# Driven Primary Regulation for Minimum Power Losses Operation in Islanded Microgrids

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Driven Primary Regulation for Minimum Power Losses Operation

_{1}, DG

_{2},…, DG

_{i}) connected to a load bus.

#### 2.1. Conventional Droop Control Method

_{Gi}and Q

_{Gi}are the real and reactive power generated by the i-th generator; K

_{Gi}and K

_{di}are the frequency and voltage droop coefficient of the i-th generator; f

_{x,i}and V

_{i}are the frequency and output voltage at the i-th generator; f

_{0i}and V

_{0i}are the frequency and voltage of the i-th generator at no load.

_{Gi}of the i-th generator is typically taken at its maximum value K

_{G}

_{maxi}, namely the ratio between the maximum output power P

_{G}

_{maxi}(rated power) and the maximum frequency deviation:

_{min}is the frequency lower limit [16].

_{xi}is the same for all the generators in the microgrid, from Equation (1) it derives that the real power sharing between the generators is function of the droop coefficients K

_{Gi}. Moreover, the microgrid operating frequency f

_{x}can be written for the generic i-th generator as it follows:

_{x}to f’

_{x}and the new value must be comprised in between the minimum acceptable frequency f

_{min}and the maximum acceptable frequency f

_{max}[23].

_{x}as a function of the real power generated by DG

_{1}, DG

_{2}, …, DG

_{i}

_{.}When the load increases, the active power of DG

_{1}changes from P

_{1}to P’

_{1}, the active power of DG

_{2}changes from P

_{2}to P’

_{2}, etc.… It is observed that, in standard linear droop control, the change of the real power demand of the generic i-th generator always stays proportional to its rated power. As shown in Figure 2, the real power demand variation leads to a slight change of the microgrid operating frequency f

_{x}and after a few oscillations, the frequency of the system is again stable at a new microgrid operating frequency f’

_{x}. The strength of conventional droop control is in its simplicity and reliability, but power sharing based on rated power cannot provide a good solution for optimization problems.

#### 2.2. Proposed Driven Primary Regulation Method

_{G}can be adjusted [24]. For example, in [25], it is proved that the coefficient K

_{G}of wind turbine is not constant. When wind direction and speed fluctuate, the output power changes and this means that the real power of the wind generator transferred to the primary frequency control changes. As a consequence, the value of K

_{G}should be picked out under various wind speeds. It is worth to highlight that, also in [2,19], different droop relations are required to resynchronize the system in different operating conditions.

_{Gi}, which is considered as the only adjustable parameter producing a new real power sharing among the two generators. The droop coefficients K

_{Gi}of all the generators are selected optimally in a given range [K

_{G}

_{mini}; K

_{G}

_{maxi}], according to the limitations of output power and frequency. For every load condition, an OPF problem is solved for finding a minimum–losses operating state, assuming that every generator is able to regulate its frequency droop coefficient.

_{bus}is the total number of buses of the microgrid and ${P}_{i({K}_{G})}$ is the injected power at bus i given by:

_{i}and V

_{j}are the voltages at buses i and j, respectively; δ

_{i}and δ

_{j}are the phase angles of the voltages at bus i, j; Y

_{ij}is the admittance of the ij branch; θ

_{ij}is the phase angle of Y

_{ij}; n

_{br}is the number of branches connected to bus i.

_{G}is the number of generators in microgrid; n

_{d}is the number of load buses; P

_{Gi}is the real power generated by DG

_{i}; P

_{Li}is the real power demand of the i-th load; P

_{loss}indicates the total real power losses of migrogrid; I

_{branchj}is the current flowing in the j-th branch of microgrid; I

_{maxbranchj}is the ampacity of the j-th branch of microgrid and n

_{branch}is the number of transmission branch in the microgrid.

_{0i}and Q

_{0i}are the real and reactive power of the load in the operating point; α, β are the real and reactive power exponents [3,28]; K

_{pf}is a coefficient ranging from 0 to 3.0; K

_{qf}is a coefficient ranging from −2.0 to 0 [27].

_{Gi}are the decision variables of the optimization problem, although they are not explicitly appearing in the objective function (5), they are contained in the expression (1) of generated powers in inverter interfaced units. The solution found for each load condition is an optimal operating point characterized the following state variables:

- The amplitude and displacement of the voltage phasors at the P–Q buses.
- The amplitude and displacement of the voltage phasors at all the P–V buses except the reference bus (Q
_{i}depends on V_{i}by (2)); - The voltage amplitude at the reference bus;
- The frequency of the system in the range [f
_{min}, f_{max}].

_{bus}nodes and 2xn

_{bus}variables. Consider the power sharing between two generators DG

_{1}and DG

_{2}, as shown in Figure 3, where the frequencies f

_{0i}are considered equal to f

_{max}.

_{2}are kept constant (continuous brown line) while K

_{G}

_{1}of DG

_{1}is varied (from the blue to the red dashed line) allowing to modify the real power contribution of each generator to the overall load demand. Finally, to ensure the stability of the system while adopting the new droop law, the frequency of the microgrid should be a monotonic function satisfying the following property [8]:

#### 2.3. Glow-worm Swarm Optimization Algorithm

- Step 1: Start.
- Step 2: Collect input data regarding the microgrid (including real power and reactive power of generators, bus voltages, features of the lines, droop parameters, etc.).
- Step 3: Initialize a population of glow-worms randomly. Every glow-worm is a potential solution of optimization problem.
- Step 4: Generate luciferin lo, local decision range ro at time t = 0.
- Step 5: The objective function is calculated by running the OPF for each solution and is stored in vector J(x).
- Step 6: Update the value of luciferin l
_{i}(t + 1) using (11):$${l}_{i}(t+1)=(1-\rho ){l}_{i}(t)+\gamma J({x}_{i}(t+1))$$ - Step 7: Find the neighborhood agents having stronger luciferin in the local decision range.
- Step 8: Update the probability of glow–worm i moving to neighbor j in the t iteration denoted by p
_{ij}(t):$${p}_{ij}(t)=\frac{{l}_{j}(t)-{l}_{i}(t)}{{\displaystyle \sum _{k\in {N}_{i}(t)}{l}_{k}(t)-{l}_{i}(t)}}$$_{i}(t) is the set of neighborhood of glow-worm i at the t-th iteration. - Step 9: Update the location of glow-worms as following:$${x}_{i}(t+1)={x}_{i}(t)+s\left(\frac{{x}_{j}(t)-{x}_{i}(t)}{\left|\right|{x}_{j}(t)-{x}_{i}(t)\left|\right|}\right)$$
- Step 10: Update the local decision range ${r}_{d}^{i}(t+1)$:$${r}_{d}^{i}(t+1)=\mathrm{min}[{r}_{s},\mathrm{max}[0,{r}_{d}^{i}(t)+\beta ({n}_{t}-|{N}_{i}(t)|)]]$$
- Step 11: Iterate the step from 5 to 10 until reach the maximum iterations number.
- Step 12: Show the results.

#### 2.4. Simulation of the Droop Control Loop

_{P}is the proportional gain constant; ${f}_{sw}$ is the switching frequency of the PWM; T

_{i}is the integral time constant and σ is defined as the symmetrical distance between 1/T

_{i}and 1/T

_{e}to crossover frequency f

_{c}. The recommended value for σ is between 2 and 4. By increasing σ, the system will have a better damping and higher phase margin, but its response will become slower [38]. The block diagram of the outer voltage PI controller is presented in Figure 5.

_{v}(s), an inner current control block G

_{C}

_{,CL}(s) and the integrator block L

_{v}(s), whose transfer functions are:

_{f}is filter parameters.

_{v}(s)

_{OL}and close loop G

_{v}(s)

_{CL}transfer functions of the current controller are defined as it follows:

_{f}and R

_{f}are the filter parameters and T

_{f}is the system time constant.

_{c}(s)

_{OL}and close loop G

_{c}(s)

_{CL}transfer functions of the current controller are defined as it follows:

## 3. Case Study

_{1}and DG

_{2}and two loads, is considered. The electrical parameters of the microgrid are reported in Table 2.

_{1}can provide real power in the range 0–0.3 pu, while DG

_{2}can operate in the range 0–0.2 pu. The no load-frequency f

_{0}is assumed the same for DG

_{1}and DG

_{2}and equal to 1.02 pu. The system frequency limits are set to f

_{min}= 0.98 pu and f

_{max}= 1.02 pu, meaning that the frequency must be within +/−1 Hz of 50 Hz.

_{G}

_{1}of DG

_{1}is varied for adjusting the output power of the generators. K

_{G}

_{1max}is assumed equal to 7.5, while the coefficient K

_{G}

_{2}of DG

_{2}is assumed invariable and equal to 5 in all the examined cases. The load at bus 4 is assumed equal to 0.1 pu while the load at bus 3 varies in the range from 0.1 pu to 0.37 pu with a step equal to +0.02 pu.

- Scenario 1, implementing the conventional droop control method
- Scenario 2, implementing the proposed optimized control method with K
_{G}_{1}selected optimally in the range [5–7.5] - Scenario 3, implementing the proposed optimized control method with K
_{G}_{1}selected optimally in the range [6–7.5]

_{1}constructed to reduce the power losses for the considered test microgrid. The first curve is built with K

_{G}

_{1}selected optimally in the range [5–7.5] (Scenario 2) and is illustrated in Figure 8a. The second is built with K

_{G}

_{1}in the range [6–7.5] (Scenario 3) and is shown in the Figure 8b. The conventional droop control curve (Scenario 1) is also represented in Figure 8 to show the improvements obtained with the proposed optimized control method.

_{G}

_{1}of the generator DG

_{1}, the power losses P

_{loss}and the frequency f as function of K

_{G}

_{1}are listed in Table 3.

## 4. Discussion

_{G}

_{1}in the range [5–7.5] gives the best results in terms of power losses reduction with respect to scenario 1. Indeed, power losses are reduced of about 8% as compared to the conventional droop control method. The improvement is illustrated clearly at low power demand where the power sharing is needed to be adjusted for optimizing the microgrid’s operation.

_{G}

_{1}constant at 7.5 (scenario 1), the frequency fluctuates from 0.9918 pu to 1.0036 pu, while with K

_{G}

_{1}in the range from 6 to 7.5, the frequency changes from 0.989 to 1.0014 and with K

_{G}

_{1}varying in the range from 5 to 7.5, the frequency only changes from 0.989 to 0.9996. In all cases, the frequency stay within the constrained operating limits from 0.98 pu to 1.02 pu. Figure 9c shows that the frequency response is smooth: system frequency fluctuates within the imposed limits from 0.992 pu to 0.998 pu, without abnormal peaks or nadir. This trend demonstrates the stability of the proposed control method.

_{maxbranch}. From the results, it can be seen that the new proposed droop control method demonstrates its powerful efficiency compared to conventional droop method, the microgrid operates more effectively at every load variation. By this way, the frequency is kept within desired limits and the volumes are relieved for secondary and tertiary regulation which have to take over from primary control, if limited load-generators variations occur in the microgrid.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations and Nomenclature

DG | Distributed generator | δ_{i} | Phase angles of the voltages at bus i |

OPF | Optimal Power Flow | θ_{ij} | Phase angle of Y_{ij} |

GSO | Glow-worm Swarm Optimization | n_{br} | Number of branches connected to bus i |

OF | Objective Function | P_{0i} | Real power of the load in the operating point |

ICT | Information and Communications Technology | Q_{0i} | Reactive power of the load in the operating point |

ACO | Ant Colony Optimization | α | Real power exponents |

PSO | Particle Swarm Optimization | β | Reactive power exponents |

PWM | Pulse Width Modulator | Y_{ij} | Admittance of the ij branch |

PLL | Phase-Locked Loop | K_{pf} | Coefficient, ranging from 0 to 3.0 |

PI | Proportional Integral | K_{qf} | Coefficient ranging from −2.0 to 0 |

P_{Gi} | Real power generated of the i-th generator | ∆P | Real power deviation |

Q_{Gi} | Reactive power generated of the i-th generator | x(t) | Location of glow-worms in the search space at iteration t |

K_{Gi} | Frequency droop coefficient of the i-th generator | l(t) | Value of luciferin at iteration t |

K_{di} | Voltage droop coefficient of the i-th generator | ρ | Luciferin decay constant |

f_{x,i} | Frequency at the i-th generator | γ | Enhancement constant |

V_{i} | Output voltage at the i-th generator | N_{i}(t) | Set of neighborhood of glow-worm i at the t-th iteration |

f_{0i} | Frequency of the i-th generator at no load | s | Step-size |

V_{0i} | Voltage of the i-th generator at no load | r_{d}^{i} | Local decision range |

K_{G}_{maxi} | Maximum value of frequency droop coefficient of the i-th generator | K_{P} | Proportional gain constant |

P_{G}_{maxi} | Rated power of i-th generator | f_{sw} | The switching frequency of the PWM |

n_{G} | Number of generators in microgrid | T_{i} | Integral time constant |

n_{d} | Number of load buses | σ | Symmetrical distance |

P_{Li} | Real power demand of the i-th load | f_{c} | Crossover frequency |

I_{branchi} | Current flowing in the i-th branch of the microgrid | L_{v}(s) | LC filter transfer function |

I_{maxbranchi} | Ampacity of the i-th branch of the microgrid | P_{v}(s) | PI controller transfer function |

n_{branch} | Number of transmission branches in the microgrid | G_{C}_{,CL}(s) | Inner current control transfer function |

f_{max} | Frequency upper limit | C_{f} | Filter parameters |

f_{min} | Frequency lower limit | L_{f}, R_{f} | Filter parameters |

P_{i} | Injected power at bus i | T_{f} | System time constant |

P_{loss} | Power losses of the microgrid | G_{v}(s)_{OL} | Open loop transfer function |

n_{bus} | Number of buses of the microgrid | G_{v}(s)_{CL} | Close loop transfer function |

V_{i} | Voltages at buses i | ∆f | Frequency deviation |

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**Figure 4.**Simulation block diagram: (

**a**) Block diagram of the control system of one inverter; (

**b**) Structure of phase-locked loop (PLL).

**Figure 8.**P-f relation curves: (

**a**) P-f relation of DG

_{1}with K

_{G}

_{1}selected optimally in the range [5–7.5]; (

**b**) P-f relation of DG

_{1}with K

_{G}

_{1}selected optimally in the range [6–7.5].

**Figure 9.**Simulation results: (

**a**) Real power of the distributed generators in the three scenarios; (

**b**) Power losses of the microgrid in the three scenarios; (

**c**) System frequency in the three scenarios; (

**d**) Current of branches in the three scenarios.

Droop Control Methods | Conventional Droop Control | Non-Linear Droop Control | Dynamic Droop Control | Proposed Droop Control |
---|---|---|---|---|

References | [9,10,11] | [5,12,13,14,15,16,17] | [18,19,20,21] | |

Simple | ✓ | - | - | ✓ |

Easy to implement | ✓ | - | - | ✓ |

Quick response | ✓ | - | - | ✓ |

No communication signals between the inverters | ✓ | - | - | ✓ |

Improved power sharing | - | ✓ | ✓ | ✓ |

Improved stability | - | ✓ | ✓ | ✓ |

Branch | R (pu) | X (pu) | R/X | I_{maxbranch} (pu) |
---|---|---|---|---|

1–3 | 0.22229917 | 0.02873961 | 7.7 | 0.5396 |

2–4 | 0.22229917 | 0.02873961 | 7.7 | 0.5396 |

3–4 | 0.22229917 | 0.02873961 | 7.7 | 0.5396 |

Scenario | Initial Load | Scenario 1 | Scenario 2 | Scenario 3 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

P_{L}_{3} | P_{L}_{4} | K_{G}_{1} | P_{G}_{1} | P_{loss} | f | K_{G}_{1} | P_{G}_{1} | P_{loss} | f | K_{G}_{1} | P_{G}_{1} | P_{loss} | f | |

1 | 0.1 | 0.1 | 7.5 | 0.1233 | 0.0049 | 1.0036 | 5.01 | 0.1022 | 0.0045 | 0.9996 | 6.01 | 0.1118 | 0.0046 | 1.0014 |

2 | 0.12 | 0.1 | 7.5 | 0.1357 | 0.0058 | 1.0019 | 5.18 | 0.1144 | 0.0055 | 0.9979 | 6.00 | 0.123 | 0.0056 | 0.9995 |

3 | 0.14 | 0.1 | 7.5 | 0.1482 | 0.0069 | 1.0002 | 5.42 | 0.1279 | 0.0066 | 0.9964 | 6.00 | 0.1343 | 0.0067 | 0.9976 |

4 | 0.16 | 0.1 | 7.5 | 0.1607 | 0.0082 | 0.9986 | 5.66 | 0.1414 | 0.0079 | 0.995 | 5.99 | 0.1456 | 0.0080 | 0.9957 |

5 | 0.18 | 0.1 | 7.5 | 0.1732 | 0.0096 | 0.9969 | 5.85 | 0.1550 | 0.0093 | 0.9935 | 5.99 | 0.1569 | 0.0094 | 0.9938 |

6 | 0.2 | 0.1 | 7.5 | 0.1858 | 0.0112 | 0.9952 | 6.02 | 0.1686 | 0.0110 | 0.992 | 6.02 | 0.1685 | 0.0110 | 0.992 |

7 | 0.22 | 0.1 | 7.5 | 0.1985 | 0.0129 | 0.9935 | 6.17 | 0.1821 | 0.0127 | 0.9905 | 6.17 | 0.1821 | 0.0127 | 0.9905 |

8 | 0.24 | 0.1 | 7.5 | 0.2112 | 0.0147 | 0.9918 | 6.32 | 0.1958 | 0.0146 | 0.989 | 6.32 | 0.1958 | 0.0146 | 0.989 |

9 | 0.26 | 0.1 | 7.5 | 0.2239 | 0.0168 | 0.9901 | 6.44 | 0.2094 | 0.0167 | 0.9875 | 6.44 | 0.2094 | 0.0167 | 0.9875 |

10 | 0.28 | 0.1 | 7.5 | 0.2368 | 0.019 | 0.9884 | 6.54 | 0.2231 | 0.0189 | 0.9859 | 6.55 | 0.2232 | 0.0189 | 0.9859 |

11 | 0.3 | 0.1 | 7.5 | 0.2496 | 0.0214 | 0.9867 | 6.65 | 0.2369 | 0.0213 | 0.9844 | 6.65 | 0.2369 | 0.0213 | 0.9844 |

12 | 0.32 | 0.1 | 7.5 | 0.2626 | 0.0239 | 0.985 | 6.74 | 0.2507 | 0.0238 | 0.9828 | 6.74 | 0.2506 | 0.0238 | 0.9828 |

13 | 0.34 | 0.1 | 7.5 | 0.2755 | 0.0266 | 0.9833 | 6.82 | 0.2645 | 0.0265 | 0.9812 | 6.82 | 0.2645 | 0.0265 | 0.9812 |

14 | 0.36 | 0.1 | 7.5 | 0.2886 | 0.0295 | 0.9815 | 7.01 | 0.2805 | 0.0295 | 0.98 | 7.01 | 0.2803 | 0.0295 | 0.98 |

15 | 0.37 | 0.1 | 7.5 | 0.2952 | 0.0311 | 0.9806 | 7.29 | 0.2918 | 0.0311 | 0.98 | 7.29 | 0.2918 | 0.0311 | 0.98 |

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## Share and Cite

**MDPI and ACS Style**

T.T Tran, Q.; Luisa Di Silvestre, M.; Riva Sanseverino, E.; Zizzo, G.; Pham, T.N.
Driven Primary Regulation for Minimum Power Losses Operation in Islanded Microgrids. *Energies* **2018**, *11*, 2890.
https://doi.org/10.3390/en11112890

**AMA Style**

T.T Tran Q, Luisa Di Silvestre M, Riva Sanseverino E, Zizzo G, Pham TN.
Driven Primary Regulation for Minimum Power Losses Operation in Islanded Microgrids. *Energies*. 2018; 11(11):2890.
https://doi.org/10.3390/en11112890

**Chicago/Turabian Style**

T.T Tran, Quynh, Maria Luisa Di Silvestre, Eleonora Riva Sanseverino, Gaetano Zizzo, and Thanh Nam Pham.
2018. "Driven Primary Regulation for Minimum Power Losses Operation in Islanded Microgrids" *Energies* 11, no. 11: 2890.
https://doi.org/10.3390/en11112890