8 flowchart.

Parameters of the Inverter | Value |
---|---|

Dc grid Voltage | 340 VDC |

DC bus capacitor | 1000 µF |

Filter capacitors | 1000 µF |

Filter Inductor | 18 mH |

Frequency | 50 Hz |

Symbols | Description | Value | Unit |
---|---|---|---|

Q | Rated Capacity | 1150 | Ah |

SOC | Initial State-of-Charge | 50 | % |

V | Nominal Voltage | 160 | V |

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**MDPI and ACS Style**

El-Shahat, A.; Sumaiya, S.
DC-Microgrid System Design, Control, and Analysis. *Electronics* **2019**, *8*, 124.
https://doi.org/10.3390/electronics8020124

**AMA Style**

El-Shahat A, Sumaiya S.
DC-Microgrid System Design, Control, and Analysis. *Electronics*. 2019; 8(2):124.
https://doi.org/10.3390/electronics8020124

**Chicago/Turabian Style**

El-Shahat, Adel, and Sharaf Sumaiya.
2019. "DC-Microgrid System Design, Control, and Analysis" *Electronics* 8, no. 2: 124.
https://doi.org/10.3390/electronics8020124