# Multi-objective optimal operation of hybrid AC/DC microgrid considering source-network-load coordination

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## Abstract

Taking the consumption rate of renewable energy and the operation cost of hybrid AC/DC microgrid as the optimization objectives, the adjustment of load demand curves is carried out considering the demand side response (DSR) on the load side. The complementary utilization of renewable energy between AC area and DC area is achieved to meet the load demand on the source side. In the network side, the hybrid AC/DC microgrids purchase electricity from the power grid at the time-of-use (TOU) price and sell the surplus power of renewable energy to the power grid for profits. The improved memetic algorithm (IMA) is introduced and applied to solve the established mathematical model. The promotion effect of the proposed source-network-load coordination strategies on the optimal operation of hybrid AC/DC microgrid is verified.

## Keywords

Source-network-load coordination Optimal operation Improved memetic algorithm Hybrid AC/DC microgrid Complementary utilization## 1 Introduction

With the increase of energy crisis and environmental pollution, renewable energy has become the focus of current research because of its inexhaustible characteristics and environmental friendliness [1, 2, 3]. However, the output power of renewable energy has significant randomness and intermittency [4]. With the increasing penetration of renewable energy in the power grid, the problems such as the voltage fluctuation, the unreliability of power supply (PS), and the inadequate utilization cannot be ignored [5, 6].

It is showed that the coordination among source, network, load and storage can effectively improve the consumption rate of renewable energy and reduce the operation cost and network loss of the grid [7]. The operation economy and the comfort level of occupants are considered at the same time for a residential building through the synergetic optimized dispatch of sources, loads, and storage devices in [8]. It is found that the coordination of energy storage systems, incentive-based and price-based demand responses has a significant effect on the economy of microgrid in [9]. Demand side response (DSR) can increase the consumption rate of renewable energy through load adjustment, and achieve a win–win situation between the power grid and the consumers [10, 11, 12, 13]. Considering the uncertainty of wind energy, the effects of allowing large, price-responsive consumers to provide reserves in a power system with high penetration of wind energy are discussed in [14].

Microgrid includes distributed generations (DGs), energy storage (ES) devices, loads, together with power electronic devices, which can realize the efficient utilization of renewable energy through the unified optimized dispatch of DGs [15, 16, 17, 18]. The optimal operation of microgrid is the focus and difficulty of current research [19, 20, 21]. Taking the operation cost of microgrid as the optimization objective, the chaotic binary particle swarm optimization is adopted to solve the established mathematical model in [22]. Based on the chance constrained programming, a new probabilistic optimization framework is developed to optimize the operation cost of microgrid in [23]. A hierarchical optimization strategy is proposed to improve the automation level of DGs in [24]. Hybrid AC/DC microgrid integrates the advantages of AC microgrid and DC microgrid and its power supply forms are more flexible and diverse, which can satisfy various load demands at the same time. The optimization problem of hybrid AC/DC microgrid has become a research hotspot and difficulty in related fields [25, 26, 27].

*l*

_{1}–norm approximation is developed in [31] that involves solving a sequence of semidefinite programs. The simulation shows that the algorithm has a shorter running time and returns a solution with a smaller gap from the global optimal solution. In order to solve the optimal power routing problem in clusters of DC microgrids, a novel cloud-based approach is proposed and its effectiveness has been verified in [32]. Memetic algorithm (MA) has the double search mechanisms, i.e., local search and global search. Compared with the conventional algorithms, MA has a significant advantage in the convergence precision [33], which is adopted in this paper. To sum up, the main contributions of this paper are as follows.

- 1)
Under the promise of meeting the constraint of customer satisfaction, the incentive-based DSR and price-based DSR are both considered on the load side. Firstly, the load is shifted to close to the output power curve of renewable energy considering the incentive-based DSR. Next, according to the time-of-use (TOU) price of the power grid, the price-based DSR is considered in the order of the peak price time to the valley price time to optimize the operation costs of hybrid AC/DC microgrid. It can improve the consumption rate of renewable energy and reduce the operation costs of hybrid AC/DC microgrid to a large extent.

- 2)
On the source side, the renewable energy is given priority to supply the load whose generation cost is not considered. While the output power of renewable energy in one area has not reached the upper limitation and the load demand in the other area is not satisfied, the complementary utilization of renewable energy is achieved between AC area and DC area. On the network side, under the premise of meeting the capacity constraint of the point of common coupling (PCC), the hybrid AC/DC microgrids can purchase the electricity from the power grid at the TOU price. When the load demands of AC area and DC area are both satisfied, the surplus power of renewable energy can be sold to the power grid if the unit generation cost of renewable energy is smaller than the selling price, which can achieve a win–win situation between the power grid and hybrid AC/DC microgrids.

- 3)
In view of the existing disadvantages of the basic MA, MA is improved in the process of initialization, distribution of the ordinary individuals, local search and global search. The improved MA (IMA) is applied to solve the established mathematical model. The correctness and effectiveness of the proposed optimal operation method and the IMA are verified through a practical case. The simulation results show that the convergence time is only 10.22 s and the IMA can find the optimal solution quickly and accurately. The consumption rate of renewable energy can reach up to 100%. Comparing with the calculation results of hybrid AC/DC microgrids without considering source-network-load coordination, the cost of hybrid AC/DC microgrids decreases from $1533.7 to $1442.4, which further proves the feasibility of the IMA.

## 2 Mathematical model of optimal operation

### 2.1 Source-network-load coordination

#### 2.1.1 Load side

- 1)
Shift load for consuming renewable energy

*t*; \(L_{\text{yc1}} (t)\) and \(L_{\text{yr1}} (t)\) is the shift-out load and the shift-in load at time

*t*, \(L_{\text{yc1}} (0){ = }0\); \(L_{\text{py}} (t)\) is the shiftable load at time

*t*; \(P_{\text{r}} (t)\) is the predictive output power of renewable energy at time

*t*; \(T\) is the optimal cycle; \(LYR(t)\) is the total power of renewable energy while the its output power is bigger than the load; and \(L_{\text{jl}} (t)\) is the value of load at time

*t*after shifting the load.

- 2)
Shift load for reducing running cost of hybrid AC/DC microgrid

*t*considering the DSR based on price; \(L_{\text{yc2}} (t)\) and \(L_{\text{yr2}} (t)\) represent the shift-out load and shift-in load at time

*t*.

#### 2.1.2 Source side

This paper studies a hybrid AC/DC microgrid which contains wind turbine (WT) and diesel generator (DEG) in AC area, and photovoltaics (PV) and ES in DC area. In the source side, the renewable energy is given priority to supply the load. When the renewable energy is difficult to meet the load demand, the output of other power sources is determined by the cost functions. The output power of WT and PV is mainly determined by the weather. The statistical data show that the wind speed obeys the Weibull distribution and the intensity of illumination obeys the Beta distribution. Through the complementary power supply of renewable energy between AC area and DC area, it can make up for the problems that the peak output power of WT and PV cannot be completely consumed and the load demand is difficult to meet when the output power of WT and PV is close to 0, which can effectively increase the consumption rate of renewable energy.

#### 2.1.3 Network side

*t*; \(\chi (t)\) is the unit generating cost of renewable energy; and \(R_{\text{s}} (t)\) is the surplus power sold to the grid.

### 2.2 Optimization objectives

#### 2.2.1 Operation cost

- 1)Initial construction cost \(F_{\text{c}}\):where$$F_{\text{c}} = \sum\limits_{t = 1}^{T} {\sum\limits_{i = 1}^{N} {\frac{{k_{{{\text{hs,}}i}} F_{{{\text{gd,}}i}} (t)}}{8760}} }$$(13)
*N*is the number of power supplies; \(k_{{{\text{hs,}}i}}\) is the investment coefficient of power supply \(i\), which is determined by the service life of the power supply; and \(F_{{{\text{gd,}}i}} (t)\) is the fixed investment costs of power supply \(i\). - 2)Operation and maintenance cost \(F_{\text{om}}\):where \(\gamma_{i}\) is the operation and maintenance coefficient of power supply \(i\); and \(P_{i} (t)\) is the output power of power supply \(i\).$$F_{\text{om}} = \sum\limits_{t = 1}^{T} {\sum\limits_{i = 1}^{N} {\gamma_{i} P_{i} (t)} }$$(14)
- 3)Fuel cost \(F_{\text{fuel}}\):where$$F_{\text{fuel}} = \sum\limits_{t = 1}^{T} {a + bP_{\text{DEG}} (t) + cP_{\text{DEG}} (t)^{2} }$$(15)
*a*,*b*,*c*are the cost coefficients of DEG; and \(P_{\text{DEG}} (t)\) is the output power of DEG. - 4)Environmental cost \(F_{\text{en}}\):where \(\tau_{e}\) represents the emission coefficient of the pollution \(e\); and \(E_{e}\) represents the emission factor of the pollution \(e\).$$F_{\text{en}} = \sum\limits_{t = 1}^{T} {\tau_{e} E_{e} P_{i} (t)}$$(16)
- 5)Subsidy cost to the customers who adjust the load demand curve \(F_{\text{py}}\):where \(\alpha\) represents the subsidy coefficient.$$F_{\text{py}} = \alpha \sum\limits_{t = 1}^{T} {\frac{{\left| {L(t) - L_{\text{jg}} (t)} \right|}}{2}}$$(17)
- 6)Renewable energy generating subsidies \(F_{\text{r}}\).$$\begin{aligned} P_{\text{R}} (t) = & P_{\text{RAC}} (t) + P_{\text{RDC}} (t) + R_{{{\text{AC}} \to {\text{DC}}}} (t) \\ & + R_{{{\text{DC}} \to {\text{AC}}}} (t) + R_{\text{s}} (t) \\ \end{aligned}$$(18)where \(P_{\text{R}} (t)\) is the output power of renewable energy; and \(\delta (t)\) is the unit generating subsidy price of renewable energy.$$F_{\text{r}} = \sum\limits_{t = 1}^{T} {\delta (t)P_{\text{R}} (t)}$$(19)

#### 2.2.2 Consumption rate of renewable energy

*t*; and

*K*is the consumption rate of renewable energy, which is the ratio of the actual output power to the maximum output power of renewable energy in the hybrid AC/DC microgrid.

The operation cost of hybrid AC/DC microgrid and the consumption rate of renewable energy are both the optimal objectives in this paper. The latter has a higher optimal priority which means the operation economy of hybrid AC/DC microgrid would be sacrificed if the consumption rate of renewable energy is influenced. While the related technologies of renewable energy become more and more mature and the consumption rate of renewable energy has met the requirements in the future, the operation economy of hybrid AC/DC microgrid can be taken as the main optimization object.

### 2.3 Constraints

- 1)Supply-load balance constraints:$$\left\{ {\begin{array}{*{20}l} {\sum\limits_{t = 1}^{T} {P_{\text{RAC}} (t) + P_{\text{DEG}} (t) + R_{{{\text{DC}} \to {\text{AC}}}} (t) + P_{\text{gridA}} (t) = L_{\text{AC}} (t)} } \hfill \\ {\sum\limits_{t = 1}^{T} {P_{\text{RDC}} (t) + P_{\text{ES}} (t) + R_{{{\text{AC}} \to {\text{DC}}}} (t) + P_{\text{gridD}} (t) = L_{\text{DC}} (t)} } \hfill \\ \end{array} } \right.$$(23)
- 2)Capacity constraint of the PCC:$$\left| {P_{\text{G}} (t)} \right| \le P_{\text{G,max}}$$(24)
- 3)Constraints of ES:$$\left\{ {\begin{array}{*{20}l} {SOC(t + 1) = SOC(t) - (\eta_{\text{ES}} P_{\text{ES}} (t))/Q_{\text{ES,max}} (t)} \hfill \\ {SOC_{\hbox{min} } \le SOC(t) \le SOC_{\hbox{max} } } \hfill \\ {SOC_{\text{start}} = SOC_{\text{end}} } \hfill \\ \end{array} } \right.$$(25)
- 4)Changing range constraint of each power supply:$$P_{i,\hbox{min} } \le P_{i} (t) \le P_{i,\hbox{max} }$$(26)
- 5)Constraints of shifting load:where \(P_{\text{gridA}} (t)\) and \(P_{\text{gridD}} (t)\) are the electricity purchased from the power grid in AC area and DC area; \(P_{\text{G}} (t)\) and \(P_{\text{G,max}}\) are the transmitting power and capacity of the PCC; \(SOC(t)\) is the state of charge (SOC) of ES at time$$\left\{ {\begin{array}{*{20}l} {\sum\limits_{t = 1}^{T} {L_{\text{yc1}} (t)} = \sum\limits_{t = 1}^{T} {L_{\text{yr1}} (t)} } \hfill \\ {\sum\limits_{t = 1}^{T} {L_{\text{yc2}} (t)} = \sum\limits_{t = 1}^{T} {L_{\text{yr2}} (t)} } \hfill \\ {\lambda = 1 - \sum\limits_{t = 1}^{T} {\left| {L(t) - L_{\text{jg}} (t)} \right|} /\sum\limits_{t = 1}^{T} {L(t)} \;\;\;\;\;\;\lambda \ge \lambda_{\hbox{min} } } \hfill \\ \end{array} } \right.$$(27)
*t*; \(P_{\text{ES}} (t)\) is the output power of ES, which is positive while discharging and is negative while charging; \(\eta_{\text{ES}}\) is the charging and discharging efficiency of ES; \(Q_{\text{ES,max}} (t)\) is the capacity of ES; \(SOC_{\hbox{min} }\) and \(SOC_{\hbox{max} }\) are the range of SOC; \(SOC_{\text{start}}\) and \(SOC_{\text{end}}\) are the initial value and the final value of SOC; \(P_{i,\hbox{min} }\) and \(P_{i,\hbox{max} }\) are the range of output power of the power supply \(i\); \(\lambda\) is the satisfaction degree of customers, which is decreased with the increase of shifting load; and \(\lambda_{\hbox{min} }\) is the lower limitation of \(\lambda\).

## 3 MA

### 3.1 Basic MA

- 1)Initialization of MAwhere$$x = x_{\hbox{min} } + rand(0,1) \times (x_{\hbox{max} } - x_{\hbox{min} } )$$(28)
*x*_{min}and*x*_{max}are the range of the individual*x*; and*rand*(0,1) is a random number which obeys uniform distribution and values in [0, 1].

- 2)
Distribution of the ordinary individuals

*a*is determined by the relative strength and the strength of each agent.

*s*

_{a}and

*s*

_{b}are the fitness values of the agent

*a*and

*b*, respectively; \(S_{a}\) and

*p*

_{a}are the relative strength and the strength of the agent

*a*, respectively; and \(M_{a,p}\) is the number of the ordinary individuals which belong to the agent

*a*.

- 3)
Local search

*b*; \(De\) is the current iteration number; \(\gamma\) is the moving coefficient;

*d*is the distance between the ordinary individual

*b*and its agent.

*M*

_{a,pr}individuals which need to be regenerated among the ordinary individuals owned by the agent

*a*.

- 4)
Global search

*ξ*is the weight value of the ordinary individuals; and

*w*

_{b}is the fitness value of the ordinary individual \(b\) which belongs to the agent \(a\).

*a*; and

*is the competition probability vector of all agents.*

**P**Let * R* be a random vector of the same dimension as

*, and each element of*

**P***is valued in [0, 1]. The competed individual would be obtained by the agent corresponding to the biggest element in the vector which is the difference between*

**R***and*

**P***.*

**R***D*, the two agents would be merged, and all the ordinary individuals of these two agents would belong to the agent with a bigger total strength.

*u*is the cooperation coefficient.

- 5)
End of MA

After the local search and global search, the agent which has no ordinary individuals would be eliminated. When there is only one agent in the algorithm, the agent is the solution of the objective function. MA would stop when the algorithm meets the requirement of convergence accuracy or reaches the maximum number of iterations.

### 3.2 IMA

The specific iterative process of IMA is shown as follows.

- 1)
Initialization of IMA

*O*times and the total number of individuals is \(O \times M\). These individuals are sorted according to their fitness values. The individuals from 1 to \(M_{\text{agent}}\) in the sequence are the agents. The individuals from \(M_{\text{agent}} + 1\) to \(M_{\text{public}}\) are the ordinary individuals. The rest individuals of the population would be eliminated. It is equivalent to screening a group of superior in the population to improve the convergence performance of the algorithm.

- 2)
Distribution of the ordinary individuals

*S*and the strength

*p*of the agent with the best fitness value are 0 in the MA. The number of ordinary individuals belonging to the agent is 0 and the agent would be eliminated, which may influence the convergence accuracy. In this paper, the calculating process of the relative strength is improved as follows:

- 3)
Local search

- 4)
Global search

- 5)
End of IMA

### 3.3 Performance test

Running results of each algorithm

Algorithm | Average result | Running time (s) |
---|---|---|

PSO | 6.6207 | 17.287467 |

MA | 2.2513 | 4.544177 |

IMA | 1.4265 | 1.332475 |

From the Table 1 and Fig. 3, it can be seen that IMA and MA have a significant advantage over PSO in the convergence precision. After the improvement in the process of the initialization, the distribution of the ordinary individuals, the local search and the global search, the convergence performance of the algorithm is greatly improved. The convergence accuracy and convergence speed of IMA can be met at the same time, which has ideal optimization performance. It is verified that IMA has the ability to solve the complex optimization problem, which is suitable to solve the multi-objective, multi-constraint, nonlinear mathematical model established in this paper.

## 4 Simulation based on engineering data

Parameters of power supplies

Supply area | Power supply | Capacity | Operation and maintenance coefficient ($/kWh) |
---|---|---|---|

AC | WT | 2 MW | 0.0044 |

DEG | 700 kW | 0.0129 | |

DC | PV | 2 MW | 0.0014 |

ES | 250 kW/1 MWh | 0.0013 |

Figure 10a, b shows the power flow situation of WT and PV, respectively. The load demand in the AC area is bigger than or equal to the power of WT at each time, so all output power of WT supplies the load in the AC area. There is no power of WT flowing to the DC area or sold to the power grid in Fig. 10a. From Fig. 10b, it is shown that the power of PV is difficult to be consumed completely in DC area because of its peak output power during the daytime. So there is part of output power of PV supplying the load in the AC area. When all load demand in the hybrid AC/DC microgrid is met, there is still the surplus power of PV. When the unit generation cost of PV is smaller than the selling price, the surplus power of PV is sold to the power grid, which not only improves the consumption rate of PV, but also can reduce the operation cost of the hybrid AC/DC microgrid.

Calculation results of each cost function

Calculation results | Mode A | Mode B |
---|---|---|

Initial construction cost | $2334.2 | $2321.9 |

Operation and maintenance cost | $145.2 | $180.6 |

Fuel cost | $155.7 | $186.5 |

Environmental cost | $323.5 | $358.1 |

Purchasing electricity cost | $868.6 | $904.2 |

Renewable energy generating subsidy | $2582.7 | $2417.6 |

Load shifting subsidy cost | $211.5 | 0 |

Profits of selling the surplus power to the grid | $13.6 | 0 |

Total operating cost | $1442.4 | $1533.7 |

Consumption rate | 100% | 82.14% |

## 5 Conclusion

In this paper, the multi-objective optimal operation method of hybrid AC/DC microgrid considering source-network-load coordination is proposed to promote the consumption rate of renewable energy and decrease the operation cost of the hybrid AC/DC microgrid. The basic MA is improved and the excellent optimization performance of the IMA is proved through the test function. Compared with the basic MA, it can be seen that the IMA has a shorter running time and more ideal running results. Simulation results show that the incentive-based DSR and the price-based DSR both consider on the load side, the complementary utilization of renewable energy between AC area and DC area, and the electricity trading between the hybrid AC/DC microgrid and the big power grid are beneficial to improve the consumption rate of renewable energy and reduce the total running cost of the hybrid AC/DC microgrid. The convergence time of IMA is only 10.22 s and the consumption rate of renewable energy can reach 100%. Comparing with the calculation results of hybrid AC/DC microgrid without considering source-network-load coordination, the cost of hybrid AC/DC microgrid considering source-network-load coordination is $1442.4, which is reduced by $91.3.

To sum up, it is necessary to consider the source-network-load coordination in the optimization operation of hybrid AC/DC microgrid, which is beneficial to the long-term development of renewable energy. Moreover, a great solving algorithm also has a significant influence on the optimal operation of hybrid AC/DC microgrid. It is the focus of future research to find the better modeling methods and solving methods.

## Notes

### Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 51577068) and the National High Technology Research and Development Program of China (863 Program) (No. 2015AA050104).

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