# Modified Chaos Particle Swarm Optimization-Based Optimized Operation Model for Stand-Alone CCHP Microgrid

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## Abstract

**:**

## 1. Introduction

## 2. Optimization Model of Stand-Alone MG

#### 2.1. An Overview of MG

#### 2.2. The CCHP Model of MT

_{MT}is the fuel cost of MT in operation time, C

_{nl}is the natural gas price to supply MT, P

_{MT}represents the electrical power produced by MT and η

_{MT}stands for the efficiency of MT.

_{MT.E}, Q

_{H}and Q

_{C}represent the residual heat of exhaust, heating and cooling capacity provided by the residual heat of exhaust severally, η

_{l}is the heat loss factor of CCHP system, η

_{H.REC}and η

_{C.REC}stand for the heating and cooling efficiency while ω

_{H}and ω

_{C}are the heating and refrigeration coefficient.

#### 2.3. Objective Function

#### 2.3.1. Operation and Maintenance Cost

_{1}(t) is the operation and maintenance cost of the whole MG, P

_{m}(t) and C

_{m}(P

_{m}(t)) are the electricity output and fuel cost of micro resource m in the tth dispatch period respectively. K

_{m}, K

_{H}, K

_{C}are the maintenance factors of micro resource m, HES and APC modules, P

_{H}(t) and P

_{C}(t) are the heat power generated by HES and the cooling power generated by AC severally, ∆t is the dispatch interval time, which is 1 h in this paper.

#### 2.3.2. Pollutant Disposal Cost

_{X}, CO

_{2}, SO

_{2}and other environmental pollutants in the generation process. Emission coefficients of pollutants are diverse for different generation units while different pollutants will cause various environmental impacts. In this paper, the environmental benefit was considered by the following conversion formulation:

_{2}(t) is the pollutant disposal cost of the whole MG, ξ

_{n}represents the conversion coefficient for different pollutants (NO

_{X}, CO

_{2}, SO

_{2}), A

_{mn}is the discharge quantity of pollutant n when micro resource m lets out unit electricity power, P is the number of pollutant types while Q is the number of generation units.

#### 2.3.3. Load Cut Compensation

_{3}(t) can be expressed by:

_{EL.c}(t) is the actual load cut power in different dispatch period and c(t) is the UIC of MG.

#### 2.4. Operation Constraint

#### 2.4.1. Power Balance Constraint

_{E.L}(t), P

_{H.L}(t) and P

_{C.L}(t) are the electricity, thermal and cooling load of the MG respectively, P

_{H}(t) and P

_{C}(t) represent the heat and cold energy generated by CCHP module.

#### 2.4.2. Output Constraint

_{m.min}and P

_{m.max}are the minimum and maximum output power of generation unit m, respectively.

#### 2.4.3. Ramp Up/Down Rate Constraint

_{m}(t) and P

_{m}(t − 1) represent the power of generation m in current and last dispatch interval, R

_{up}and R

_{down}stand for the ramp up and down rate of micro resource m, respectively.

#### 2.4.4. Battery Operation Constraint

_{SOC}(t), P

_{SB}(t) are the state of charge (SOC) and output power of battery in the tth dispatch period, B

_{soc.min}and B

_{soc.max}represent the minimum and maximum SOC while η

_{SB.C}and η

_{SB.D}are the charge/discharge efficiency for the battery, λ

_{C}and λ

_{D}stand for the maximum charging/discharging proportion in one hour, and S

_{B}is the capacity of the battery.

#### 2.4.5. Load Cut Constraint

_{cut.max}is the upper limit of load cut quantity, which is determined by the actual system.

#### 2.5. Modified CCHP Dispatch Strategy

## 3. Modified Chaos Particle Swarm Optimization

#### 3.1. Basic PSO

_{best}and population optimal solution g

_{best}converge to global optimal solution during iteration. The jth dimension of the velocity and position for particle i at moment t are updated as follows:

_{1}and s

_{2}are learning factors while rand

_{1}and rand

_{2}are random numbers between 0~1, d is the dimension of the optimization model, p

_{i}

_{,}

_{j}and p

_{g}

_{,}

_{j}stand for the individual and population optimal solution, respectively.

#### 3.2. Chaotic Optimization

- (1)
- Assume h = 0, and map the decision variables z
_{j}^{h}, j = 1, 2, …, m into chaotic variables $c{h}_{j}^{h}$ between 0 and 1 for every dimension of the solution, where z_{max,j}and z_{min,j}represent the upper and lower search bounds of the jth dimension, m is the dimension number of solution.$$c{h}_{j}^{h}=\frac{{z}_{j}^{h}-{z}_{min,j}}{{z}_{j}^{h}-{z}_{max,j}},j=1,2......m$$

- (2)
- Calculate the chaotic variables of next iteration by the following formula:$$c{h}_{j}^{h+1}=4\times c{h}_{j}^{h}\left(1-c{h}_{j}^{h}\right),j=1,2......m$$

- (3)
- Transform chaotic variables ch
_{j}^{h+}^{1}into decision variable ${z}_{j}^{h+1}.$$${z}_{j}^{h+1}={z}_{min,j}+c{h}_{j}^{h+1}\left({z}_{max,j}-{z}_{\mathrm{min},j}\right),j=1,2......m$$

- (4)
- Evaluate the new solution according to decision variable ${z}_{j}^{h+1}$. If the new solution is better than the initial or the chaotic search has reached the maximum iterations, the new solution will be the result of chaos search, otherwise, set h = h + 1 and turn to the second step.

#### 3.3. Elite Retention Strategy

#### 3.4. Steps of MCPSO

- (1)
- Initialize the position and velocity of each particle in the population.
- (2)
- Evaluate the fitness of each particle; save current particles’ positions and fitness values into p
_{best}of each particle; save the position and fitness value of the optimal individual in current population into g_{best}. - (3)
- Update the position and the speed of each particle.
- (4)
- Calculate the objective function value of each particle; preserve the top 20% of the best individuals with the best fitness values.
- (5)
- Search the selected particles with chaos optimization; update p
_{best}and g_{best}of the population. - (6)
- If the search accuracy is satisfied or the iteration number is reached, stop the search and output the result, otherwise, turn to step 7.
- (7)
- Regenerate the remaining 80% of the particles; calculate the fitness values and replace the last 10% of the individuals with the worst fitness by the top 10% of the good individuals obtained in step 4 and transfer to step 2 then.

## 4. Case Studies

#### 4.1. The Framework of Stand-Alone MG

#### 4.2. Results Analysis

#### 4.3. Comparison Analysis

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**The structure of micro-gas turbine’s (MT’s) combined cooling-heating-power (CCHP) mode. APC: absorption chiller; HES: heat-exchanging system.

**Figure 6.**The structure of stand-alone MG; photovoltaic (PV), wind turbine (WT), MT and energy storage (ES), fuel cell (FC), diesel engine (DE).

**Figure 7.**The load demand and output prediction of renewable energy in four scenarios. OPBH: ordering power by heat; EL: electric load.

**Figure 8.**The dispatch optimization results for MG in each period for four scenarios; LCQ: load cut quantity.

Type | P_{e} (kW) | P_{max}/P_{min} (kW) | R_{up}/R_{down} (kW/min) | K ($/kWh) |
---|---|---|---|---|

DE | 155 | 180/10 | 20 | 0.01258 |

FC | 135 | 160/10 | 10 | 0.00419 |

MT | 100 | 125/10 | 10 | 0.00587 |

ES | 25 | - | - | 0.01241 |

Type | Disposal Cost ($/lb) | DE (lb/kWh) | FC (lb/kWh) | MT (lb/kWh) |
---|---|---|---|---|

NOx | 4.2 | 2.18 × 10^{−2} | 3 × 10^{−5} | 4.4 × 10^{−4} |

SO_{2} | 0.99 | 4.54 × 10^{−4} | 6 × 10^{−6} | 8 × 10^{−6} |

CO_{2} | 0.014 | 1.43 × 10^{−3} | 1.078 × 10^{−3} | 1.596 × 10^{−3} |

Scenario | (a) | (b) | (c) | (d) |
---|---|---|---|---|

Modified Strategy ($) | 28.926 | 506.816 | 13.043 | 824.484 |

Traditional Strategy ($) | 30.201 | 521.794 | 13.639 | 844.073 |

Decreased Percentage (%) | 4.22 | 2.87 | 4.37 | 2.32 |

Initial Load Demand (kW) | 1201.761 | 1268.601 | 1201.761 | 1268.601 |

Actual Power Output (kW) | 1159.959 | 1273.904 | 1156.716 | 1266.460 |

Decreased Percentage (%) | 3.48 | 0.42 | 3.75 | 0.17 |

**a**) Sunny-working day; (

**b**) Sunny-weekend; (

**c**) Rainy-working day; (

**d**) Rainy-weekend.

Algorithms | Total Cost | Average Convergence Time/s | |
---|---|---|---|

Average Cost/$ | Standard Deviation/$ | ||

PSO | 851.146 | 1.972 | 254.84 |

CPSO | 833.564 | 1.496 | 267.35 |

MCPSO | 824.732 | 0.358 | 243.28 |

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## Share and Cite

**MDPI and ACS Style**

Wang, F.; Zhou, L.; Wang, B.; Wang, Z.; Shafie-khah, M.; Catalão, J.P.S. Modified Chaos Particle Swarm Optimization-Based Optimized Operation Model for Stand-Alone CCHP Microgrid. *Appl. Sci.* **2017**, *7*, 754.
https://doi.org/10.3390/app7080754

**AMA Style**

Wang F, Zhou L, Wang B, Wang Z, Shafie-khah M, Catalão JPS. Modified Chaos Particle Swarm Optimization-Based Optimized Operation Model for Stand-Alone CCHP Microgrid. *Applied Sciences*. 2017; 7(8):754.
https://doi.org/10.3390/app7080754

**Chicago/Turabian Style**

Wang, Fei, Lidong Zhou, Bo Wang, Zheng Wang, Miadreza Shafie-khah, and João P. S. Catalão. 2017. "Modified Chaos Particle Swarm Optimization-Based Optimized Operation Model for Stand-Alone CCHP Microgrid" *Applied Sciences* 7, no. 8: 754.
https://doi.org/10.3390/app7080754