# Decentralised Active Power Control Strategy for Real-Time Power Balance in an Isolated Microgrid with an Energy Storage System and Diesel Generators

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## Abstract

**:**

## 1. Introduction

- Given extreme disturbances (such as a trip of the DGs), real-time power balance in an isolated microgrid is achieved without using communication systems.
- It has a simple structure and hence can be easily implemented in the outer control loop of the grid-forming BESS while ensuring the normal operations of inner control loops and, consequently, the device-level stability.
- Only the CVCF control is activated under normal operating conditions, minimising the fluctuation of microgrid frequency and active power of other DGs.

- Supplementing detailed explanations on the proposed control method and its simulation results, as well as the test bed with respect to load models and diesel generators
- Performing simulation case studies with consideration of practical microgrid components such as dead-bands and maximum/minimum limiters.

## 2. System Description

#### 2.1. Geocha Island Microgrid

^{2}and 2.29 km

^{2}in area, respectively.

#### 2.2. Grid-Forming BESS

_{c}and recovers it to the reference value with the internal voltage and current controller. In the conventional CVCF control scheme, the dq voltage and frequency references are set to their rated values: i.e., V

_{d}* = 1 pu, V

_{q}* = 0, and f* = 1 pu. The active and reactive power outputs of the BESS are indirectly controlled to maintain the bus voltage to the rated value. In this study, the frequency reference is calculated to share active power with other DERs by the proposed voltage-frequency proportional controller (VFPC), based on the level of voltage deviation, as explained in Section 3 in detail.

#### 2.3. Diesel Generator

_{ref}is the reference frequency of a generator and f

_{set}and P

_{set}are the presets of microgrid frequency and active power determined by the microgrid operator, respectively. P

_{m}is a measured value of active output power of a generator and K

_{p}is a droop coefficient that can be determined considering the operating frequency range in a microgrid as:

_{max}and f

_{min}are the maximum and minimum values of the grid frequency, respectively. Moreover, P

_{nom}is the nominal active power of a generator and a is a constant for determining the droop coefficient.

_{ref_di}and the PI controller is used to track the reference signal by comparing ω

_{ref_di}and ω

_{m_di}. Note that ω

_{m_di}is the measured angular frequency of a diesel generator.

_{q}as:

_{ref}is the reference value of the bus voltage of a diesel generator. The values of V

_{set}and Q

_{set}correspond to the preset values of bus voltage and reactive power, respectively. In addition, Q

_{m}and Q

_{nom}are the measured and nominal reactive powers of a generator. Moreover, V

_{max}and V

_{min}denote the maximum and minimum voltages of the system and b is a constant for determining the reactive power droop coefficient.

#### 2.4. Basic Load Model

_{0}and Q

_{0}are active and reactive power demands at the rated operating voltage V

_{0}. In addition, P and Q are active and reactive power demands for actual bus voltage V. Furthermore, n

_{p}and n

_{q}are the exponents that vary depending on the inherent characteristics of the load devices. These exponents essentially represent the sensitivities of the load demands with respect to the bus voltage V: i.e., ∂P/∂V and ∂Q/∂V at V = V

_{0}. Equations (1) and (2) can then be represented equivalently using a ZIP model [41] that has been commonly adopted in power system analysis as:

_{p}, I

_{p}, and P

_{p}are the constant impedance, constant current, and constant power coefficients of active power demand, respectively. Similarly, Z

_{q}, I

_{q}, and Q

_{q}are the ZIP coefficients of reactive power demand. The sum of the three coefficients must be equal to one, as shown in Equations (8) and (10), to meet the rated operating condition. Note that in this paper, we focus on the active power management in an isolated microgrid. In [42], the average value of n

_{p}was known to be between 1.1 and 1.7. In isolated microgrids, n

_{p}is expected to be larger due to the high proportion of resistive loads such as heating and lighting [42]. Therefore, n

_{p}has been set to 2. This assumed that the isolated microgrid only includes constant impedance loads (i.e., Z

_{p}= 1, I

_{p}= 0, and P

_{p}= 0).

#### 2.5. Active Power Balance Equation in an Isolated Microgrid with CVCF Control

_{BESS}and ΔP

_{DG}are the variations in the active power outputs of the grid-forming BESS and the DGs, respectively. ΔP

_{Load}is the variation in the rated load demand and ΔP

_{Loss}is the variation in active power losses in the microgrid. In contrast, the active power output of the BESS reaches its limit when the BESS does not have a sufficient power reserve. This limit can be estimated as:

_{BESS_max}is the maximum variation in the active power output of the BESS. In Equation (12), I

_{d_max}and I

_{d_set}are the maximum and preset values, respectively, of d-axis current. In this situation, the BESS cannot recover the voltage completely and, consequently, the load shedding is initiated by the bus voltage reduction to achieve the active power balance in the microgrid, as shown in Equations (13) and (14):

_{Load_VR}is a decrease in the total load demand at under-voltage buses. A shown in Equation (14), the value of n

_{pi}significantly affects the value of V

_{i}at which the power balance in Equation (13) is satisfied. The smaller n

_{pi}, the smaller V

_{i}that is required to induce the enough reduction of the load demand, causing the degradation of voltage stability and even voltage collapse. This implies that for the microgrid with less voltage-dependent loads, the proposed VFPC becomes more effective in alleviating the power shortage and consequently mitigate the voltage reduction. Moreover, with less voltage-dependent loads, the proposed VFPC is capable of adjusting the frequency more successfully by inducing active participations of other diesel generators in the real-time frequency regulation via their P-f droop controllers.

## 3. Proposed Control Method

#### 3.1. Frequency Control of BESS with VFPC

_{nom}is the nominal frequency and f

_{ref}is the reference frequency of the grid-forming BESS. The reference frequency is determined as:

_{c}is the variation in the AC voltage estimated by subtracting the actual AC voltage from the reference voltage of the BESS. The coefficient K

_{v}denotes the proportional gain of the VFPC, which can be expressed as:

#### 3.2. Proposed Autonomous Active Power Management

_{c}is not fully recovered to V

_{nom}when the BESS has insufficient the active power reserve and hence cannot compensate for all power imbalance in the microgrid. The BESS controls the frequency (i.e., f

_{set}to f

_{ref}) proportional to ΔV

_{c}, as shown in Figure 8(Left), and then controls the diesel generators with active power droop curves (i.e., P

_{set}to P

_{ref}), as illustrated in Figure 8(Right). Considering the VFPC operation, a new power balance equation is represented as follows:

_{Load_FR}is a variation in the load demand for the change in the microgrid frequency and ΔP

_{DG_Droop}is the variation in the active power generation by droop control. In large-scale power systems, the load demand variation with respect to the frequency deviation can be characterized using the sensitivity coefficient K

_{pf}in Equation (18), which varies for the range from 0 to 3.0 [41]. However, in this paper, the load demand is assumed to remain unchanged for the frequency deviation for simplicity. This assumption is also valid because the reference frequency of the BESS is controlled to vary within a very small range, resulting in a slight variation in the microgrid frequency. For the VFPC, Equation (19) can then be derived from Equations (1) and (15). Equation (17) also can be expressed as:

- The situation in which the remaining primary reserve of the BESS (ΔP
_{BESS_max}) is not enough to cover the active power balance occurs due to a rapid increase in the net demand (e.g., sudden disconnection of a DG). - The overall bus voltage in the microgrid is reduced, inducing load reduction (ΔP
_{load_VR}). This leads to the reduction of variations in the maximum power output of the BESS (see Equations (12) and (13)). - The BESS recognises the power shortage based on ΔV
_{c}and reduces f_{ref}(see Equation (15)) by the VFPC. The diesel generator increases its active power with the P-f droop controller (see Equation (1)). - The participation of diesel generator, acting as a slave unit, enables the power shortage to be compensated for and consequently the microgrid voltages and load demand to be recovered. The reserve of the BESS is also procured and the microgrid starts operating with new levels of V and f (see Equation (20)).

## 4. Case Studies and Simulation Results

#### 4.1. Simulation Results under the Normal Condition (t < 9 s)

_{BESS}and f

_{BESS}at the rated values in the microgrid during 0 s ≤ t ≤ 9 s. Specifically, during 0 s ≤ t ≤ 3 s, the bus voltages at the WT and PV system increased to levels slightly higher than 1 pu. The voltages at the BESS were maintained at almost 1 pu, as shown in Figure 11. Figure 12, Figure 13, Figure 14 and Figure 15 compare the profiles of the microgrid frequency at the main transformer, the reference frequency of the BESS, the total load demand, and the reactive power outputs in the microgrid for Cases 1 and 2. As shown in Figure 14, the actual load demand was observed at approximately 243 kW, which was greater than 238 kW at the rated bus voltages; the voltages at several load buses were higher than 1 pu, increasing the load demand due to the load-voltage dependency, as shown in Equation (14). In Figure 15, the reactive power outputs of the BESS and the diesel generator were maintained at an almost constant level due to the small variations in the reactive power loss and the feeder voltage.

#### 4.2. Simulation Results under the Abnormal Conditions (t ≥ 9 s)

_{set}and the diesel generator could not detect the power imbalance with only its local measurement, as shown in Figure 10, Figure 12 and Figure 13. Consequently, the total load demand was significantly reduced to 282 kW, which is about 67% of the nominal demand, owing to the severe voltage reductions beyond the lower voltage limit of 0.9 pu: i.e., V

_{aBESS}= 0.847 pu, V

_{aDiesel}= 0.836 pu, V

_{aWT}= 0.824 pu, and V

_{aPV}= 0.817, as shown in Figure 11 and Figure 14. Moreover, the reduction of the bus voltage at which the BESS is located also affected the active power output of the BESS, as shown in Equation (12). This is illustrated in Figure 10 where the active power output of the BESS is about 212 kW; it is lower than the rated active power. This further decreased the bus voltage. The large reduction of the feeder voltage caused the excessive compensation of the Q-V droop controller for the reactive power. Since the BESS is located close to the diesel generator in the remote microgrid, the excessive compensation could be immediately balanced using the BESS. It can be seen that the total reactive power supply and the reactive power loss increased mainly because of a further increase in the power flowing from the west island to the east island.

_{aBESS}= 0.944 pu, V

_{aDiesel}= 0.926 pu, V

_{aWT}= 0.913 pu, and V

_{aPV}= 0.905 pu) and the load reduction (about 72 kW, about 17% of the nominal demand).

#### 4.3. Simulation Results with Less Voltage-Dependent Loads

_{p}was reduced to approximately 1.65 at t = 0 s. After the constant impedance load of 180-kW was connected at the Dong-Yuk bus at t = 3 s, n

_{p}increased from 1.65 to 1.81. The power shortage then led to larger decreases in the feeder voltages and consequently in the microgrid frequency during t ≥ 9 s, compared to the original condition (i.e., Case 2) where only the constant impedance loads were considered. Figure 16, Figure 17, Figure 18 and Figure 19 and Table 2 show that the lower n

_{p}, the lower active power output of the BESS, further reducing the bus voltage, the frequency, and actual total load demand, particularly when the diesel generator failed to completely follow the command of the master BESS owing to the insufficient reserve capacity. In Figure 16, Figure 17, Figure 18 and Figure 19, the full and dotted lines represent the cases of n

_{p}= 2 and 1.81, respectively.

_{p}to approximately 1.24 at t = 0 s. After the constant impedance load of 180-kW was connected at the Dong-Yuk bus at t = 3 s, increasing n

_{p}from about 1.24 to 1.56. The power shortage occurred at t = 9 s in the microgrid, resulting in n

_{p}= 1.56. It led to the bigger drop in the voltage and consequently caused the larger decrease in the frequency, in comparison to Case 2*. The maximum variation in the power output of the BESS was also reduced owing to the voltage drop, as shown in Equation (12). The diesel generator measured the frequency, which was further reduced, and increased its output power larger than those in Case 2*. This allowed the power shortage to be better compensated for and, consequently, the microgrid voltages and total load demand to be more recovered. Figure 20, Figure 21, Figure 22 and Figure 23 then show that the lower n

_{p}, the higher active power supply when the diesel generators had the sufficient reserve capacities and succeeded in following completely the command of the master BESS. This mitigated the reduction of actual load demand. Note the full and dotted lines represent the cases of n

_{p}= 2 and 1.56, respectively. Table 2 shows that although the bus voltage, microgrid frequency, and BESS power output were reduced at t = 12 s for n

_{p}= 1.56, the output power of the diesel generator and the total load demand were higher in Case 4 than those in Case 2*.

_{p}is reduced, particularly, under the power shortage condition. This implies that the proposed controller is more effective in alleviating the power shortage problem and voltage stability issue for a remote microgrid with less voltage-dependent load. The effect of the proposed controller becomes more evident when the slave units have sufficient reserve capacities.

#### 4.4. Discussion

## 5. Conclusions

- The proposed VFPC can be easily applied to the existing CVCF controller of the grid-forming BESS and enables the coordinated control with other DERs that operate with conventional P-f droop controllers.
- The proposed VFPC can be activated based on the local measurement of its bus voltage, not active power, even when sudden and severe imbalance of active power takes place in the microgrid.
- The proposed controller is activated only during the period of active power imbalance Unlike the conventional f-P droop method, the CVCF controller can still reduce the fluctuation of frequency and active power under the normal microgrid condition.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Parameters | Symbols | Values | Units |

Inertia coefficient | J | 3.35 | kg·m^{2} |

Friction factor | F | 0 | N·m·s |

Pole pairs | p | 2 | - |

Stator resistance per phase | R_{s} | 1.66 × 10^{−2} | Ω |

Stator leakage inductance | L_{l} | 1.68 × 10^{−4} | H |

d-axis magnetizing inductance viewed from stator | L_{md} | 5.86 × 10^{−3} | H |

q-axis magnetizing inductance viewed from stator | L_{mq} | 5.05 × 10^{−3} | H |

Field resistance | R_{f} | 5.25 × 10^{−3} | Ω |

Field leakage inductance | L_{lfd} | 6.82 × 10^{−4} | H |

d-axis resistance of Damper | R_{kd} | 1.53 × 10^{−1} | Ω |

d-axis leakage inductance of Damper | L_{lkd} | 3.40 × 10^{−3} | H |

q-axis resistance of Damper | R_{kq1} | 4.06 × 10^{−2} | H |

q-axis leakage inductance of Damper | L_{lkq1} | 6.08 × 10^{−4} | H |

P gain of PI controller for active power control | K_{pp} | 20 | - |

I gain of PI controller for active power control | K_{ip} | 60 | - |

P gain of PI controller for reactive power control | K_{pq} | 5 | - |

I gain of PI controller for reactive power control | K_{iq} | 13 | - |

Parameters | Symbols | Values | Units |

Time constant of diesel engine | T_{d} | 0.5 | s |

Time constant of valve actuator | T_{v} | 0.05 | s |

P-f droop coefficients of the diesel generator | K_{p} | 4.0 × 10^{−6} | - |

Amplification gain of the exciter | K_{e} | 70 | - |

Time constant of the exciter | τ_{e} | 2.0 × 10^{−3} | - |

Q-V droop coefficient of the diesel generator | K_{q} | 2.5 × 10^{−6} | - |

P gain of PI controller for active power control | K_{pp} | 20 | - |

I gain of PI controller for active power control | K_{ip} | 60 | - |

P gain of PI controller for reactive power control | K_{pq} | 5 | - |

I gain of PI controller for reactive power control | K_{iq} | 13 | - |

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**Figure 6.**Flow chart of the proposed VFPC for the autonomous active power management at a primary control level.

**Figure 8.**Comparison between (

**Left**) the proposed control strategy (i.e., VFPC) of the grid-forming BESS) and (

**Right**) the conventional control strategy (i.e., droop controller) of the diesel generators.

Parameter Name | Symbol | Value | Units |
---|---|---|---|

Rated voltage of the system | V_{nom} | 1 | pu |

System nominal frequency | f_{nom} | 60 | Hz |

Minimum reference frequency | f_{min} | 59.4 | Hz |

Dead-band of the VFPC of the BESS | - | ±0.01 | |

Rate limit of the reference frequency | - | 0.3 | Per s |

V-f proportional gain | K_{v} | 6 | - |

Maximum limit of d-axis current in the BESS | I_{d_max} | 1 | pu |

d-axis voltage reference of the BESS | V_{d}* | 1 | pu |

q-axis voltage reference of the BESS | V_{q}* | 0 | pu |

Sample time of the simulation | T_{s} | 5 × 10^{−5} | s |

**Table 2.**Comparisons between the simulation results acquired for different load demand and compositions at t = 12 s.

n_{p} | P_{load_0} (kW) | V_{aBESS} (pu) | V_{aDiesel} (pu) | P_{BESS} (kW) | P_{Diesel} (kW) | P_{load} (kW) | f_{MTR} (Hz) | |
---|---|---|---|---|---|---|---|---|

Case 2 | 2 | 418 | 0.944 | 0.926 | 236.1 | 145.9 | 345.6 | 59.68 |

Case 3 | 1.81 | 418 | 0.927 | 0.910 | 231.8 | 145.9 | 340.8 | 59.58 |

Case 2* | 2 | 388 | 0.975 | 0.955 | 243.8 | 135.4 | 343.7 | 59.86 |

Case 4 | 1.56 | 388 | 0.969 | 0.949 | 242.3 | 143.7 | 350 | 59.83 |

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## Share and Cite

**MDPI and ACS Style**

Moon, H.-J.; Kim, Y.J.; Chang, J.W.; Moon, S.-I.
Decentralised Active Power Control Strategy for Real-Time Power Balance in an Isolated Microgrid with an Energy Storage System and Diesel Generators. *Energies* **2019**, *12*, 511.
https://doi.org/10.3390/en12030511

**AMA Style**

Moon H-J, Kim YJ, Chang JW, Moon S-I.
Decentralised Active Power Control Strategy for Real-Time Power Balance in an Isolated Microgrid with an Energy Storage System and Diesel Generators. *Energies*. 2019; 12(3):511.
https://doi.org/10.3390/en12030511

**Chicago/Turabian Style**

Moon, Hyeon-Jin, Young Jin Kim, Jae Won Chang, and Seung-Il Moon.
2019. "Decentralised Active Power Control Strategy for Real-Time Power Balance in an Isolated Microgrid with an Energy Storage System and Diesel Generators" *Energies* 12, no. 3: 511.
https://doi.org/10.3390/en12030511