Wavelet neural network–based wind speed forecasting and application of shuffled frog leap algorithm for economic dispatch with prohibited zones incorporating wind power

Abstract

Wind speed and wind power generation are characterized by their inherent variability and uncertainty. To overcome this drawback, an accurate prediction of wind speed is essential. The purpose of this article is to develop a hybrid wavelet neural network model for wind speed forecasting and thus, in turn, for wind power generation. The combined optimal economic scheduling of the wind generators and conventional generators has also been investigated in this article. This article proposes shuffled frog leap algorithm for solving economic dispatch problem in power systems. The non-linear characteristics of the generator such as prohibited operating zone and non-smooth functions are considered. The feasibility of the proposed algorithm is demonstrated for 5 units, 6 units and 15 units systems and it is compared with the existing solution techniques. The results show that the proposed algorithm is indeed capable of handling economic dispatch problems.

Keywords

Wavelet neural network shuffled frog leap algorithm economic dispatch wind speed forecasting

Introduction

The increasing energy demand and decreasing energy resources have necessitated the optimum use of available resources. Economic dispatch (ED) is an optimization scheme that intends to find the generation outputs that minimize the total operating cost while satisfying several unit and system constraints. Prior to the widespread use of alternate sources (solar, wind) of energy, the ED problem involved only conventional generators. In recent years, wind power has experienced a rapid growth and has shown great potential in fuel savings and environmental protection. However, its uncertainty and variability also makes it challenging to find a proper dispatch scheme for a wind-penetrated power system. The key issue associated with the incorporation of wind power is how to deal with its variable nature, considering the required reliability and security of power systems. Up to now, different authors have proposed models to solve ED (or unit commitment) problems for wind-penetrated power systems (Jadhav et al., 2012; Villanueva et al., 2012). To effectively use wind power, researchers usually forecast the wind speed or wind generation over a time horizon in advance and then obtain the statistic distribution of wind speed or wind generation. Based on the distribution function and estimated loads, researchers can determine the dispatch scheme. Hetzer et al. (2008) presented an ED model incorporating wind power with the stochastic wind speed characterization based on the Weibull probability density function (PDF). Penalty costs for overestimation and underestimation of available wind energy are also considered.

Various conventional methods such as bundle method, non-linear programming, mixed integer linear programming, dynamic programming (Fiacco et al., 1968), quadratic programming, Lagrange relaxation method, network flow method and direct search method reported are used in the literature (Hazra and Sinha, 2011; Hejazi et al., 2011; Sinha et al., 2003) to solve ED problem. Practically, ED problem is non-linear, non-convex type with multiple local optimal points due to the inclusion of valve point loading effect, multiple fuel options with diverse equality and inequality constraints. Normally, conventional methods have failed to solve such problems as they are sensitive to initial estimates and converge into local optimal solution. Modern heuristic optimization techniques proposed by researchers based on operational research and artificial intelligence (AI) concepts, such as evolutionary programming (Sinha et al., 2003), genetic algorithm, simulated annealing, ant colony optimization, Tabu search, neural networks, particle swarm optimization (PSO), differential evolution, bacterial foraging technology and shuffled frog leap algorithm (SFLA), provide better solution for ED.

This article presents the ED problem formulation with wind generators. So far, the conventional technique primal-dual interior point (PDIP) is not applied for ED with non-linearities such as valve point effect and prohibited zones. Hence, in this article, two solution techniques, namely, PDIP and SFLA are applied for solving ED problem. The effectiveness of these solution techniques is compared with respect to operational cost and time.

This article is organized as follows: section ‘Wind speed forecasting’ explains about the forecasting of wind speed by wavelet neural network (WNN). Section ‘ED problem formulation including wind generators’ presents the formulation of the ED problem with wind generators and thermal generators possessing prohibited zones. Section ‘Solution techniques’ presents the solution algorithms PDIP and SFLA. Section ‘Simulation results’ deals with the simulation results of three test systems, and section ‘Conclusion’ concludes the work.

Wind speed forecasting

Over the last few decades, several methods for wind speed forecasting including artificial neural network (ANN), probabilistic neural network (PNN) and the general regressive neural network (GRNN) have been proposed. In general, the ANNs are trained under supervision with the backpropagation (BP) algorithm. The basic BP algorithm is a gradient descent one (Lee and Park, 1992; Sinha, 2000), which adjusts the network weights along the steepest descent direction of error function. The other forecasting techniques, PNN and GRNN, described in Dhivya et al. (2011) are also considered for comparison and analysis.

All these methods involve the limitations of obtaining monolithic global models for a time series (Ulagammai et al., 2007). To enhance the ability of the ANN in learning the signals, the hidden patterns, that is, all the frequency components, should be extracted from the data, which can be achieved by introducing a multi-resolution decomposition technique such as wavelet transform.

Wavelet transform, a scalable windowing technique, breaks the signals into shifted scaled versions of the original wavelet signal, using the timescale region instead of the time–frequency region. To improve the accuracy of the ANN, they are combined with the wavelet to set the hybrid model (Ulagammai et al., 2007). First, the wind speed is decomposed into several sub-serials using wavelet. Each neural network is then constructed to forecast each sub-serial. The final forecasting speed result is obtained as the sum of all the sub-serial forecasting results. A given signal s(t) is decomposed into several other signals with different resolution levels by dyadic wavelet transform (DWT), and the DWT of s(t) is defined as follows (Justus et al., 1978)

s (m, n) = 2^{\frac{m}{2}} \int s (t) φ^{*} (\frac{t - n 2^{m}}{2^{m}}) d t

(1)

where * denotes a complex conjugate, m and n are scale and time-shift parameters, respectively, and f(t) is a given basis function (mother wavelet). The DWT is implemented using a multi-resolution pyramidal decomposition technique.

The WNN forecasting procedure shown in Figure 1 comprises the development of a preliminary forecast model followed by pre-signal processing, signal prediction and post-signal processing (Ulagammai et al., 2007).

Figure 1.

Three stages of the WNN forecast model.

Stage 1: Pre-signal processing

In pre-signal processing, the historical wind speed data are fed into the model proposed as time-series signals. The non-decimated wavelet transform (NWT) is used as the pre-signal processor, and based on the selected resolution level, the respective time-series signals are decomposed into several wavelet coefficients. These decomposed coefficients are then normalized and fed as inputs to the signal predictor (neural networks) for either training or forecasting.

Stage 2: Signal prediction

Signal prediction in the forecast model is achieved using the ANN. The number of ANN needed for the model is determined by the number of wavelet coefficient signals at the pre-processor output. For each wavelet coefficient signal (including the approximation component), one ANN is required to perform the corresponding prediction.

Stage 3: Post-signal processing

In post-signal processing, the same wavelet technique and resolution level utilized for pre-signal processing are used. In this stage, the signal predictor (ANN) outputs are combined to obtain the final predicted output, as the sum of all the predicted wavelet coefficients.

Modelling of wind speed

The wind speed profile at a given location closely follows the Weibull distribution. The Weibull distribution function with a shape factor of 2 is also termed the Rayleigh distribution. The advantages of the Weibull distribution (Justus et al., 1978) include the following features: (1) it is a two-parameter distribution, more general than the single parameter Rayleigh distribution, but less complicated than the five-parameter bi-variate normal distribution; (2) the observed data of wind speeds have already been proven to follow a Weibull distribution and (3) if the k and c parameters are known at one height, it is possible to find the corresponding parameters at another height. The PDF for a Weibull distribution is given as follows

f_{v} (v) = (\frac{k}{c}) {(\frac{v}{c})}^{k - 1} e^{{\frac{v}{c}}^{k}}

(2)

Using curve fitting and maximum likelihood estimation, the parameters of Weibull distribution curve are estimated for the forecasted wind speed data.

Wind power calculation

After the hourly wind speed is obtained, the next step is to determine the power output of wind turbine. The function is described by the operational parameters of wind turbine. The parameters commonly used are cut-in speed, cut-out speed and rated wind speed. The following equations (Arabali et al., 2013) are used to obtain hourly wind power output from the forecasted hourly wind speed

W_{i} = {\begin{matrix} 0 0 \leq v < v_{i} \\ (A + B * v + C * v^{2}) v_{i} \leq v < v_{r} \\ W_{r} v_{r} \leq v < v_{o} \\ 0 v > v_{o} \end{matrix}

(3)

From the study by Arabali et al. (2013), the operational parameter–dependent constants A, B and C are determined.

ED problem formulation including wind generators

The ED problem can be mathematically expressed as an optimization problem in which the objective is to minimize the total cost of generation. If the power sources are fully controllable as happens with thermal units, the generation can coincide with the demand. But if the network includes wind generators, sometimes the scheduled and available wind power may not coincide because the wind speed cannot be controlled. Therefore, when the wind generators are involved, the cost minimization problem includes more terms to account for the variable nature of wind power. The optimal dispatch of the wind power is also the outcome of ED problem in addition to the optimal dispatch of thermal generators. The wind power and ED are coupled together in this work. When we decouple both the problems, then wind power has to be reflected as negative load, or in other words, the load that has been forecasted has to be modified according to the forecasted wind power. Under these circumstances, there is no provision to handle the operating cost associated with wind generation and also the forecasted errors of wind power (such as overestimation and underestimation). By integrating the scheduling of wind generators in the thermal ED problem, there is flexibility to accommodate the cost of wind generation and its associated forecasted errors. Therefore, when wind generators are involved, the problem of cost minimization will involve more terms than conventional ED problem because the wind power available may vary from the scheduled power. It is essential to consider the consequences when the wind power available is not used completely, that is, when there is excess wind power available, more than the scheduled power. In such a case, a penalty cost is applied, which is the payment to the wind power producer for the additional power. On the other hand, if the scheduled wind power is not achieved, or in other words, when the wind power available is less than expected, a reserve power source must provide the difference. Therefore, a reserve cost needs to be considered when wind generators are involved in the electrical network.

To get more practical results, fuel cost function is modified with the inclusion of valve point loading effect. The generating units with multiple valves in steam turbines are available. The opening and closing of these valves are helpful to maintain the active power balance. However, it adds the ripples in the cost function, which makes the objective function highly non-linear. In addition, the prohibited operating zones in the input–output curve of generator are due to steam valve operation or vibration in a shaft bearing. The best economy is achieved by avoiding the operation in those prohibited areas. Hence, these two constraints must be taken into account to achieve true economic operation.

Considering the above constraints, the objective function is given as follows

F_{T} = \sum_{i = 1}^{N G} a_{i} P_{g i}^{2} + b_{i} P_{g i} + c_{i} + d_{i} \sin (e_{i} (P_{g i \min} - P_{g i})) + \sum_{j = 1}^{M} d_{j} W_{j} + k_{p j} \int_{W_{j}}^{W_{r j}} (W - W_{j}) f_{w} (w) + k_{r j} \int_{0}^{W_{r j}} (W_{j} - W) f_{w} (w)

(4)

where d_i and e_i are the coefficients of generator i considering valve point loading effect.

Subject to the constraints

P_{g i \min} ⩽ P_{g i} ⩽ P_{g i 1} and P_{g i 2} ⩽ P_{g i} ⩽ P_{g i \max}

(5)

where $P_{g i 1} ⩽ P_{g i} ⩽ P_{g i 2}$ is the prohibited zone $i = 1, 2, \dots, N G$

W_{j \min} \leq W_{j} \leq W_{j \max} i = 1, 2, \dots, M (MW)

(6)

\sum_{i = 1}^{N G} P_{g i} + \sum_{j = 1}^{M} W_{j} = P_{D} (MW)

(7)

Solution techniques

This section describes about the two solution techniques: PDIP and SFLA.

PDIP algorithm

Interior point methods have proven to be a viable alternative for the solution of power system optimization problem. The ED problem described by equation (3) can be compactly written as general non-linear constrained problem

Min f (x) subject to g (x) = 0 and h (x) \geq 0

(8)

where x = [P₁, P₂, …, P_n; W₁, W₂, …, W_m]^T, g(x) is the power balance equality constraint and h(x) is a vector of the physical limit inequality constraints.

PDIP has four steps to obtain optimality conditions as explained in the study by Capitanescu et al. (2006).

Set the iteration count k = 0; initialize y⁰ (slack and dual variables should be strictly positive).

Solve the linearized Krush Kuhn Tucker conditions by taking the first-order derivative as given below, and the second-order derivative (Hessian matrix) of Lagrange function is derived from $\nabla f (x)$

\nabla f (x) = [\begin{matrix} \begin{matrix} \begin{matrix} 2 a_{i} * P_{i} + b_{i} - λ \\ \frac{\partial (U E + O E)}{\partial P_{i}} \\ \sum (P_{i}) - P_{d} \end{matrix} \\ π_{1} - \frac{μ}{s_{1}} \end{matrix} \\ - π_{2} - \frac{μ}{s_{2}} \\ \sum (P_{i} - P_{\max} + s_{1}) \\ \sum (P_{\min} - P_{i} + s_{2}) \end{matrix}] with respect to [\begin{matrix} P_{i} i = 1 to n \\ P_{i} i = 1 to n w \\ λ \\ s_{1} \\ s_{2} \\ π_{1} \\ π_{2} \end{matrix}]

(9)

Determine the maximum step length α ^k along the Newton direction ∆y^k such that (s^k + 1, π^k + 1) > 0; $α^{k} = \min {1, γ \min_{Δ s_{i}^{k} < 0} (- s_{i}^{k} / Δ s_{i}^{k}), γ \min_{Δ π_{i}^{k} < 0} (- π_{i}^{k} / Δ π_{i}^{k})}$ , where γ є (0, 1) is a safety factor aiming to ensure strict positiveness of the slack and dual variables. Update the solution as follows

s^{k + 1} = s^{k} + α^{k} Δ s^{k}, π^{k + 1} = π^{k} + α^{k} Δ π^{k}, x^{k + 1} = x^{k} + α^{k} Δ x^{k} and λ^{k + 1} = λ^{k} + α^{k} Δ λ^{k}

(10)

Check convergence. A locally optimal solution is found and the process terminates when (1) the primal feasibility and (2) objective function variation from one iteration to the next fall below some tolerances (Granville, 1994).

If convergence is not achieved, update the barrier parameter (Irrisari et al., 1997), and go to step 2.

SFLA

It is a memetic algorithm inspired by the food-hunting behaviour of frogs. It is based on the evolution of memes carried by the interactive frogs and by the global exchange of information among themselves. It is a combination of deterministic and random approaches. It also combines the benefits of both the genetic-based memetic algorithm and social behaviour-based PSO algorithm. It can be used to solve many complex optimization models that are non-linear and non-differentiable.

The first step of this algorithm is to generate initial population P of frogs randomly in search space. The position of ith frog is represented as X_i = [X_i,₁, … X_i,_D], where D is the number of variables. Then, the frogs are sorted in descending order according to their fitness. After that, the entire population is partitioned into m subsets referred as memeplexes each containing n frogs (P = m*n). The strategy of the partitioning is as follows. The first frog goes to first memeplex, second goes to second memeplex, the mth frog to mth memeplex and (m + 1) frog goes to first memeplex and so forth. In each memeplex, the position of frogs with the best and worst are identified as X_b and X_w, respectively. Also, the position of the frog with global best is X_g. Then, within each memeplex, a process similar to PSO algorithm is applied to improve only the frog with worst fitness in each cycle using the following equation. Change in frog position is given as follows

D_{i} = r a n d () * (X_{b} - X_{w})

(11)

New position X_{w} = Current position of X_{w} + D_{i} where D_{i m a x} \geq D_{i} \geq - D_{i m a x}

(12)

where rand( ) is the random number between 0 and 1, and D_imax is the maximum allowed change in a frog’s position.

Fitness function to be evaluated is given as follows

F_{T} + λ (P_{d} ~ \sum_{i = 1}^{N + M} P_{i})

(13)

Figure 2 illustrates the memeplex partitioning process, and Figure 3 shows the flow chart for SFLA.

Figure 2.

Memeplex partitioning process.

Figure 3.

SFLA flow chart.

Simulation results

Wind speed prediction

The training data set and test data set comprise temperature, humidity, dew point, pressure, wind direction and wind speed. To evaluate the proposed model for wind speed prediction, data sets are collected from the automatic weather station, and the study is carried out for 24 h ahead. The sampled time series used in the model consists of 1000 data in total, corresponding to 30 min mean data. The time series is divided into two folders: one is the training set with 964 samples used for the model’s training and the other is the test set that contains the rest, namely, 36 samples, which are used to verify the accuracy during the prediction period. Some of the data in the study by Dhivya et al. (2011) are purposely multiplied by a constant (*10, *100 or *1000) to avoid storage of floating point numbers and the same data are considered.

Different AI techniques such as feed-forward backpropagation (FFBP), cascade-forward backpropagation (CFBP), PNN, GRNN and k-nearest neighbours (KNN) are applied to the developed model in the author’s previous paper (Dhivya et al., 2011) and are given in Table 1.

Table 1.

Comparison of performance measure by different techniques.

	FFBP	CFBP	PNN	GRNN	KNN	WNN
MSE	6.748	6.8177	3.795	2.856	5.882	2.77
MAPE (%)	5.1097	5.2671	2.9729	2.3000	0.9104	1.50

Bold value represents the best value.

FFBP: feed-forward backpropagation; CFBP: cascade-forward backpropagation; PNN: probabilistic neural network; GRNN: general regressive neural network; KNN: k-nearest neighbours; WNN: wavelet neural network; MSE: mean squared error; MAPE: mean absolute percentage error.

In WNN, the number of ANNs required depends upon the wavelet family and the resolution level. The wavelet family is chosen as Db2 with a resolution level of 2. Hence, the number of neural networks constructed for WNN is 3. The number of input neurons for ANN1, ANN2 and ANN3 is 6, 6 and 9, respectively, and the number of output neurons for all the ANNs is 2.

The resultant relationships between the predicted and the actual values of the wind speed for different ANN techniques are given in the study by Dhivya et al. (2011). Figure 4 displays the wind speed predicted by WNN. The performance measures adopted are the mean squared error (MSE), mean absolute percentage error (MAPE) and the linear regression. According to the forecasted errors, it is clearly seen that WNN is the optimal model because of the lowest MSE. Second comes GRNN followed by PNN and KNN, respectively (Meyyappan and Pandu, 2015).

Figure 4.

Wind speed forecasting using WNN.

Thus, WNN is found to be the better technique for predicting the wind speed compared to the ANN techniques. From the predicted wind speed, Weibull distribution is applied for wind speed. The wind speed distribution is converted into wind power distribution using equation (3). The Weibull parameters assumed are as follows: k = 2, c = 10, v_i = 2, v_o = 45 and v_r = 15. The wind power is predicted for each hour by approximating the area under the wind power PDF curve. It is assumed that the distribution is trapezoidal, and the area of the trapezoid is calculated.

ED results

Three test systems, namely, the IEEE 5-unit, 6-unit and 15-unit systems, are considered for the simulation along with three wind-generating units. Each wind farm rating is assumed to be 260 MW. Techniques used for this case study are PDIP and SFLA. In SFLA, the control parameters are power generated by the thermal and wind units. The population size for SFLA is assumed to be 50 with 5 memeplexes. The maximum number of iterations is 100. System data are taken from the study by Somasundaram et al. (2003).

IEEE 5-unit system

The 5-unit system includes five thermal and three wind-generating units and a load demand of 1175 MW. The prohibited zones for the 5-unit system are given in Table 2.

Table 2.

Prohibited zones for IEEE 5-unit system.

Unit	Zone 1 (MW) (P_Z₁, P_Z₂)	Zone 2 (MW) (P_Z₃, P_Z₄)
1	(240, 275)	(315, 375)
2	(210, 270)	(300, 390)
3	(200, 250)	(290, 370)

Since PDIP cannot handle the prohibited zone constraints directly, different combinations are run with each prohibited zone as upper and lower limits of the generators with prohibited zones. For PDIP, different combinations of prohibited zone areas such as (P_min, P_Z₁), (P_Z₂, P_Z₃) and (P_Z₄, P_max) of the generators are analysed. Each generator can operate in any of these three areas, and the different possible combinations are given in Appendix 2. Some combinations resulted in infeasible solution. The feasible combinations are considered, and the best combination from the feasible solutions is considered as the optimal solution. From the optimal scheduling results presented in Table 3, it is observed that the SFLA converges to the best cost of INR 11,486 and 10,786 without and with wind generators, respectively, whereas PDIP converges to a cost of INR 11,231 with wind generators. Since PDIP undergoes several combinations, time taken for PDIP is 118 s. If the number of prohibited zone areas increases, then the number of combinations and the execution time for PDIP also increases. When compared to the existing methods, SFLA results in the less production cost. Inclusion of wind generators further reduces the production cost. The execution time for SFLA without and with generators is 7.2 and 32 s, respectively. The execution time includes the wind speed forecasting, algorithm convergence and also the calculation of under- and overestimation costs in the case of wind generators.

Table 3.

Optimal scheduling for 5-unit system.

Units	P (MW)
Units	PDIP	SFLA
1	128.3539	122.51
2	124.5988	121.289
3	126.3208	120.759
4	104.0278	130.6687
5	112.5179	127.0020
WG1	183.0412	229.1693
WG2	198.0674	146.1736
WG3	198.0735	177.4016
Total demand	1175
Total cost (INR/h)	11,231	10,786
Execution time (s)	118	92 (100 trials)

PDIP: primal-dual interior point; SFLA: shuffled frog leap algorithm.

IEEE 6-unit and 15-unit systems

IEEE 6-unit system comprises six thermal units and three wind units with all the thermal units possessing prohibited zones. SFLA algorithm converged in 37 s with the total production cost of 12,090 INR/h. For IEEE 15-unit system, total number of thermal and wind units is 18 (15 thermal + 3 wind), and units 2, 5, 6 and 12 have prohibited zones. From the results obtained, it is prominent that the total cost obtained by SFLA algorithm is less (32,525 and 31,710.56 INR/h without and with wind generators, respectively) when compared to the existing methods (Somasundaram et al., 2003). The optimal scheduling for 6- and 15-unit systems is given in Tables 4 and 5, respectively. Convergence characteristics for IEEE 5-unit and 15-unit systems are given in Figures 5 and 6, respectively.

Table 4.

Optimal scheduling for 6-unit system.

Units	P (MW)
Units	PDIP	SFLA
1	210.0000	103.6681
2	110.0000	65.3523
3	150.0000	176.7118
4	80.0000	77.5416
5	129.8776	59.9338
6	50.0000	114.5619
WG1	177.7074	220.9626
WG2	177.7073	195.3960
WG3	177.7077	249.0946
Total demand (MW)	1263
Total cost (INR/h)	12,567	12,090
Execution time (s)	146	107 (100 trials)

PDIP: primal-dual interior point; SFLA: shuffled frog leap algorithm.

Table 5.

Optimal scheduling for 15-unit system.

Units	P (MW)		Units	P (MW)
Units	PDIP	SFLA	Units	PDIP	SFLA
1	202.9362	170.1246	12	40	24.0222
2	335	182.9788	13	25	73.0517
3	106.1846	42.2281	14	15.0708	23.2318
4	128.7594	44.5326	15	15	39.2041
5	335	438.7991	WG1	83.3182	224.7090
6	395	407.0850	WG2	117.5852	172.6559
7	464.9798	178.4475	WG3	98.0725	221.3444
8	60	176.2637	Total demand (MW)	2650
9	114.0432	114.4071	Total cost (INR/h)	32,390	31,710
10	34.0506	68.5580	Execution time (s)	212	139.58 (100 trials)
11	79.9996	48.3706

PDIP: primal-dual interior point; SFLA: shuffled frog leap algorithm.

Figure 5.

SFLA convergence characteristics of IEEE 5-unit system.

Figure 6.

SFLA convergence characteristics of IEEE 15-unit system.

The performance of the proposed algorithm for solving the ED problem is compared with the algorithms that are available in the literature (Somasundaram et al., 2003). Table 6 reveals that the execution time for SFLA is less when compared with other conventional techniques. This technique also results in the reduction in the production cost in all the cases. Furthermore, the inclusion of wind generators reduces the total fuel cost for all the test cases and it has become apparent that there is a need for alternatives to thermal energy power generation. From the cost and the computational efficiency point of view, the proposed algorithm is found to be very effective for solving ED problems. Cost comparison of existing literature techniques with SFLA is shown in Figure 7.

Table 6.

Cost comparison of existing literature techniques with SFLA.

Method		5-unit system		15-unit system
Method		Generation cost (INR/h)	Execution time (s)	Generation cost (INR/h)	Execution time (s)
Somasundaram et al. (2003)	Λ-δ iterative method	11,492.5	12.1	32,544.9	34.7
	Λ-δ iterative method	11,492.5	4.6	32,544.99	11.5
	PDIP			323,990	212
	SEPA method	11,493.23	2750	32,545.2	3000
	FCEPA method	11,492.5	5.4	32,544.97	9.4
Proposed	SFLA method without wind grs	11,486.2	7.2	32,525.32	8
Proposed	SFLA method with wind grs	10,786	32	31,710.56	39.58

Bold value represents the best value.

FCEPA: fast computation evolutionary programming algorithm; grs: generators; PDIP: primal-dual interior point; SEPA: simulated evolutionary programming algorithm; SFLA: shuffled frog leap algorithm.

Figure 7.

Cost comparison of existing literature techniques with SFLA.

Conclusion

Due to the variable nature of wind power production, wind speed prediction presents to be one of the challenging tasks to the researchers. The 1-h ahead prediction is suitable for small power systems operations and 1-h electricity markets. However, 1-day prediction is appropriate for interconnected power system operations such as unit commitments, conventional generators scheduling as well as 1-day electricity markets. Therefore, 24-h forecasting model is developed for wind speed. New improved ANN prediction tools such as CFBP, PNN, KNN, GRNN and WNN are proposed for 24-h ahead prediction of average wind speed. The test results from the models reveal the performance and the precision of the used neural network algorithms. The hybrid WNN model has proven to be an effective way for wind speed forecasting. With the forecasted results of wind speed and power, and with the integration of wind generators, the ED problem is solved using PDIP and SFLA. Conventional technique, PDIP, is also used to get the solution of ED problem that considers thermal units with valve point effects and prohibited zones. The generation cost and execution time for all test systems are obtained and are compared. AI techniques search for the global optimum and converge to the optimal solution, and an average cost saving of 2%–3% is accomplished. From the results, it is also clear that the major benefit of wind energy is that after the initial land and capital costs, there is essentially no cost involved in the production of power from wind energy conversion systems (WECS). The SFLA technique searches for global optimum and converges to an optimal solution with a minimum cost than conventional techniques. From the results, it can be noted that time taken for SFLA is on a par with FCEPA.

Footnotes

Appendix 1

Appendix 2

Unit	Combination 1	Combination 2	Combination 3
1	(P_min, 240)	(275, 315)	(375, P_max)
2	(P_min, 210)	(270, 300)	(390, P_max)
3	(P_min, 200)	(250, 290)	(370, P_max)

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship and/or publication of this article.

References

Arabali

Ghofrani

Etezadi-Amoli

(2013) Cost analysis of power system using probabilistic optimal power flow with energy storage integration and wind generation. Electric Power and Energy Systems 53: 832–841.

Capitanescu

Glavic

Ernest

et al . (2006) Interior point based algorithms for the solution of optimal power flow problems. Electric Power Systems Research 77: 507–518.

Dhivya

Meyyappan

Pandu

KDR

(2011) Performance evaluation of different ANN models for medium term wind speed forecasting. International Journal of Wind Engineering 35(4): 433–444.

Fiacco

McCormick

(1968) Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Hoboken, NJ: John Wiley & Sons.

Granville

(1994) Optimal reactive dispatch through interior point methods. IEEE Transactions on Power Systems 9: 136–142.

Hazra

Sinha

(2011) A multi-objective optimal power flow using particle swarm optimization. European Transactions on Electrical Power 21(1): 1028–1045.

Hejazi

Mohabati

Hosseinian

et al . (2011) Differential evolution algorithm for security constrained energy and reserve optimization considering credible contingencies. IEEE Transactions on Power Systems 26(3): 1145–1155.

Hetzer

Bhattarai

(2008) An economic dispatch model incorporating wind power. IEEE Transactions on Energy Conversion 23(2): 603–612.

Irrisari

Wang

Tong

et al . (1997) Maximum loadability of power systems using interior point nonlinear optimization methods. IEEE Transactions on Power Systems 12: 162–172.

10.

Jadhav

Bhandari

Dalal

et al . (2012) Economic load dispatch including wind power using plant growth simulation algorithm. In: Proceedings of the 11th international conference on environment and electrical engineering (EEEIC), Venice, 18–25 May 2012, pp. 388–393. New York: IEEE.

11.

Justus

Hargraves

Mikhail

et al . (1978) Methods for estimating wind speed frequency distributions. Journal of Applied Meteorology 17: 350–353.

12.

Lee

Park

(1992) Short-term load forecasting using artificial neural networks. IEEE Transactions on Power Systems 7: 124–130.

13.

Meyyappan

Pandu

KDR

(2015) Wavelet neural network-based wind-power forecasting in economic dispatch: A differential evolution, bacterial foraging technology and primal dual-interior point approach. Electric Power Components and Systems 43(13): 1–12.

14.

Sinha

(2000) Short-term load forecasting using artificial neural networks. In: Proceedings of IEEE international conference on industrial technology, vol. 1, Goa, India, January 2000, pp. 548–553.

15.

Sinha

Chakrabarti

Chattopadhyay

(2003) Evolutionary programming techniques for economic load dispatch. IEEE Transactions on Evolutionary Computation 7(1): 83–94.

16.

Somasundaram

Kuppusamy

Kumudini Devi

(2003) Economic dispatch with prohibited operating zones using fast computation evolutionary programming algorithm. Electric Power Systems Research 70: 245–252.

17.

Ulagammai

Venkatesh

Kannan

et al . (2007) Application of bacterial foraging technique trained artificial and wavelet neural network in load forecasting. Journal of Neurocomputing 70: 2659–2667.

18.

Villanueva

Feijoo

Pazos

(2012) Simulation of correlated wind speed data for economic dispatch evaluation. IEEE Transactions on Sustainable Energy 3(1): 142–149.