# Energy Coordinative Optimization of Wind-Storage-Load Microgrids Based on Short-Term Prediction

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## Abstract

**:**

## 1. Introduction

## 2. Topological Structure of Microgrid System and Model Description

#### 2.1. Topological Structure of the Microgrid System

_{w}(t) denotes the power output of the wind turbine at time t, and P

_{l}(t) refers to the power consumption of the load. If P

_{g}(t) and P

_{b}(t) are positive values, they indicate the power output of the external grid and storage battery, respectively, and otherwise, they indicate power input.

#### 2.2. External Characteristic Model of DGs

#### 2.2.1. The External Characteristics of Wind Turbine

_{w}is the radius of the wind turbine blade, πR

_{w}

^{2}denotes the swept area of blade, ${P}_{w-\mathrm{M}}$ is the mechanical power output of the wind turbine and ${C}_{p}\left(\mathrm{\lambda},\mathrm{\beta}\right)$ represents the function relevant to the tip speed ratio λ and blade angle β.

_{1}, λ

_{2}, λ

_{3}denote correlation coefficients of the wind turbine which can be calculated via curve fitting.

#### 2.2.2. Mathematical Model of a Storage Battery

_{b}(t) represents the state of charge(SOC) of energy stored at time t, τ is the hourly self-discharge decay, ${P}_{b}^{C}(t),$ ${P}_{b}^{D}(t)$ are the charge or discharge power of storage battery at time t, respectively.

_{b}is negative, and otherwise indicates discharging, η

_{C}and η

_{D}denote the charge and discharge efficiency of the storage battery, respectively, K

_{C}and K

_{D}indicate the hourly maximum charge and discharge ratio of the storage battery, respectively. Detailed parameters of the storage battery are listed in Table 1.

Parameter | Characterization | Numerical Value |
---|---|---|

τ | hourly self-discharge decay | 0.0001 |

η_{C} | charge efficiency | 0.9 |

η_{D} | discharge efficiency | 1.0 |

K_{C} | hourly maximum charge ratio | 0.1 |

K_{D} | hourly maximum discharge ratio | 0.1 |

#### 2.3. Inverter Model

_{abc}and filter capacitor C

_{abc}(the line impedance is ignored). U

_{1abc}and i

_{1abc}are the three-phase export voltage and current of inverter, respectively, and U

_{2abc}and i

_{2abc}are the three-phase voltage and current after filtering, respectively.

#### 2.4. Spot Power Price Model

Hours (h) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

Price | 0.2294 | 0.1692 | 0.1243 | 0.0926 | 0.0287 | 0.1626 | 0.259 | 0.3693 |

Hours (h) | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

Price | 0.4932 | 0.5028 | 0.7742 | 0.9558 | 0.9462 | 1.4241 | 0.9462 | 0.7551 |

Hours (h) | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |

Price | 0.3823 | 0.3486 | 0.3427 | 0.3948 | 0.4251 | 0.3326 | 0.2867 | 0.2125 |

## 3. Energy Coordinative Optimization of a Microgrid System Based on Short-Term Prediction

#### 3.1. The Optimization Control in Receding Horizon

_{r}in the receding horizon. The aim is to obtain the optimum control sequence u

_{k}in a limited horizon. The first optimum control value is used as input for the current moment t. Then the above process are repeated in the next receding time domain. The process of receding horizon optimization is shown in Figure 5.

#### 3.2. The Grey Prediction Model of Wind Power and Load with Residual Modification

^{(0)}(k) be the historical data series and x

^{(1)}(k) be the accumulating generation operator (AGO) series;

^{(1)}:

_{1}) of residual sequence as well as the variance $\left(\overline{x}\right)$ and standard deviations (S

_{2}) of the original accumulated sequence are figured out.

Grade of Prediction Precision | P | C |
---|---|---|

Good | >0.95 | <0.35 |

Qualified | >0.8 | <0.5 |

Barely qualified | >0.7 | <0.45 |

Unqualified | ≤0.7 | ≥0.65 |

**Figure 6.**The predictive and actual wind and load power: (

**a**) The predictive wind power curve within 24 h; (

**b**) The predictive load power curve within 24 h.

#### 3.3. Energy Coordinative Optimization Management Model of Microgrid System

#### 3.3.1. Objective Function

_{Sell}(t) refers to the spot power price when the electricity is sold to the external grid; e

_{Buy}(t) to the spot power price at which the electricity is bought from the external grid; e

_{bat}(t) to the management cost of storage batteries; P

_{g}

^{Buy}(t) to the electric power absorbed by the external grid (negative sign) at time t; P

_{g}

^{Sell}(t) to the electric power generated by the external grid (positive sign) at time t; P

_{bat}(t) to the active power of the storage batteries at time t; and Δt to the time interval of system operation (Δt = 1 h).

#### 3.3.2. Constraints

_{w}(t) refers to the power output of a wind turbine unit at the time t and P

_{l}(t) to the power consumption at the time t. When positive values, P

_{g}(t) and P

_{b}(t) will represent the power output of external grid and storage battery at the time t, respectively; conversely, they will represent the power input.

_{g}

^{min}and P

_{g}

^{max}constitute the lower and upper limits of the power during the energy exchange between the microgrid system and the external grid.

_{b}

^{min}and P

_{b}

^{max}represent the minimum and maximum output power of the storage batteries, respectively.

^{−4}).

^{min}(t) and △E

^{max}(t) denote the minimum and maximum values of the charge and discharge rates.

^{min}(t) and E

^{max}(t) refer to the minimum and maximum values of storage battery capacity, respectively.

#### 3.4. Energy Coordinative Optimization of Microgrid System Based on GA

#### 3.4.1. The Objective Function of the Energy Coordinative Optimization of a Microgrid System

_{g}(t). If P

_{g}(t) is positive, the external grid outputs power to the microgrid, on the other hand, if negative, the power flow reverses. The time step is denoted by s. The corresponding equation is Equation (29):

_{Sell}(t)·P

_{g}(t) when P

_{g}(t) is a positive value, but the cost will become −e

_{Buy}(t)·P

_{g}(t) when it is a negative value.

#### 3.4.2. The RHC Optimization Based on a Genetic Algorithm

_{r}and the receding step being 1 h. At time t, a solution for the optimization within the receding horizon [t t + t

_{r}] should be found, and the objective function should be minimized through calculating the optimal control sequence within receding horizon. In view of this, receding optimization range is added to Equation (29) to calculate the system operation cost during t and t + t

_{r}, which emerges in the following equation as a new objective function:

#### 3.5. Linearization of the Non-Linear Model in Energy Coordinative Optimization of Microgrid System

#### 3.6. The Specific Steps of a Microgrid System’s Energy Coordinative Optimization

- Step 1
- Establish the microgrid model, including wind turbine model, storage battery model, spot power price model; initialization of the parameters involving the predictive wind power and the load demand values obtained in the predictive range and state variables P
_{w}(t), P_{g}(t), P_{b}(t) and P_{l}(t). - Step 2
- Establish the constrained objective function of economical optimization according to the actual demand by the microgrid’s energy coordinative optimization.
- Step 3
- Find a solution for the minimization problem within a limited horizon in the optimization range of [t t + t
_{r}]; in this step, every receding optimization will bring into existence a control sequence U(t) = {u(t|t),…,u(t + t_{r}|t)}, whereby the solution for the control variable u(t|t) can be found at the first step in current moment; that is, P_{g}(t|t) at the first step constitutes the variables for the energy exchange between the external grid and microgrid and P_{b}(t|t) is the variable for the charge and discharge energy of the storage battery. - Step 4
- The optimization horizon keeps receding: t = t + 1, return to Step 3.
- Step 5
- Output the optimal result within the limited horizon [t, t + t
_{n}] after the receding optimization stops.

## 4. Experimental Results and Analysis

#### 4.1. Main Parameters

Number | Parameter | Power Upper Limit (kW) | Power Lower Limit (kW) |
---|---|---|---|

1 | P_{g} | 25 | −20 |

2 | P_{b} | 20 | −20 |

3 | E | 60 | 20 |

4 | △E | 30 | −30 |

#### 4.2. The Inverter Control Optimization Result

**Figure 11.**The effect of PQ control on a storage battery and wind turbine: (

**a**) Active power of the storage battery and wind turbine; (

**b**) Reactive power of the storage battery and wind turbine; (

**c**) Effective values of phase voltage and line current output from the storage battery.

**Figure 12.**The effect of V/f control on the storage battery: (

**a**) Active and reactive output power of the storage battery; (

**b**) The phase voltage, line current and frequency output from the storage battery.

#### 4.3. The Result Analysis of RHC Based on Prediction

**Figure 13.**The optimization result of a GA for different prediction lengths: (

**a**) The optimization result of the external grid and battery power; (

**b**) The optimization result of the battery’s SOC capacity.

**Figure 14.**The optimization result when MILP’s prediction length is 5: (

**a**) MILP’s receding optimization result of the grid and battery power; (

**b**) MILP’s receding optimization result of the battery’s remaining capacity.

#### 4.4. The Comparison about Optimization Results of GA and MILP

**Table 5.**The comparison about the 24-h optimization results without implementing RHC based on prediction strategy.

Number | Method | Optimization Result |
---|---|---|

1 | GA | 45.6 |

2 | MILP | 48.49 |

**Figure 15.**Comparison between the prediction-based results of different strategies: (

**a**) The results of GA and MILP based on prediction; (

**b**) The difference values of the prediction-based results of GA and MILP.

Number | Method | Prediction Length t_{r} | |||||||
---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | ||

1 | GA | 80.093 | 76.095 | 55.107 | 50.628 | 50.053 | 50.089 | 50.055 | 50.054 |

2 | MILP | 80.093 | 72.949 | 54.334 | 51.044 | 50.147 | 50.147 | 50.147 | 50.147 |

3 | Difference values | 0 | 3.146 | 0.773 | −0.416 | −0.094 | −0.058 | −0.092 | −0.093 |

## 5. Conclusions

- (1)
- Based on the characteristics of microgrids, this paper proposes a method for energy coordinative optimization which focuses on the improvement of the economic benefits of microgrids in the prediction framework.
- (2)
- The generation power of wind turbines and load power are predicted through building a grey prediction model with residual modification, which has eliminated the unstable influence of wind power on energy optimization. Meanwhile, the data such as spot power price, wind power and predicted load power are applied in the optimization algorithm.
- (3)
- Comparing GA with MILP in finding the optimal solutions, MILP has higher computing speed, but non-linear computing become difficult after model becomes more complex. A GA can efficiently figure out the optimum solution in predictive horizon for the complex non-linear coordination control model of microgrids. The effectiveness and feasibility of the proposed method which integrates RHC and GA is verified by example.
- (4)
- As for future work, we think that energy coordinative optimization model of microgrids and various constraints such as economy, environment and maintenance cost need to be improved. Furthermore, the charge and discharge frequency of the storage battery and centralized, distributed and decentralized optimization algorithms need to be discussed.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Hu, C.; Luo, S.; Li, Z.; Wang, X.; Sun, L.
Energy Coordinative Optimization of Wind-Storage-Load Microgrids Based on Short-Term Prediction. *Energies* **2015**, *8*, 1505-1528.
https://doi.org/10.3390/en8021505

**AMA Style**

Hu C, Luo S, Li Z, Wang X, Sun L.
Energy Coordinative Optimization of Wind-Storage-Load Microgrids Based on Short-Term Prediction. *Energies*. 2015; 8(2):1505-1528.
https://doi.org/10.3390/en8021505

**Chicago/Turabian Style**

Hu, Changbin, Shanna Luo, Zhengxi Li, Xin Wang, and Li Sun.
2015. "Energy Coordinative Optimization of Wind-Storage-Load Microgrids Based on Short-Term Prediction" *Energies* 8, no. 2: 1505-1528.
https://doi.org/10.3390/en8021505