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Multi-objective optimization of multi-microgrid power dispatch under uncertainties using interval optimization

  • *Corresponding author: Xiuping Guo

    *Corresponding author: Xiuping Guo

This work is partially supported by the National Natural Science Foundation of China [grant number 71471151] and by the Open Foundation of State key Laboratory of Networking and Switching Technology (Beijing University of Posts and Telecommunications) [SKLNST-2021-2-01]

Abstract Full Text(HTML) Figure(13) / Table(6) Related Papers Cited by
  • The microgrid technology, which can dispatch power independently, is an effective way to increase the efficiency of energy utilization meanwhile develop and utilize the clean and renewable energy. However, the power generation of a single microgrid is unstable, because it is greatly affected by the external environment. Therefore, the development and application of the multi-microgrid system have gradually drawn various countries' attention. In order to minimize the operating cost and gaseous pollutant emission of the multi-microgrid system, which is composed of renewable energies and electric vehicles and so on, this paper builds a 24 hours day-ahead multi-objective complex constrained optimization model, using interval optimization to handle uncertainties of renewable energies. In view of the model characteristics, the metaheuristic strategies about initialization and repair of solution are designed. Furthermore, the fuzzy membership degree and Chebyshev function are used in parallel to decompose the multi-objective optimization problem, thus a multi-objective evolutionary algorithm based on hybrid decomposition (MOEA/HD) is constructed. Finally, the effectiveness of the metaheuristic strategies can be verified by analyzing the simulation results in this paper. Moreover, the results prove that the MOEA/HD is more efficient, which can get a higher-quality Pareto optimal solution set when compared to other algorithms.

    Mathematics Subject Classification: Primary: 49M37; Secondary: 68W50.

    Citation:

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  • Figure 1.  The framework of the multi-microgrid system

    Figure 2.  Three possible relations between an interval and a real number

    Figure 3.  The flow chart about the repair of ESU's power dispatch scheme

    Figure 4.  The flow chart about the repair of EV's power dispatch scheme

    Figure 5.  Power prediction intervals of PVs and WTs in 24 h

    Figure 6.  The objective values of the Pareto optimal solutions

    Figure 7.  The boxplot group of the $ CS $ metric values

    Figure 8.  A group of three-dimensional Surface of the mean of $ CS $ metric values

    Figure 9.  Run time of each algorithm

    Figure 10.  The scatter diagram of non-dominated set

    Figure 11.  Cost and emission interval in each period

    Figure 12.  Active power of DG, ESU and EV in each period

    Figure 13.  Energy exchange

    Table 1.  The difference between this paper and existing relevant research

    Research field Differences
    Interval Existing research   Existing studies on IO, such as literature [29], mostly don't consider the risk preference of decision makers.
    Optimization This paper   Considering the risk preference of decision makers, this paper creates a multi-objective IO model with the possibility degree.
    Handling Existing research   In existing studies, such as literature [16], the method of handling complex constraints is lack of detailed description
    Constraints This paper   In this paper, the metaheuristic strategies about initialization and repair of solution are designed to deal with the complex constraints.
    MOEA/D Existing research   The existing studies, such as literature [36], mostly use Chebyshev function as the decomposition strategy, and do not apply hybrid decomposition strategy to update the solution.
    This paper   In this paper, Chebyshev function and fuzzy membership are used in parallel to improve the conventional MOEA/D to MOEA/HD to solve the complex constrained model.
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    Table 2.  The real-time market prices

    Periods $ {\boldsymbol{S_{\rm{Mac}}}} $(CNY/kwh)
    00:00-08:00 0.3
    08:00-12:00 0.95
    12:00-17:00 0.56
    17:00-21:00 0.95
    21:00-24:00 0.56
     | Show Table
    DownLoad: CSV

    Table 3.  The parameters of PVs and WTs

    Bus No. Name $ {\boldsymbol{P_{rate}}} $(kW) $ {\boldsymbol{Q_{min}}} $(kvar) $ {\boldsymbol{Q_{max}}} $(kvar)
    3 PV1 30 -15 15
    5 WT1 35 -10 10
    7 WT2 35 -10 10
    8 PV2 30 -15 15
    10 WT3 45 -10 10
    11 PV3 30 -15 15
    12 PV4 40 -20 20
    13 WT4 45 -10 10
    14 PV5 40 -20 20
     | Show Table
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    Table 4.  The parameters of MOEA/HD

    Control parameter Combination Number
    1 2 3 4 5 6 7 8 9
    CN 100 100 100 200 200 200 300 300 300
    ps 0.6 0.8 0.9 0.6 0.8 0.9 0.6 0.8 0.9
    pm 0.05 0.08 0.1 0.08 0.1 0.05 0.1 0.05 0.08
    Z 20 50 100 100 20 50 50 100 20
     | Show Table
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    Table 5.  $ Sa $ metric value

    Possibility degree $ \xi $=0 $ {\boldsymbol{Sa }}$ metric value
    2MGs 3MGs 4MGs 5MGs 6MGs 7MGs 8MGs 9MGs 10MGs
    MOEA/CD 0.341 0.442 0.556 0.384 0.553 0.607 0.490 0.418 0.535
    Best MOEA/FD 0.429 0.486 0.545 0.545 0.475 0.476 0.498 0.623 0.454
    value NSGAII 0.549 0.562 0.684 0.559 0.442 0.745 0.554 0.608 0.526
    MOEA/HD 0.365 0.382 0.460 0.425 0.441 0.502 0.559 0.420 0.413
    MOEA/CD 0.598 0.731 0.662 0.758 0.808 0.795 0.547 0.540 0.599
    Worst MOEA/FD 0.462 0.622 0.583 0.682 0.587 0.592 0.601 0.640 0.626
    value NSGAII 0.648 0.737 1.110 0.606 1.058 0.875 0.742 1.148 0.590
    MOEA/HD 0.485 0.487 0.555 0.518 0.499 0.675 0.580 0.711 0.574
    MOEA/CD 0.428 0.588 0.606 0.582 0.713 0.679 0.513 0.492 0.576
    Mean MOEA/FD 0.443 0.560 0.567 0.620 0.540 0.516 0.552 0.633 0.551
    value NSGAII 0.597 0.665 0.830 0.581 0.795 0.791 0.652 0.903 0.551
    MOEA/HD 0.433 0.434 0.504 0.463 0.467 0.562 0.570 0.613 0.509
    MOEA/CD 0.120 0.118 0.043 0.154 0.113 0.083 0.024 0.053 0.029
    Standard MOEA/FD 0.014 0.056 0.016 0.057 0.048 0.054 0.042 0.007 0.072
    deviation NSGAII 0.040 0.075 0.199 0.019 0.259 0.059 0.077 0.223 0.028
    MOEA/HD 0.050 0.043 0.039 0.040 0.024 0.080 0.008 0.137 0.069
    ${\boldsymbol{ \xi}} $=0.5
    MOEA/CD 0.435 0.320 0.454 0.602 0.502 0.556 0.543 0.498 0.535
    Best MOEA/FD 0.409 0.535 0.553 0.419 0.387 0.535 0.546 0.458 0.483
    value NSGAII 0.530 0.408 0.686 0.766 0.475 0.566 0.664 0.680 0.506
    MOEA/HD 0.442 0.469 0.439 0.444 0.396 0.390 0.488 0.449 0.444
    MOEA/CD 0.456 0.561 0.600 0.796 0.543 0.685 0.726 0.784 0.572
    Worst MOEA/FD 0.538 0.570 0.910 0.555 0.687 0.590 0.789 0.824 0.907
    value NSGAII 0.611 0.790 0.750 1.170 0.780 0.686 1.062 0.704 0.829
    MOEA/HD 0.699 0.494 0.576 0.731 0.578 0.516 0.647 0.649 0.757
    MOEA/CD 0.447 0.456 0.527 0.690 0.525 0.633 0.641 0.632 0.552
    Mean MOEA/FD 0.491 0.547 0.764 0.490 0.537 0.569 0.635 0.632 0.666
    value NSGAII 0.574 0.658 0.715 0.951 0.637 0.634 0.839 0.691 0.708
    MOEA/HD 0.570 0.485 0.500 0.597 0.468 0.459 0.559 0.550 0.616
    MOEA/CD 0.009 0.101 0.058 0.080 0.017 0.056 0.075 0.117 0.015
    Standard MOEA/FD 0.058 0.016 0.153 0.056 0.122 0.024 0.109 0.150 0.178
    deviation NSGAII 0.033 0.177 0.026 0.167 0.125 0.051 0.166 0.010 0.144
    MOEA/HD 0.105 0.012 0.057 0.118 0.079 0.052 0.066 0.082 0.130
    $ {\boldsymbol{\xi }}$=1
    MOEA/CD 0.435 0.320 0.454 0.602 0.502 0.556 0.543 0.498 0.535
    Best MOEA/FD 0.409 0.535 0.553 0.419 0.387 0.535 0.546 0.458 0.483
    value NSGAII 0.530 0.408 0.686 0.766 0.475 0.566 0.664 0.680 0.506
    MOEA/HD 0.442 0.469 0.439 0.444 0.396 0.390 0.488 0.449 0.444
    MOEA/CD 0.456 0.561 0.600 0.796 0.543 0.685 0.726 0.784 0.572
    Worst MOEA/FD 0.538 0.570 0.910 0.555 0.687 0.590 0.789 0.824 0.907
    value NSGAII 0.611 0.790 0.750 1.170 0.780 0.686 1.062 0.704 0.829
    MOEA/HD 0.699 0.494 0.576 0.731 0.578 0.516 0.647 0.649 0.757
    MOEA/CD 0.447 0.456 0.527 0.690 0.525 0.633 0.641 0.632 0.552
    Mean MOEA/FD 0.491 0.547 0.764 0.490 0.537 0.569 0.635 0.632 0.666
    value NSGAII 0.574 0.658 0.715 0.951 0.637 0.634 0.839 0.691 0.708
    MOEA/HD 0.570 0.485 0.500 0.597 0.468 0.459 0.559 0.550 0.616
    MOEA/CD 0.009 0.101 0.058 0.080 0.017 0.056 0.075 0.117 0.015
    Standard MOEA/FD 0.058 0.016 0.153 0.056 0.122 0.024 0.109 0.150 0.178
    deviation NSGAII 0.033 0.177 0.026 0.167 0.125 0.051 0.166 0.010 0.144
    MOEA/HD 0.105 0.012 0.057 0.118 0.079 0.052 0.066 0.082 0.130
     | Show Table
    DownLoad: CSV

    Table 6.  MS metric value

    Possibility degree $ {\boldsymbol{\xi }}$=0 ${\boldsymbol{ MS }}$ metric value
    2MGs 3MGs 4MGs 5MGs 6MGs 7MGs 8MGs 9MGs 10MGs
    MOEA/CD 0.948 0.857 0.940 0.948 0.929 0.895 0.820 0.885 0.906
    Best MOEA/FD 0.958 0.953 0.881 1 0.976 1 0.899 0.927 0.910
    result NSGAII 0.654 0.614 0.606 0.683 0.700 0.627 0.522 0.647 0.686
    MOEA/HD 1 1 1 0.985 1 1 1 1 0.991
    MOEA/CD 0.880 0.831 0.907 0.822 0.896 0.801 0.795 0.865 0.888
    Worst MOEA/FD 0.935 0.868 0.832 0.944 0.914 0.942 0.782 0.899 0.857
    result NSGAII 0.599 0.550 0.515 0.621 0.677 0.490 0.473 0.617 0.612
    MOEA/HD 0.913 0.965 0.925 0.944 0.961 0.991 0.959 0.896 0.967
    MOEA/CD 0.916 0.844 0.923 0.887 0.914 0.844 0.805 0.874 0.898
    Mean MOEA/FD 0.946 0.923 0.854 0.974 0.942 0.967 0.823 0.909 0.889
    value NSGAII 0.633 0.590 0.556 0.657 0.689 0.576 0.504 0.627 0.642
    MOEA/HD 0.959 0.985 0.956 0.971 0.987 0.997 0.983 0.96 0.978
    MOEA/CD 0.028 0.011 0.014 0.052 0.013 0.039 0.010 0.008 0.008
    Standard MOEA/FD 0.009 0.038 0.020 0.023 0.025 0.024 0.054 0.013 0.023
    deviation NSGAII 0.024 0.029 0.038 0.026 0.009 0.061 0.022 0.014 0.032
    MOEA/HD 0.036 0.015 0.032 0.019 0.018 0.004 0.018 0.046 0.01
    ${\boldsymbol{ \xi }}$=0.5
    MOEA/CD 0.884 0.901 0.882 0.901 0.945 0.838 0.921 0.912 0.913
    Best MOEA/FD 0.870 1 1 1 0.919 0.975 0.956 1 0.987
    value NSGAII 0.629 0.576 0.748 0.774 0.587 0.66 0.672 0.575 0.617
    MOEA/HD 1 1 1 0.957 1 1 1 0.966 1
    MOEA/CD 0.435 0.320 0.454 0.602 0.502 0.556 0.543 0.498 0.535
    Worst MOEA/FD 0.409 0.535 0.553 0.419 0.387 0.535 0.546 0.458 0.483
    value NSGAII 0.530 0.408 0.686 0.766 0.475 0.566 0.664 0.680 0.506
    MOEA/HD 0.442 0.469 0.439 0.444 0.396 0.390 0.488 0.449 0.444
    MOEA/CD 0.864 0.832 0.869 0.876 0.872 0.822 0.871 0.895 0.905
    Mean MOEA/FD 0.862 0.994 0.966 0.973 0.888 0.952 0.921 0.99 0.949
    value NSGAII 0.610 0.543 0.726 0.720 0.554 0.647 0.604 0.560 0.601
    MOEA/HD 0.987 0.974 0.942 0.937 0.987 0.971 0.968 0.960 0.975
    MOEA/CD 0.017 0.051 0.011 0.018 0.052 0.012 0.039 0.020 0.051
    Standard MOEA/FD 0.006 0.009 0.029 0.019 0.022 0.025 0.040 0.010 0.030
    deviation NSGAII 0.017 0.025 0.017 0.038 0.031 0.013 0.051 0.011 0.012
    MOEA/HD 0.018 0.028 0.049 0.014 0.018 0.041 0.034 0.004 0.035
    ${\boldsymbol{ \xi }}$=1
    MOEA/CD 0.886 0.972 0.8794 0.882 0.963 0.780 0.889 0.950 0.784
    Best MOEA/FD 0.909 0.921 0.954 1 0.990 0.890 0.987 1 1
    value NSGAII 0.540 0.802 0.571 0.631 0.615 0.558 0.913 0.754 0.772
    MOEA/HD 1 0.970 1 1 0.968 1 1 1 1
    MOEA/CD 0.843 0.779 0.855 0.861 0.826 0.808 0.827 0.867 0.900
    Worst MOEA/FD 0.858 0.982 0.930 0.957 0.869 0.917 0.865 0.976 0.912
    value NSGAII 0.587 0.515 0.708 0.692 0.512 0.629 0.549 0.550 0.586
    MOEA/HD 0.962 0.936 0.881 0.924 0.962 0.912 0.921 0.956 0.926
    MOEA/CD 0.826 0.938 0.847 0.814 0.957 0.747 0.872 0.868 0.727
    Mean MOEA/FD 0.903 0.902 0.899 0.929 0.966 0.871 0.964 0.998 0.902
    value NSGAII 0.520 0.773 0.532 0.589 0.611 0.515 0.870 0.720 0.669
    MOEA/HD 0.987 0.961 0.958 0.979 0.957 0.936 0.995 0.941 0.988
    MOEA/CD 0.045 0.025 0.038 0.049 0.005 0.028 0.018 0.058 0.052
    Standard MOEA/FD 0.005 0.025 0.041 0.060 0.0310 0.022 0.026 0.002 0.069
    deviation NSGAII 0.017 0.022 0.034 0.030 0.004 0.031 0.030 0.0280 0.0930
    MOEA/HD 0.018 0.007 0.036 0.021 0.014 0.056 0.005 0.044 0.011
     | Show Table
    DownLoad: CSV
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