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With the rapid and large-scale development of renewable energy, the lack of new energy power transportation or consumption, and the shortage of grid peak-shifting ability have become increasingly serious. Aiming to the severe wind power curtailment issue, the characteristics of interactive load are studied upon the traditional day-ahead dispatch model to mitigate the influence of wind power fluctuation. A multi-objective optimal dispatch model with the minimum operating cost and power losses is built. Optimal power flow distribution is available when both generation and demand side participate in the resource allocation. The quantum particle swarm optimization (QPSO) algorithm is applied to convert multi-objective optimization problem into single objective optimization problem. The simulation results of IEEE 30-bus system verify that the proposed method can effectively reduce the operating cost and grid loss simultaneously enhancing the consumption of wind power.

Wind power industry has been rapidly developed. Wind power generation reached 241 billion kW∙h that has been 30% year-on-year growth accounting for 4% of the total electricity generation in China. Among them, new energy installed capacity accounted for more than 30% of the total installed capacity of the local power supply in Gansu, Ningxia, Xinjiang, Qinghai, which has shown favourable prospects in reducing fossil energy consumption and pollutant emissions [_{2} emission under multiple constraints. A fuzzy modeling for dynamic economic dispatch is presented in [

1) Interactive load characteristics

2) Interactive load model

・ Shiftable load

The dispatching center calculates the optimal power dispatching plan according to the information provided by the intention chart which determine the optimal dispatch time of the load user and the shiftable load involved in shifting the peak. Therefore, for the rth shiftable load, the decision variable is the start variable U s r t : If it starts in the t period, then U s r t = 1 ; If it starts at other times, then U s r t = 0 ; t s r is the start time of the rth shiftable peak load [

The shift cost curve characterizes denotes the compensation price that the user should obtain from the grid company after providing the shift service. The mathematical description is as follows:

C s r t = { m s r ( t s r 0 − t ) 0 ≤ t < t s r 0 m s r ( t − t s r 0 ) − m s r T s r o t > t s r 0 + T s r 0 0 t s r 0 ≤ t ≤ t s r 0 + T s r 0 (1)

where is C s r t the peak cost of the rth shiftable peak load in the t period of the peak; m s r is the compensation factor for the load of the rth shiftable peak load that is determined by the load control agreement signed from the user and the power company in advance; t s r 0 and T s r 0 are the number of the original power load start time and load duration before the peak which belong to known parameters.

・ Interruptible load

Users through the auction to declare interruptible capacity and compensation prices as well as the dispatch center by calculating the optimal power generation scheduling program to determine the interruptible users and the optimal capacity. Dispatching the hth interruptible load of the user’s compensation cost as shown in Equation (4) [^{ }

C I h t = C I h 0 P I h t I I h t (2)

where C I h 0 is the unit to reduce load costs of the hth interruptible load in the contract; P I h t is the load reduction of the hth interruptible load in the t period ; and I I h t is variable dispatch for interruptible load. The interruptible load was whether to dispatched basing on I I h t = 1 and I I h t = 0 .

The problem of economic power dispatch with wind penetration consideration can be formulated as a multi-objective optimal dispatch model. The two conflicting objectives, i.e., operating cost and system power loss, should be minimized simultaneously while fulfilling certain system constraints. This problem is formulated mathematically in this section.

・ Objective 1: Minimization of operational cost

min C 1 = C G i + C W i (3)

C G i = ∑ t = 1 T ∑ i = 1 N c { U G i t [ a i + b i P G i t + c i ( P G i t ) 2 ] + C U i t ( 1 − U G i t − 1 ) + C R i t } (4)

C W i = ∑ t = 1 T ( ∑ j = 1 N S C S r t + ∑ i = 1 N I C I h t ) (5)

where T is the number of hours during system dispatching; N C is the number of generating units; and P G i t , U G i t are the active output and the state variables of the ith generator in the

・ Objective 2: Minimization of system power loss

The dispatch of interactive load will inevitably cause the change of power flow distribution, which will have some influence on the system power loss. Thus, the minimize of power loss is one goal of optimal dispatching. Here the use of B-coefficient method to calculate the power loss [

min C 2 = ∑ t = 1 T ( ∑ i = 1 K ∑ j = 1 K P i t B i , j P j t + ∑ i = 1 K B i , 0 P i t + B 0 , 0 ) (6)

where K is the number of system nodes; B i , j , B i , 0 , B 0 , 0 are the second term , which are the first term and the constant term of the coefficient; and P i t , P j t are active power of node i and j.

・ Constraint 1: Power balance constraint [

・ Constraint 2: Spare constraints

・ Constraint 3: Unit constraint

・ Constraint 4: Interactive load constraint [

The objective of this model is to minimize the operating cost and the grid loss as much as possible under all constraints. Therefore, when the operating cost and the network loss are lower, the fitness value of the fitness function is greater. Where the fitness function can be defined as [

μ ( C i ) = { 1 C i ≤ C x C i 2 + m C i + n C x < C i ≤ C x + Δ C i 0 C i > C x + Δ C i (7)

m = ( − 2 C x Δ C i − Δ C i 2 − 1 ) / Δ C i (8)

n = 1 − C x 2 − C x ⋅ [ ( − 2 C x Δ C i − Δ C i 2 − 1 ) / Δ C i ] (9)

Δ C i = C i − C x (10)

where C i is the ith objective function value; C x is the ith objective function ideal value. Δ C i is the ith objective function added value. The fitness function diagram is shown in

Thus, where the fitness index can be defined as:

μ = min { μ ( C 1 ) , μ ( C 2 ) } (11)

where m is the minimum value for all fitness functions.

The multi-objective problem is transformed into a single objective nonlinear optimization problem that satisfies the fitness value of all constraints:

max μ s . t . C 1 + μ Δ C 1 ≤ C 1 + Δ C 1 C 2 + μ Δ C 2 ≤ C 2 + Δ C 2 (12)

In this paper, the quantum particle swarm optimization (QPSO) [

In this study, a IEEE 30-bus system with 1-wind farm of grid-connected is used to investigate the effectiveness of the model. The system configuration is shown in

The system parameters including generator capacities, spare cost and fuel cost coefficients are listed in

The interruptable capacity, compensation price, interruptable times and duration for interruptible load are listed in

1) There are 100 wind turbines in the wind farm with a total installed capacity of 200 MW. Conventional unit positive and negative rotation standby demand for the maximum unit capacity of 15%.

2) The particle size scale of QPSO algorithm is 100 and the maximum number of iterations is 500.

3) The prediction curves and load forecast curves of the wind power during the last 24 hours are shown in

4) The willingness curve and the peak cost of the shiftable load are shown in

It can be seen from

Unit No. | Power generation cost factor | Spare cost factor | Up/down Output limit | Output | |||||
---|---|---|---|---|---|---|---|---|---|

a_{i} | b_{i} | c_{i} | d_{i} | e_{i} | P_{Gi,up} | P_{Gi,down} | P_{Gi,max} | P_{Gi,min} | |

1(1) | 786.1 | 38.4 | 0.152 | 16 | 19 | 50 | 50 | 200 | 50 |

2(5) | 1048.9 | 40.3 | 0.028 | 13 | 12 | 15 | 15 | 60 | 15 |

3(13) | 1355.2 | 38.1 | 0.018 | 9 | 10 | 15 | 15 | 40 | 15 |

No. | P_{IH }/MW | λ_{HK}/[$/(MW∙h)] | Times | T_{IH},_{cont}/h |
---|---|---|---|---|

1(7) | 4.3 | 10 | 2 | 2 |

2(19) | 2.2 | 5 | 2 | 2 |

3(21) | 3.6 | 8 | 2 | 4 |

μ | μ ( C 1 ) | μ ( C 2 ) | C 1 | C 2 |
---|---|---|---|---|

0.434 | 0.870 | 0.434 | 636147 | 147.95 |

0.513 | 0.846 | 0.513 | 636652 | 144.12 |

0.695 | 0.832 | 0.695 | 636946 | 130.17 |

0.826 | 0.828 | 0.826 | 637030 | 129.47 |

The results are compared using the conventional optimal scheduling model and the interactive load multi-objective optimal scheduling model.

It can be seen from

In the following, the results of the traditional optimization scheduling model and the multi-objective optimization scheduling model considering the interactive

Calculation | Generation | Spare | Interactive | total |
---|---|---|---|---|

Traditional | 585909 | 69818 | 0 | 655727 |

Optimization | 541285 | 21218 | 74527 | 637030 |

Calculation method | Power loss /MW |
---|---|

Traditional model | 139.06 |

Optimization model | 129.47 |

load are compared in

It can be seen from

The operation cost of power grid will become increased when the capacity of wind power which have fluctuation and randomness is increased. The solution of this problem is the interactive load which is adjusted the power grid to interact with user. The interactive load decreased the operation cost because it can be a part of the reserve capacity of electric power system. In addition, on the basis that bring the interaction load into the optimalscheduling of the system which include the wind farm, a multi-objective optimization scheduling model based on the minimum operation cost and network loss are established. A quantum particle swarm optimization (QPSO) algorithm is utilized to solve the optimization objective of the model which achieve minimum of system power loss and operational cost. Simulation results show the interactive load’s ability to reduce the cost of reserve capacity due to the random fluctuations in wind power. Experimental results demonstrated that the model was successfully implemented.

The authors would like to thank the financial support from National Natural Science Foundation of China (51267011), and partly financed by Gansu Electric Power Research Institute (271733-KJ-07).

Shi, X.X., Bao, G.Q., Ding, K. and Lu, L. (2018) Multi-Objective Optimal Dispatch Considering Wind Power and Interactive Load for Power System. Energy and Power Engineering, 10, 1-10. https://doi.org/10.4236/epe.2018.104B001