94 a network.
Considering these issues, a multi-objective planning problem is formulated. The optimization objectives are: (i) maximization of peak load shaving for radial distribution networks with the placement of PV-BESS-UPQC-O, (ii) minimization of cost of placement of PV-BESS-UPQC-O, and (iii) minimization of total power loss during peak load demand with the placement of PV-BESS-UPQC-O. These objectives are optimized subject to the active and reactive power balance constraints, bus voltage magnitude constraint, thermal constraint, and minimum reactive power compensation constraint. The PSO-based multi- objective planning algorithm is used to solve the problem. The Pareto-dominance principle [137] is used to find out a set of non-dominated solutions called Pareto-approximation set.
There are many variants of Pareto-based multi-objective evolutionary algorithms, out of which the SPEA2 [138] is an efficient approach and it is extensively used in solving various multi-objective optimization problems including the power system optimization problems.
The Pareto-based MOPSO is used in various applications for solving optimization problems, for example, distribution network planning [141], design of stand-alone micro- grid system considering wind, PV, and fuel cell [154-155], design of UPQC for energy loss minimization of distribution networks [73], design of controller for microgrid system [156]
etc. In this work, SPEA2-MOPSO is chosen as the solution tool to solve the proposed planning optimization problem. The contribution of this work is the development of multi- objective planning approach for the peak load shaving of radial distribution networks keeping a desired PQ level intact with the optimal allocation of PV-BESS-UPQC-O in distribution networks. The simulation study is performed using 33-bus and 69-bus radial distribution networks.
5.2 Modelling of PV-BESS-UPQC-O for peak load shaving of distribution networks
Multi-Objective Planning for the Allocation of PV-BESS Integrated Open UPQC for Peak Load Shaving…..
voltage sag mitigation. However, the shunt inverter is mathematically modelled using Eqs.
(2.63)-(2.71) to provide active power, reactive power, and harmonic compensations. These inverters share a common communication link to decide the respective set points as shown with the dotted lines. The respective VAr set points are decided using Eqs. (2.1) and (2.2).
The BESSs connected to the series and shunt inverters are used to maintain the dc-link voltage constant and to provide the active power to the network, respectively. Each BESS is charged with a PV system as shown in Fig. 5.1. These all constitute PV-BESS-UPQC-O system. The phasor diagrams for the series and shunt inverters are shown in Figs. 2.4(a) and 2.5, respectively. The determination of the rating requirements of PV and BESS to be connected to the series and shunt inverters of PV-BESS-UPQC-O is explained in the subsequent section.
5.2.1 PV and BESS rating requirements
The rating of BESS is computed considering the maximum depth of discharge of BESS (%𝐷𝑂𝐷𝑚𝑎𝑥). The depth of discharge (DOD) of BESS at any instant of time is complement of the state of charge (SOC) of BESS. SOC provides the information of present available BESS capacity at any instant of time in terms of percentage of total/actual BESS capacity [157]. The PV generation in a day is usually interminent in nature. Thus, in this work, the PV rating requirement for charging the BESS is computed considering the CUF of PV system. CUF is defined as the actual output of PV to the maximum/peak output of PV in a day/year. Since the BESS connected to the series inverter is to supply the compensating energy required in sag mitigation and inverter losses, its rating depends upon
Fig. 5.1: Schematic diagram for the placement of PV-BESS-UPQC-O in a 5-bus radial distribution network (dotted line represents communication link)
96
the amount of voltage sag to be mitigated and the inverter loss to be compensated. The amount of energy required for this is computed as:
𝐸𝑆𝑒 = (𝑘𝑡𝑆𝑎𝑔∑𝑖𝜖[2,..,N]𝑃(𝑖)
3600 + 𝐼𝑁𝑉𝐿𝑃𝑒𝑎𝑘𝑆𝑒 𝑡1) (5.1)
where, 𝐼𝑁𝑉𝐿𝑆𝑒𝑃𝑒𝑎𝑘 = 𝛾𝑙𝑜𝑠𝑠𝑆𝑆𝑒 (5.2)
The first part of Eq. (5.1) shows the amount of energy required to mitigate the 𝑘 amount of voltage sag for maximum duration of 𝑡𝑆𝑎𝑔. However, second part shows the amount of energy required to compensate the inverter losses during peak demand hours. The actual rating of BESS connected to the series inverter is computed as:
𝑃𝐵𝑆𝑒 = 𝐸𝑆𝑒( 100
%𝐷𝑂𝐷𝑚𝑎𝑥) (5.3)
The PV rating requirement for the charging of BESS connected to the series inverter is computed as:
𝑃𝑃𝑉𝑆𝑒 = ( 𝐸𝑆𝑒
24𝐶𝑈𝐹) (5.4)
where, 𝐸𝑆𝑒 is the actual energy required for the charging of BESS connected to the series inverter.
The rating of BESS connected to the shunt inverter is determined based on the amount of active power to be supplied during peak hours and the inverter loss to be compensated. The total amount of energy required by the shunt inverter for this is computed as:
𝐸𝑆ℎ = (𝑃𝑆ℎ𝑡1
ɳ𝐼𝑁𝑉) (5.5)
where, the numerator shows the active power to be supplied through the shunt inverter during peak load demand hours and denominator shows the efficiency of shunt inverter.
The actual rating of BESS to be connected to the shunt inverter is computed as:
𝑃𝐵𝑆ℎ = 𝐸𝑆ℎ( 100
%𝐷𝑂𝐷𝑚𝑎𝑥) (5.6)
The PV rating requirement for the charging of BESS connected to the shunt inverter is computed as:
𝑃𝑃𝑉𝑆ℎ = ( 𝐸𝑆ℎ
24𝐶𝑈𝐹) (5.7)
Multi-Objective Planning for the Allocation of PV-BESS Integrated Open UPQC for Peak Load Shaving…..
where, 𝐸𝑆ℎ is the actual energy required for the charging of BESS connected to the shunt inverter.
The total BESS and PV rating requirements of PV-BESS-UPQC-O are computed as:
𝑃𝐵𝑇𝑜𝑡 = 𝑃𝐵𝑆𝑒+ 𝑃𝐵𝑆ℎ (5.8)
𝑃𝑃𝑉𝑇𝑜𝑡 = 𝑃𝑃𝑉𝑆𝑒+ 𝑃𝑃𝑉𝑆ℎ (5.9)
5.2.2 Assumptions/consideration
The following assumptions are considered in this planning:
The distribution networks are assumed to be balanced and radial.
It is assumed that the operational hours of PV and peak demand hours do not coincide to each other. This is true for the network with domestic loads, in which the peak demand usually occurs during evening time.
BESS is to be fully charged during operational hours of PV so that it can be discharged during peak hours.
BESS is to be charged and discharged only once in a day.
The series inverter location is fixed at bus 2 so as to protect all the downstream loads from the voltage sag.