Optimal sizing and control of hybrid energy storage system for wind power using hybrid Parallel PSO-GA algorithm

Abstract

This paper proposes a frequency-based method for sizing the hybrid energy storage system in order to smoothen wind power fluctuations. The main goal of the proposed method is to find the power and energy capacities of the hybrid energy storage system that minimizes the total cost per day of all the systems. The energy management strategy used in this paper is designed as a two-level energy distribution scheme: the first level is responsible for setting the output power of hybrid energy storage system, the second level manages the power flow between the battery and supercapacitor. The hybrid parallel particle swarm optimization-genetic algorithm (PSO-GA) optimization algorithm is proposed to solve the control parameters of energy management strategy. In addition, the proposed method uses the piecewise fitting function to describe the lifetime of battery. Obtained results show that the hybrid energy storage system with the proposed energy management strategy is able to offer the best performances for the wind power system in terms of cost and lifetime.

Keywords

Optimization algorithm hybrid energy storage system optimal sizing energy management strategy smoothing fluctuations

Introduction

Wind energy has been a main stream of sources for emerging energy. According to the Global Wind Energy Council (GWEC), the cumulative wind power installation in the world at the end of 2016 was 486.8 GW, especially in China the cumulative capacity was 168.7 GW, which have become an important portion of generation mix with a capacity of 3.9% of net electricity generation (GWEC, 2017). However, variable wind speed has restricted its power quality and system stability for the output power of Wind Turbine Generators (WTG) (Jannati et al., 2014). This phenomenon significantly restricts the wind energy integration with the grid. Comparatively, energy storage system (ESS) offers a relatively better solution and is assumed to be a good solution to smoothen power fluctuation, maintain the power and energy balance as well as to improve the power quality (Khalid and Savkin, 2014). However, different types of ESSs have huge differences in character, the ESS by a single type has some shortcomings for using smoothing fluctuation. For example, battery has a high-energy density but limited power density, and supercapacitor (SC) has a high-power density but limited energy density. Therefore, utilizing both battery and SC provides a compromise of a high-power density and high-energy density hybrid energy storage system (HESS), resulting in improving the technical performance of the wind power generation (Schaltz et al., 2009). Since the cost of energy storage is a strong function of their power and capacity, and too high cost is prohibitive to engineering acceptance, a method for optimizing the size and control of HESS to fit application constraints is a key issue.

Sizing the ESS is finding the proper ESS power and energy capacity to satisfy the special technical requirements of the wind power system. During the past year, some researchers carried out significant works on this issue. Parra et al. (2015) presented control strategies for sizing ESS to comply with the constraint of power ramp rate (PRR). Khalid and Savkin (2014) proposed a semi-distributed ESS scheme to optimize ESS size and operation with a wind power smoothing model. Arabali et al. (2014) studied a combined sizing optimization method using the pattern search and Monte Carlo simulation. Zhang et al. (2015) presented a strategy to allocate the capacity within HESS by applying the Ragon plots. They did not consider the cost of ESS. Meanwhile, other researchers formulated the objective function of the sizing optimization problem and found the solution using the heuristic algorithm or the hybrid algorithm. For instance, Fossati et al. (2015) acquired the power and energy capacities by the genetic algorithm (GA) and the lifetime prediction model of ESS. Bahmani-Firouzi and Azizipanah-Abarghooee (2014) presented a new improved bat algorithm for determining optimal sizing of battery storage system. García-Triviño et al. (2016) calculated the optimal result by the particle swarm optimization (PSO) considering cost, efficiency and lifetime. Those optimal techniques also have some downsides such as trapping in local optima or convergence to the global optima over a long time. Consequently, choosing a robust optimal algorithm to solve the complex problem is important.

In this paper, we propose a hybrid Parallel PSO-GA (PPSO-GA) optimization method to smooth wind power fluctuation. The energy management strategy (EMS) in this paper is designed as a two-level energy distribution scheme. The first level is based on the spectrum analysis and technical rules of PRR for connecting wind farm to power system in China that is used to set the output power of HESS. The second level deploys the output power of the battery and SC according to the battery operation period and cutoff frequency of battery output power, where the goal to find the optimal sizing of HESS to balance the costs and the ESS lifetime. For this purpose, the hybrid PPSO-GA algorithm is suggested to achieve an optimal sizing. Furthermore, owing to the great influence that the depth of discharge (DOD) has on battery lifetime and therefore on the cost of HESS, a lifetime prediction model as constrains parameter is integrated with the algorithm.

This paper is organized as follows: In the next section, the system model of the HESS is explained. Then, the EMS is presented. The hybrid PPSO-GA optimization algorithm is proposed and tested next. This is followed by a section where the simulation result is shown by MATLAB. Finally, conclusions are drawn.

System model

In this paper, the proposed wind power system with the introduced HESS model is used as described in Figure 1.

Figure 1.

Layout of wind power system with the introduced HESS.

In Figure 1, the HESS is used to absorb the extra generated energy from the TG or releases the stored energy to the point of common coupling (PCC) of power system. The basic operation of HESS can be described as

P_{pcc} (t) = P_{w} (t) + P_{hess} (t)

(1)

where P_w is the MPPT output power of the wind farm. P_hess is the charge/discharge output power of the HESS. P_pcc is the combined output power to the power system.

HESS constraints

In this paper, one of the aims is to find the desired output power of wind power system with HESS P_pcc,ref which satisfis the technical rule of the PRR. It is assumed that the P_pcc,ref is determined, and the desired output power of the HESS P_hess,ref can be calculated as

P_{hess,ref} (t) = P_{pcc,ref} (t) - P_{w} (t)

(2)

P_hess,ref contains numreous high-frequency components. The P_hess,ref can be absorded by battery and SC, which can reduce the battery lifetime lose owing to the frequently deep charge–discharge cycle (Dufo-López et al., 2014). The absorbed power of the battery and SC can be written as

P_{hess,ref} (t) = P_{b,ab} (t) + P_{sc,ab} (t)

(3)

Based on the charge–discharge effciency, the output power of the battery and SC (P_b/P_sc) can be expressed as

{\begin{array}{l} P_{b} (t) = {\begin{matrix} \frac{P_{b,ab} (t)}{η_{d,b}}, & P_{b,ab} (t) \geq 0 & (discharge) \\ P_{b,ab} (t) η_{c,b}, & P_{b,ab} (t) < 0 & (charge) \end{matrix} \\ P_{sc} (t) = {\begin{matrix} \frac{P_{sc,ab} (t)}{η_{d,sc}}, & P_{sc,ab} (t) \geq 0 & (discharge) \\ P_{sc,ab} (t) η_{c,sc}, & P_{sc,ab} (t) < 0 & (charge) \end{matrix} \end{array}

(4)

where η_c,b and η_d,b are the charge and discharge effciencies of battery, respectively; η_c,sc and η_d,sc are the charge and discharge effciencies of SC, respectively. In general, the rated power of the battery and SC in HESS (P_b,rated/P_sc,rated) is given as

{\begin{array}{l} P_{b,rated} = \max (| P_{b} (t) |) \\ P_{sc,rated} = \max (| P_{sc} (t) |) \end{array}

(5)

In order to satisfy the safety of ESS, the energy stored at any tth commitment interval E(t) must be limited as

{\begin{array}{l} 0 \leq E_{b} (t) \leq E_{b,base} \\ 0 \leq E_{sc} (t) \leq E_{sc,base} \end{array}

(6)

where E_b,base and E_sc,base are the base capacity of the battery and SC, which can be expressed as

{\begin{array}{l} E_{b,base} = \frac{\max (E_{b} (t)) - \min (E_{b} (t))}{S_{b,U} - S_{b,L}} \\ E_{sc,base} = \frac{\max (E_{sc} (t)) - \min (E_{sc} (t))}{S_{sc,U} - S_{sc,L}} \end{array}

(7)

where S_b,U and S_b,L are the upper limit and lower limit of state of charge (SOC) of the battery, S_sc,U and S_sc,L are the upper limit and lower limit of SOC of SC. Based on equation (7), the SOC limit of HESS can be satisfied, the rated capacity of SC is equal to E_sc,base. In addition, the adjustment factor is introduced in this paper to increase the lifetime of the battery, and the rated capacity of the battery and SC is defined as

{\begin{array}{l} E_{b,rated} = k_{b} \cdot E_{b,base} \\ E_{sc,rated} = E_{sc,base} \end{array}

(8)

where k_b is the adjustment factor of the battery. When k_b > 1, the battery capacity is overrated, it will reduce the DOD to prolong the lifetime of the battery. In this paper, the range of the factor is k_b ∈ [1,3].

HESS lifetime model

The battery lifetime highly depends on the DOD, charge and discharge cycle, rate of discharge, temperature, equivalent series resisor, charging method, etc. (Layadi et al., 2015). To simplify, the impacts of the most important parameters, DOD and the number of the charge and discharge cycles are studied. In this paper, the preferred reference battery is a 12-V, 2.1-kWh valve-regulated lead-acid (VRLA) battery. The data of cycles to failure N_cyc for a given DOD can be described in Table 1 from the reference battery data sheet.

Table 1.

Cycles to failure and amount of throughput energy versus DOD.

DOD (%)	10	20	30	40	50	60	70	80	90	100
N _cyc	3800	2850	2050	1300	1050	900	750	650	600	550
E_thro (kWh)	798	1197	1292	1092	1103	1134	1103	1092	1134	1155

DOD: depth of discharge.

To build the battery lifetime model, it is necessary to obtain a continuous function of the cycle to failure, which can be fitted by the data sheet value. Usually, the number of cycles to failure versus DOD can be expressed by exponential, power and polynomial in Figure 2. These curves have similar shape to describe the characteristic of the number of cycles to failure, and it is difficult to evaluate the applicability of these fitting functions by only one parameter. Hence, we introduce the amount of throughput energy E_thro for testing these fitting functions. The amount of throughput energy at a specific DOD can be expressed as

E_{thro} (D O D_{s}) = E_{Nom} \cdot D O D_{s} \cdot N_{cyc} (D O D_{s})

(9)

where E_Nom is the nominal battery capacity and N_cyc(DOD_s) is the number of cycle to failure at DOD_s. The reference E_thro is calculated for the reference battery with discharge from full state of charge to DOD of data sheet, which is shown in Table 1.

Figure 2.

Cycles to failure versus depth of discharge.

In order to evaluate the applicability of different functions, the three series of throughput energy which are calculated based on exponential, power and polynomial are shown in Figure 3. In Figure 3, three throughput curves have great errors with the reference E_thro, but the power function can better fit the reference data at DOD > 40% and the exponential function has better result at DOD ≤ 40%. Hence, the number of cycles to failure versus DOD can be expressed as

N_{cyc} (D O D) = {\begin{matrix} 5143.53 e^{- D O D / 25} + 440.31, & D O D \leq 40 % \\ 24205.73 D O D^{- 0.7775} - 125, & D O D > 40 % \end{matrix}

(10)

Figure 3.

Throughput energy versus depth of discharge.

During the operation of the battery, it is almost impossible to discharge on a certain DOD level all the time, the battery lifetime cannot be directly calculated by equation (10). In this paper, the number of cycles in the different DOD levels is obtained by a rainflow counting method (Sauer and Wenzl, 2008). After one operated cycle of HESS, the battery lose lifetime is defined as

L_{b,loss} = \sum_{i = 1}^{m} \frac{N_{b,ct} (D O D_{i})}{N_{cyc} (D O D_{i})}

(11)

where N_b,ct(DOD_i) is the counting of cycles corresponding to DOD_i (insplit in m intervals) by rainflow counting method. N_cyc(DOD_i) corresponding to the DOD_i is the number of cycles to failure obtained from equation (11). Accordingly, when the L_b,loss=1, the end of the lifetime of battery is reached.

The SC has high-power density, fast charging and discharging, and long life more than 5 × 10⁴–10⁵ cycles with virtually no maintenance. The SC lifetime is influenced by some factors, and the main factor is the number of cycles of charging and discharging (Zhang et al., 2016). To simplify, the supercapcitor lose lifetime is defined as

L_{sc,loss} = \frac{N_{sc,ct}}{N_{sc,max}}

(12)

where N_sc,max is the nominal maximum number of cycels of charging and discharging. N_sc,ct is the number of cycles charging and discharging in an operated period of HESS. In this paper, the N_sc,ct is calculated by peak-value counting method. The end of the lifetime of SC is reached when the L_sc,loss=1.

Objective function

In this paper, the main goal is to minimize the operating cost of HESS. For this reason, the estimation function of cost which consists of initial investment cost and management & operating (M&O) cost must be determined.

The initial investment cost C_iv may be expressed as a function of the rated capacity and power of ESS (Fossati et al., 2015; Kaldellis and Zafirakis, 2007) and can be constructed as

{\begin{array}{l} C_{iv} = C_{b,iv} + C_{sc,iv} \\ C_{b,iv} = C_{b,P} P_{b,rated} + C_{b,E} E_{b,rated} \\ C_{sc,iv} = C_{sc,P} P_{sc,rated} + C_{sc,E} E_{sc,rated} \end{array}

(13)

where C_b,iv and C_sc,iv are the initial investment cost. C_b,P and C_sc,P are the power cost per unit of the battery and SC (¥/kW). C_b,E and C_sc,E are the capacity cost per unit of the battery and SC (¥/kWh).

The M&O cost C_mo can be split into the fixed maintenance cost C_fm in normal operation and the variable replacement cost C_re (Han et al., 2013) and can be expressed as

C_{mo} = L (C_{b,mo} E_{b,rated} + C_{sc,mo} E_{sc,rated})

(14)

C_{re} = q_{b} C_{b,iv} + q_{sc} C_{sc,iv}

(15)

where C_b,mo and C_sc,mo are the maintenance costs of the battery and SC (¥/kWh). L is the designed lifetime of the total system (year). q_b and q_sc are the replacing times of battery and SC.

The time horizon of the research sample was set as 24 h. Then, considering the interest rate for financing and system lifetime, the objective function can be expressed by the following equation.

Minimize total cost per day

\min (C_{total}) = \min [\frac{1}{365} (\frac{r {(1 + r)}^{L}}{{(1 + r)}^{L} - 1} (C_{iv} + C_{re}) + \frac{C_{mo}}{L})]

(16)

where r is the interest rate for financing.

Energy management strategy

The EMS was divided into two energy schemes: one was applied to produce the appropriate output power to alleviate the fluctuations and the other was to separate the power between the battery and SC.

First level of EMS

For the requirement of grid-connected, the output power that satisfies technical rules of PRR was set as the first level of EMS. The PRR is defined as

R_{prr, Δ t} = \frac{P_{max, Δ t} - P_{min, Δ t}}{P_{n}} \times 100 %

(17)

where P_n is the rated power of the wind farm, P_max _, _Δ _t and P_min,Δ _t are the maximum and minimum power of wind farm in the interval Δt (10 min), respectively, R_prr _, _Δ _t is the PRR in interval Δt. Then, the maximun PRR of 10-min interval is 33.33% (Technical rule for connecting wind farm to power system, 2012) and R_prr,10 of the desired output power of wind power is limited by equation (18)

\max (R_{prr,10}) \leq 33.33 %

(18)

The first level strategy is designed based on the cutoff frequency control. The key of the first level strategy selects the proper cutoff frequency f_c to achieve the dispatched power to HESS, and further ensures the wind power output to meet equation (18). This method calculates the desired output power P_pcc,ref by the spectrum analysis result of P_w and the selected f_c. In addition, f_c is obtained by the recursive calculation. According to P_pcc,ref, the desired output power of HESS P_hess,ref is determined (Pang et al., 2016). The flowchart representing the calculated P_hess,ref is described in Figure 4.

Figure 4.

Flowchart of the calculated desired output power of HESS.

Second level of EMS

According to the first level, the desired output power of HESS P_hess,ref is calculated. Taking into consideration P_hess,ref contains numerous high-frequency components, the second level is in charge of managing the P_hess,ref power flow between the battery and SC. In this strategy, the battery works at low frequency range and provides more energy to the system, and the SC deals with the fast peak powers. In order to prolong the lifetime of the battery, the controlled battery by EMS outputs a certain power value for a battery operation period T_b,op in this paper. It is assumed that an output power of battery in T_b,op is determined, the absorbed power of the battery P_b,ab can be definded as

P_{b,ab} (t) = {\begin{array}{l} P_{b,op} (t), & t = T_{b,op}, & 2 T_{b,op}, \dots, ⌊ \frac{T_{d}}{T_{b,op}} ⌋ \\ P_{b,op} (n T_{b,op}), & t \in [n T_{b,op} + 1, (n + 1) T_{b,op}], & n =0,1,2,3, \dots \end{array}

(19)

where P_b,op is the output power of the battery at T_b,op. T_d is the time of the system regulation period. According to equation (3), when t is equal to an integer times of T_b,op, the united output power of the battery and SC P_u is shown as

P_{u} (t) = P_{hess,ref} (t) = P_{b,op} (t) + P_{sc,ab} (t), t = T_{b,op}, 2 T_{b,op}, \dots, ⌊ \frac{T_{d}}{T_{b,op}} ⌋

(20)

The second level of EMS’s core mission is to control the battery worked at the low frequency band. Due to the characteristics of output power of battery at T_b,op, the P_b,op can be extracted from P_u by a low-pass filter with bandwidth f_b,c. Additionally, the amplitude frequency characteristic of P_b,op is given by

f f t (P_{b,op}) = {\begin{array}{l} {[f f t (P_{u})]}_{f_{u}}, & f_{u} \leq f_{b,c} \\ 0, & f_{u} > f_{b,c} \end{array}

(21)

where fft(P_u) is the amplitude frequency characteristic of P_u by fast Fourier transform (FFT). f_u is the sequence of frequency of P_u from FFT. f_b,c is the cutoff frequency of the battery output power. It is assumed that the f_b,c is known, the P_b,op can be calculated based on the inverse Fourier transform. Further, the output power of the battery and SC P_b(t), P_sc(t) are determined by equations (3) and (4).

In this level strategy, the key factors of the power sharing between the battery and SC are the battery operation period T_b,op and the cutoff frequency of battery output power f_b,c, which are obtained, thanks to the hybrid PPSO-GA optimization algorithm in order to improve the cost and lifetime of battery. The hybrid PPSO-GA optimization algorithm will be detailed in the next section.

Hybrid PPSO-GA optimization algorithm

In this study, the battery and SC are selected to smooth wind power fluctuation. However, it is a highly complex problem as to how the power is distributed between the battery and SC under the constraints of cost, lifetime, charging and discharging effciencies, output power and EMS’s control parameters.

A hybrid PPSO-GA optimization algorithm is proposed to solve the optimal sizing and control parameters of the HESS. This algorithm consists of two synchronized parallel algorithms of PSO, and enhances the global and local searching ability to modify the populations results of two PSO based on GA. This section describes the hybrid optimization algorithm.

Particle swarm optimization

PSO is one of the most important meta-heuristic algorithms developed by James Kennedy and Russell Eberhart (Amer et al., 2013; Mesbahi et al., 2017). Compared with other meta-heuristic algorithms, PSO is simple, easy to implement and it needs fewer parameters (Sharafi and Elmekkawy, 2014). In this method, the PSO works with a swarm of particles. Each particle in the population has two characters: position and velocity. For each particle i, its own past best position pbest_i and the entire swarm’s best overall position gbest are recorded. The velocity and position of each particle in PSO updating rules (Liu et al., 2010; Ramadan et al., 2017) are given by

{\begin{cases} v_{i} (k + 1) = w v_{i} (k) + c_{1} r_{1} (p b e s t_{i} - x_{i} (k)) + c_{2} r_{2} (g b e s t - x_{i} (k)) \\ x_{i} (k + 1) = x_{i} (k) + v_{i} (k + 1) \\ w = w_{\max} - (k - 1) (w_{\max} - w_{\min}) / (k_{\max} - 1) \end{cases}

(22)

where k is an iteration number. v_i(k) is the velocity. x_i(k) is the position of particle i at iteration k. k_max is the maximum number of iterations. w is an inertia weight. c₁ and c₂ are the two positive constants to weigh the relative importance of pbest_i and gbest. r₁ and r₂ are the random numbers in [0,1].

Genetic algorithm

GA is also a meta-heuristic algorithm, which simulates the evolution of a population of solutions to optimize a problem based on the genetic theory of Darwin evolution (Roberge et al., 2013). The solution in the GA is similar to the living organisms adapting to their environment by crossover and mutation. The GA operator is selection, crossover and mutation. The initializing population occurs randomly. At every generation, the parents are selected for the next generation by the fitness value. And children solution is subject to a crossover based on the crossover probability. If the mutation probability is met, the parents change randomly to produce children (Ismail et al., 2013).

Hybrid PPSO-GA algorithm

In this section, hybrid PPSO-GA is introduced in detail. In order to solve the optimization problem, it is designed that the two PSOs search the solution independently, and the GA is responsible for the interaction between the two PSOs under the setting rules and obtain the global search results. In this method, the two PSOs of populations with the same search size NP and the same dimension D are used. The two individual populations of two PSO are created randomly and the initial pbest¹_i, pbest²_i, gbest₁ and gbest₂ are found out. At each generation, the two positions of the particle i from two PSOs: x1 i=(x1 i1,x1 i2,…,x1 iD), x2 i=(x²_i1,x²_i2,…,x²_iD) (i = 1,2,…,NP) are generated by equation (22). Further, the x1 iand x2 iare sorted in descending order according to the fitness values. Based on the GA theory, the crossover process is to randomly determine the position of the crossover, and then to interchange the best fitness values form x¹_i(or x²_i) with the worst fitness values form x²_i(or x¹_i) when the random probability p_r1 satisfies the setting crossover probability p_cr. Following crossover, if the random probability p_r2 has met the setting mutation probability p_m, the mutation process is to randomly select the position and quantities of the mutation about the x1 iand x2 i, and to assign the random value within a range for increasing the diversity. The optimal result of this method is the best solution from the two populations by competition. The flowchart representing the hybrid PPSO-GA optimization algorithm is shown in Figure 5.

Figure 5.

Flowchart of hybrid PPSO-GA optimization algorithm.

As shown in Figure 5, the aim of PSO1 and PSO2 is to search the more potential probability areas. To improve the local search capability, the better solutions are used to replace the corresponding inferior solutions between the both PSOs. The x¹_rand (or x²_rand) is assigned random value rand1 (or rand2) (rand1,2 = x_min + rand(0,1)(x_max − x_min)) in mutation to avoid premature convergence. Meanwhile, excessive particles in mutation destroy the better solutions, so that the mutation rate r_m is limited to 20% of the NP in this paper. The parameters of the hybrid PPSO-GA optimization algorithm are illustrated in Table 2.

Table 2.

Parameters of the hybrid PPSO-GA optimization algorithm.

	PSO 1,2				GA
Parameter	w _min	w _min	c ₁	c ₂	p _cr	p _m	r _m
value	0.6	0.9	2	2	0.7	0.3	0.2

The Ackley function was applied to test the robustness and convergence. In this case, the number of population and maximum iteration was set to 500, 10,000, respectively. The hybrid PPSO-GA GA and differential evolution (DE) can be evaluated and compared by solving testing function with 100 and 200 dimensions. In Figure 6, it is clearly demonstrated that the convergence solution of the hybrid PPSO-GA algorithm is significantly better and faster than the other two algorithms.

Figure 6.

Convergence characteristics of the tested algorithm GA, DE and hybrid PPSO-GA.

Simulation and discussion

The algorithm and system simulation model are implemented by m-files with MATLAB R2014a and run on a PC with Intel I7-3770 CPU and 8 GB of RAM under Windows 7. In this paper, the optimal sizing of HESS using the wind power history date is simulated. The rated power of WTG is 1500 kW. The sample period is 1 min, and the regulation period is 24 h (T_d =24 h). The maximum and minimum output powers of the sample (P_w) are 1513.8 kW and 0 kW, respectively. The average of P_w is 406 kW. In Figure 7(a), the blue line is the output power of P_w. Using equation (17) to evaluate the P_w, we can obtain the maximum PPR of 10-min interval of P_w, the value is 76.15% and far exceeds the requirements of equation (18).

Figure 7.

(a) The profile of wind power and system desired output power and (b) The profile desired power and amplitude-frequency of HESS.

The desired power of wind power system is calculated by the first level of EMS. Since the sample frequency f_s is 16.667 mHz, the cutoff frequency f_c is limited in 0 to 8.333 mHz (Nyquist frequency f_N = f_s/2). By the recursive calculation, the optimal cutfoff frequecy f_c is 1.367 mHz, and the max (R_prr,10) fell to 33.15%. The PRR before and after the optimal is shown in Figure 8. It is clearly shown that the all PRR in any time step are less than the limit value after smoothing. Further, the desired output power of wind power system P_pcc,ref is calculated by equation (2) as indicated by the red dash dot line in Figure 7(a). Using equation (3), the desired output power of the HESS P_hess,ref can be obtained as shown in Figure 7(b).

Figure 8.

The profile of the PRR of 10-min interval.

From Figure 7(b), the amplitude–frequency characteristics can obviously be seen that the P_hess,ref has high-frequency fluctuation (approximately >1.3 mHz), which can damage the lifetime of the battery. In this study, to prolong the lifetime, the P_hess,ref is dispatched to lead-acid battery and SC. The characteristics of the lead-acid battery and SC is shown in Table 3 (Castillo and Gayme, 2014; Chen et al., 2009; Han et al., 2013; Zhao et al., 2015).

Table 3.

Characteristics of the lead-acid battery and SC.

Parameters	Lead-acid	SC
Efficiency (%)	80	90
Lifetime (cycles)	550	5 × 10⁵
SOC limited (%)	20–80	10–90
Capital cost per power (¥/kW)	2700	1500
Capital cost per capacity (¥/kWh)	640	27,000
Maintenance cost per capacity (¥/kWh)	0.05	0.05
Interest rate (%)	4	4

The optimal results are obtained by the designed EMS and hybrid PPSO-GA algorithm. In this simulation, the number of population NP is 200, the maximum number of iterations is set to 500. The parameters of hybrid PPSO-GA are shown in Table 2. For the purpose of comparison, GA and DE are also used to solve the same objective function. For the GA, crossover rate, mutation rate and discretization precision are chosen to be 0.7, 0.3 and 1 × 10⁻⁴, respectively. For the DE, crossover rate and mutation rate are selected to be 0.9 and 0.5, respectively. In this simulation, the battery operation period T_b,op is defined as an integer and the range is 1 to 60 min. The range of values for battery cutoff frequency f_b,c is 0 to 8.333 mHz. The range of adjustment factor k_b is 1 to 3. Considering the above variable limits, the results of the three methods are shown in Figure 9. It is clear that the hybrid PPSO-GA algorithm converges in 239 iterations that achieve the best objective function value of ¥18,546.95 in less time than that of other tested algorithms. Moreover, the hybrid PPSO-GA algorithm obtains the optimal value of T_b,op, f_b,c and k_b as 2 min, 1.623 mHz and 1.9, respectively. The optimal parameters of HESS are listed in Table 4.

Figure 9.

Convergence characteristics of the three algorithms for simulation.

Table 4.

The optimal parameters of HESS.

Parameters	T_b,op (min)	f_b,c (mHz)	k_b	P_b,rated (kW)	E_b,rated (kWh)	P_sc,rated (kW)	E_sc,rated (kW)	C_total (¥)
Value	2	1.623	1.9	327.14	978.91	783.85	425.19	18,546.95

According to T_b,op, f_b,c, k_b and the parameters of Table 3, P_b,ab is calculated by equations (19) to (21), and P_sc,ab is determined by equation (3). Taking into consideration the charge/discharge efficiency of the battery and SC, P_b,rated and P_sc,rated are obtained using equations (4) and (5). For prolonging the lifetime of battery, the SOC of the battery is settled within the band margin of ±20% and the SOC of the SC is settled within the band margin of ±10% for safety. The optimal sizing of HESS can be determined, which is shown in Table 4.

In order to evaluate the efficiency of the HESS, the single ESS uses lead-acid battery for reference. By calculation, the single ESS sizing is 972.92 kW/656.12 kWh. During the frequent charge and discharge conditions, the lifetime of the battery rapidly declines. In this simulation, the nominal lifetime of the battery is 550 times at DOD = 100%, the lifetime of the battery is only 0.23 years on this operation condition. For the above reason, the battery ESS has a high cost, where the total cost per day is 4.5926 × 10⁴. As shown in Table 4, it is obviously show that the HESS can effectively reduce costs, the cost of HESS is only 40.38% of the battery ESS. Meanwhile, the lifetime of the battery can be prolonged for 1.82 years because the high-frequency fluctuations are absorbed by SC. Although the sizing of HESS is greater than the battery ESS, the total cost per day is significantly reduced owing to the prolonged lifetime.

Figure 10 shows that the battery operation period T_b,op has obviously influenced the minimum total cost per day. When T_b,op = 2 min, the total cost can get the optimal value. While T_b,op increases, the total cost also increases. This phenomenon is due to the extra power caused by the battery works in constant power output in T_b,op. Although increasing T_b,op can decline the frequence of the battery output power and prolong lifetime, the cost will increase with the T_b,op.

Figure 10.

Minimum total cost per day versus the battery operation period T_b,op.

Figure 11 illustrates the relationship between the total cost per day and the f_b,c at T_b,op =2 min and k_b =1.9. As the battery cutoff frequency increases, the battery sizing also increases and the battery cost is improved, but the change trend is opposite for SC. When f_b,c = 1.623 mHz, the optimal cost is obtained. From Figure 12(a), it is clearly seen that the frequency of the output power of the battery is far lower than SC. Figure 12(b) shows that the SOC of HESS meets the system setting requirements: 20%≤S_b≤80% and 10%≤S_sc≤90%.

Figure 11.

Total cost per day versus the battery cutoff frequency f_b,c at T_b,op= 2 min, k_b=1.9.

Figure 12.

Output power and SOC of HESS at T_b,op= 2 min, f_b,c=1.623 mHz, k_b=1.9.

The impact of adjustment factor of the battery k_b on the relative DOD, lifetime and cost is shown in Figure 13. When k_b > 1, the oversizing of the battery has a significant positive effect on its lifetime. When adjustment factor k_b=1.9, the DOD is lower than 55% and the lifetime increases from 1.12 to 1.82 years. With k_b increasing from 1.9 to 3, the DOD is lower than 40% and the lifetime improves to 2.86 years, but the cost also increases from ¥18,546.95 to ¥21,441.31. The simulation results show that the optimized sizing of HESS satisfies the requirements of smoothing fluctuations of the wind power and lower system cost.

Figure 13.

The impact of adjustment factor k_b on the relative DOD, lifetime and cost at T_b,op = 2min, f_b,c = 1.623mHz: (a) DOD statistics in terms of various k_b and (b) lifetime and cost versus k_b.

Conclusions

In this paper, a hybrid optimization method combining PSO and GA was proposed to alleviate the fluctuations of wind power energy. By using the proposed method, it is used to find the optimal power and energy capacities of the HESS. We have proposed a two-level EMS based on the cutoff frequency. In first level EMS, the desired output power of HESS is obtained. In second level EMS, the sizing of HESS can be calculated according to the battery operation period and the battery cutoff frequency. We also have proposed the hybrid PPSO-GA optimization algorithm for guaranteeing a feasible optimal solution in terms of cost and lifetime. In addition, we used the piecewise fitting function to estabilsh the relationship between DOD and cycles to failure.

According to the analysis of the simulation results, the optimal sizing of HESS reduces the total cost per day by 59.62% compared to the single battery ESS, whereas the lifetime increases to 1.82 years. Results show that the lifetime is a major factor to influence the cost of all the systems. And the several factors can influence the optimality and reliability of the result such as temporal resolution of sample power, filtering function of power and battery features.

The future works will concentrate on developing the model and EMS, which considers the wind power uncertainty, load and emission objectives.

Footnotes

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) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (Grant No. 51605385) and the Fundamental Research Funds for the Central Universities (Grant No. 3102017zy008).

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