A HEURISTIC MODEL FOR PLANNING OF SINGLE WIRE EARTH RETURN POWER DISTRIBUTION SYSTEMS Geofrey Bakkabulindi1*, Mohammad R. Hesamzadeh2, Mikael Amelin2, Izael P. Da Silva1, Eriabu Lugujjo1 1Makererere University P. O. Box 7062, Kampala, Uganda. 2Royal Institute of Technology Teknikringen 33, Stockholm, Sweden. 1*Email: gbakkabulindi@tech.mak.ac.ug ABSTRACT The planning of distribution networks with earth return is highly dependent on the ground’s electrical properties. This study incorporates a load flow algorithm for Single Wire Earth Return (SWER) networks into the planning of such systems. The earth’s variable conductive properties are modelled into the load flow algorithm and the model considers load growth over different time periods. It includes optimal conductor selection for the SWER system and can also be used to forecast when an initially selected conductor will need to be upgraded. The planning procedure is based on indices derived through an iterative heuristic process that aims to minimise losses and investment costs subject to load flow constraints. A case study in Uganda was used to test the model’s practical application. KEY WORDS Power distribution planning, Power flow analysis, Single Wire Earth Return, Rural electrification 1. Introduction Since the pioneering work on Single Wire Earth Return (SWER) by Lloyd Mandeno in 1925 [1], the technology has proven to be very cost effective in electrifying scattered rural areas. Countries like New Zealand, Australia, Brazil and South Africa, among others, have several thousand kilometres of SWER lines installed with several lines having been in operation for well over 25 years [2]. However, many developing countries especially in sub-Saharan Africa have yet to mainstream SWER into their distribution networks despite prevailing low electrification rates. The major challenges facing these countries are lack of awareness, insufficient capacity for the required technical analysis and implementation as well as inadequate framework within which to design and plan these low-cost networks [3]. Considerable research has been done on SWER systems [1 - 3, 5, 9 -12] as well as power distribution system planning [4, 14, 15]. However, the planning of SWER distribution systems based on earth return load flow constraints has not been widely covered. The general objective of the distribution planning is to minimise the capital investment and operation costs of distribution substations and feeders to create a network that meets the projected load growth reliably and securely. This is achieved only if the constraints associated with equipment capacities, voltage limits, technical losses, and radial configuration are met [4]. SWER distribution systems use the earth as current return path. As such, the planning of these networks largely depends on an area’s ground conductive properties which are, in turn, a function of soil type and humidity [5]. By using a heuristic approach, this paper presents a simple iterative procedure for planning SWER distribution systems. A dynamic planning model is used to consider the impact of load growth over several time periods on system performance. By using a load flow algorithm for earth return networks, optimal conductor selection is carried out for the initial case and the algorithm presents the possibility to determine when the initial conductor will need upgrade. The aim was to minimise the costs of distribution losses, initial installation costs for feeders and subsequent upgrades subject to load flow constraints. The model is applied to a case study in Uganda to test its performance. All mathematical model formulations were done using the General Algebraic Modelling System (GAMS). 2. System Model Formulation 2.1 SWER Distribution Line Model The SWER distribution line model was based on Carson’s line [6]. This model considers a single conductor parallel to the earth with unit length and carrying a current with return path through the ground. The earth return is considered to be a single conductor beneath the earth’s surface with 1 m geometric mean radius (GMR), uniform resistivity and infinite length [5, 6]. The geometric mean distance (GMD) between the overhead conductor and the earth return path is a function of the soil resistivity, ρ [5, 7]. The total impedance, Zaa, of the overhead line as a result of the earth presence was derived in [5] and is given by (1). The ground self impedance, zgg, and the mutual impedance, zag, between the earth return and the phase conductor are given by (2) and (3) [5, 7]. agggaaaa z2zzZ −+=                   (1)  ) 105.6198 2ln(f10j4π f108πj0.0386f10πz 3 4 442 gg − − − ⋅⋅⋅⋅ +⋅⋅−×=     (2)  f/ hln102jz a4ag ρπ ⋅⋅= −        (3) Where f is the network frequency, ha is the height of the overhead line in meters and the units of (1) to (3) are Ω/km. The self impedance of the overhead line was calculated using the Simplified Carson Method given by (4) [5, 8]. The details of the full development of the Carson line model are not included here for brevity but can be found in [5, 6, 8]. ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛⋅×+= − a a4 aaa GMR h2lnf104jrz π Ω/km (4) Where, ra is the resistance of the phase conductor a (Ω/km) and GMRa is the geometric mean radius of conductor a (m). The impedances of the sending and receiving earth connections were considered to be negligible compared to the conductor and ground values. SWER lines are characterised by long span lengths since they supply scattered rural loads spread over large distances. As a result, line charging currents due to the Ferranti effect are quite pronounced in these systems compared to conventional distribution lines [9]. The voltage rise with distance results into voltage regulation problems at distant consumer load points [10]. The line shunt admittance, Y, normally neglected in conventional distribution lines was included in the line model to reflect the above phenomenon. The overhead line shunt capacitance, C, was computed using (5) [8]. Equation (5) was used to compute the capacitive reactance from which the shunt admittance was then derived. ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛= a a o GMR h2ln 2C πε (5) 2.2 Load Model All loads were modelled as constant power loads. It was assumed that the loads were proportional to the sizes of the distribution transformers with a power factor of 0.8 lagging. As such, changes in power factor due to transformer inductances as well as losses due to the distribution transformers were considered as part of the load while ignoring voltage drops beyond the transformers to customer points [11]. 3. Load Flow Algorithm Although SWER lines can be connected directly to the rest of the three-phase distribution grid, an isolation transformer is often used to electrically isolate them from their energising feeders. This allows earth leakage protection to be used on the rest of the network and ensures that the energising feeders do not carry zero sequence currents [12]. In this study, an infinite bus was added at the isolating transformer output terminals to form the slack bus [11]. The isolation transformer itself was not included in the model. The load flow algorithm was based on the forward/backward sweep method whose steps are as explained below [13]. In the first step all nodal current injections due to loads, capacitor banks, if any, and shunt elements are calculated based on initial voltages. In subsequent iterations, updated voltages are used to calculate the nodal currents. For the single wire earth return case, the calculation of nodal currents is given by (6) [5]. )1k( ig iaia )k( ia )1k( iaia )k( ig ia V V 0 Y I )V/S( I I −− ⎥⎦ ⎤⎢⎣ ⎡ ⎥⎦ ⎤⎢⎣ ⎡− ⎥⎥⎦ ⎤ ⎢⎢⎣ ⎡ − ∗=⎥⎦ ⎤⎢⎣ ⎡ (6) Where, Iia and Iig are the current injections at node i for the overhead line and earth return respectively, Sia is the specified complex power load at node i, Via and Vig are the complex voltages at node i for the overhead conductor and earth return respectively, Yia is the shunt admittance of the overhead line at node I, and k refers to the iteration index. The second step is the backward sweep which calculates branch currents starting from the end nodes of the radial distribution network (RDN) backwards to the source node following Kirchoff’s Current Law (KCL) [13]. The current, J, flowing through branch l is calculated according to (7) [5]. ∑ ⎥⎦ ⎤⎢⎣ ⎡+ ⎥⎥⎦ ⎤ ⎢⎢⎣ ⎡−=⎥⎦ ⎤⎢⎣ ⎡ ∈Mm k mg ma k jg ja )k( lg la J J I I J J (7) Where, j is the end node of branch l and M is the set of all branches connected downstream from node j. A branch- to-node matrix was used to keep track of all the branches and nodes connected downstream from any branch. In the third step, the forward sweep, bus voltages are updated using the current values obtained from the backward sweep starting at the root node towards the end nodes [13]. Nodal voltage calculations in the forward sweep were calculated using (8) [5]. k lg la ggag agaa k ig ia )k( jg ja J J ZZ ZZ V V V V ⎥⎦ ⎤⎢⎣ ⎡ ⎥⎥⎦ ⎤ ⎢⎢⎣ ⎡−⎥⎦ ⎤⎢⎣ ⎡= ⎥⎥⎦ ⎤ ⎢⎢⎣ ⎡ (8) Where, i and j are the incoming and outgoing nodes of branch l respectively. The impedances are calculated as in (1) to (4). The above method was formulated as an optimisation algorithm in GAMS to obtain a solution to the network load flow following convergence. The objective of the optimisation was to minimise the difference between the specified and calculated load power injections at each bus [5] subject to the constraints given in (6) to (8). The objective function formulations to be minimised for the earth return load flow solution are given in (9) and (10). ia 2k ia * ia k ia k ia k ia SVY*)I(VS −−=Δ (9) *)I(VS kig k ig k ig =Δ (10) All parameters and variables in (6) to (10) are complex. 4. Methodology A forward planning approach was used in the planning model. Using an iterative process shown in figure 1, the load flow algorithm developed above was used to test different system scenarios. Performance indices were formulated to test the suitability of each scenario starting from a base case and multiple simulations of the load flow algorithm were used to test each case. The performance of different feeders was measured against load growth for different time periods, t, up to the horizon year of the planning period, tmax. This was in turn used to determine the need for upgrade on existing feeders and the time period during which this would be required, if at all. The annual load growth was calculated using (11) [14]. t ot )g1(SS +×= (11) Where St is the load after time t in years, So is the initial load in the base year, g is the percentage annual load growth rate and t is the number of years. The planning algorithm was intended to identify the branches exhibiting weak points in the network given load growth. The performance indices were based on voltage profile, feeder losses, conductor utilisation and cost. The different indices were combined using an overall index which reflected the proportional contribution of each index to the general system performance. The above approach is summarised in figure 1. The proposed procedure was based on the assumption that only the peak load was considered for the successive time periods. Furthermore, it was assumed that the feeder route and different conductor options were known in advance and their costs of installation estimated. 4.1 Voltage index An index for the voltage profile was developed to monitor the node voltage deviations for different conductor options given increasing load. This index, given by (12), was formulated as the difference between the actual bus voltage magnitude and the nominal voltage, Vo (1 p.u), in a given time period using conductor c [15]. %100 tn VV I max n 1i t 1t oc,t,i c,volt max ×⋅ ∑ ∑ − = = = (12) Where Ivolt,c is the voltage index for conductor c, Vi,t,c is the actual voltage at bus i using conductor c, tmax is the total number of years in the planning period and n is the total number of buses on the network. Figure 1. Flow diagram of proposed methodology The allowable voltage limits for SWER distribution transformers are slightly different from those of ordinary distribution transformers and should be within the range 0.907 to 1.027 p.u [11]. The voltage index in (12) was only used for bus voltages within that range. It follows that the smaller the overall voltage deviation from the nominal 1 p.u, the better the system performance. Start  Read data on topology, conductors, load and earth return. Set k= 0, t=0. Run load flow for case scenario Indices within range? k=k+1 t=t+1 Calculate voltage profile index Calculate power loss index Calculate utilisation index Calculate overall performance index t