1. Introduction
To address the energy crisis and environmental pollution caused by the growth of the economy and society, hybrid renewable energy systems (HRES) have become popular and wise choices, especially for remote or island areas, where renewable energy is abundant, and where power electricity construction cost is high [
1,
2]. With their complementary characteristics and matured technologies, HRES consisting of photovoltaics (PV), wind turbines (WT) and battery systems (BS) have become one of the most popular power generation modes [
3]. The optimal capacity of HRES is a key and complicated issue [
4] because it always contains multiple optimization objectives and is influenced by many factors, such as characteristics of the energy source, technical specifications and environmental conditions [
5].
Many researchers have been keen to address the capacity optimization problem. Scholars have applied mathematical programming to solve capacity optimization problems. Linear programming was utilized for capacity optimization of a standalone PV/WT HRES in [
6], mixed-integer linear programming was applied for the design for an isolated PV/WT/BS/DG (diesel generator) HRES in [
7] and dynamic programming was utilized for storage capacity optimization of PV/WT/BS HRES in [
8]. There are also scholars solving the problem by iteration. An iterative algorithm [
9] and an enumeration-based iterative algorithm [
10] were implemented for component capacity optimization of micro-grids. However, the methods above have the drawbacks that they can only handle single objective optimization and are susceptible to falling into local optimum solutions [
11].
Many other researchers utilized software tools to solve this problem. HOMER [
12,
13] is one of the most popular tools. It was used for capacity optimization, techno-economic and sensitivity analyses of a PV/BS HRES in [
14] and a PV/DG/BS HRES in [
15]. In [
16], the techno-economic feasibility of replacing a completely DG power supply by a standalone PV/WT/BS/DG was analyzed by HOMER. In [
17], the performance of a WT/BS/DG HRES impacted by different battery technologies was analyzed by HOMER. It was applied for the investigation of possible renewable power generation systems for Gadeokdo Island in South Korea in [
18]. In [
19], component capacities of PV/BS/DG HRES was optimized under different load profiles. In [
20], the optimal sizing of fuel cell/PV HRES was performed by HOMER with the components cost calculated by fuzzy logic program. Homer is good software for scenario investigation, but some scenarios need to be re-calculated individually for the specific situation because this tool can only handle single-object optimization [
21], the flexibility is limited, and is easy to fall into local optimum solutions [
22].
Intelligent optimization algorithms, having the superiority of global optimization and the capacity to handle multi-objective problems easily, have been intensively studied in the optimal capacity problem [
11]. In [
23], an artificial bee colony algorithm was used for finding the optimal capacities of a PV-biomass HRES with the minimum levelized cost of electricity (LCOE), and the results proved it outperformed HOMER. The discrete bat search algorithm [
24] and grasshopper optimization algorithm [
25] were used for PV/WT/DS/BS HRES. Many researchers have considered multiple objective functions in capacity optimization, and have applied multi-objective intelligent optimization algorithms to obtain solutions. In [
26], a multi-objective differential evolution algorithm was applied for the capacity optimization of a PV/WT/DG/BS HRES in Yanbu, where the objective functions were minimizing LCOE and loss of power supply probability (LPSP) simultaneously. A non-dominated sorting genetic algorithm (NSGA-II) was applied for optimal sizing of an off-grid PV/WT/BS HRES where economic and reliability indicators were simultaneously considered in [
27]. Many scholars considered additional indicators, except for economic and reliability indicators; for example, an environmental indicator was involved in the optimal sizing of a PV/WT/fuel cell HRES in [
28] and a PV/WT/BS HRES in [
29].
With the rapid development of HRES, intelligent optimization algorithms with better performance are urgently needed [
11]. Multi-objective evolution algorithms based on decomposition (MOEA/D) [
30] provide a new approach to multi-objective optimization [
31] and have received growing attention as they can incorporate the techniques used in single-objective optimization algorithms well. In this paper, a novel multi-objective optimization algorithm, namely MOEA/DADE, is proposed for better optimization performance. In this algorithm, a differential evolution mechanism with parameter self-adaptation is integrated in decomposition framework and its effectiveness is verified by algorithm contrasts with NSGA-II and MOEA/D on benchmark problems. Then, the algorithm is applied for techno-economic optimization of a standalone PV/WT/BS HRES located in Xining, China and its applicability for this problem is also validated by comparisons with NSGA-II and MOEA/D. Lastly, techno-economic and sensitivity analyses of the initial capital of wind turbines, photovoltaics and battery systems are performed.
The paper is organized as follows: component models of the HRES and energy management strategy (EMS) are introduced in
Section 2, MOEA/DADE algorithm and algorithm comparisons with MOEA/D and NSGA-II on benchmark problems are presented in
Section 3, techno-economic optimization and sensitivity analyses of PV/WT/BS HRES are performed in
Section 4; finally, conclusions are drawn in
Section 5.
2. Component Models and Energy Management Strategy
The HRES is consisted of five major components: PV systems, WT systems, a converter, BS and grid loads. Its structure diagram is shown in
Figure 1.
2.1. Wind turbine
The relationship between a WT’s output power (
) and wind speed can be described by a piecewise function as Equation (1) [
13]:
where
(kW) represents the WT’s rated output power,
(m/s) represents wind speed at the turbine hub height,
(m/s) is the cut-in speed,
(m/s) is the rated speed, and
(m/s) is the cut-out speed.
,
and
are assumed to be 2 (m/s), 9 (m/s) and 24 (m/s) respectively.
As the anemometer is not at the same altitude as the turbine hub,
can be obtained by Equation (2):
where
(m),
(m) are the installation altitude of the turbine hub and the anemometer respectively,
(m/s) is the wind speed measured by anemometer,
is a constant number between 0.1 and 0.25 [
13]. In this paper, the anemometer height is 10 m, the hub height is 25 m and
is assumed 0.25.
2.2. PV Panel
Ignoring the temperature effects, the PV’s output power (
) can be calculated by Equation (3) [
13],
where
(kW) and
(1 kW/m
2) represent the power output and solar radiation under standard test conditions,
(kW/m
2) represents the actual solar incident radiation on the PV array in time
t, and
(%) is the PV derating factor.
2.3. Battery System
The electric power stored into the BS in time
t is described as Equation (4):
where
(kW) represents the electrical load,
represents the converter efficiency.
If
is greater than 0, the BS will be charged to store the surplus power energy, otherwise, it will be discharged to make up for the electricity shortage. The BS’s state of charge (SOC) for
t period is shown as Equation (5):
where
(kW∙h) is the BS’s SOC,
t represents time index, and
is the dissipation coefficient. Assume that the charge efficiency (
) and discharge efficiency (
) remain unchanged,
can be obtained by Equation (6).
Moreover, the BS’s SOC should satisfy the constraint described as Equation (7):
where
(kW∙h) means the maximum allowable amounts of energy that can be stored by the BS,
DOD (%) is the BS’s allowable depth of discharge.
2.4. Load Profile
To make the inherently statistical power load more realistic, the load in each time step is obtained by multiplying its annual average value with a perturbation factor
[
32] shown as Equation (8):
where
denotes the daily variation percent,
denotes the hourly variation percent.
2.5. Economic Model
The life cycle cost (LCC) of the
k-th component of the HRES is described as Equation (9). It includes initial capital cost (
), maintenance and operation cost (
), replacement cost (
) and salvage value (
).
,
,
,
can be calculated according to Equations (10)–(15), where
(kW for WT, PV and converter, and kW∙h for BS) means the component capacity,
,
and
mean initial capital cost, maintenance and operation cost, replacement cost per unit respectively and their units are
$/kW for WT, PV and converter and
$/kW∙h for BS,
N (year) and
Nk (year) mean the system life time of the system and the
k-th component respectively,
(year) means the surplus life of the
k-th component when the system ends,
(year) means the last replaced time of the
k-th component, INT(.) is a function that returns the smallest integer that is greater than or equal to the input number, and the relationship of the real discount rate
(%), nominal discount rate
r (%) and expected inflation rate
u (%) is shown as Equation (16):
Capital recovery factor (CRF) shown as Equation (17) is applied to convert LCC into the annualized cost of the HRES. Assuming that the amount of electricity generated by the HRES per year stays the same over the project’s lifetime, LCOE is shown as Equation (18) [
24]:
where
NC is the number of components in the HRES and
(kW∙h) is the annual power output.
2.6. Rule-Based Energy Management Strategy
EMS is one main criterion for HRES [
25]. To coordinate various components’ output power, a rule-based EMS is designed and its flow chart is shown as
Figure 2.
Firstly, a binary variable (
Sp) is defined to represent whether the electric power generated is sufficient, and a binary variable (
Sc) is defined to represent whether the converter capacity is sufficient. Their definitions are shown as Equations (19) and (20).
Secondly, according to the combination values of Sp and Sc, the rule-based EMS is designed with four case scenarios as follows: Case 1,the electric power generated and the converter capacity are both sufficient (); Case 2, the electric power generated is sufficient while the converter capacity is insufficient (); Case 3, the electric power generated is insufficient while the converter capacity is sufficient (); and, Case 4, the electric power generated and the converter capacity are both insufficient ().
Finally, update the BS’s SOC and calculate the loss of power supply (LPS) for different cases according to the follow rules:
Case 1: the load will be completely satisfied (LPS = 0), and the extra power used for charging the battery is calculated by Equation (4) and a new temporary SOC of the BS (soc_new) can be obtained by Equation (5), if , set , otherwise, set and the extra energy will be discarded.
Case 2: the power output of the HRES will be
, LPS and the power used for charging the BS (
) can be calculated by Equations (21) and (22) respectively.
then, update the BS’s SOC as Case 1.
Case 3: the battery will be discharged to supply as much electricity as possible and whether the load can be satisfied with the BS’s support is calculated according to Equation (23).
If
, the load will be completely satisfied (LPS = 0), and the charge power of BS (
) and BS’s SOC are calculated by Equations (4) and (5) respectively, otherwise, set
and calculate LPS by Equation (24).
Case 4: the load will not be completely satisfied and the battery will be discharged. Firstly, whether the power output can reach to converter capacity with the BS’s support is calculated according to Equation (25).
If , the power output of the HRES will be , LPS is calculated by Equation (21), the charge power of BS () and BS’s SOC can be calculated by Equation (22) and Equation (5) respectively, otherwise, set and calculate LPS by Equation (24).
2.7. Objective Function and Constraints
The objective functions described as Equation (26) are to maximize system reliability (represented by minimizing LPSP) and economy (represented by minimizing LCOE) simultaneously,
where
,
,
, and
are decision variables that mean the capacity of PV, WT, converter and BS respectively,
,
and
are their upper bounds, and LPSP is calculated as Equation (27),
where
t is a time period index, T (8760 h) represents the total hours of a year.
5. Conclusions
In this paper, we focused on the techno-economic optimization of a standalone PV/WT/BS HRES in Xining, China. To find out the optimal LCOE under different LPSP, a novel multi-objective optimization algorithm, namely MOEA/DADE, is proposed. In this algorithm, a differential evolution mechanism with parameter self-adaptation is implemented in the decomposition framework. Algorithm comparisons with NSGA-II and MOEA/D on benchmark problems verify that MOEA/DADE is superior to NSGA-II and MOEA/D. The applicability of MOEA/DADE on the capacity optimization problem was also validated by comparisons. Then, MOEA/DADE was applied for techno-economic and sensitivity analyses of the HRES. Techno-economic analyses from the PF shows the economic benefits are significant by reducing reliability requirements when LPSP is less than 0.5%, and are not obvious when LPSP is larger than 0.5%. The system’s LCOE can fall from 0.2348 ($/kW∙h) to 0.2225 ($/kW∙h), falling by 0.0123 ($/kW∙h) as LPSP increases by 0.1% when LPSP is 0, however, it can only fall from 0.2041 ($/kW∙h) to 0.2008 ($/kW∙h), falling by 0.0033 ($/kW∙h) as LPSP increases by 0.1% when LPSP is 0.5%. Sensitivity analyses for the components’ initial capital show PV’s initial capital has the greatest impact while WT’s initial capital has the least impact on LCOE. When the components’ initial capital falls to 80% of its initial value, the LCOE can fall by 3.97% for the PV case, 2.19% for the BS case and 2.07% for the WT case, and when components’ initial capital increases to 120% of its initial value, the LCOE can increase by 6.05% for the PV case, 4.77% for the BS case and 2.50% for the WT case. The results indicate that reducing the PV’s initial capital produces more obvious economic benefits.