Optimal power flow incorporating wind power and optimally allocated energy storage

Abstract

The rapid growth of wind power poses new challenges for power system operators and electricity marketers. The benefits of using wind power are emission reduction and decrease in consumption of conventional resources. But the inherent nature of wind energy poses challenges in the power system operation and planning. In order to consider the wind power as firm power, auxiliary energy storage is added as a backup to encounter the variations in wind power. In this article, optimal power flow with wind and energy storage is developed. The energy storage systems are installed as a standby of wind generators to meet the demand consistently. The objective is to minimize the loss by optimal location and sizing of energy storage systems. With the optimally located energy storage systems, optimal power flow is carried out using shuffled frog-leaping algorithm technique and tested on IEEE 30 bus system.

Keywords

Wavelet neural network shuffled frog-leaping algorithm optimal power flow energy storage systems wind speed forecasting

Introduction

The aim of the optimal power flow (OPF) is to optimize a certain objective function, subjected to the network power flow equations and system and equipment operating constraints. The optimal condition is reached by fine-tuning the available controls to minimize an objective function subjected to specified operating and security requirements. Objective function involves fuel cost, transmission losses, and reactive source allocation. Usually, the objective function aims toward the minimization of total production cost of scheduled generating units. It reflects current economic dispatch practice, and importantly, cost-related aspect is always ranked high among operational requirements in power systems.

Wind energy is likely to account for a big share of renewable energy source but wind is variable and wind energy capacity does not directly turn into wind power generation. In order to increase the renewable energy penetration into the grid, utilities should have a costly reserve capacity online. As an alternative of this vital source, many researchers have proposed energy storage solutions that can be connected with the renewable source. Energy storage significantly increases the use of the renewable source and makes this energy dispatchable as needed, resulting in a significant increase in the renewable energy value proposition. At present, there are several types of energy storage technologies, which have different characteristics, for example, energy and power density, efficiency, cost, lifetime, and response time. Examples of energy storage systems (ESSs) are ultracapacitors, superconducting magnetic energy storage systems (SMESs), flywheel, batteries, compressed air, pumped hydro, fuel cells, and flow batteries.

In terms of joint scheduling model for wind power and ESS, Wu et al. (2013) in their article considered the power generation unit and energy storage unit constraints and built a static model for wind power and energy storage joint operation. The uncertainty of wind power is ignored. Hu et al. (2012) combined the opportunity constraint theory and built a joint scheduling model of wind power and ESS considering wind power uncertainty. Ding et al. (2012) developed a wind storage joint scheduling model considering risk constraints and used Monte Carlo simulation method.

In terms of solution technique, numerous methods have been suggested in the literature to solve the power flow problem. The OPF problem is solved by several classical techniques such as primal dual interior point (Capitanescu et al., 2006), dynamic programming (Price et al., 2005), linear programming, and non-linear programming. These algorithms are applied for continuous differentiable functions and not for non-smooth cost functions. The past two decades has seen the introduction of other methods based on artificial intelligence (AI) techniques including genetic algorithm (GA), particle swarm optimization (PSO), differential evolution (DE), and hybrid DE (Bhattacharya and Chattopadhyay, 2012) which have also been proposed to solve the OPF problem. This article presents an evolutionary technique named shuffled frog-leaping algorithm (SFLA) which combines the benefits of the genetic-based mimetic algorithms and the social behavior–based PSO algorithms for solving OPF with wind and ESSs.

This article is organized as follows. Wind speed forecasting and characterization are given in section “Wind speed forecasting and characterization.” OPF problem formulation including wind generators and ESSs is presented in section “OPF problem formulation with wind and energy storage.” Section “SFLA solution technique” describes the SFLA solution technique. Section “Results and discussions” presents the simulation results for IEEE 30 bus system. Section “Conclusion” concludes the article.

Wind speed forecasting and characterization

In last few decades, several methods for wind speed forecasting such as the artificial neural network (ANN), probabilistic neural network (PNN), and the general regressive neural networks (GRNNs) have been proposed. In general, ANNs are trained in a supervised fashion with the back propagation (BP) algorithm. The basic BP algorithm is a gradient descent one (Lee and Park, 1992), which adjusts the network weights along the steepest descent direction of the error function. Other forecasting techniques such as PNN and GRNN explained in Dhivya et al. (2011) are also considered for comparison and analysis.

All these methods suffer from obtaining monolithic global models for a time series (Ulagammai et al., 2007). To enhance the ANNs’ ability in learning the signals, the hidden patterns of all the frequency components from the data should be extracted. Hence, to do this, a multi-resolution decomposition technique such as wavelet transform is introduced.

Wavelet transform is a scalable windowing technique. It breaks the signals into shifted scaled versions of the original wavelet signal. It uses time-scale region instead of time-frequency region. In order to improve the accuracy of ANNs, they are combined with wavelet to set hybrid model (Ulagammai et al., 2007). The wind speed is first decomposed into several sub-serials using wavelet. To forecast each sub-serial, each neural network is constructed. The final wind speed forecasting result can be obtained by summing up all the sub-serial forecasting results. A given signal s(t) is decomposed into several other signals with different levels of resolution by dyadic wavelet transform (DWT), and the DWT of s(t) is defined as follows

s (m, n) = 2^{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 the scale- and time-shift parameters, respectively; and s(t) is a given basis function (mother wavelet). The DWT is implemented using a multi-resolution pyramidal decomposition technique.

The wavelet neural network (WNN) forecasting procedure comprises a development of a preliminary forecast model followed by pre-signal processing, signal prediction, and post-signal processing (Price et al., 2005).

Stage 1: pre-signal processing

In pre-signal processing, historical wind speed data are fed to proposed model as time-series signals. The non-decimated wavelet transform (NWT) is used as the pre-signal processor and depending on the selected resolution level, the respective time-series signals are decomposed into a number of 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

ANNs are used for signal prediction in the forecast model. The number of ANNs needed for the model is determined by the number of wavelet coefficient signals at the output of the pre-processor. 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 as mentioned in pre-signal processing are used. In this stage, the outputs from the signal predictor (ANNs) are combined to form the final predicted output. This is achieved by summing all the predicted wavelet coefficients.

The wind speed profile at a given location closely follows Weibull distribution. The Weibull distribution function with a shape factor of 2 is also known as the Rayleigh distribution. In Hetzer et al. (2008), the advantages of the Weibull distribution are noted as follows: (1) it is a two-parameter distribution, which is more general than the single-parameter Rayleigh distribution, but less complicated than the five-parameter bi-variate normal distribution; (2) it is already proven that the observed data of wind speeds follow a Weibull distribution; and (3) if the k and c parameters are known at one height, a methodology exists to find the corresponding parameters at another height. The probability density function (PDF) for a Weibull distribution is given by

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

(2)

Once the uncertain nature of the wind is characterized as a random variable, the output power of the wind energy conversion systems (WECSs) may also be characterized as a random variable through a transformation from wind speed to output power. Ignoring minor nonlinearities, the output of the WECS with a given wind speed input may be stated as (Hetzer et al., 2008)

W = 0 for v < v_{i} and v > v_{o}

(3)

W = W_{r} \frac{(v - v_{i})}{(v_{r} - v_{i})} for v_{i} \leq v \leq v_{r}

(4)

W = W_{r} for v_{r} \leq v \leq v_{o}

(5)

The wind speed has the Weibull distribution, and it has to be converted as wind power distribution. This is achieved by linear transformation given below (Peebles and Prabab, 2001)

W = T (V) = a V + b

(6)

where T is the transformation, W is the wind power random variable, and V is the wind speed random variable. After the transformation, the Weibull PDF of wind power output random variable in continuous range takes the following form (Hetzer et al., 2008)

f_{w} (w) = (\frac{k l v}{c}) {(\frac{(1 + ρ l) v_{i}}{c})}^{k - 1} e^{- {(\frac{(1 + ρ l) v_{i}}{c})}^{k}}

(7)

Then, the area under the power distribution curve is calculated using trapezoidal rule and the discrete values of wind power are obtained as in author’s previous paper (Meyyappan and Kumudini Devi, 2015).

OPF problem formulation with wind and energy storage

Need for energy storage

In order to effectively reduce CO₂ emissions, fossil fuel will be gradually replaced by renewable source to produce electrical power. Wind and solar are the most abundant renewable sources for electric power generation. Energy converted from wind and solar becomes more and more competitive in power markets due to the improvement in technology. However, the variable nature of renewable energy limits its large-scale penetration in the power system. Additional spinning reserves are always assigned with renewable generators committed to the system to ensure system reliability. The extra cost and emission of reserve units becomes another economic and environmental issue. However, energy storage could be a solution to these issues. Akhavan-Hejazi and Mohsenian-Rad (2014) provided reliability evaluations for energy storage along with large-scale wind generation and observed some potential benefits for both the power system operator and the wind farm owners.

Energy storage for power systems has recently attracted significant interest and attention from researchers and the power industry. An ESS is treated as a generator (i.e. pumped hydro or stationary batteries) with a negative or positive output during its charging or discharging period, respectively. With fast response time and low operating cost, energy storage is viewed as an attractive resource to compensate the variable nature in the wind-penetrated power system and as an essential resource to enable integration of large amounts of renewable resources into the electric grid. Examples of ESSs are ultracapacitors, SMESs, flywheel, batteries, compressed air, pumped hydro, fuel cells, and flow batteries.

Problem formulation

The objective of multi-period (dynamic) OPF is to minimize the cost of generation and optimally utilize the renewable generation.

The objective function is given by

M i n F_{T} = \sum_{t = 1}^{24} (\sum_{i = 1}^{N G} a_{i} P_{g i, t}^{2} + b_{i} P_{g i, t} + c_{i} + \sum_{j = 1}^{M} C_{o p w} W_{j, t} + \sum_{k = 1}^{N E} C_{o p s} E_{s t o r a g e k, t})

(8)

Subjected to the equality and inequality constraints

\sum_{t = 1}^{24} (P G_{i, t} - P_{D i, t} - V_{i, t} \sum_{j = 1}^{N} V_{j, t} [G_{i j} \cos (δ_{i, t} - δ_{j, t}) + B_{i j} \sin (δ_{i, t} - δ_{j, t})] = 0)

(9)

\sum_{t = 1}^{24} (Q G_{i, t} - Q_{D i, t} - V_{i, t} \sum_{j = 1}^{N} V_{j, t} [G_{i j} \sin (δ_{i, t} - δ_{j, t}) + B_{i j} \cos (δ_{i, t} - δ_{j, t})] = 0)

(10)

where PG_i,t and QG_i,t are, respectively, the sum of the real power and reactive power injections (thermal, wind, and energy storage) at bus i at time t

P_{g i m i n} \leq P_{g i, t} \leq P_{g i m a x} i = 1, 2, \dots, N G

(11)

V_{g i m i n} \leq V_{g i, t} \leq V_{g i m a x} i = 1, 2, \dots, N G

(12)

Q_{g i m i n} \leq Q_{g i, t} \leq Q_{g i m a x} i = 1, 2, \dots, N

(13)

W_{j m i n} \leq W_{j, t} \leq W_{j m a x} j = 1, 2, \dots, M

(14)

E_{s t o r a g e, k m i n} \leq E_{s t o r a g e k, t} \leq E_{s t o r a g e k m a x} k = 1, 2, \dots, N E

(15)

S_{i, t} \leq S_{i m a x} i = 1, 2, \dots, n o . o f l i n e s

(16)

Further state of charge of energy storage for an hour, t + 1, is given as

E_{s t o r a g e i, t + 1} = S O C_{i, t + 1} = {\begin{matrix} S O C_{i, t} + η_{d i s} P_{K}^{S t} i f P_{K}^{S t} < 0 \\ S O C_{i, t} + η_{c h} P_{K}^{S t} i f P_{K}^{S t} > 0 \end{matrix}

(17)

where $P_{K}^{S t}$ is the power required from the kth ESS at time t. It may take positive or negative value depending on the availability of the wind power. If the availability of the wind power is less than the expected, then the energy storage starts discharging to meet the wind deficit and hence $P_{K}^{S t}$ takes negative value and vice versa.

In short time scales, it is not possible for a conventional generator to considerably deviate from current operating point. Therefore, we limit the amount of change in generation depending on the ramp rate of individual generators. The constraints are given as follows:

When generation increases

P_{g i, t} - P_{g i, (t - 1)} \leq U R_{i}

(18)

When generation decreases

\begin{array}{l} P_{g i, (t - 1)} - P_{g i, t} \leq D R_{i} \\ for i = 1, 2, \dots, N G \end{array}

(19)

where UR_i and DR_i are the ramp-up and ramp-down limits of ith unit in MW.

Optimal location and sizing of ESS

The determination of optimal location and size of ESS is posed as an optimization problem. The problem can be stated as follows.

To find the optimal location and size of ESS by minimizing transmission losses while satisfying equality and inequality constraints

\begin{matrix} M i n \\ x \end{matrix} P_{l o s s}

(20)

where x = [P_g₂ … P_gNG, W₁ … W_M, E_storage ₁ … E_{storage NE}], subjected to constraints (11) to (17).

The optimization problem is executed for different wind power penetrations. The location and size of ESS is the super set of all the optimal solutions. OPF analysis considering the entire wind power distribution is carried out using fmincon and SFLA technique.

SFLA solution technique

It is a memetic algorithm inspired by the food hunting behavior 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 behavior–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 = [Xi_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 best and worst positions of frogs 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 by

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

(21)

N e w p o s i t i o n X_{w} = C u r r e n t p o s i t i o n o f X_{w} + D_{i}

(22)

where $D_{i m a x} \geq D_{i} \geq - D_{i m a x}$ , here D_imax is the maximum allowed change in a frog’s position, and rand( ) is the random number between 0 and 1.

Fitness function to be evaluated is given by

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

(23)

Figure 1 illustrates the memeplex partitioning process, and Figure 2 shows the flowchart for SFLA.

Figure 1.

Memeplex partitioning process.

Figure 2.

SFLA flowchart.

Results and discussions

Wind speed prediction

The training dataset and test dataset comprise temperature, humidity, dew point, pressure, wind direction, and wind speed. To evaluate the model proposed for wind speed prediction, datasets are collected from the automatic weather station and the study is conducted for 24 h ahead. The sampled time series used in the model includes 1000 data in total, corresponding to 30 min of mean data. The time series is distinguished into two folders: one is the training set containing 964 samples used for the model’s training and the other is the test set that includes the rest, namely, 36 samples, used to verify the accuracy during the prediction period. Some of the data in Ding et al. (2012) are deliberately multiplied by a constant (×10, ×100, or ×1000) to avoid storage of the floating point numbers and the same data are considered.

Different AI techniques such as feed forward back propagation (FFBP), cascade forward back propagation (CFBP), PNN, GRNN, and k-nearest neighbor (KNN) are applied to the model developed in the author’s previous paper (Ding et al., 2012). In WNN, the number of ANN required depends on the wavelet family and the resolution level. With a resolution level of 2, the wavelet family is chosen as db2. Hence, three neural networks are constructed for WNN. The individual ANN is constructed depending on the wavelet coefficients. In general, db2 wavelet family produces four filter coefficients for single decomposition. By linear convolution, number of approximations (A) and detail coefficients (D) are given by (m + n − 1)/2, where m is the input data size (number of inputs in this case is 15) and n is the filter coefficient size.

In this case, the number of A and D in the first-level decomposition is, for example, A = D = (15 + 4 − 1)/2 = 9. For the second-level decomposition, the number of coefficients is (9 + 4 − 1)/2 = 6. Thus, the input neurons are 6, 6, and 9 for ANN1, ANN2, and ANN3, respectively. A total of 10 hidden neurons and 1 output neuron (wind speed) are selected for all neural networks (Bhattacharya and Chattopadhyay, 2012).

The resultant relationships between the predicted and the actual values of the wind speed for the different ANN techniques are presented in Ding et al. (2012). Figure 3 displays the wind speed predicted by WNN. Performance measures such as mean square error (MSE), mean absolute percentage error (MAPE), and linear regression are used to compare the various methods that are applied for wind speed predictions. These measures can be calculated using the equations in Ding et al. (2012) and the comparison results are given in Table 1.

Figure 3.

Wind speed forecasting using WNN.

Table 1.

Comparison of performance measures for different ANN techniques.

	FFBP	CFBP	PNN	GRNN	KNN	WNN
MSE	6.748866	6.817727	3.795714	2.856825	5.882085	2.778
MAPE (%)	5.109752	5.267151	2.972917	2.300082	0.91048	1.5075

ANN: artificial neural network; FFBP: feed forward back propagation; CFBP: cascade forward back propagation; PNN: probabilistic neural network; GRNN: general regressive neural network; KNN: k-nearest neighbor; WNN: wavelet neural network; MSE: mean square error; MAPE: mean absolute percentage error.

According to the forecasted errors, WNN has the lowest MSE and MAPE; hence, the WNN model is used for wind speed prediction. GRNN is ranked second followed by PNN and KNN, respectively. Thus, WNN is found to be the better wind speed predicting technique compared with the other ANN techniques. The shape factor and scale factor of Weibull distribution for the predicted wind speed are obtained as 2.24 and 8.83, respectively. The cut-in speed, cut-out speed, and rated speed in the Weibull distribution are considered as 2, 10, and 15 m/s, respectively. The wind power is predicted for every hour using equation (3).

OPF results

Simulations are carried out using IEEE 30 bus system using SFLA technique. The standard IEEE 30 bus system has 6 generators and 22 load buses. A wind generator of capacity 260 MW is integrated at bus 7 which has high short-circuit level. In SFLA, the control parameters are power generated by the thermal and wind units. Hence, the number of control variables for this test system is 7 (6 thermal + 1 wind generator). The population size for SFLA is assumed to be 50 with 5 memeplexes. The maximum number of iterations is 100. Results of OPF with wind using SFLA is given in Table 2.

Table 2.

OPF results of IEEE 30 bus system with wind generator (P_d = 283.4 MW).

Control variables	SFLA
P₁ (MW)	26.12
P₂ (MW)	21.72
P₅ (MW)	14.58
P₈ (MW)	16.13
P₁₁ (MW)	17.54
P₁₃ (MW)	30.82
P₇ (MW)	166.09
V₁ (pu)	1.06
V₂ (pu)	1.04
V₅ (pu)	1.00
V₈ (pu)	1.01
V₁₁ (pu)	1.01
V₁₃ (pu)	1.05
V₇ (pu)	1.05
Cost (INR/h)	784.23
Losses (MW)	9.36
Exe. time (s)	124

OPF: optimal power flow; SFLA: shuffled frog-leaping algorithm.

The computational time for SFLA is around 124 s for 100 trials. It can be seen from the table that the operational cost gets reduced with the inclusion of wind power. The operational cost and loss without wind generator using PSO is 800.41 INR/h and 12.96 MW, respectively (Abido, 2010). But with the inclusion of wind power, the operational cost gets reduced from 800.41 to 794.57 INR/h. Also, the transmission losses get reduced from 12.96 to 9.36 MW.

OPF with wind and energy storage

This section presents about the determination of optimal location and sizing of ESS with loss minimization as objective. For this case, different wind power penetrations are considered. Hence, discrete values of wind power are considered. Three distinct values of wind power allowing 10% of forecast errors are considered for OPF: (1) forecasted wind power (wp), (2) wp + (0.1 × wp), and (3) wp − (0.1 × wp) are taken and presented in Table 3 and shown in Figure 4. Along with these wind power values, two extreme cases, nil wind and rated wind power, are also considered for allocation of ESSs. Initially, SFLA initializes a random ESS size for each bus and the size at each bus will be updated by SFLA. At the end, the size of ESSs at some buses becomes zero, which means that these buses do not need to install any ESS. The remaining ESSs converge to their optimal allocations. The total operational cost and power loss is reduced, and voltage profiles are improved; the results are presented in Table 4. The objective function considered here is the minimization of the losses. The installation of ESSs at proper locations may reduce the transmission losses.

Figure 4.

Discretization of wind power.

Table 3.

Discretization of wind power.

Wind power (MW)	0	69.3	77.03 (mean)	84.06	260 (rated)
Probability	7.12	23.67	38.39	21.9	8.92

Table 4.

OPF with ESS considering discretized wind power.

Bus no.	Deterministic OPF
	Wind power (MW)
	0	69.3	77.03 (mean)	84.06	260 (rated)
	PG (MW)	PG (MW)	PG (MW)	PG (MW)	PG (MW)
1	96.63	99.38	86.432	83.123	8.23
2	0	17.12	77.03	157.09	260
3	13.8983	18.4	0	0	0
4	0	0	0	0	0
5	6.7939	8.88	5.73	7.12	3.37
6	0	3.67	1.73	2.62	0
7	10.911	8.76	7.138	6.073	0
8	9.4697	12.46	10.34	11.39	0
9	0	0	0	0	0
10	0	0	0	0	0
11	17.67	13.67	11.681	10.734	2.13
12	0	0	0	0	0
13	32.98	29.67	31.68	25.43	0
14	0	0	0	0	0
15	5.54	0	0	0	0
16	10.87	5.5	0	0	0
17	0	0	0	0	0
18	0	0	0	0	0
19	11.795	10.86	13.738	5.67	2.156
20	13.059	12.156	14.368	7.156	1.95
21	0	0	0	0	0
22	14.7986	15.87	16.13	6.8	3.67
23	0	0	0	0	0
24	5.9658	6.86	4.794	1.12	4.37
25	14.3177	11.32	12.034	7.32	0
26	0	0	0	0	0
27	11.7016	13.70	11.070	0	0
28	0	0	0	0	0
29	8.18	7.17	5.17	4.2	5.12
30	7.37	6.17	7.18	1.3	0
Losses (MW)	8.7901	8.64	8.412	8.23	7.98

OPF: optimal power flow; ESS: energy storage system.

From the results, it is obvious that injection of power at the buses 11, 19, 20, 22, 24, and 29 (the highlighted bus locations in Table 4) is needed to reduce the losses. Hence, these buses are considered as the optimal location for installing ESSs. From the values of generations obtained, the capacity of each ESS can be fixed as 20 MW each. For optimal allocation of generation and for the minimization of the loss, six ESSs are installed with a total capacity of 120 MW.

From the above results, the ESS locations are identified as 11, 19, 20, 22, 24, and 29 with a maximum rating of 20 MW each. OPF is run considering entire wind power distribution, and the results are presented in Table 5 for IEEE 30 bus system.

Table 5.

OPF with wind and optimally located ESS.

IEEE 30 bus (P_d = 283.4 MW)
Control and dependent variables	SFLA
P₁ (MW)	32.51
P₂ (MW)	14.09
P₅ (MW)	29.82
P₈ (MW)	28.45
P₁₁ (MW)	39.14
P₁₃ (MW)	18.376
Sum of six ESSs (MW)	83.8
Wind, P₇ (MW)	45.2
V₁ (pu)	1.060
V₂ (pu)	1.02
V₅ (pu)	1.030
V₈ (pu)	1.01
V₁₁ (pu)	1.00
V₁₃ (pu)	1.010
V₇ (pu)	0.998
Average V (pu) of all ESSs	1.102
Cost (INR/h)	775.21
Losses (MW)	8.56
Exe. time (s)	(100 trials)

OPF: optimal power flow; ESS: energy storage system; SFLA: shuffled frog-leaping algorithm.

The above obtained results with and without ESS are compared and given in Table 6. From the comparison analysis, with the installation of ESS, the cost obtained is slightly less than the cost without ESS. The bus voltages for all the cases are within their limits. Losses obtained with optimal location of ESS are 9.98 and 8.56 MW, respectively, by primal dual interior point method (PDIP) and SFLA. Around 2% of the loss reduction can be achieved with the help of optimally located ESSs.

Table 6.

Comparison of OPF with and without ESS.

Case study	Cost (INR/h)	Loss (MW)
OPF without ESS	784.23	9.36
OPF with optimally located ESS	775.21	8.56

OPF: optimal power flow; ESS: energy storage system.

Conclusion

As wind penetration continues to increase in the power grids, it becomes important to consider the uncertainty of wind power when optimizing the placement and size of ESSs. In this research, SFLA algorithm is proposed to determine the optimal ESS allocation in wind-penetrated power systems. Unlike many other optimization methods which only consider the worst-case (zero-wind) scenario, the entire wind power distribution is considered here. A five-point estimation method is implemented to discretize the continuous wind power distribution. IEEE 30 bus and 118 bus systems are considered as case studies. The results show that the proposed SFLA is able to find proper location and size of ESS, minimize the total operational cost and losses, and also improve voltage profiles.

Footnotes

Appendix 1 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.

ORCID iD

Ulagammai Meyyappan

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