The substantial penetration of wind power from Wind Turbine Generators ( WTGs) into the power distribution system, combined with variations in load demand, has caused issues such as voltage instability, voltage deviations, and high-power losses. Operators of the distribution system are required to improve the technical performance of the system at a minimum cost. Superconducting Magnetic Energy Storage (SMES) units have been shown to be very efficient in addressing these problems by enhancing voltage stability and improving power quality in the distribution system. Despite the merits of the SMES, it has a high investment cost. This scenario has paved the way for the development of a multiobjective optimization platform to address this techno-economic issue. The weighted sum Multi-objective Function (MOF) is formulated to improve the techno-economic performance of the distribution system by determining the optimal location and size of WTGs and SMESs units in a distribution system to enhance the voltage stability and minimize voltage deviation, power loss and annual total cost using the Voltage Sensitivity Factor (VSF) and the Grasshopper Optimization (GO) algorithm. The weight factors are not left to the preference of the decision maker but are determined through an analytical test conducted on the IEEE 33-bus distribution system to ascertain their most effective values. The simulation results of the proposed technique demonstrate a significant improvement in voltage stability by 28.56% when one WTG and one SMES were installed, 29.43% when two WTGs and two SMESs were installed and 30.14% when three WTGs and three SMESs were installed when compared to their base cases. The voltage deviations were reduced by 50.67% when one WTG and one SMES were installed, 52.59% when two WTGs and two SMESs were installed, and 54.68% when three WTGs and three SMESs were installed when compared to their base cases. The energy losses were reduced by 29.34% when one WTG and SMES were installed, 37.76% when two WTGs and two SMESs were installed, and 41.56% when three WTGs and three SMESs were installed when compared to their base cases. The proposed algorithms for optimal location and sizing of WTGs and SMESs units have been validated on the IEEE 33-bus distribution system, considering time-varying voltage-dependent loads as well as variable wind speed. The results obtained are compared with those of the Equilibrium Optimizer (EO) and Particle Swarm Optimization (PSO) algorithms. The obtained results show that the proposed GO algorithm is remarkably effective in determining the optimal locations and sizes of the WTGs and SMESs by obtaining the optimal values of the MOF impact indices.
Abstract
High power losses, voltage sag, and low voltage stability are the issues that the system faces because of the widespread use of intermittent wind-turbine generating (WTG) in the electric distribution system and the substantial changes in load demand. To overcome the problem in the distribution system superconducting magnetic energy storages (SMESs) is used which helps to reduce these issues. In this work, a multi-objective-function based optimization method is used to determine the best positioning and sizing of WTGs and SMESs in a distribution system. The approach is effective by using Grasshopper Optimization (GO) and the hybrid concept since it relies on both the loss sensitivity factor (LSF) and the algorithm. The weighted-sum multi-objective function (MOI) is developed to simultaneously reduce energy loss, voltage deviation, cost* and enhance voltage stability as performance indicators for distribution systems.
The weighting factor presumptive or subject to the decision maker's preferences and calculated as part of the IMO index optimization process to find the best locations and sizes for WTGs and SMESs. The performance of the proposed approach is validated on IEEE 33-bus radial distribution system with time-varying voltage-dependent load models for mixed, residential, industrial, and commercial loads as well as variable wind-speed. To verify the efficiency of GO, the results from the algorithm are compared with particle swarm optimization (PSO.
1. Introduction
Due to its high-power output (up to 10 MW per wind turbine), low cost per kWh, and favorable environmental effects, wind energy has grown in popularity [1][2],due to public's support for green projects, growing fuel prices, and a focus on using wind energy are a few factors that contribute to the global trend toward increasing the usage of wind turbines to produce electric power. Wind energy sources are unpredictable and intermittent in nature, notwithstanding the advantages of wind turbine power generation systems. Low voltage stability, voltage variation, and power loss are only a few of the problems that arise because of increasing the penetration levels of wind turbine power generation in a distribution system [3][4]. An efficient solution to these issues is possible by integration of energy storage systems (ESS) into the distribution system.
Different ESS types are employed to address the issues related to the utilization of wind power producing systems. These include battery energy storage systems (BESS) [5], flywheel energy storage systems (FWS) [6], fuel cell energy storage systems (FC) [7], compressed air energy storage systems (CAES) [8], compressed carbon dioxide energy storage systems (CCES) [9], and superconducting magnetic energy storage systems (SMES) [10]. Despite being the industry standard, the BESS has several disadvantages, including a lower lifespan, voltage and current restrictions, potential environmental concerns, and a poor response time. The SMES has several benefits over the ESS, including high storage efficiency (95–98%), high power density (0.1–10 MW), the absence of moving parts, short response times, long lifespans, and no restrictions on the number of charging and discharging cycles [11].
Due to the main drawback of SMES being its high cost, a multi-objective optimization platform has been developed to study its techno-economic patterns. The use of High Temperature Superconductors (HTS) can lessen this drawback. HTS are cooled by liquid nitrogen at 77 o K as opposed to 4.2 oK (LTS) for Low-Temperature Superconductors [12]. In comparison to LTS, HTS systems are more reliable and have reduced refrigeration expenses. Recently, an overview of the design and development of high temperature SMESs for power applications was published [13]. In order to reduce the degradation of superconductor performance at high temperatures, several investigations have been done on SMESs cooling methods and thermal management strategies based on thermal energy storage materials [14]– [19].
The SMES unit is a substantial superconducting coil that can store electrical energy in the magnetic field created by a direct current (dc) flowing through it [20]. According to the power requirement of the distribution system, real and reactive power can be absorbed or released from the SMES coil. The magnetic field is produced by DC current passing through a superconducting coil. This energy can be released from a SMES unit in a nanosecond for several hours because it is held as a circulating current [12], [21], [22]. As shown in Figure 1, the SMES unit is made up of a cryogenic refrigerator, a power conditioning unit (PCU), and a superconducting coil [23].
FUGURE 1: Components of the SMES unit [23]
The effectiveness of SMES units for enhancing transient stability has been examined in [2], [33]– [36], as well as changes in the output power and voltage of WTGs [37]–[39]. On the other hand, little is known about the optimal allocation and sizing of WTG and SMES units. To increase the voltage stability in the test system, the authors in [27] use a genetic algorithm to position a SMES unit in an IEEE14-bus transmission system. To increase the stability of a distribution power system with PV generation, the optimal size of the SMES was calculated using a simplex method in [40]. A straightforward case study using the field measurement data for PV module temperature and irradiation in the Power System Computer Aided Design Software (PSCAD) is used to assess the performance of SMES at its ideal size. In [41], the author put forth a technique to use loss sensitivity in an example power system while considering a daily load profile to determine the best location for the superconducting device to minimize the system loss. In [42], the authors proposed a method to minimize the operating cost of thermal units in an IEEE 10-unit thermal transmission system by optimal sized SMESs using the Lagrange Relaxation PSO algorithm for a daily varying load. Authors in [23] proposed a multi-objective optimization technique for allocation and sizing of wind turbine generators and SMESs in a distribution system using the Equilibrium Optimizer (EO) and loss sensitivity factor in an IEEE 33-bus distribution system with time-varying voltage-dependent load models as well as variable wind speed. The weighted sum multi-objective index was formulated for the simultaneous minimization of energy loss, voltage deviation, and enhancement of voltage stability.
In the proposed approach GO algorithm is suggested for the optimal placement and sizing of WTGs and SMESs in the IEEE 33-bus distribution system for improving voltage stability, minimizing voltage deviation, power loss, and annual total cost considering voltage-dependent load demand, variable wind speed, and power loss compared with PSO.
2. Methodology
The optimization problem for the optimal location and sizing of WTGs and SMESs is formulated as a weighted-sum multi-objective function for enhancement of voltage stability, minimization of voltage variations, power loss and annual total cost combined with optimization algorithm. Mathematically, this multi-objective function can be stated as shown in equation (1).
Minimize F = (1)
w.r.t
Subject to
where is a vector of control variables that will be optimized in the process. , and are the vectors denoting the location of the WTGs and SMESs, respectively. and are the vectors denoting the capacities (sizes) of the WTGs and SMESs, respectively. The terms and denote the equality and inequality constraints to account for the technical restrictions and operating strategies, respectively. Note that the control variables include both integer and positive real values. The impact indices and the equality and inequality constraints are presented in the following subsections.
The first objective function is defined as the Voltage Stability Index (VSI) as in equation (2) [51].
(2)
The VSI is determined as follows:
(3)
where is the voltage stability index at bus k and is the line reactance between i and k buses.
The second objective function is defined as in equation (4).
(4)
where is number of buses, is the voltage at bus i, and is the reference voltage being equal to 1 p.u.
The third objective function is defined as the active power loss as in equation (5).
(5)
where is number of transmission lines in the investigated distribution system.
The fourth objective function is defined as the annual total cost power loss expressed in equations (6) through (10).
(6)
(7)
where,
(8)
(9)
(10)
denotes the unit investment cost of WTGs and SMESs units in USD/kW or USD/kWh, whereas denotes the annual operation and maintenance costs of the units in USD/kW-yr or USD/kWh-yr. It should be noted that is the estimated lifetime of the units in years, is the size of installed SMES unit; and represents the energy and power rating of the SMES units. The subscripts f and v in denote the fixed and the variable operation and maintenance costs of SMES units respectively. The number of WTGs and SMESs are represented by and , respectively. Finally, is the capacity recovery factor of a unit having a lifetime of , with an interest rate of r.
The annual total cost comprises of the annual investment, operation, and maintenance costs. The costs of the WTGs and SMESs are influenced by the market economy and the site location of the installation. While the cost of SMES is influenced by both its power and energy ratings, the cost of WTG is determined by its power rating. Therefore, it is preferable to express the cost of WTGs and SMESs separately [52], [53]. The WTGs and SMESs parameters are shown in Table 1.
TABLE 1: WTGs and SMESs cost parameters [3], [54][52]
|
Maximum = 1, 2 and 3 Maximum NSMES =1, 2 and 3 |
0.00025-0.0005 |
|
|
= 25 |
(MUSD$/kW-yr): 0.08 - 0.25 |
(MUSD$/kW-yr): 1x |
|
= 0.0002 |
= 30 |
(MUSD$/kW-yr): 0.0000185 |
|
Maximum WTGs rated power limit: 0.4 - 4.0 MW |
= 0.0005 |
|
|
SMES rated power limit : 0.01- 4.0 MW |
SMES rated capacity limit: 0.001- 10.0 MWh |
|
2.1 Weighted-Sum Multi-Objective Index
A weighted-sum multi-objective index (MOI) is formulated to accommodate the above indices with appropriate weights as shown in equation (11).
MOI (t) = μ1F1 +μ2F2 +μ3F3 +μ4F4 (11)
Where , denote weight factors, each weight factor has the range from zero to one and whose summation is equal to one as in equation (12).
(12)
The determination of MOI(t) at each hour is performed using load flow analysis of the distribution system. The Average Multi-Objective Function (AMOF) over the total day hours (T=24) is expressed as shown in equation (11)
(13)
The lowest AMOF value identify the best sizes of WTGs and SMESs for enhancing voltage stability, minimizing voltage deviation, power loss, and annual total cost.
2.2 Load Profile
The normalized hourly load demand profile for residential customer [23] of 1 p.u peak is considered in the study as shown in Figure 2. The loads are of time-varying voltage-dependent type with active load- voltage exponent of 4.04 and reactive load-voltage exponent of 0.92 [44].
FIGURE 2: Normalized hourly load demand profile [44]
The time-varying voltage-dependent load model at bus k of the distribution network is expressed in equations (14) and (15):
(14)
(15)
where and are, respectively, the real and reactive powers injected at the kth bus, and are, respectively, the real and reactive loads at the same bus but at nominal bus voltage, is the voltage at the bus, and and respectively.
2.3 WTG Modeling
The WTG generated outpower at wind speed is determined as shown in equation (16).
0 if
if (16)
if
where is the rated output power and , , and are the cut-in speed, cut-out speed, and rated speed of the WTG, respectively. Equation (16), which represents the WTG characteristic power curve, demonstrates that there is no WTG output power when the wind speed is lower or higher than the cut-in and cut-out wind speeds, respectively.
2.4 SMES Unit Modeling
SMESs can store the excess or surplus energy produced by the WTGs and release it to meet peak load demand during the day. The SMESs can function as loads to store energy during charging mode and generators to release load or supply energy during discharge mode. When wind power generation is low and the load exceeds 75% of the peak load demand, the SMESs are permitted to discharge. Reactive power can be delivered or absorbed by it as well. The SMES are mounted on the same bus as the WTG to get power from it.
Charging mode:
This mode occurs when WTG power is higher than the load demand (i.e., ).
(17)
(18)
Discharge mode:
This mode occurs when the load demand is higher than the WTG power .
(19)
(20)
Where is the exchanged power of the SMES at period t, which has negative, positive, and equal to zero during charging mode, discharging mode, and idle mode of the SMES unit respectively and where and are the charging and discharging efficiencies, respectively; The difference between load demand and WTG output is known as ∆ ; denotes the power rating of the SMES; denotes its energy storage capacity of the SMES unit at period t; and denote the minimum and maximum energy storage capacity limits of the SMES unit respectively; and t represents the time interval (one hour) [5], [42], [48], [49].
2.3 Load Flow Analysis
FIGURE 3: Backward-Forward load flow
The backward and forward sweep algorithm's simplicity, low memory demand, speed, and computational correctness make it the most efficient technique for solving load flow studies in power distribution systems [Kawambwa S. et al. 2021]. Consider two buses linked by a branch, which has sending and receiving buses are designated bus 't' and 't+1', respectively. Equations (20) and (21) utilized to determine the real power loss and reactive power loss flowing in the feeder segment between buses 't' and 't + 1' [Thangaraj Y. and Kuppan R. 2017].
(20)
(21)
Where, and are the over-all effective active and reactive power delivered beyond the bus t+1 respectively. The and are the active and reactive power losses between the bus’ t ‘and ‘t+1’ respectively computed using (21) and (22),
(22)
The sum of losses in all feeder sections, stated by (23) and (24), can be used to compute the total real and reactive power losses,
(23)
(24)
2.4 Problem Constraints
The AMOF expressed in (26) is subjected to the following constraints:
2.4.1 System Operation Constraints
i. Power balance constraint
The algebraic sum of all input and output active and reactive power flow through the investigated distribution system should be equal as shown in equations (25) and (26)
(25)
(26)
where and represents substation active and reactive power at time t, respectively, and are active and reactive power losses of line at time t, and are active and reactive powers of load demand at bus i at time t [55].
ii. Bus Voltage Constraint
The voltage magnitude at each bus must be kept within an acceptable range at all times as shown in equation (27).
(27)
where and are the minimum and the maximum voltage limits with values of 0.95 p.u. and 1.05 p.u., respectively.
iii. Line current constraint
The current magnitude of each line at any time t must remain within acceptable operating limits in order to avoid any excessive thermal stress of the line is shown in equation (28).
(28)
iv. Reverse Power Flow Constraint
This constraint defines that the reverse power flow never exceeds 0.6 of the substation rating (R) is shown in equation (29) [55].
(29)
2.4.2 Wind Turbine Constraints
The wind turbine constraint is shown in equation (30).
(30)
where is equal to 0 and is equal to maximum rated output power of the WTGs.
2.4.3 SMES System Constraints
Charging-discharging power limit constraint
The charging-discharging power limit constraint is shown in equation (31).
(31)
where the negative and positive polarities of refers to charging and discharging of SMESs, respectively.
2.4.4 Storage Capacity Constraint
The storage capacity constraint is shown in equation (32).
(32)
where and are taken as 0.1 and 0.9 times rated capacity respectively [1], [42], [56].
2.4.5 Capacity Balance Constraint
For continuous utilization in the next day, the final storage capacity of SMES unit at the end of the day should be equal to the initial storage capacity for the next day as shown in equation (33).
(33)
3. OPTIMIZATION ALGORITHM
Optimization algorithms are mathematical techniques used to find the best solution to a problem from a set of possible solutions. In this proposed approach we have used three algorithms,
I. Grasshopper Optimization
II. Particle Swarm Optimization
III. Equilibrium Optimizer
3.1 Grasshopper Optimization Algorithms
In this work, the first algorithm uses GO algorithm for the optimal location and sizing of WTGs and SMESs in a distribution system. The GO algorithm, a novel and fascinating swarm intelligence system that imitates grasshopper foraging and swarming behaviors, was introduced by Saremi et al. in [59]. Insects called grasshoppers do extensive damage to agricultural goods. They go through two stages in their life cycle: nymph and adult. The nymph phase is characterized by short steps and smooth motions, whereas the adult phase is characterized by lengthy steps and abrupt movements. Movements made by nymphs and adults are what the GO algorithm uses to determine its intensification and diversification phases.
3.2 Particle Swarm Optimization (PSO)
Particle Swarm Optimization (PSO) is a population-based optimization algorithm that is inspired by the social behavior of birds and fish. It is used to find optimal or near-optimal solutions to optimization and search problems. The key idea behind PSO is to model a population of potential solutions (particles) that move through the search space to find the best solution through social interactions and individual learning. The basic optimization stages for PSO are initialization of particles with random values matching the dimensions of the problem, initialization of initial and final velocities.
The flow chart of the GO algorithm for optimal location and sizing of WTGs and SMESs is shown in Figure 6.
Table 5: The parameters of GO algorithm
|
Parameter |
Symbol |
Value |
|
Number of Search Agent |
S |
100 |
|
Max Iteration |
Iter |
100 |
|
Lower bound |
|
0 |
|
Upper bound |
|
100 |
|
Maximum value of decreasing factor |
|
0 |
|
Minimum value of decreasing factor |
|
0.0004 |
The step procedure for the PSO algorithm as follows:
Results and Discussions
The proposed approach is tested on IEEE 33 bus system in four different load models i.e., Residential, Commercial, Industrial and Mixed. Using HP personal computer with an Intel Core (TM) i7, 16 GB of RAM, and a 64-bit operating system with the MATLAB R2020b the performance of GO and PSO algorithm is evaluated and compared.
Residential Load
Industrial Load
Commercial Load
MIXED
