ORIGINAL ARTICLE
Flower pollination–feedforward neural network for load flow
forecasting in smart distribution grid
Gaddafi Sani Shehu1• Nurettin Çetinkaya2
Received: 11 October 2017 / Accepted: 3 March 2018 / Published online: 13 March 2018 Ó The Natural Computing Applications Forum 2018
Abstract
Nature-inspired population-based metaheuristic flower pollination algorithm is proposed in solving load flow forecasting problem in smart distribution grid environment. The efficient approach involves training a feedforward neural network (FNN) with a new flower pollination algorithm (FPA). The idea is to perform short-term load flow forecasting in smart distribution network, thus maintaining system security due to intermittency of renewable energy penetration and power flow demand. Application of optimization algorithms such as FPA in training neural network improves accuracy, over-comes generalization ability of neural network, requires less data and prevents premature convergence problem in artificial intelligence solutions due to nonlinearity of parameters. The real load flow data are collected through distribution man-agement system of Konya Organized Industrial Zone. The result obtained indicates strong improvement in error reduction using flower pollination optimization algorithm in training FNN for short-term load flow forecasting in smart distribution grid; the model is compared against FNN model and efficient support vector regression.
Keywords Flower pollination algorithm Feedforward neural network Load flow forecasting Smart distribution grid
1 Introduction
Over the past few decades, electricity sector is confronted with growing energy demand and high level of renewable energy penetration and couples with total deregulations of power sector as commodity enterprises. In other hand, high aggregated power losses and power flow forecasting con-stitute critical challenges to the industry. These challenges lead to development of new power system technology called smart grid; the new grid is to ensure efficiency and sustainability in meeting electricity generation, transmis-sion and distribution demand with reliability and best of
quality at optimal cost. The term smart grid has been coined to define the present day development of power system, accommodation of renewable energy integration, user’s activities to the network, and those that do both in order to deliver efficiently sustainable, economic and secure electricity supplies [1]. As such other innovations focusing on connecting low-voltage meters to be remotely controlled are raising new chances for load flow forecast-ing. Currently short-term load forecasting is a major col-umn in everyday life of power networks for maintaining energy demand and component system security. An accu-rate prediction is necessary to issue short- and long-term network operation plans. Hence, any inaccuracy or devia-tion may result in a loss of significant power in MW or million amount of operational cost for the utility company [2]. Load flow is performing to ascertain power system economic operations and component security. For optimal utilization of power system, state of operation ought to be well known in the present and several hours or day onward to overcome security margins and plan equipment maintenance.
Forecasting method is popular among many researchers especially in power system load demand, several & Gaddafi Sani Shehu
gsshehu@selcuk.edu.tr Nurettin C¸ etinkaya ncetinkaya@selcuk.edu.tr
1 Graduate School of Natural and Applied Science, Selc¸uk
University, Alaeddin Keykubat Yerles¸kesi, Akademi Mah. Yeni I˙stanbul Cad. No: 369, 42130 Selc¸uklu, Konya, Turkey
2 Electrical and Electronics Engineering Department, Selc¸uk
University, Alaeddin Keykubat Yerles¸kesi, Akademi Mah. Yeni I˙stanbul Cad. No: 369, 42130 Selc¸uklu, Konya, Turkey https://doi.org/10.1007/s00521-018-3421-5(0123456789().,-volV)(0123456789().,-volV)
forecasting method employed autoregressive model, neural network approach, and many artificial intelligence method [3–8]. The author in [9] presented detailed review of decision-making tools in electric load forecasting from classical method to artificial intelligence model, without single optimization algorithms heuristic or metaheuristic in the review. A full load flow forecasting approach using neural network with multilayer perception is discussed in [10]. Artificial intelligence based on short-term load fore-casting (STLF) in distribution structures is presented in [11]; the paper describes the design of a class of machine learning models, namely neural networks, for load fore-casting of medium-voltage/low-voltage substations. Hybrid methods using artificial neural network (ANN), genetic algorithm (GA), and support vector machines (SVM) are discussed by many authors in [12–14]. Metaheuristic methods are presented using particle swam optimization (PSO) [15], and firefly algorithm (FA) in hybrid with support vector regression (SVR) model is discussed in [16, 17], while a short-term high-resolution distribution load forecasting based on SVM with hybrid parameter optimization is detailed in [18]. An improved hybrid backpropagation neural network (BPNN) with a modified flower pollination algorithm for STLF based on decom-position technology is reported in [19], and flower polli-nation algorithm (FPA) is employed to cater for unstable factors and larger deviation associated with using single BPNN for capturing complex electrical time series data. Recently, STLF in smart grid takes another dimension with different algorithms and objectives. STLF using clustering regression model in smart grid is reported in [20], with main objective to manage the issue of big data problem for short-term load flow forecasting with high accuracy. The authors applied load characteristic curve for each cluster to scale the data, since each cluster represents electrical feature of various users; the model is realized by using Apache Spark machine learning library with improved accuracy. Another STLF in smart grid is a combined model to improve accuracy and reduce training time; the proposed model combined BPNN, multi-label algorithm based on nearest neighbor (NN) and K-means. Each individual algorithm is tested separately, but combined result shows significant improvement [21]. Due to various activities taken place in modern smart grid, it is a difficult task to forecast load accurately; with this notion, a behavior learning algorithm using recurrent neural network is proposed; the approach takes into account individual resident volatility, the accuracy of the algorithm notably improved, with drawback of including individual mea-surement in data training [22].
In this paper, a short-term load flow forecasting in smart grid is treated on Konya Organized Industrial Zone using flower pollination optimizations algorithms in training
simple feedforward neural network (FNN) to enhance forecasting to optimum level. Konya Industrial Zone is one of the leading industrial areas in Turkey, and it covers an area of 11.7 million square meters of industrial zone with plan extension; the industrial zone’s yearly energy growth rate is about 15%. The power distribution system supplying the industries is integrated with distribution management system for load flow control and renewable integration management, at the same instance supporting demand response and price forecasting, but the smart distribution grid lacks load flow forecasting capabilities. The main objective behind this study is to conduct a load flow forecasting in smart distribution grid for security assess-ment leading to accuracy of planning ahead due to renewable energy (RE) fluctuation, and equipment loading capacity assurance. The paper is divided into 5 sections, introduction in section one gives brief account of previous related works; section two explains data requirement for load flow in smart distribution grid including error analysis and provides brief review of SVR algorithm; section three gives review of FPA and its application for modeling analysis; results and discussion are presented in sections four; and finally section five concluded the paper. The analyses are carried out in MATLAB environment.
2 Load flow forecasting in smart
distribution grid
Smart distribution grid is an upgraded traditional grid that enables bidirectional communication and power exchange between utility company and consumer; incorporation of communication interface and sensors allowed remote operation and at the same time reduced system failure. The load flow idea is for the system operator to understand necessary planning, economic scheduling, and control of existing system and future planning. However, load flow forecasting in smart grid is for the purpose of assessing system security both in the present state and several hours ahead, so as to check how reliable state of operation and intermittency of renewable energy integration can affect network components. Data requirement for load flow forecasting is four inputs: generating unit schedule data for transmission grid both active and reactive power genera-tion, voltage control buses and its corresponding phase angle in either case. Active and reactive power consump-tion flow is typically needed for each bus; in this case, a load flow is set to be accomplished on request, and shunt compensation and transformer tap setting are sometime needed. In this work, a real smart distribution grid of Konya Industrial Zone is considered as a case study. The is a medium-voltage grid with three separate transformers of 100 MVA at 33.5 kV, 50 MVA at 31.5 kV, and 100 MVA
at 31.5 kV; solar power plants of size 4350 kW are inte-grated, and Fig.1shows the load flow topology of the test grid.
Performance measurement and data fitting problem are required to determine method quality and results proved that finding a proposed approach does not happen by chance, especially in the field of metaheuristic algorithms. Mean absolute error, mean absolute percentage error, and standard deviation are enough for this kind of analysis [23]. Mean absolute error (MAE) It is the most affordable and frequent way to evaluate any success load forecasting problems and depends on mean of difference among observations and real values. MAE is calculated using Eq. (1): MAE¼1 n Xn i¼1 abs yimbyif ð1Þ
where yim is ith the measure value andbyif is the ith
fore-casted value under considerations.
Mean absolute percentages error (MAPE) It represents the percentage of average absolute error occurred.
MAPE is independent of the scale of dimension, but affected by data conversion and is given in Eq. (2): MAPE¼100 n Xn i¼1 abs yimbyif byif : ð2Þ
Root-mean-squared error (RMSE) It is a measure of average deviation or a judgment criterion of fit of fore-casted values. It penalizes extreme errors occurred while
forecasting. RMSE is calculated by Eq. (3). Basically, the smaller the errors are, the fitter the forecast is:
RMSE¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 n Xn i¼1 yimbyif 2 s ð3Þ
Support vector regressions (SVR) Support vector machine (SVM) is rooted in statistical learning problems and can be generalized to solve a regression problem which is generally classification problems. Support vector regression (SVR) is well suited in classification problems with characteristics of using kernel, sparse solution. Rarely widespread than SVM, SVR is demonstrated to be an operational tool in real-value function approximation. One great advantage of SVR is that computation capability is independent of dimensionality of input space; it has pos-sessed generalization with prediction accuracy [24]. SVM achieved classification problems by finding maximum margin separating hyperplane using support vectors, while generalization to SVR is achieved by introducing e-sensi-tive area within the function [25]. SVR make effort to predict linear regression function as in Eq. (4) that can best describe the actual output data with error tolerance e, while most of the real-world scenarios including load forecasting have nonlinear dimension; in this case, data dimension has to be mapped into higher vector spaces, so that training data may exhibit linearity and thereafter linear regression can be applied [26]:
f xð Þ ¼ w:; xð Þ þ b ð4Þ where ; xð Þ is the mapping function from nonlinear to linear space, b is the bias term, and w is the minimum norm values to be calculated subject to given condition con-straints as in Eq. (5): min w;bmni;ni 1 2w 2þ CX n i niþ ni for si[ 0 ð5Þ s:t: yi f xð Þ e þ ni f xð Þ yi e þ ni ni;ni 0 8 < : ð6Þ
where C is penalty parameter on errors, e is the tolerance error greater than niand n
i a kind of trade-off; since SVR
back bone is kernel trick, a widely used Gaussian kernel function is adopted as in [26,27], given in Eq. (7):
k xi;; xj ¼ exp xi x2j 2o2 0 @ 1 A ¼ exp c xi x2j ð7Þ xi;and xjare the input samples, ando2is variance width of
the parameter of kernel function; amongst important parameters of SVR are C, e, and c¼ 1
2d2 which are highly
required to be specified, selected at the same time for minimum estimated errors, the parameters are adopted according work in [26], due to minimum forecasting error output at this parameter setting among various kernel functions. SVR algorithm for load forecasting application was first introduced in the year 2001, and thereafter its finds recognition from several researchers in various applications [28, 29]. Two strategy approaches for STLF using SVR algorithm to reduce operator interaction in model design procedure are proposed; based on the approach an improved accuracy is observed compared to artificial neural network (ANN) [30]. A nonlinear dynamic model of customer load demand is forecasted using SVR in smart grid environment, and an SVR with single set of kernel is applied with no prior assumption about data standing; prediction results of SVR are compared with that of ANN, and times series analysis techniques shows high accuracy [31]. With following properties, SVR is well fit-ted for STLF in smart distribution grid.
3 Flower pollination–feedforward neural
networks for load flow forecasting
In numerous design applications, finding optimal solutions is a difficult task due to highly complicated constraint; sometimes nonlinearity and multi-dimension make it
impossible to find optimal solutions. Especially in training artificial intelligence, such problems are encountered; nat-ure-inspired optimization algorithms play significant role in tackling such kinds of problems [32]. Majority of clas-sical algorithms are deterministic; in case of stochastic algorithms, most types are heuristic and metaheuristic; with small differences heuristics mean finding solution by guessing of many trials, and on the other hand meta-heuristic algorithms mean finding advanced-level solutions beyond good solutions, and these algorithms usually exe-cute well than simple heuristics [33]. In practice meta-heuristic algorithms custom certain trade-offs of randomization and local search. Randomization offers worthy chance of algorithms deviation at local optimum trap to focus search on a global level [34]. Intensification and diversification are two key constituents of all meta-heuristic optimizations algorithms. Diversification is to produce different outputs so that search space is explored on a global optimum. Intensification allowed exploiting search focus in region of local space that a good solution is within reach [35]. This two major components guarantee the emergence of the best solutions, whereas diversification through randomization evades best fitness confined to local region, and this increases diversity of solutions. FPA can be categorized as population based and trajectory based, which all use multiple agents or particles [36].
A recent emerging nature-inspired population-based optimization algorithm FPA is developed by Yang [37], enthused by pollination process of flower, which is the transfer of pollen that is linked to natural biohabitant. Two important characters of flower pollination are abiotic and biotic, with 90% biotic pollination and the rest abiotic which requires no pollinators. For FPA to solve FNN training optimization problems such as load flow fore-casting, a random weighted sum is added to combine a number of objectives so to become composite sole objec-tive [32]. The FPA can be expressed in four rules for updating equations mathematically:
Rule 1 global pollination and (Rule 3) flower constancy are expressed in Eq. (8):
xtþ1i ¼ xt
iþ cL kð Þ g xti
ð8Þ where xt
i is i solution vector xi at iteration t, and g is the
present best solution, c is a scaling factor of step size control, L(k) is a step size parameter. Rule 2 and Rule 3 both are local fertilization and are expressed in Eq. (9): xtþ1i ¼ xt iþ 2 x t j x t k ð9Þ where xt jand x t
kare pollen from diverse flowers with similar
plant species. If xt
j and xtk are from exact species and
population, this becomes local search with 2¼ 0; 1½ uni-formly drawn.
Rule 4 is switching probability control between local and global pollination of value p2 0; 1½ . The above pro-cedure is summarized in Fig.2. FPA as population-based metaheuristic algorithm operates on multiple candidates to be optimized on global search scale and is used to train FFN to generate low-level error of weight and bias with accurate network structure arrangement.
FPA developed in 2012 attracts little attention on parametric studies and why FPA works on global opti-mization problems. A review on applications of FPA in comparison with other metaheuristic algorithms is pre-sented in [38]. Another detailed review considers FPA and other algorithm application in single- and multi-objective problem; findings reveal that FPA outperforms most of counterparts [39]. Local and global exploration searching ability of FPA makes it possible to solve most of the engineering problems. Authors in [40] compared FPA with four other algorithms and found FPA to be energy-efficient and superior. A comprehensive study based on mutation operators of FPA subjected to statistical tests compared five recent metaheuristic algorithm based on mutation; again FPA proved better with high accuracy [41]. Quali-tative and quantiQuali-tative analyses of FPA and its variant with some extension of it using CEC 2013 benchmarks to solve real-parameter continuous optimization and then by applying it on some CEC 2011 benchmarks for real-world optimization problems proved FPA to be suitable [42]. In addition, for FPA based on opposition-based learning and modification of the movement equation in the global pol-lination operator, the authors in [39, 43] concluded that basic FPA has been found to offer more-than-average performances when compared to state-of-the-art algo-rithms, and for hybrid extensions FPA reached best results;
a comprehensive review for variant analysis on FPA since 2012 acknowledges superiority of FPA.
3.1 FPA for training FNN
Feedforward neural network (FNN) is the distinct category of neural network structure; the structural organization design of FNN makes it attractive since it permits identifying a computational classic in a structural/network arrangement; it has universal capabilities of approximating continuous functions [44]. The FNN structure consists of large number of neurons arranged into layer-by-layer form; these neurons have weight from the previous neurons layer [45]. Meta-heuristic algorithms analyzed FNN organs into an opti-mization problem to obtain near-optimum solutions [46]. The best reliable model for load flow forecasting method is to train a simple neural network with a minimum structure. In this work feedforward neural network (FNN) with one hid-den layer is proposed; two-layer-structured FFN is shown in Fig.3. Usually, three design procedures are applicable in training neural network using a FPA algorithm. The first procedure in this process employs FPA algorithms applica-ble for discovering an arrangement of weights and biases that generate lowest output error for the entire networks. The second procedure is whereby metaheuristic algorithms are utilized to locate a good arrangement of structure for network within a certain problem consideration. The third technique allows FPA to adjust gradient-based learning parameters of an algorithm. The first method maintained fixed structure for training FNN; the algorithm’s duty is to discover an appro-priate value for all connected weights and biases for the overall error minimization training. In the second situation, the structures of FNN are altering; algorithm application is training and construction of best possible structure for a specific problem.
Altering the structure can be accomplished by influ-encing the connections between neurons, the number of
Initialize a population of n pollen gametes with random solutions Find the best solution in the initial population
Define a switch probability p [0, 1] while (t <MaxGeneration)
for i = 1 : n (all n flowers in the population) if rand < p,
Draw a step vector L which obeys a Lévy distribution Global pollination via
else
Draw from a uniform distribution in [0,1] Randomly choose j and k among all the solutions Do local pollination via
end if
Evaluate new solutions
Update population with new solution end for
Find the current best solution end while
Fig. 2 Pseudoflowchart of the proposed FPA
hidden layers, and the number of hidden nodes in each layer of the neural network [47]. In this case the first method is employed for FPA to train the FNN using a combination of weights and biases to provide the lowest possible error for the network structure. With this approach the structure of the neural network is not altered in any form. In this respect the objective function that fits to data with minimum error fitness for FNN is described in Eq. (10), and details are explained in [48]. The FNN requires encoding strategy agent applicable to meta-heuristic algorithm to encode the weight and bias. The number of input nodes is equal to n, and the number of hidden node neurons is equal to h; then, the total number of neurons of the hidden layer is 2 h ? 1, and the number of output nodes is m [19,49]. In each epoch of learning, the output of each hidden node is calculated as follows:
F yj ¼ 1= 1 þ exp X n i¼1 wij:xi hj !!! ; j¼ 1; 2; . . .:h ð10Þ yj¼ Xn i¼1 wij:xi hj ð11Þ
where Eq. (11) represents the function in yj, wij is the
connection weight from the ithnode in the input layer to the jthlayer node in the hidden layer, hj is the bias (threshold)
of the jthhidden node layer, and xiis the ithinput; finally, the calculated hidden node output producing the final output is presented in Eq. (12):
Ot¼ Xh i¼1 wtj F yj ht; t¼ 1; 2; . . .m ð12Þ
where wtjis the connection weight from the jthhidden node to the tthoutput node and htis the bias (threshold) of the tth output node. The learning error is determined by (13): Et¼ Xm t¼1 Oti dt i 2 ð13Þ E¼X L t¼1 Et L ð14Þ
where L is the number of input sample for training,dt iis the
required output at ithinput unit when the tthtraining sample is applied, and Ot
i is the actual output of the ithinput unit when the tthtraining sample is used.
The final stage of the model is to encode the weights and bias of the FNN for every agent of the algorithms used. Matrix method of encoding strategy has been used; in this method every single agent is encoded as matrix, because the decoding process is easy even though for neural net-work with complicated structure the encoding is difficult
and time-demanding. The load flow forecasting training algorithms are shown in Fig.4. The algorithms work flow initialized value randomly to generate solution by the first iteration when FNN algorithm is run. Generated weight and bias are checked; otherwise, new random values are gen-erated and thereafter proceed to calculate the best fitness functions. The best candidate is selected; optimization algorithms are applied to obtain global best value for each one of the algorithms; the procedure is repeated until the maximum iteration or convergence of the algorithm is reached. Optimization common parameters are generation number and population size, and other parameters are explicitly stated; these parameter settings are obtained after several runs, and of course due to randomization, a better result becomes a worst result in some run. The best can-didate is selected, and optimization algorithms are applied to obtain global best value for each one of the algorithms; the procedure is repeated until the maximum iteration or convergence of the algorithms is reached. List of setting and construction parameters is presented in Table1.
4 Results and discussion
In this approach robustness and efficiency of new emerging FPA nature-inspired population-based optimization algo-rithms in training an FNN for load flow forecasting prob-lems analysis are investigated. The works proposed a smart distribution gird of Konya Industrial Zone, to verify load flow forecasting in smart distribution grid environment. In the optimization procedure initial independent variables are assigned randomly to perform load flow forecasting, while dependent variables are set automatically. The optimal solution is achieved using FPA setting parameters; the procedure is explained in Fig.4. The best trained candi-dates are selected, and optimization algorithm is applied to obtain global best value for the algorithm; the procedure is repeated until the maximum iteration or convergence of the algorithm is reached. Optimization common parameters are generation number and population size, and other param-eters are explicitly stated; these parameter settings are obtained after several runs, and of course due to random-ization a better result becomes a worst result in some run. Population size = 20, generation size = 1000, probability switch p = 0.8, scaling factor c = 0.1, and k = 1.5 as sug-gested for most engineering problems by Yang to represent local search operator by 0.8 and global search operator by 0.2, a claim supported by Rohit in his comprehensive review on mutation operators to FPA [41]. The load flow data case study is done for 7 weeks; the real load flow data in Konya Industrial Zone employed to compare the fore-casting performances are shown in Fig.5, while reactive power can be compensated locally. These data are divided
into 2, 6 weeks for training and 1 week for testing, so as to forecast the next week a head corresponding to 168-h period of testing data as shown in Fig.6; the effect of RE fluctuation is evidently present especially during the night hours equivalent to no production time.
Real and reactive power for 1-week period testing data is shown in Fig.6; the prevalence effect peak period and working days are well captured. For the purpose of clarity individual cases are presented in separate figures (Figs.7,
8,9) and are combined in Fig. 10for snap clear and easier observation. It is pertinent to observe that in Fig.7 FNN forecasted results are compared against actual real power flow as a first step; it can be observed that forecasted result follows closely to actual data with relatively clearly visible residual at all time frames, with exception of some few point. The accuracy level in terms of performance mea-surement is as follows: MAE is 3.09 MW, MAPE is found to be 3.56%, and RMSE is equal to the value of 2.18; these values are within acceptable limit in traditional grid, but in smart grid best maximum accuracy is inherently required. In Fig.8SVR forecasted results are shown; at initial stage it is more evident that the algorithm deviated from the actual data. From 10- to 50-h time interval more deviations are present; SVR adjust effectively for tracking real shape before forecasting at minimum error compared to middle point time to the end time with minimum ripples at tip end. In this case measurement error parameters are as follows: MAE is found to be 1.83 MW, MAPE is 2.13%, while RMSE is 1.97. For the case of FPAFNN model forecasted results are shown in Fig.9; the proposed approach follows Training_Algorithm (Max_Iterations, Max_Solutions, Load_Data)
Parameters List: Num_Iteration: generation counter; : solution counter;
Load_Data: training data and testing data
Best_solution: value for best solution; Min_Fitneess: fitness for best solution SOLUTIONS array that holds current generation of solutions
Generate_Solutions():Sub-function that generate new solutions Neural_Network(): Sub-function that performs training analysis Optimization_Operators():Sub-function that breeds the new solutions
01 INITIALIZE Num_Iteration =1; =1;
02 Neural_Network(parameters(n, net, input, target)):
03 Run_ Neural_Network()
04 SET =Generate_Solutions( weights and biases);
05 LOOP WHILE Num_Iteration <= Max_Iterations
06 LOOP WHILE <= Max_Solutions
07 SET Solution= 08 SET 09 IF < Min_Fitneess 10 SET Min_Fitneess= 11 Best_solution= Solution 12 END 13 SET = +1 14 END
15 SET =Generate_Solutions(weights and biases);
16 RUN Optimization_Operators();
17 SET Num_Iteration= Num_Iteration+1
18 END
19 RETURN Best_solution (weights and biases)
Fig. 4 Proposed pseudocode for training algorithm
Table 1 Parameter setting of each method
Method Name of function or parameter Function or Value FFN Number of neurons of input layer 4
Number of neurons of hidden layer 9 Number of neurons of output layer 1
Hidden layer transfer function Sigmoid (logsig) Output layer transfer function Linear (purelin)
Training function Feedforwardnet
SVR Variance constant (c) 0.0266
Error tolerance (e) 0.001
Penalty factor (C) 5.309
FPA Population size 20
Generation 1000
Scaling factor 0.1
Step size 1.5
more closely related pattern with almost similar curve except in some instance, with curve deviating from the actual data with small margin. The proposed model gives more accurate forecasted result in terms of measurement error parameters as follows: MAE is 1.01 MW, MAPE shows significant improvement of 1.42%, while RMSE in this case is 1.800; with this index value optimal accuracy is
guarantee. All the forecasted method results are summa-rized in Table2.
The combined figures of different methods are shown in Fig.10, representing all scenarios at a forecasting time; it is clearly observed that FPAFNN method tracks the real actual pattern effectively with little deviation and then all the other methods. Even though errors exist especially during the first 20 h, thereafter FPAFNN optimization
100 200 300 400 500 600 700 800 900 1000 1100 100 120 140 160 180 200 220 Number of Hours Power (MW)
Seven weeks actual Data
Fig. 5 Hourly actual collected real power flow data plot for 7 weeks 0 20 40 60 80 100 120 140 160 100 120 140 160 180 200 220 Number of Hours Power (MW)
One Week Real Testing Data
Fig. 6 One-week actual testing data plot of the Konya Industrial Zone 0 20 40 60 80 100 120 140 160 -50 0 50 100 150 200 Number of Hours Power (MW)
Actual load flow FNN Forecasted Forecasted Error Fig. 7 Comparison of actual
0 20 40 60 80 100 120 140 160 -50 0 50 100 150 200 Number of Hours Po w e r (M W )
Actual load flow SVR Forecasted Forcasted error Fig. 8 Comparison of actual
load flow and SVR forecasted
0 20 40 60 80 100 120 140 160 -50 0 50 100 150 200 Number of Hours Power (MW)
Actual load flow FPAFNN Forecasted Forecasted error Fig. 9 Comparison of actual
load flow and FPAFNN forecasted 0 20 40 60 80 100 120 140 160 100 120 140 160 180 200 220 Number of Hours Power (MW)
Actual load flow FNN Forecasted SVR Forecasted FPAFNN Forecasted Fig. 10 Comparison of actual
load flow, FNN, SVR and FPAFNN forecasted
algorithm parameter settings keep maximum tracking of the actual data with little deviation until forecasting period elapses. The FPAFNN algorithm shows level of superiority numerically and graphically.
The key future to forecasting analysis is the minimum output error; the error assessment using 1-week load flow forecasting generally exhibits good performance; this may be collaborated due to the fact that training data are col-lected with high resolution for 1-week look-ahead fore-casting. For further error analysis the output errors for FNN and FPAFNN model are shown in Fig.11; the ideal error is to be at zero level; in this regard, the error output of FPAFNN model is closer to the best line than of FNN error output model. Breaking forecasted deviation from the original values in hours and days for the FPAFNN model
gives more detailed information of how the model delivers optimal accuracy.
In Fig.11, the difference between the medians of the hour group’s data is not equal to one, due to the fact that hourly result is highly variable hour to hour, and thus is more during the peak working hours. Considering Fig. 12, the difference between the medians of the working day is approximately equal. Since the notches in the box plot do not overlap, it can be concluded that, with 95% confidence the true medians do differ on Saturday and Sunday due to less power on these days; therefore, minimum errors are observed.
5 Conclusions
Short-term load flow forecasting using nature-inspired metaheuristic algorithm in smart distribution grid envi-ronment is carried out. The problem of learning process for finding the best combination of weight and biases con-nection that requires huge data with trial and error in FNN has been overcome. Both parametric experimental results proved that the finding does not happen by chance, but by an independent non-bias results comparison. FNN algo-rithm performs below average compared to SVR algoalgo-rithm, Table 2 Evaluation of forecasted method
Method MAE (MW) MAPE (%) RMSE
FNN 3.09 3.56 2.18 SVR 1.83 2.13 1.97 FPAFNN 1.01 1.42 1.80 -20 -10 0 10 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Number of Hour a day
Errors (MW)
Fig. 11 FPAFNN error rate forecasted by hours of day
-15 -10 -5 0 5 10 15 20
Sun Mon Tue Wed Thu Fri Sat
Errors by week a day
Errors (MW)
Fig. 12 FPAFNN error rate forecasted by days of the week
while FPAFNN performs better than SVR algorithm. The results indicate that FPAFNN outperforms FNN and SVR simultaneously, even though the error between the algo-rithms is within acceptable limit in load flow forecasting analysis; in this regard, optimal accuracy outcomes are preferred. FPAFNN proposed model can efficiently be applied independently in load flow forecasting problems in smart distribution grid environment with much differences; the MAE load flow forecasting error is 3.09 MW for FNN model and 1.01 MW for FPAFNN model; same improve-ment is seen in respect of MAPE and RMSE values in each case. For the sake of comparison a well-reported SVR algorithm for forecasting problems is tested on the same data; the algorithm proved superior against FNN with improved accuracy value of MAE 1.83 MW and other error criteria of MAPE and RMSE values; a significant improvement in error reduction compared to FNN is observed. Both FNN and SVR algorithm models are sig-nificantly behind FPAFNN model measure using all the three error forecasting techniques, an illustration capability of our proposed approach. The accuracy of results among the algorithms shows a strong selection in parametric turning capabilities. As discussed above FPAFNN algo-rithm model provides better optimal accuracy in compar-ison with FNN and SVR models.
Acknowledgements The authors acknowledge the effort of Konya Organized Industrial Zone Directorate for providing access to system data, and support of Scientific and Technological Research Council of Turkey (TUBITAK)
Compliance with ethical standards
Conflict of interest The authors declare that they have no conflict of interest.
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