Network impact of increasing distributed PV hosting: A utility-scale case study

Depósito de Investigación de la Universidad de Sevilla https://idus.us.es This is an Accepted Manuscript of an article published by Elsevier in Solar Energy, Vol. 217, on March 2021, available at: https://doi.org/10.1016/j.solener.2021.01.066 Copyright 2021 Elsevier. En idUS Licencia Creative Commons CC BY-NC-ND Network impact of increasing distributed PV hosting: 1 a utility-scale case study 2 3 Gabriel Tévar-Bartolomé1, Antonio Gómez-Expósito2,*, Angel Arcos-Vargas2 and Manuel Rodríguez-Montañés1. 4 5 (2) University of Seville 6 (1) Endesa 7 8 9 (*) Corresponding author. [email protected] 10 11 Abstract 12 13 14 This paper presents a methodology to assess the cost of upgrading the LV network so that it can host increasing levels of 15 PV distributed generation. The cost is valued in terms of investment, operation and maintenance and losses. A real scale 16 case study (80,000 customers from urban and rural areas, 460 GWh of demand and 3,600 km of MV&LV lines/cables) is 17 thoroughly analysed, using the actual network topology along with the hourly demand of each supply point, provided by 18 smart meters. With the help of a planning-oriented load flow solver, technical violations (congestions and overvoltages) 19 are quantified and classified for different PV penetration scenarios. Then, a heuristic procedure is implemented aimed at 20 identifying the most cost-effective investment solution that sequentially eliminates the previously ranked excessive 21 congestions, assuming that mild congestions and other operational problems, can be addressed without extra investments, 22 either through network switching practices or through the implementation of local flexibility markets. Specifically, it has 23 been found that the direct costs (investment and O&M) arising from the massive deployment of PV generation amount to 24 2.73 €/kWp and 10.18 €/kWp for scenarios with 30% and 50% PV penetration levels, respectively. No additional 25 investments needed in digitization, monitoring, automation and systems have been considered. 26 27 Keywords: 28 Distributed energy; PV; grid congestion; overvoltage; investment, grid losses. 29 Highligths: 30 31  A methodology to evaluate network congestions & overvoltages due to massive distributed PV penetration is 32 developed. 33  The method is applied to a utility-scale planning case study, comprising 80,000 supply points. 34  The cost of removing the congestions originated by increasing levels of rooftop PV is evaluated. 35  For PV penetration levels not exceeding 33% of the annual demand, the induced cost is negligible. 36  Some recommendations have been proposed to help policy makers in future PV developments. 37 38 39 1. Introduction 40 41 One of the most important energy and environmental objectives of the European Union [1,2] is to achieve greater 42 penetration of distributed electric generation, especially with photovoltaic (PV) technology. Some countries like Germany 43 have significantly promoted this kind of thecnologies by implementing feed-in-tariff policies [3]. Other important 44 objetives are the promotion of electric mobility, increased energy efficiency and a greater participation of consumers in 45 demand response. All these levers will boost the objective of decarbonizing the economy and thus reducing CO2 emission 46 levels. Although large PV power plants are more efficient, due to the existence of significant economies of scale, other 47 2 factors are driving individuals to install small PV facilities on their rooftops [4]. Indeed, a large-scale rooftop PV system, 48 integrated along with a conventional (hydrothermal) generation system can achieve great energy-cost savings [5]. In turn, 49 this trend is reducing the costs of distributed PV significantly [6]. 50 51 In this context, the role of distribution networks is of paramount importance in facilitating the integration of these new 52 distributed resources, while at the same time ensuring that current quality and continuity of supply indices are kept intact 53 [7]. 54 55 This new scenario completely changes and complicates the way distribution networks are operated, since they turn from 56 "distribution" to "contribution" networks. As analysed by Haque and Wolfs in [8], Barker and De Mello in [9] and Karimi 57 et al. in [10], dispersed PV generation gives rise to voltage fluctuations, imbalances, harmonics, reverse power flows, 58 obsolescence of the protection systems etc. Moreover, beyond certain PV penetration levels, it may lead to increasing 59 losses, congestion of network elements and overvoltage at different supply points. 60 61 In a previous work (Tévar et al. [11]), the authors have evaluated on a case study the impact of different rooftop PV 62 penetration levels on network losses and congestions (ampacity and overvoltages). This was performed under the “constant 63 network” hypothesis which, being useful to draw certain conclusions (e.g. how network losses evolve with increasing PV 64 power), does not seem to be acceptable if very high penetration levels are considered. Indeed, when the amount of rooftop 65 PV exceeds a certain threshold, the underlying distribution system has to be upgraded to a larger or lesser extent. 66 67 The primary objective of this paper is to evaluate the impact that increasing levels of distributed PV generation have on 68 the distribution system, when it is reinforced to eliminate excessive technical constraints violations. The assessment 69 includes the evolution of losses with respect to the base case scenario (no PV) as well as the investment and operation and 70 maintenance costs (O&M) associated with the involved network upgrading, aimed at maintaining the current level of 71 service quality. The scope of this paper considers a long-term network planning perspective, assuming that the DSO can 72 resort to suitable operational tools in order to enforce customary network constraints. Therefore, the issues related to short- 73 term network operation and individual asset assessment are beyond the scope of this paper. A real and sufficiently 74 representative distribution network, incorporating actual consumption and PV generation data, is used as case study, thus 75 complementing the previous work [11]. In this work, the existing Spanish regulation has been taken as a reference [12, 76 13]. 77 78 Several works have previously addressed this issue. In addition to the aforementioned studies [8, 9, 10], analysing the 79 most significant effects on voltage fluctuations, imbalances, reverse power flows, etc., other related works reviewed in the 80 sequel deal with the following topics: 81 (a) Simplified high-voltage (HV) or medium-voltage (MV) models: works that resort to HV-MV case studies, 82 with simplified demand models, to assess the impact on losses and other factors [14, 15, 16, 17]. 83 (b) Assessment of losses for different PV penetration levels, by using different network case studies [18, 19, 20, 84 21]. 85 (c) Analysis of the impact of PV penetration on real LV networks [22, 23, 24, 25, 26, 27, 28]. 86 (d) Research on the impact of PV penetration on the operation of the network [29, 30, 31, 32, 33]. 87 (e) Analysis of voltage and congestion violations for different PV scenarios [34, 35]. 88 (f) Assessment of the investment needs related to the increase in PV generation [36, 37, 38, 39, 40, 41]. 89 90 (a) Simplified HV and MV models, such as those of Quezada et al. [14], Bastiao et al. [15] and Wang and Lan [16], study 91 the impact on losses caused by the penetration of different renewable generation technologies, using mainly case studies 92 with simplified demand models. Those works already anticipate the importance of the specific location of PV facilities, 93 as far as the resulting losses and the amount of energy that can be integrated are concerned. A broader view is provided 94 by Bastiao et al. [15], who examine how distributed PV generation can affect the stability of the grid, the voltage variations, 95 the useful life of transformers and the protection system, among other topics. Morvaj et al. [17] use a simplified demand 96 model with three residential buildings and two single-family dwellings to verify how, through both demand management 97 and storage (hot water storage), greater levels of PV can be integrated into the grid, without the need for additional 98 investment. 99 100 (b) Regarding the influence of PV in network operation, the works by Borges and Falcäo [18] and Osorio et al. [19] can 101 be highlighted. They use different network and demand models to verify that losses can be reduced if generation facilities 102 are installed in some locations for certain penetration levels. Mandis et al. [20] analyse the potential for improving 103 3 reliability and reducing voltage drops, proposing an algorithm that identifies the connection points and power that optimize 104 the overall system. Yang et al. [21] develop a stochastic power flow study, using the standard IEEE 39 bus testing system 105 and trhee case studies (8, 16 and 24 % PV penetration), to conclude, among other things, that high penetration of renewable 106 energy sources has a negative effect on ampacities and overvoltages, and also for system power losses if generation is far 107 from load centers. 108 109 (c) A different set of studies analyse the impact of renewable generation on the low voltage network, using real demand 110 and network information. In this respect, it is relevant to highlight the contribution of Chiandone et al. [22] that verifies 111 the positive impact of PV generation on losses, at least for low penetration levels, achieving up to 20% reduction in losses 112 when the location of the generation is optimized. Other works that use actual LV networks across extensive distribution 113 areas are those by Cohen and Callaway [23, 24], Westacott and Candelise [25], Eguía et al. [26] and García-Villalobos 114 et al. [27, 28]. Some of those works use very detailed generation profiles, allowing for instance to assess the effect of 115 passing clouds [24] or voltage fluctuations. Using a more detailed demand model (hourly curves for eight typical days of 116 the year), Eguía et al. [26] and García-Villalobos et al. [27, 28] estimate losses by performing a full-scale analysis for a 117 real LV network, extrapolating the results to the rest of the market. The conclusions reinforce the previous findings, namely 118 that losses decrease for low concentrations of PV generation, but then increase significantly for higher levels, especially 119 if PV production is concentrated. 120 121 (d) Concerning the influence of PV generation on network operation, several works focus on the possible dynamic or 122 operational effects that intermittent PV distributed generation can cause on the network, including losses, as already 123 discussed for previous works. For example, Nguyen et al. [29] use a very detailed generation model with solar radiation 124 data obtained every 30 s by means of a sky imaging system, which enables them to simulate the passage of clouds over 125 areas with real networks of a certain size. In a nutshell, they conclude that a uniform generation model for an entire area 126 tends to overestimate the amount of losses. Ebad and Grady [30] model generation ramps that are comparable to clouds 127 passing across broad areas, with production voltage drops of up to 70% in less than 10 s. They conclude that large 128 centralised PV plants can produce greater network voltage instability. From a different perspective, Rodríguez-Calvo et al. 129 [31], by performing load flows by phases and considering different connection scenarios for PV generation, conclude that 130 LV network losses for an unbalanced system can be from 2.5 to 3.8 times higher than losses in a balanced system. Kreuwel 131 et al. [32] use different direct measurements of high frequency fluctuations of the PV power to demonstrate that, in short 132 time intervals (some seconds), short-term peaks or ramps of PV power can occur much higher than those traditionally 133 calculated in long-term planning scenarios (hours on days of maximum radiation with clear skies), exceeding voltage 134 limits in short intervals of time and threatening the stability of the network. Gastalver-Rubio et al. [33] show how using 135 the capability of today’s PV inverters to individually inject active and reactive power in each phase, network operators 136 could reduce to a large extent some of the operational problems mentioned above, such as phase unbalances. 137 138 (e) Regarding the analysis of voltage and ampacity constraints violation, in addition to the authors' previous work [11], 139 other relatively recent works explore the capacity of the existing network to accommodate different levels of distributed 140 generation penetration. Bottacciolia et al. [34] use a PV generator simulator that incorporates digitized information of land 141 surfaces, orientations and shadows from an urban area of Milan, which is integrated into a real-time network simulator to 142 analyse voltage changes that would arise on different days of the year with different levels of PV penetration. One of their 143 main conclusions is that the current grid may not be prepared to incorporate all the PV generation that could potentially 144 be installed, as this could lead to operational constraints violations. Mateo et al. [35] evaluate the overvoltages and 145 congestion violations that take place in MV and LV networks for different PV penetration scenarios, but they do not 146 evaluate possible solutions for those violations. To simulate the network behaviour they use a Reference Network Model 147 (RNM), capable of building from scratch idealized or theoretical MV and LV networks that serve real distribution areas, 148 and use hourly consumption curves to calculate load flows for the day of the year with the highest solar radiation. Similar 149 works, such as the one by EPRI [45] and Wang and Tisdale [46], develop methodologies to identify network locations 150 where the connection of a certain capacity of PV generation could be integrated without leading to voltage violations or 151 congestions. 152 153 (f) The last category of studies deals with investment evaluation models, derived from the potential network 154 reinforcements that make PV penetration possible. Xiang and others [36] raise the need to modify the current planning 155 criteria, both static and dynamic, in order to accommodate this new type of generation, including tools such as demand 156 management. Pudjianto et al. [37] parameterize the PV generation effect through 15 more sophisticated theoretical models, 157 quantifying the network improvements needed to assume different penetration levels. In the case of Spain, they estimate 158 a reinforcement cost of 0.28 €/MWh generated for 2% penetration, which raises to 1.04 €/MWh for 4% penetration. 159 4 Schmalensee et al. [38] use a RNM to design various prototype theoretical networks where different predetermined PV 160 penetration scenarios are considered. Through a brownfield network model they obtain the costs and losses of future 161 upgradings required to accommodate the new dispersed generation. They found that, for 20% PV generation with respect 162 to the annual demand, the total distribution cost increase could vary between USD 10 and USD 30 per installed kWp of 163 PV capacity, depending on the network type. This cost is exclusive of losses, but does include investment and operation 164 costs for LV networks, including substations. 165 166 Other works use real distribution networks or areas to quantify the impact on network investments owing to the presence 167 of distributed PV generation. From a different perspective, Cohen et al. [39] estimate the network investment savings that 168 can be achieved by implementing different levels of PV penetration for a real size feeder in California. The evaluation 169 method for investment savings is based on a previous quotation provided by the company to forecast future demand, and 170 the evaluation of investment delay due to the adjustment of peak demand as PV penetration grows. The evaluation is 171 performed just up to the PV generation that matches the peak demand for each feeder. Therefore, as reverse power flows 172 seldom happen, the expected impact on network investments is negligible. 173 174 Gomes and Saraiva [40] propose a methodology that, using a Transmission Expansion Planning (TEP) model on an IEEE 175 study network, and assuming four PV penetration scenarios (0%, 10%, 15% and 20% PV), search for optimal constructive 176 solutions by means of an Evolutionary Particle Swarm Optimisation (EPSO) model. By only evaluating the impact on the 177 transmission network, the work confirms that there is virtually no impact at these voltage levels, for the PV penetration 178 considered. To conclude this review, Freitas et al. [41] perform power balances at the MV/LV transformer level for an 179 urban area of Lisbon to quantify the number of transformers that may need upgrading under different scenarios. Essentially 180 two scenarios are considered: a base case in which all available rooftop surfaces, according to cartographic data and 181 considering shadows, are covered with PV panels, and a second case in which well-oriented facade surfaces are also 182 included. The conclusion, albeit not quantified, is that the capacity of current secondary substations may not be sufficient 183 in case all the PV potential for the urban area is materialized. 184 185 This paper completes the previous ones, by providing a more realistic and comprehensive quantitative assessment of the 186 impact that the different degrees of distributed PV penetration would have on the LV distribution network. Instead of 187 using theoretical models, the assessment is performed with an actual distribution network that supplies over 80,000 188 consumers, each located according to its actual geographic coordinates. Smart meters and solar irradiation data are used 189 to carry out an energy balance (consumption minus generation) for each LV consumer over the 8,760 hours of the year. 190 Then, the impact of the PV generation is quantified in detail, in terms of technical losses variations, network upgrading 191 and expansion investments and the associated O&M costs. For this purpose, beyond the methodology presented in [11], a 192 heuristic procedure has been developed to sort out the alternative upgrading solutions which can solve the unacceptable 193 violations detected for each PV penetration scenario. In order to assess and rank the severity of technical constraints 194 violations, a RNM has been adopted [42], mimicking the one used by the Spanish Regulator (CNMC). In fact, as the 195 results have been obtained with a large enough representative network, using actual hourly demand and PV, the main 196 conclusions reached in this study should be of interest also for policy makers. 197 198 The rest of this paper is organized as follows: section 2 describes the notation, methodology and main procedures 199 underpinning this study, as well as the hypotheses adopted to construct different scenarios for the grid, PV generation and 200 demand. Section 3 outlines the data corresponding to the case study, while section 4 presents the main results obtained, 201 including the impact on the network in terms of variation of technical losses, investment needs and O&M costs. Finally, 202 a summary of the main findings is provided in section 5, followed by the most important conclusions and possible 203 regulatory recommendations. 204 2. Methodology and Hypotheses 205 206 This work further elaborates on the methodology developed in [11], intended to evaluate the losses and congestions for 207 increasing degrees of rooftop PV penetration on an hourly basis. More specifically, for all the scenarios considered, a 208 heuristic, RNM-based procedure is proposed to determine cost-effective reinforcement measures, to be implemented on 209 the base-case network so that major overvoltages and congestions are eliminated. Then, a cost assessment of the necessary 210 investments and resulting losses is performed. 211 212 5 Starting from the baseline (0% PV) case, the methodology adopted in this work sequentially applies the following five 213 steps for each scenario of increasing PV penetration (the first two steps embed the methodology presented in [11]) 214 215 (1) Determination of hourly energy balances for each point of supply: 216 217 The hourly energy balances are determined at each point of supply, including the electricity generated, the self- 218 consumed energy, the energy taken from the network and the excess energy injected into the network. By properly 219 aggregating the individual hourly balances, the energy delivered to the LV circuits by each MV/LV secondary 220 substation, or injected to the MV subsystem in case of excessive LV generation, is obtained, and hence the energy 221 flows through each MV feeder section. The customers connected to LV grids who decide to deploy a rooftop PV 222 installation for self-consumption are randomly selected from among those located in the zone of interest. 223 224 225 (2) Load flow solution at the feeder and hourly level to individually identify technical constraints violations (overvoltages 226 and/or congestions): 227 228 Using the ANETO RNM tool [42], a load flow is run for each of the 8,760 hours of the year, assuming that all LV 229 loads are three-phase balanced supplies. Then, all supply points facing overvoltages above regulatory limits (>7%) 230 and all congested feeder sections (loading >100%) are identified. Yang et al. [21] propose a set of indices to quantify 231 the system performance including active and reactive power losses, voltage deviation and line loading indices. 232 However, as our work prioritizes network reinforcing investments intended to solve severe violations (assuming mild 233 or moderate violations have been addressed through operational actions), we have adopted the severity metrics 234 developed in [11], comprising the Length-cumulated Section Saturation Index (LSSI) and the Energy-cumulated 235 Voltage Violation Index (EVVI, defined for each LV feeder j, as follows: 236 237 238 239 Length-cumulated Section Saturation Index (LSSI): 240 241 𝐿𝑆𝑆𝐼𝑗= ∑ (𝐿𝑖,ℎ ∗ %𝜟𝑆𝑖,ℎ) 𝐻,𝑁𝑆 ℎ,=1,𝑖=1 , where (1) 242 243 o i, h: Feeder section and hour indices 244 o NS: Total number of feeder sections 245 o %𝜟𝑆𝑖,ℎ: Overload in % of section i recorded at hour h. 246 o 𝐻: Hours of the year when section i of the feeder j is overloaded 247 o 𝐿𝑖,ℎ: Length of the section i (in meters) where an overload exists at hour h. 248 249  Energy-cumulated Voltage Violation Index (EVVI): 250 251 𝐸𝑉𝑉𝐼𝑗= ∑ (𝐸𝑖,ℎ ∗ %𝜟𝑉𝑖,ℎ) 𝐻,𝑁𝑃 ℎ=1,𝑖=1 , where (2) 252 253 o i, h: Point of supply and hour indices 254 o NP: Total number of supply points fed by the feeder j 255 o %𝜟𝑉𝑖,ℎ: Overvoltage in % at point i recorded at hour h. 256 o 𝐻: Hours of the year when the voltage is above 7% (regulatory limit) at supply point i 257 o 𝐸𝑖,ℎ: Energy demanded by supply point i at time h in which an overvoltage takes place 258 259 260 where j denotes the respective LV feeder, h is the number of hours for which overvoltages/congestions are detected, 261 and H is the set of 8,760 hours (the indices are computed for a whole year). Next, the LV feeders are preliminarily 262 ranked according to their separate violation indices and classified as being subject to either excessive or moderate 263 violations. As in the previous work [11], the following thresholds are adopted: 264 265  Constraints violations are deemed as excessive if: 266 6 o 𝐸𝑉𝑉𝐼 ≥ 1 𝑀𝑊ℎ ∗ 10% or, (3) 267 o 𝐿𝑆𝑆𝐼 ≥ 100 𝑚 ∗ 100 ℎ ∗ 120% (4) 268 269  Constraints violations are deemed as moderate if 270 o 0 < 𝐸𝑉𝑉𝐼 < 1 𝑀𝑊ℎ ∗ 10% and (5) 271 o 0 < 𝐿𝑆𝑆𝐼 < 100 𝑚 ∗ 100 ℎ ∗ 120% (6) 272 273 274 275 (3) Characterization of the overall severity of technical constraints violations at the feeder level: 276 277 Assume there are two nearby LV feeders, j and k, for which excessive violations are detected. Each of them can face 278 the most severe violation at different hours of the year, or they can be subject to different degrees of violation severity 279 depending on whether the overvoltage or congestion index is considered. Furthermore, an upgrading solution initially 280 intended to solve the violations of circuit j, might also solve to a certain extent the violations of circuit k. For these 281 and other reasons, it is not obvious or straightforward to determine, based solely on the yearly feeder indices defined 282 by (1) and (2), which constraint violations (overvoltage or ampacity), or which hours of the year, should the analysis 283 be focused on, and consequently which upgrading choices are most effective. 284 285 Therefore, after trying and discarding other alternatives, a normalized severity index indicator, computed at the feeder 286 level and intended to guide the selection and assessment of upgrading alternatives, is introduced as follows: 287 288  Let F denote the set of all LV feeders (or circuits) under study, Fx the subset of feeders for which excessive 289 violations are detected according to the annual indices (LSSI, EVVI), and hm(j) the hour of the year at which 290 the LSSI indicator for feeder j reaches its maximum value. 291 292  Then the index EX j hm(j), representing the normalized (weighted) sum of ampacity and overvoltage violations 293 at hour hm(j), is defined for each LV circuit j as follows, where the normalization is based on the whole set 294 F of LV feeders. 295 296 EXj hm(j) =LSSIj hm(j) ∑LSSIi hm(i) i∈F +EVVIj hm(j) ∑EVVIi hm(i) i∈F (7) 297 298 The introduced severity index is computed also for the entire set of feeders F and the critical subset Fx: 299 300 301 EXF=∑EXj hm(j) j∈F (8) 302 303 EXFx =∑EXj hm(j) i∈Fx (9) 304 305 As long as EXFx > 0, a series of candidate reinforcement actions are considered, aimed at reducing EXF under the 306 condition that EXjhm(j) does not increase for any feeder in F. The candidate upgrading actions and the way the most 307 cost-effective action is chosen are explained in the following step. 308 309 (4) Assessment and selection of reinforcement actions required to correct excessive violations of technical constraints: 310 311 As findin g the truly optimal sequence of upgrading measures, capable of solving all technical constraints at minimum 312 cost, is a very hard combinatorial problem, a much simpler heuristic procedure is proposed that prioritizes and 313 sequentially solves all excessive violations arising in the studied area. For this purpose, the following additional 314 notation is introduced: 315 316  “Spotlighted feeder” (SF) is the feeder for which upgrading solutions to solve excessive violations are being 317 sought. The buses with unacceptable overvoltages, or those fed by congested sections of the SF are termed the 318 “involved nodes”. Note that all circuits initially included in the set Fx will eventually become “spotlighted 319 7 feeders”, unless their violations have vanished as a consequence of previously implemented reinforcement 320 actions. 321  Given a SF, a subset of “candidate feeders” (CF) is identified to be potentially involved in the solutions required 322 to solve the SF violations. This subset corresponds to all subsidiary LV circuits of the MV/LV secondary 323 substation from which the SF is fed, plus the LV circuits of the three closest secondary substations. 324 325 For each involved node the following upgrading/reinforcement alternatives are just considered: 326 327 1. Reinforcement of the upstream feeder section: this consists of upgrading the master section that feeds the 328 involved node, all the way from the secondary substation, by increasing the conductor ampacity. 329 2. Additional link (or interconnection) from neighbour feeders: a new section that connects the involved 330 node, and its downstream sections, to any other node belonging to the CF set is considered (to keep the 331 radiality of operation, it is assumed that the involved node is disconnected from its original master section). 332 All possible options are analysed and compared. 333 3. Splitting of the upstream feeder section: a new feeder, running from the MV/LV secondary substation in 334 parallel with the congested one, is added to take on just the load of the downstream buses (the original 335 section remains feeding only the involved node). 336 337 The cost of each alternative measure is evaluated based on reference unitary investment costs for each network asset 338 type. For this purpose, the reference unitary costs stablished by the Spanish regulator in [43] are adopted. Moreover, 339 for each candidate upgrading action, the benefit in terms of EXF reduction (EXF) is also obtained. This implies 340 recalculating the 8,760 load flows for the affected feeders (SF and eventually CF), by duly considering the network 341 model modifications involved in the reinforcement measures being analysed. Note also that, while handling the 342 constraints violations of the SF, only those actions that do not worsen the violation indicators of other LV circuits 343 are deemed acceptable. 344 345 Once the list of candidate actions is available, and the associated investment costs are computed, the one that offers 346 a greater reduction of the EXFx/cost ratio is chosen and implemented. Then, the 8,760 load flow solutions are run 347 again for the upgraded network, the parameters EXFx and EXF are recomputed and a new list of network adaptation 348 candidates is generated. This process is repeated until EXFx is zero or no suitable upgrading actions are found to 349 further reduce EXFx. 350 351 Finally, once the whole set of LV feeders is upgraded for each PV penetration scenario, it is checked whether any 352 MV/LV secondary substation remains serving a load that exceeds 120% of its rated power over more than 100 hours 353 per year. In that case, the secondary transformer is replaced by another one with the minimum power strictly needed 354 to eliminate the congestion, among those available in the standardised catalogues for that type of transformer. 355 356 (5) Economic assessment of the solution: 357 358 In order to assess the economic impact of the grid reinforcement solutions found in step (4), at least three cost 359 components should be considered: 1) the variation of losses with respect to the scenario without PV generation, 2) 360 the investment costs associated with the network upgrading actions required to maintain the current level of service 361 quality, and 3) the O&M costs related with them. A brief discussion on each of those three factors follows. 362 363  Economic assessment of losses: once all LV circuit violations are solved for each PV penetration scenario, the 364 solution of 8,760 load flows provides the hourly losses at the feeder level and, through accumulation, the resulting 365 annual losses. Also, multiplying hourly losses by the hourly price of the wholesale energy market, and adding for 366 all hours of the year, the cost of annual losses is obtained. The difference between the resulting losses and those 367 registered in the baseline scenario (0% PV), in both kWh and euros, yields the impact (positive or negative) on 368 the LV network losses for every PV penetration level. It is worth noting that the results shown below are different 369 from those obtained in [11], as the network has been adapted in this work to remove violations, whereas in [11] 370 the grid was always the same. 371 372  Economic assessment of investment costs needed to upgrade the network: as a result of the procedure described 373 in points (3) and (4) above, the reinforcements required to prevent excessive violations for increasing PV 374 8 penetration levels are determined. This may include new feeder sections, interconnections among neighbour 375 feeders or secondary substations. Therefore, a list is created of all physical units that have been added to the 376 network in the area (km of new LV lines, km of sections with upgraded conductor, kVA of more transformation 377 capacity). Applying the reference unitary investment costs provided by the Spanish regulator [43] to the resulting 378 physical units yields the associated investment in the whole area. 379 380  Evaluation of O&M costs: the Spanish regulation also provides reference unitary costs for operation and 381 maintenance of each type of network asset [43]. Applying these unitary costs to the physical units obtained in 382 points (3) and (4) yields the annual O&M costs associated to each PV scenario. The cost saving arising from the 383 LV network sections that have been removed and replaced with new ones is also taken into account. It is worth 384 noting the recurrent nature of those annual costs, until the end of the useful life of the installations. 385 386 In order to obtain the total cost, the three cost components have to be referred to the same time basis. While the 387 investment cost is incurred only once, for each increasing PV penetration, O&M costs and losses are recurrent and 388 repeat annually. Given that, from a regulatory point of view, the distribution activity considers a useful life of network 389 assets of 40 years, and assuming the hypothesis that the demand remains constant for all PV penetration scenarios, 390 the Total Cost (TC) is defined as: 391 392 TC%PV = I%PV + OM40%PV + L40%PV (10) 393 394 where: 395 396 I%PV: Investment to adapt the distribution network for an increase in the %PV level from the previous one. 397 398 OM40%PV: Present value of increased annual operation and maintenance costs for an increase in the %PV 399 level from the previous one, calculated for 40 years with an internal rate of return (IRR). 400 401 L40%PV: Present value of the increase in annual losses due to the increase in %PV level from the previous 402 one, calculated for 40 years with an internal rate of return (IRR). 403 404 Figure 1 provides a flow chart summarising the methodology outlined above. 405 15 Overall, taking on 50% of PV penetration requires upgrading and/or expanding 1.4% of the existing network in the area, 499 with an investment cost representing 1.5% of the replacement value (value as new) of the existing assets. Accommodating 500 90% PV generation, requires that 6.1% of the LV network be upgraded, with an investment cost of 9.3% of the value as 501 new. 502 503 The investment required to adapt the network implies also an increase of the network capacity and, consequently, a 504 reduction in technical losses. This can be seen in Figure 6, representing the total LV network losses (secondary substations 505 included) for increasing PV generation scenarios, both for the baseline network (i.e., assuming the violations seen in 506 previous sections), and for the gradually upgraded network. Losses are expressed in % over the total energy delivered. 507 Logically, the losses increase at slower rates with PV generation when the network is reinforced. For example, for a 508 scenario with 50% PV penetration, adapting the network to correct excessive violations reduces the losses from 4.86% to 509 4.57% (6% reduction of total losses), whereas for a scenario with 90% PV penetration the total reduction would be 10% 510 (from 6.62% to 5.93%). As a result, while approximately 30% of PV penetration was the threshold point at which losses 511 began to exceed those of the baseline scenario under the constant network hypothesis [11], when the network upgrading 512 is considered such a threshold shifts to slightly above 40% PV penetration. 513 514 515 Figure 7 separately shows the evolution of losses for LV circuits and MV/LV secondary substations. It can be noticed that 516 all components of losses grow at a slower rate when the grid is gradually adapted, except for the transformer core losses, 517 which are independent of the transformer charge but increase with its capacity. 518 Figure 6 Annual losses for increasing PV penetration scenarios in two cases: with and without grid upgrading 16 4.4. Impact of network upgrading in terms of overall network cost 519 520 As explained in section 2, all cost components (losses, investment and O&M costs) associated to every level of PV 521 penetration, and the resulting reinforced grid, can be translated into uniform units (euros) and then added up on the same 522 time basis (40 years of useful life for installations). Figure 8 shows the evolution of the three cost components versus the 523 PV penetration degree, when a 5.58% internal rate of return (IRR) for distribution assets 4 is considered in expression (6). 524 525 As clearly seen, the total direct costs are negative for small PV penetration levels, which means that rooftop PV has a 526 positive impact on the distribution network. The maximum profit for the network occurs at approximately 18% penetration 527 level, whereas the impact is neutral again for 33% of PV penetration. Beyond this point, direct costs grow nearly 528 quadratically with PV penetration, investment costs being the largest component followed by the costs of losses. The 529 O&M costs benefit from the fact that, while new installations are considered, the cost of dismantled assets is subtracted. 530 531 4 This value is proposed by the Spanish Regulator (CNMC, 2018). Figure 7 Annual losses split by main network components for increasing PV scenarios in two cases: with and without grid upgrading 17 532 533 534 It is worth stressing that this work has not considered other relevant issues and associated costs that could also grow as 535 the distributed PV generation flourishes. These include several operational problems, such as rapid voltage changes due 536 to passing clouds, phase imbalances, generation of harmonics and flickers, power flow reversals and the need to readjust 537 protection co-ordinations, premature ageing of certain network components, etc. In addition, unresolved moderate 538 violations will involve other measures not quantified in this paper, such as network control actions or the implementation 539 of local flexibility markets 5 [48, 49]. Altogether, in order to properly address all those issues, additional investments in 540 digitization, monitoring, automation and systems are needed. 541 542 Figure 9 shows the total direct costs (ignoring losses) per installed PV for each PV penetration scenario. Those values 543 range from approximately 0.50 €/kWp for 10-15% PV penetration degrees (15-20% in terms of PZeroD), to 10.18 €/kWp 544 for PV penetration levels as large as 50%. 545 546 547 548 549 550 551 552 553 554 555 556 557 558 5 Decentralized flexibility resources such are electric vehicle, storage devices, electrical heating and cooling, public lighting loads, etc. Figure 8 Total direct costs split by its components for increasing PV penetration scenarios 18 559 5. Summary of Findings 560 561 The methodology developed in this work, when applied to an actual case study comprising approximately 562 80,000 customers, each characterized by its hourly consumption curves throughout a year, including approximately 4,300 563 LV feeders (2,200 km), fed by 1,800 MV/LV secondary substations, has provided a bunch of results regarding the impact 564 of different rooftop PV generation scenarios on the LV distribution network, which can be summarised as follows: 565 566  Up to approximately 30% of PV penetration (45% in terms of PZeroD), no significant structural actions 567 (upgrading or expansion) are needed to maintain the ampacity violations and overvoltage levels on the LV 568 network within acceptable limits, which can be hopefully handled through operational control actions or by 569 deploying local flexibility markets. 570  Beyond 40-50% PV penetration, the cost of structural actions required to maintain the LV network saturation 571 and overvoltage levels within acceptable limits increases quadratically. For instance, to be able to reach 50% of 572 PV penetration requires an investment representing 1.5% of the value as new of the base case network. In order 573 to incorporate 90% of PV generation the required investment would be 9.3% of that value. 574  Investment in the upgrading and network expansion contributes also to reducing the technical losses with respect 575 to those that would arise in the base case network, for the same PV penetration. As a result, while approximately 576 30% of PV penetration was the point, under the constant network hypothesis [11], at which losses began to 577 exceed those of the baseline scenario, such threshold point lies beyond 40% PV penetration when the network 578 is gradually upgraded. 579  Regarding the impact in terms of total cost (investment, O&M and losses), it is concluded that, for low 580 penetration levels, PV generation produces a positive impact (profit) on the distribution network, which reaches 581 a maximum at approximately 18% PV penetration. Such positive impact vanishes (null total cost) at 582 approximately 33% PV penetration whereas, beyond that point, the additional distribution costs grow 583 quadratically with PV generation. This excludes other operational costs that could be incurred to address related 584 problems, such as rapid voltage fluctuations, imbalances, generation of harmonics, readjustment of protections 585 to safely accommodate reverse power flows, etc. 586  Neglecting losses, the total direct costs per installed PV power amounts to 2.73 €/kWp for scenarios with 30% 587 PV and 10.18 €/kWp for 50% PV penetration. 588  No additional investments needed in digitization, monitoring, automation and ICT systems have been valued, 589 nor the need to implement local flexibility markets or alternative control actions intended to solve the remaining 590 moderate violations. 591 Figure 9 Reinforcement and repowering plus O&M cost vs. PV installed 19 As pointed out in the introduction, it is worth stressing that those findings stem from a long-term planning perspective and 592 for a large-scale geographical area. Local or short-term effects, such as phase imbalances, cloud induced PV fluctuations 593 or spatial load concentrations, may have also detrimental effects, which could be solved through the implementation of 594 local flexibility markets, by network switching/operational actions, or even by resorting to the features provided by current 595 PV inverters. We implicitly assume that those solutions would not involve significant additional investments, provided 596 suitable regulatory measures are adopted. 597 598 6. Conclusions 599 600 In this work a methodology is presented to assess the impact on the LV distribution network arising from the expansion 601 of distributed PV generation, mainly from rooftop self-consumption installations. The assessment considers the direct 602 investment costs associated to the expansion/upgrading of the network, which is required to maintain the network 603 congestions and overvoltage levels within acceptable limits, as well as the corresponding O&M costs and the variation in 604 losses. The methodology has been applied to a large-scale, real distribution network comprising approximately 80,000 605 customers with an annual demand of 460 GWh, almost 2,200 km of LV lines and over 1,800 secondary substations. 606 607 For low PV penetration levels, the average energy flowing through the LV network tends to decrease, even though local 608 congestions or overvoltages may still arise to a lesser extent. Starting at around 30% PV (45% using the base PZeroD), 609 investments are increasingly necessary to solve unacceptable overvoltages or congestions, the growing rate being nearly 610 quadratic beyond that point. 611 612 Regarding the losses, thanks to the reduction in transmitted energy from the initial stages of PV penetration, they get 613 reduced and reach their lowest level at approximately 20% PV penetration. The investments necessary to eliminate 614 excessive congestions and voltage violations also favour the reduction of losses. As a result, the global losses do not 615 exceed again those of the baseline scenario until the PV penetration level is beyond 40%. 616 617 Overall, considering the total direct costs, including losses, low PV penetration levels lead to a distribution cost saving 618 that peaks at 18%. Beginning at 33%, the distributed generation leads to an increase in distribution cost that grows more 619 than proportionally with PV penetration. Specifically, without losses, the total costs per installed PV power amounts to 620 2.73 €/kWp for scenarios with 30% PV and 10.18 €/kWp for 50% PV penetration. 621 622 From a regulatory standpoint, until more efficient dynamic rates are developed, based on remote information provided by 623 smart meters, our findings suggest that PV-based self-consumers should be subject to extra charges only in those areas 624 where the degree of PV penetration is greater than 30%. Other indirect costs not evaluated in this work, such as those 625 arising from the need of greater monitoring and remote control, amongst others, should be somehow recognised under the 626 remuneration scheme for the distribution activity. 627 628 7. Acknowledgements 629 630 This work has been performed within and supported by the Department of Regulations of Endesa, under the direction of 631 Dr. Juan J. Alba-Ríos. 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