Abstract
The significance of situation awareness (SA) in power systems has increased to enhance the utilization of grid-connected renewable energy power generation (REPG). This paper proposes a real-time calculation architecture based on the integration of robust optimization (RO) and artificial intelligence. First, the time-series simulation of the REPG consumption capacity is carried out under the current grid operating conditions. RO is employed in this simulation, given the randomness of the REPG output and the grid load. Then, the radial basis function neural network (RBFNN) is trained with the results under different parameters using the artificial fish swarm algorithm (AFSA), enabling the neural network (NN) to be the replacement for the time-series simulation model. The trained NN can quickly perceive the REPG absorption situation within the predefined grid structure and period. Moreover, the Sobol’ method is adopted to conduct the global sensitivity analysis for different parameters based on the input-output samples obtained by the trained NN. Finally, the simulation experiments based on the modified IEEE 14-bus system prove the real-time performance and accuracy of the proposed SA architecture.
THE injection of renewable energy power generation (REPG) into the power grid is crucial for improving energy security and achieving carbon neutrality [
The direct consequence of insufficient consumption of the REPG is electricity curtailment. In 2019, the curtailment in China and Germany reached 16869 GWh and 6273 GWh [
An absorption analysis based on stochastic scenarios for WP is proposed in [
The above methods all have shortcomings. The calculation results of the multi-scenario method do not consider the timing characteristics of the power system, and the probabilistic method cannot incorporate some essential constraints such as the ramping rate of the conventional units. In addition, since the span of the time-series simulation is usually more than one year and some iterations may be required, the calculation time can be pretty long. Although the time-series simulation results can guide offline planning, this method cannot be applied to online situation awareness (SA), which supports the scheduling decision [
The probabilistic method has revealed the existence of an analytical relationship between the absorption results and the parameters that influence the REPG absorption in a specified power grid and during a specified period [

Fig. 1 Main contributions of this paper.
1) We address the volatility and randomness of the REPG and load by developing a time-series simulation model based on robust optimization (RO). We change input parameters to obtain simulation results under various conditions. These samples are then used to train a radial basis function neural network (RBFNN) employing the artificial fish swarm algorithm (AFSA). The trained NN can accurately predict real-time absorption results within the set grid.
2) We carry out the global sensitivity analysis using Sobol’ method to investigate the impact of different parameters on the absorption results. This method considers the interaction between various parameters based on variance [
The rest of this paper is organized as follows. Section II develops the time-series simulation based on RO. Section III proposes the online SA based on AFSA-RBFNN. Section IV introduces the global sensitivity analysis of REPG absorption by Sobol’ method. Section V conducts the simulation experiments, and Section VI summarizes the paper.
While the current work based on the time-series simulation has considered the volatility of the REPG, the randomness is often neglected. It is imperative to note that the REPG output cannot be regarded as a definitive curve in the day-ahead unit commitment since it is not entirely predictable. Although the reserve capacity of conventional power generation can cover some prediction errors, the optimized results could not meet the up/down ramping constraint, resulting in the curtailment of the REPG and the loss of load [

Fig. 2 Process of time-series simulation based on RO.
The objective function is given as:
(1) |
where is the output of conventional generation i in time interval t; NG is the number of conventional units; NT is the value of time intervals in each time window; and are the maximum outputs of PV and WP in time interval t, respectively, which have uncertainties; and are the sets of their possible values, respectively; and is the random value of grid load in time interval t, while is the set of its values. Reducing the power of conventional generations can promote the REPG utilization, so the curtailment of WP and PV can be lower.
Constraints of the conventional generations include the max-min output, ramping capacity, and on-off time:
(2) |
(3) |
(4) |
(5) |
where and are the maximum and minimum outputs of generation i, respectively; is a binary variable representing the on-off states of generation i in time interval t as 1-0; and are the maximum ramping up and ramping down capacities, respectively; and are the binary variables, and generation i will start or halt in time interval t if or equals 1; and and are the shortest durations of consecutive on and off states, respectively.
(7) |
(8) |
The power flow transfer factor is adopted to depict the influence of node b on the power flow of line l.
(9) |
where is the number of grid nodes; and is the maximum TLC of line l.
We regard the parameters related to the REPG and load as random variables in RO. When these parameters change within a specific range, all the constraints should still be satisfied. RO is an NP-hard problem but can be calculated using the algorithms such as column and constraint generation (C&CG) [
The limitation of the time-series simulation is its extended computational time for online scheduling decision support and generation of a significant number of samples, which are essential for global sensitivity analysis. Hence, based on the time-series simulation, this subsection develops a method for online SA toward the REPG absorption employing NN. The framework of the NN-based online SA is illustrated in

Fig. 3 Framework of NN-based online SA.
First, the parameters that may influence REPG absorption will be input into the time-series simulation based on RO. We select ten parameters in this paper: prediction error of load (PEL), peak load (PL), peak-valley difference of load (PVDL), amount of flexible load (AFL), TLC, REPG capacity (REC), prediction error of REPG (PERE), capacity of conventional generation (CCG), minimum output of conventional generation (MICG), and ramping rate of conventional generation (RRCG). Then, the absorption results will be calculated for the specified grid and period. We can obtain multiple input-output data sets as training samples by adjusting the parameters.
Second, the RBFNN will be trained based on the samples acquired from the time-series simulation. Thus, the trained RBFNN can perceive the REPG absorption results of the prescribed power grid during the specified period according to the characteristic parameters.
Finally, we generate a large number of parameter sets through Sobol’ sampling. The corresponding absorption results can be achieved based on the trained RBFNN, which provides numerous samples for global sensitivity analysis. Therefore, we can quantitatively reveal the comprehensive influence of various characteristic parameters on REPG absorption.
Artificial NNs have emerged as a powerful tool in the research and practice of power systems. The specific tasks determine the form of NN utilized. For example, long short-term memory (LSTM) NN, which can effectively process time series, is good at forecasting load and REPG output [
We utilize the Gaussian kernel function as the activation function:
(10) |
where is the input sample; and and are the center vector and the neuron width of the hidden layer, respectively. The output result v is the sum of the products of the weight vectors and the corresponding .
, , and are the crucial parameters of RBFNN, of which the general training method can be found in [

Fig. 4 AFSA-RBFNN training method.
Sobol’ method finds wide application in the fields such as economy, environment, and society [
The global sensitivity analysis can obtain the independent influence of different parameters on the absorption results and consider each parameter’s effect when coupled with the others. The Sobol’ method conducts the global sensitivity analysis based on variance, calculated by decomposing the input-output function as:
(11) |
The sensitivity coefficient can be expressed as:
(12) |
where D is the total variance; and is the partial variance caused by various parameters (); is the first-order sensitivity coefficient of parameter k; and is the second-order sensitivity coefficient which represents the cross-influence of k1 and k2. The total sensitivity coefficient of k equals the sum of its various orders.
Based on (11) and (12), to calculate the first-order and total sensitivity coefficients of each parameter, the variance is then estimated by Monte Carlo simulation according to (13):
(13) |
where N is the number of samples; the superscripts (1) and (2) represent two dimensional sampling matrices; represents all columns of matrix without the sampled values of parameter k; is the estimated value of variance caused by changes of parameters except k; and ^ represents the estimated value. Therefore, the total sensitivity coefficient of k is given as:
(14) |

Fig. 5 Sobol’ sampling based global sensitivity analysis.
A. Comparison Between Results of Time-series Simulation Based on Robust and Deterministic Optimization
The time-series simulations are based on a modified IEEE 14-bus system presented in

Fig. 6 Modified IEEE 14-bus system.
In the time-series simulation based on RO, the uncertainties of the PV output, the WP output, and the grid load are considered, unlike in the time-series simulation based on deterministic optimization, where the predicted value is directly used as input parameters for each optimization.

Fig. 7 Curves and uncertain ranges of REPG output and grid load.
Constraint violations must occur during this time window if the RO model cannot be solved successfully. In such cases, the REPG CR of this time window is regarded as zero, and the number of times this situation occurs is conunted during the whole simulation span.
We conducted all experiments on a personal computer with an Intel Core i7-9700 CPU and 32 GB of RAM using MATLAB 2019a with MOSEK. The time-series simulation based on RO took 192.62 s, while the deterministic algorithm only took 52.12 s. The simulation considering randomness needs more calculation time for its complexity.
The REPG CR derived by the RO algorithm is 71.41%, and the constraints are violated 23 times. However, the CR is 94.46% with the deterministic optimization-based simulation, where the constraint violations occur only ten times.

Fig. 8 Histograms of CRs in various time windows. (a) RO. (b) Deterministic algorithm.
The simulation period is adjustable. Thus, by adjusting the duration and number of time windows, the REPG absorption results of this the modified IEEE 14-bus system for different periods can be obtained.
We achieve different results of REPG absorption with various parameters through time-series simulation based on RO, which provides training and test samples for the RBFNN. The value ranges of the parameters are shown in
Parameter | Value range |
---|---|
PEL | |
PL | 210-300 MW |
PVDL | 1.1-1.4 |
AFL | 0-40 MW |
TLC | 65-85 MW |
REC | 70-110 MW |
PERE | |
CCG | 220-300 MW |
MICG | 0.1-0.5 |
RRCG | 0.2-0.6 |
Within the value ranges of parameters, 900 different data sets are randomly selected as the input of the time-series simulation based on RO, which takes approximately 48 hours to complete.

Fig. 9 Negative correlation between REPG CR and CVR.
Seventy percentage of the results from the time-series simulation are randomly selected as the training set, while the remaining 30% are used as the test set. The AFSA is adopted to train the RBFNN, while another NN with a tansig activation function is trained by the error back propagation NN (BPNN) as a control. The parameters of the AFSA are set as follows: the number of artificial fishes is 30, the maximum number of attempts is 10, the vision is 2, the step size is 0.5, and the crowding factor is 0.618. We present the structures of the RBFNN trained by the AFSA and BPNN in Fig. SA4 of Supplementary Material. All the NNs are implemented based on MATLAB.
The performance of different algorithms on the training set is shown in
Algorithm | MSE | Training time (s) |
---|---|---|
BPNN | 0.0030 | 4.070 |
RBFNN | 0.0150 | 0.741 |
AFSA-RBFNN | 0.0013 | 11.797 |
The comparison of performance on test set between AFSA-RBFNN and BPNN is illustrated in

Fig. 10 Comparison of performance on test set between AFSA-RBFNN and BPNN. (a) AFSA-RBFNN. (b) BPNN.
To further demonstrate the advantages of AFSA-RBFNN in the application scenarios of this paper, we gradually increase the number of neurons in the hidden layer of BPNN from 10 to 60.

Fig. 11 MSE of BPNN on training and test sets. (a) Training set. (b) Test set.
Generate 100000 sets of parameters within the ranges in

Fig. 12 Results of global sensitivity analysis of CVR and CR to different parameters. (a) CVR. (b) CR.
According to
1) The time-series simulation based on RO obtains a lower CR than deterministic optimization due to the strict restriction of uncertainty. The results of the stochastic optimization are supposed to be bounded between them. Rather than the scheduling plan, this paper estimates the REPG and analyzes the key factors affecting absorption. Therefore, the time-series simulation based on RO, which can account for various parameters, is suitable for this application scenario and can provide high-quality learning samples for RBFNN training.
2) BPNN and AFSA-RBFNN have their advantages in the training set. However, the performance of the AFSA-RBFNN is significantly better on the test set, which proves its strong generalization ability. This ability comes from the characteristics of RBFNN and the underlying mathematical relationship between input parameters and absorption results. It is difficult for the NN to obtain the absorption results entirely consistent with the time-series simulation. In contrast, it enables the operators to quickly perceive the REPG absorption situation in real time since the calculation time of the trained RBFNN is less than 1 ms. On the test set, the Pearson correlation coefficients between the results of RBFNN and the time-series simulation are close to 1 (0.9882 and 0.9839), i.e., they have incredibly high consistency.
3) We find that the first-order sensitivity coefficients of most parameters are much smaller than the total sensitivity coefficients, especially parameters such as PERE, REL, and CCG. It illustrates that although the independent influence of these parameters is small, they can also change the absorption results by coupling with other parameters. The discovery of this hidden relationship is also the significance of the global sensitivity analysis.
This paper proposes an architecture combining the AFSA-RBFNN and the time-series simulation based on RO for online SA and sensitivity analysis of the REPG absorption. First, RO is adopted to consider the influence of the uncertainties of REPG and grid load. The calculation results are more suitable for analyzing the absorption expectation. Then, we introduce the RBFNN trained by AFSA to effectively fit the input-output relationship of the time-series simulation based on RO, making it possible to conduct the online SA of the REPG absorption with different parameters within the specified power grid and period.
The global sensitivity analysis based on Sobol’ method shows that the peak regulation capacity of conventional generations, TLC, and flexible load significantly impacts the absorption results.
The trained RBFNN and sensitivity analysis results apply to the given power grid and period. However, this analysis procedure described in this paper is universal, i.e., online applications in different times and spaces using NNs can be supported by their corresponding offline time-series simulations.
References
Y. Wolde-Rufael and E. M. Weldemeskel, “Environmental policy stringency, renewable energy consumption and CO2 emissions: panel cointegration analysis for BRIICTS countries,” International Journal of Green Energy, vol. 17, no. 10, pp. 568-582, Aug. 2020. [Baidu Scholar]
S. Ma, L. Lu, H. Zhang et al., “Multi-regions bundled planning of wind farm, thermal, energy storage with renewable energy consumption,” in Proceedings of 2021 3rd Asia Energy and Electrical Engineering Symposium (AEEES), Chengdu, China, Mar. 2021, pp. 1130-1135. [Baidu Scholar]
J. Zhu, Y. Yuan, and W. Wang, “Multi-stage active management of renewable-rich power distribution network to promote the renewable energy consumption and mitigate the system uncertainty,” International Journal of Electrical Power & Energy Systems, vol. 111, no. 1, pp. 436-446, Oct. 2019. [Baidu Scholar]
R. Palma-Behnke, F. Valencia, J. Vega-Herrera et al., “Synthetic time series generation model for analysis of power system operation and expansion with high renewable energy penetration,” Journal of Modern Power Systems and Clean Energy, vol. 9, no. 4, pp. 849-858, Jul. 2021. [Baidu Scholar]
A. Q. Al-Shetwi, M. A. Hannan, K. P. Jern et al., “Grid-connected renewable energy sources: review of the recent integration requirements and control methods,” Journal of Cleaner Production, vol. 253, p. 119831, Apr. 2020. [Baidu Scholar]
Y. Yasuda, L. Bird, E. M. Carlini et al., “C-E (curtailment-energy share) map: an objective and quantitative measure to evaluate wind and solar curtailment,” Renewable and Sustainable Energy Reviews, vol. 160, p. 112212, Feb. 2022. [Baidu Scholar]
F. Liu, X. Zhang, N. Li et al., “Research on optimal matching scheme of renewable energy based on renewable energy consumption ability,” in Proceedings of IEEE Conference on Energy Internet and Energy System Integration (EI2), Beijing, China, Oct. 2018, pp. 1-6. [Baidu Scholar]
A. Yazdaninejadi, A. Hamidi, S. Golshannavaz et al., “Impact of inverter-based DERs integration on protection, control, operation, and planning of electrical distribution grids,” The Electricity Journal, vol. 32, vol. 6, pp. 43-56, Jul. 2019. [Baidu Scholar]
W. Xuan, H. Li, Z. Liu et al., “Urban renewable energy consumption capacity quantitative and improving approach,” in Proceedings of IEEE Student Conference on Electrical Machines and Systems (SCEMS), Jinan, China, Dec. 2020, pp. 853-857. [Baidu Scholar]
Q. Xu, C. Kang, N. Zhang et al., “A probabilistic method for determining grid-accommodable wind power capacity based on multi-scenario system operation simulation,” IEEE Transactions on Smart Grid, vol. 7, no. 1, pp. 400-409, Jan. 2016. [Baidu Scholar]
H. Zhou, H. Wu, C. Ye et al., “Integration capability evaluation of wind and photovoltaic generation in power systems based on temporal and spatial correlations,” Energies, vol. 12, no. 1, pp. 1-12, Jan. 2019. [Baidu Scholar]
W. Zhang, H. Qiu, and S. Sheng, “Comprehensive assessment method of new energy consumption considering steady and dynamic active power equilibrium constraints,” in Proceedings of International Conference on Automation, Mechanical and Electrical Engineering (AMEE), Shanghai, China, Jul. 2018, pp. 474-482. [Baidu Scholar]
Z. Zhang, W. Wang, G. Zhang et al., “Assessment method of accommodation capacity of renewable energy based on non-time-series model,” Automation of Electric Power Systems, vol. 43, no. 20, pp. 24-32, Dec. 2019. [Baidu Scholar]
M. Fan, V. Vittal, G. T. Heydt et al., “Probabilistic power flow studies for transmission systems with photovoltaic generation using cumulants,” IEEE Transactions on Power Systems, vol. 27, no. 4, pp. 2251-2261, Nov. 2012. [Baidu Scholar]
M. Aienab, A. Hajebrahimic, and M. Fotuhi-Firuzabad, “A comprehensive review on uncertainty modeling techniques in power system studies,” Renewable and Sustainable Energy Reviews, vol. 57, no. 1, pp. 1077-1089, May 2016. [Baidu Scholar]
C. Liu, J. Qu, and W. Shi, “Evaluating method of ability of accommodating renewable energy based on probabilistic production simulation,” Chinese Journal of Electrical Engineering, vol. 40, no. 10, pp. 3134-3144, Mar. 2020. [Baidu Scholar]
L. Ye, C. Zhang, H. Xue et al., “Study of assessment on capability of wind power accommodation in regional power grids,” Renewable Energy, vol. 133, no. 1, pp. 647-662, Apr. 2019. [Baidu Scholar]
E. Nycander, L. Södera, J. Olauson et al., “Curtailment analysis for the Nordic power system considering transmission capacity, inertia limits and generation flexibility,” Renewable Energy, vol. 152, no. 1, pp. 942-960, Jun. 2020. [Baidu Scholar]
C. Sun, Z. Bie, and Z. Zhang, “A new framework for the wind power curtailment and absorption evaluating,” International Transactions on Electrical Energy Systems, vol. 26, no. 10, pp. 2134-2147, Oct. 2016. [Baidu Scholar]
H. Li, N. Zhang, C. Kang et al., “Analytics of contribution degree for renewable energy accommodation factors,” Proceedings of the CSEE, vol. 39, no. 4, pp. 1009-1017, Feb. 2019. [Baidu Scholar]
X. Li, Y. Wang, Y. Huang et al., “Research on the quantitative evaluation method of wind power and photovoltaic power curtailment in real-time market transactions,” in Proceedings of International Conference on Power System Technology (POWERCON), Guangzhou, China, Nov. 2018, pp. 1564-1572. [Baidu Scholar]
J. Zhu, K. Shi, Q. Li et al., “Time series production simulation and renewable energy accommodation capacity evaluation considering transmission network power flow constraints,” Power System Technology, vol. 46, no. 5, pp. 1947-1955, May 2022. [Baidu Scholar]
M. Panteli and D. S. Kirschen, “Situation awareness in power systems: theory, challenges and applications,” Electric Power Systems Research, vol. 122, no. 1, pp. 140-151, May 2015. [Baidu Scholar]
S. Nitish, H. Geoffrey, K. Alex et al., “Dropout: a simple way to prevent neural networks from overfitting,” Journal of Machine Learning Research, vol. 15, no. 1, pp. 1929-1958, Jun. 2014. [Baidu Scholar]
D. Efimov and H. Sulieman, “Sobol sensitivity: a strategy for feature selection,” in Proceedings of International Conference on Mathematics and Statistics (ICMS), Sharjah, United Arab Emirates, Apr. 2015, pp. 57-75. [Baidu Scholar]
C. Zhao, J. Wang, J. P. Watson et al., “Multi-stage robust unit commitment considering wind and demand response uncertainties,” IEEE Transactions on Power Systems, vol. 28, no. 3, pp. 2708-2717, Aug. 2013. [Baidu Scholar]
Z. Zhang, Z. Chen, Q. Zhao et al., “Multi-level cooperative scheduling based on robust optimization considering flexibilities and uncertainties of ADN and MG,” Energies, vol. 14, no. 21, pp. 7376-7398, Nov. 2021. [Baidu Scholar]
H. Zhou, Y. Zhou, J. Hu et al., “LSTM-based energy management for electric vehicle charging in commercial-building prosumers,” Journal of Modern Power Systems and Clean Energy, vol. 9, no. 5, pp. 1205-1216, Sept. 2021. [Baidu Scholar]
M. Mohammed and G. V. M. Istemihan, “Post-fault prediction of transient instabilities using stacked sparse autoencoder,” Electric Power Systems Research, vol. 164, no. 1, pp. 243-252, Nov. 2018. [Baidu Scholar]
F. Fernandez-Navarro, C. Hervas-Martinez, P. A. Gutierrez et al., “Generalised Gaussian radial basis function neural networks,” Soft Computing, vol. 17, no. 3, pp. 519-533, Mar. 2013. [Baidu Scholar]
T. Xie, H. Yu, and B. Wilamowski, “Comparison between traditional neural networks and radial basis function networks,” in Proceedings of IEEE International Symposium on Industrial Electronics (ISIE), Gdansk, Poland, Jun. 2011, pp. 1194-1199. [Baidu Scholar]
R. Kumar, S. Srivastava, and J. R. P. Gupta. “Time series prediction using focused time lagged radial basis function network,” in Proceedings of International Conference on Information Technology (InCITe), Noida, India, Oct. 2016, pp. 121-124. [Baidu Scholar]
D. Yu and D. Yu, “Neural network control of multivariable processes with a fast optimisation algorithm,” Neural Computing & Applications, vol. 12, no. 1, pp. 3-4, Dec. 2003. [Baidu Scholar]
Z. Zhang, “Pattern classification based on radial basis function neural network,” in Proceedings of International Conference on Smart Grid and Electrical Automation (ICSGEA), Zhangjiajie, China, Jun. 2020, pp. 213-216. [Baidu Scholar]
W. Shen, X. Guo, C. Wu et al., “Forecasting stock indices using radial basis function neural networks optimized by artificial fish swarm algorithm,” Knowledge-based Systems, vol. 24, no. 3, pp. 378-385, Apr. 2011. [Baidu Scholar]
Z. Huang and Y. Chen, “Log-linear model-based behavior selection method for artificial fish swarm algorithm,” Computational Intelligence and Neuroscience, vol. 2015, no. 10, pp. 1-10, Jan. 2015. [Baidu Scholar]
J. Nossent, P. Elsen, and W. Bauwens, “Sobol’ sensitivity analysis of a complex environmental model,” Environmental Modelling & Software, vol. 26, no. 12, pp. 1515-1525, Dec. 2011. [Baidu Scholar]
X. Xu, Z. Yan, M. Shahidehpour et al., “Power system voltage stability evaluation considering renewable energy with correlated variabilities,” IEEE Transactions on Power Systems, vol. 33, no. 3, pp. 3236-3245, May 2018. [Baidu Scholar]
K. N. Hasan and R. Preece, “Influence of stochastic dependence on small-disturbance stability and ranking uncertainties,” IEEE Transactions on Power Systems, vol. 33, no. 3, pp. 3227-3235, May 2018. [Baidu Scholar]
G. Mavromatidis, K. Orehounig, and J. Carmeliet, “Uncertainty and global sensitivity analysis for the optimal design of distributed energy systems,” Applied Energy, vol. 214, no. 1, pp. 219-238, Mar. 2018. [Baidu Scholar]