4.3 Multi-objective planning for simultaneous optimization of PVHC and energy loss of
4.3.3 SPEA2-MOPSO based solution approach
This section describes the MOPSO-based multi-objective planning algorithm to determine the optimal PV generation capacity in each bus, except the substation bus and the optimal locations for the series and shunt inverters of UPQC-O. The basics of PSO algorithm are discussed in subsection 2.5.1. The SPEA2-based MOPSO is described in the subsequent section.
4.3.3.1 Assumptions
The following assumptions/considerations are used for the operation of rooftop PV and UPQC-O in the proposed model:
All rooftop PV arrays are always operating at unity power factor. Thus, they are capable of injecting only active power into the network during the operational hour.
The PV generation hours and the peak demand hours do not coincide with each other.
The peak demand takes place during evening 6 to 10 PM and this duration is named as peak hour. The rest of the time is treated as off-peak hour. The peak and off-peak demand refer to the average load demand during the peak and off-peak hours, respectively.
The PV generation is directly injected into the network during operational hours of PV arrays. There is no provision for storage.
Modelling and Allocation Planning of Inverters of Open UPQC to Improve the Rooftop PV Hosting Capacity…
4.3.3.2 SPEA2-MOPSO
MOPSO is a version of PSO algorithm which is used to solve the multi-objective optimization problems. In this algorithm, multiple fitness values corresponding to the multiple objectives are assigned to each particle. In literature, many MOPSO variants are found. The state-of-the-art review on MOPSO is available in [140]. The most of the MOPSO approaches are based on the Pareto-dominance principle. All these approaches are used to find out a set of non-dominated solutions. The plot of the non-dominated solutions is called Pareto approximation front (PAF). In SPEA2-MOPSO, the non-dominated solutions obtained with the MOPSO algorithm are stored in an elite archive. This elite archive is utilized to assign fitness to each member of the archive itself and the current population undergoing evolution according to the fitness assignment scheme of SPEA2 [138]. Single fitness value is assigned to each particle according to its non-domination rank and solution density [137, 141].
4.3.3.3 MOPSO based planning algorithm
The overall MOPSO-based planning algorithm uses the FBSLF subroutine incorporating UPQC-O and PV models. A particle of MOPSO consists information of maximum PV generation capacity in each bus, except the substation, and the locations for series and shunt inverters. The flow chart for the overall planning algorithm is shown in Fig. 4.9. In this work, each particle consists of two fitness values corresponding to the following functions,
Fitness 1: max {ℱ1} =∑∑𝑖=2,…,𝑁𝑃𝑃𝑉𝑃(𝑖)(𝑖)
𝑖=2,…,𝑁 (4.16)
Fitness 2: min {ℱ2} =∑𝑐∈𝜓𝑇𝐸𝐿𝑃𝐿𝑐𝑡𝑐
𝑏𝑎𝑠𝑒 (4.17)
The two objective functions as shown in Eqs. (4.13) and (4.14) are normalized with the total peak active power demand of base-case network and the total energy loss of base-case network in a day (𝑇𝐸𝐿𝑏𝑎𝑠𝑒), respectively to obtain Eqs. (4.16)-(4.17). 𝑇𝐸𝐿𝑏𝑎𝑠𝑒 is determined by summing up the energy loss of a distribution network during peak demand hours and off-peak demand hours without any compensation. The maximization of first fitness function provides the information of total PV generation capacity that a network can accommodate with respect to the total peak active power demand of the base-case network.
Y Y Start
Input Bus data and Line data of the distribution network
Calculate PVSML, and VA-ratings of series and shunt inverters corresponding to each location in the network
Update position and velocity of the particle using Eqs. (2.94) and (2.95), respectively
Input PSO parameters and different planning parameters
Initialize position and velocity of the particles of size 𝑁𝑃𝑜𝑝 Calculate fitness values for each
particle of MOPSO
Find the initial set of non-dominated solutions and store it in an elite archive
The particle violating constraints is to be penalized
End 𝑖𝑡 ≥ 𝑁𝑃𝑜𝑝
N
𝑖𝑡𝑟 = 1
𝑖𝑡𝑟 = 2
Determine initial 𝐿𝐵𝑒𝑠𝑡 and 𝐺𝐵𝑒𝑠𝑡
𝑖𝑡 = 1
Perform FBSLF with PV and UPQC-O models Calculate fitness values
𝑖𝑡 = 𝑖𝑡 + 1
𝑖𝑡𝑟 ≥ 𝑖𝑡𝑟𝑚𝑎𝑥 Determine 𝐿𝐵𝑒𝑠𝑡 and 𝐺𝐵𝑒𝑠𝑡 Find the set of non-dominated solutions
and update the elite archive 𝑖𝑡𝑟 = 𝑖𝑡𝑟 + 1
Fig. 4.9: Flow chart for the SPEA2-MOPSO-based multi-objective planning algorithm
N
Modelling and Allocation Planning of Inverters of Open UPQC to Improve the Rooftop PV Hosting Capacity…
The minimization of second fitness function results in the energy loss of network with PV in a day with respect to the energy loss of the base-case network in a day. These objectives are optimized under the constraints shown in Eqs. (2.88-2.89), (2.90), (2.91), (2.93), and (4.15).
4.3.3.4 FBSLF subroutine incorporating the PV generation and inverters models In this approach, the FBSLF algorithm is also used incorporating the PV generation and inverters models to determine the network operational parameters, such as, bus voltage, line current flow [74] etc. The algorithmic steps of FBSLF are given in subsection 2.3.1.
The incorporation of PV generation model at any bus modifies the active power demand of that bus, as shown in Eq. (4.8). However, the incorporation of series and shunt inverters models modifies the reactive power demand of corresponding buses, as shown in Eqs. (4.9- 4.10). The amount of hourly average PV generation at bus ‘𝑖’ during the PV operational hours is computed by using Eq. (4.18),
𝐶𝑈𝐹 =𝑃24𝑃𝑃𝑉𝐴𝑣𝑔(𝑖)𝑡4
𝑃𝑉(𝑖) (4.18)
where, 𝐶𝑈𝐹 is the capacity utilization factor of PV; 𝑡4 is the operation hours of PV;
𝑃𝑃𝑉𝐴𝑣𝑔(𝑖) and 𝑃𝑃𝑉(𝑖) are the hourly average PV generation and the maximum PV generation capacity at bus ‘𝑖’, respectively. The CUF is defined as the ratio of actual PV energy generation to the total PV energy generation capacity over a year. It is used to determine the hourly average PV generation {𝑃𝑃𝑉𝐴𝑣𝑔(𝑖)} which is to be used to compute the energy loss.