Multi-year Optimal Investment Planning For Active Distribution Networks Wrapped As An Energy Application For DSOs

Posted on 8 Oct 2025 — CC-BY 4.0 — https://doi.org/10.36227/techrxiv.175993219.92328791/v1 — e-Prints posted on TechRxiv are preliminary reports that are not peer reviewed. They should not b... Multi-year Optimal Investment Planning For Active Distribution Networks Wrapped As An Energy Application For DSOs Andreas Gatos1, Athanasios Rafail Lagos1, Angeliki Lydia Antonia Syrri1, Aris Dimeas1, and Nikos Hatziargyriou1 1School of Electrical and Computer Engineering, National Technical University of Athens Athens October 08, 2025 1 Multi-year Optimal Investment Planning For Active Distribution Networks Wrapped As An Energy Application For DSOs Andreas Gatos, Athanasios Rafail Lagos, Angeliki Lydia Antonia Syrri, Aris Dimeas, Nikos Hatziargyriou School of Electrical and Computer Engineering National Technical University of Athens Athens, Greece Abstract—This paper introduces an optimization algorithm for optimal planning of infrastructure reinforcements for a mediumvoltage distribution network to accommodate connections of new distributed energy resources (DER) and demand growth for a long-term planning horizon. This algorithm suggests optimal reinforcement of lines, transformers & substations and the optimal year for each upgrade to be implemented, considering also the procurement of flexibility to minimize or postpone the necessary investments. This software solution is offered to Distribution System Operators (DSOs) as an ”energy-as-a-service”, in the form of a Digital Twin (DT) and an accompanying energy application, that can operate based on the DSO’s datasets available on some private or shared Energy Data Space (EDS). The application offers a friendly interactive environment where the end-user can investigate different planning scenarios by defining accordingly the levels of demand growth and the location, capacity and time of installation of new DERs, EVs and batteries. Index Terms—Network Planning, Optimization, Multi-stage Planning, Active Distribution Network, Digital Twin, Energy Application, Energy Data Spaces NOMENCLATURE Binary Variables zl i,a,y Decision to upgrade line ito type a Continuous Variables Isqr i,y,d,h Squared current of line i Pi,y,d,h, Qi,y,d,h Active and reactive power flow at line i Vsqr i,y,d,h Squared bus voltage of bus i Indices y, d, h Indices for year/day/hour Parameters aflex load/gen,i Flexibility capacity of generator/load i CLR,b Cost per km of installing a line of type b fgen/load,↑ i,y,d,h , fgen/load,↓ i,y,d,h Upwards/downwards flexibility of generator/load at bus i Inft, InttInflation & Investment rate at year t liLength of line i pD i,y,d,h, qD i,y,d,h Active/reactive power demand at bus i This paper is funded by SYNERGIES project, European Union’s Horizon Innovation. Actions under Grant Agreement 101069839 Email: [email protected]; a r [email protected]; angel- [email protected]; [email protected]; [email protected] pG i,y,d,h, qG i,y,d,h Active/reactive power generation at bus i pfgen/load iPower factor of generator/load i Prflex,↑ y,d,h , Prflex,↓ y,d,h , Prreactive y,d,h Price of upwards/downwards flexibility & reactive power Prloss y,d,h Price of active & reactive power losses rc, xcResistance/Reactance per km of line type c Smax,L i,y Maximum capacity of Line iat year y Vmax, Vmin Maximum and Minimum voltage of buses wdWeight coefficient of characteristic day d Sets DSet of characteristic days ΦLR Set of lines to be upgraded ΨLR Set of available types of lines NB/L Set of buses/lines I. INTRODUCTION The rapid evolution of energy systems and the increasing integration of distributed energy resources necessitate a paradigm shift in the planning and operation of distribution networks. Transitioning existing distribution networks into active, future-ready systems requires careful optimization and scheduling of investments, while maximizing the utilization of existing capacities. This shift also demands addressing operational constraints and embracing advanced digital tools. Modern distribution networks face significant challenges, including increasing yet uncertain load growth (e.g., EVs penetration), variability in renewable energy generation, and the need to make the best use of capital investments. These challenges highlight the importance of leveraging flexibility services offered by flexibility service providers. By combining such services with optimal planning strategies, it becomes possible to minimize capital (CAPEX) and operational expenditures (OPEX) over multi-year planning horizons. This paper proposes a robust, multi-year optimization algorithm tailored to active distribution networks. The algorithm aims to minimize the combined costs of network reinforcements and flexibility acquisition while ensuring compliance with technical constraints. Presented as a digital twin and 979-8-3315-2503-3/25/$31.00 ©2025 European Union energy application, the solution enables distribution system operators to simulate and analyze different future demand-growth and RES penetration scenarios to derive optimal planning strategies. By offering an interactive environment for scenario design and visualization, this approach facilitates effective decision-making and supports the long-term sustainability of distribution networks. Supported by the European Union’s Horizon Innovation program under the SYNERGIES project, this research focuses on leveraging digital technologies, such as energy dataspaces and tailored optimization algorithms, to address the complexities of modern distribution network planning. By providing modular and user-centric tools, the proposed solutions enable distribution system operators to adapt to evolving energy demands and integrate renewable resources efficiently. II. MULTI-YEAR OPTIMAL PLANNING FOR ACTIVE DISTRIBUTION NETWORKS Distribution network planning has evolved significantly with the growing need to integrate renewable energy and provide operational flexibility. Advanced optimization techniques such as mixed integer linear programming (MILP) are used to balance the cost of infrastructure investments with the operational costs associated with flexibility services, ensuring a costefficient expansion of distribution networks [1], [14]. Recent studies not only improve the efficiency of grid operations but also aim to balance the investments in network infrastructures with investments in smart technologies, ensuring that modern distribution networks are more adaptable and sustainable in the face of uncertain future conditions. Active Distribution Networks (ADNs), employ solar generation, storage, wind farms, and demand side management for instance to help balance supply and demand [1], [6], while also ensuring grid stability. Given the variability and uncertain nature in renewable energy generation, many studies incorporate stochastic and scenario-based optimization methods. These methods simulate multiple possible future scenarios to ensure that networks are optimized under various conditions [7], [14]. These allow planners to optimize network expansions and operations under different future scenarios [7]. Other models implement bi-level optimization, where one level addresses strategic investment decisions, while the lower level focuses on operational decisions such as load balancing, reconfiguration, and storage management. This ensures optimal long-term planning while accommodating operational needs [1]. Multistage approaches allow gradual decision making and revisiting expansion plans over time as new data and technologies emerge. This reduces the risks associated with long-term planning under uncertainty [3]. Different RES penetration scenarios are also considered in [1], to ensure that the grid can handle them. Typical criteria considered for network expansion are aimed at optimizing reliability, cost, and flexibility. Currently, minimizing both investment (CAPEX) and operational expenditures (OPEX) is typically a central objective in cases where regulation dictates minimization of TOTEX expenses. These costs are balanced against potential savings from flexibility services, such as energy storage and demand-side management [1], [5]. Additionally, many studies incorporate reliability metrics such as EENS and SAIDI into optimization models, ensuring that investments not only minimize cost but also maintain high reliability standards [1]. The integration of flexibility services like battery storage and demand-side management can be proven essential for maintaining the stability of the grid, especially during periods of high demand or low renewable generation [6], [7]. Finally, the incorporation of efficient and accurate load forecasting models could ensure that grid expansion plans meet future energy needs without overbuilding infrastructure [9]. III. DIGITAL TWIN AND ENERGY APPLICATION DESIGN The main novelty of this work, compared to the existing solutions, is the deployment of the planning tool as an ”energyas-a-service” solution, in a modular manner with the purpose to be offered to DSOs either as an independent solution or within an Energy Data Space (EDS) framework. It means that DSOs can purchase this service from an energy services marketplace and run it on their private premises (private cloud) using datasets stored there, or run it in a proper Energy Data Space environment, where their datasets will be available and optionally shared with other stakeholders of the energy value chain (e.g., TSOs, FSPs, prosumers). In that framework, stakeholders’ data can be accessed through the Energy Data Space and AI analytics can be purchased from the on-demand service platform as presented in the SYNERGIES project [15]. The solution consists of a data-driven DT for ADNs and an accompanying energy application, with a user-friendly interface where the user can select actions to be taken and results to be visualized. A. Long-term Asset Sizing Digital Twin The DT can retrieve and process both raw data, provided through the EDS directly by a DSO, and forecasts for the demand and generation, provided by pre-trained AI models. The DT comprises an engine called ”Long-Term Asset Sizing”, which is based on the exploitation of datasets (such as distribution network topology) and forecasts from the analytics and includes tools to assess long-term evolution scenarios and support optimal investment planning decisions via efficient mathematical programming techniques. The DT consists of the following sub-components: •Ingestion of long-term demand/generation forecasts - which can be either developed independently by the DSO or constructed and purchased from an AI analytics marketplace •Ingestion of network evolution scenarios (for demand and generation growth for the planning horizon) - which are constructed by the DSO using the application •Execution of the algorithm for the ADN planning problem based on the optimization formulation presented in the following Section IV •Identification of necessary network reinforcements and flexibility requirements B. Investment planning and prioritization Energy application The application allows the DSO to construct demand and generation evolution scenarios and communicates with the “Long-term planning engine” of the DT to derive suggestions for optimal planning. Finally, it allows the user to visualize the planning results for the different scenarios defined. The application consists of two components: •The future scenario design manager - which is responsible for the design of demand and generation evolution scenarios (example in Fig. 1, Sec. V). It is a userfriendly, interactive environment, where end-users can define the expected annual increase of generation and demand for the following 5/10 years. Moreover, the installation of new assets (RES, EVs, batteries), as well as their placement and capacity, can be defined by the user. This tool sends the created scenarios to the DT to be assessed in terms of feasibility and the necessary network reinforcements to be derived. •The planning results visualization engine - which is responsible for the presentation of the results of the DT per scenario (example in Fig. 2, Sec. V). This component receives the optimization results from the DT and presents the necessary network reinforcements, with all their technical specifications, in a dashboard. Moreover, it presents the assessment (positive or negative) of the investments for the installation of new assets and an indicative comparative assessment of the different evolution scenarios defined. IV. MULTI-YEAR INVESTMENT PLANNING FORMULATION A. Planning Criteria The multiyear optimization problem for the distribution network planning considered in this work has the following objective function: min f= T X y=1 (Ry−DLR y)ICLR y+Ry(Cflex y+Closs y)(1) where Ry=Qy t=1 1+Inft 1+Inttis the net present value coefficient, DLR y=RTELLR−(T−y) ELLR is the depreciation of the equipment at the end of the time horizon T(where ELLR is the expected lifespan of a line). The first term stands for the CAPEX of upgrading lines (Eq. (2)). While the OPEX consist of the flexibility acquisition costs Cflex y=CP G y+CQG y+CL y(Eq. (3)-(5)) and the costs of losses (6). ICLR y=X i∈ΦLR X b∈ΨLR CLR,bli⌊zl i,c,y −zl i,c,y−1⌋(2) CP G y=X d∈D wd 24 X h=1 X i∈NB (Prflex,↑ y,d,h fgen,↑ i,y,d,h +Prflex,↓ y,d,h fgen,↓ i,y,d,h) (3) CQG y=X d∈D wd 24 X h=1 Prreactive y,d,h |qgen i,y,d,h|(4) CL y=X d∈D wd 24 X h=1 X i∈NB (Prflex,↑ y,d,h fload,↑ i,y,d,h +Prflex,↓ y,d,h fload,↓ i,y,d,h) (5) Closs y=X d∈D wd 24 X h=1 X i∈NL Prloss y,d,h(ri,y +xi,y)Isqr i,y,d,h (6) Where, ⌊x⌋=xif x > 0, else 0. The set of characteristic days Dconsists of 4 days in this study, modeling worstcase scenarios that stress more the ADN. Specifically, these days are the ones with max/min load and max/min generation per annum respectively, based on the available forecasts. Moreover, the flexibility prices are taken as input timeseries based on proper forecasts. The DistFlow equations are considered for modeling the power flows of distribution networks: X k:i→k Pk,y,d,h =Pi,y,d,h −ri,yIsqr i,y,d,h +pD i,y,d,h −pG i,y,d,h (7) X k:i→k Qk,y,d,h =Qi,y,d,h −xi,yIsqr i,y,d,h +qD i,y,d,h −qG i,y,d,h (8) Vsqr i,y,d,h =Vsqr πi,y,d,h −2ri,yPi,y,d,h −2xi,yQi,y,d,h + (r2 i,y +x2 i,y)Isqr i,y,d,h (9) Isqr i,y,d,hVsqr πi,y,d,h ≥P2 i,y,d,h +Q2 i,y,d,h (10) Constraint (10), stands for the power balance per line, which is nonconvex in its original form (as equality). It has been relaxed here (SOCP relaxation) for convexifying the optimization problem. The relaxation is exact since the minimization of the power losses is considered in the objective (see Appendix A in [16]). The demand and generation flexibility procurement margins are the following: 0≤fload,↑ i,y,d,h, fload,↓ i,y,d,h ≤αflex load,iPload i,y,d,h (11) pload i,y,d,h =Pload i,y,d,h +fload,↑ i,y,d,h −fload,↓ i,y,d,h (12) qload i,y,d,h =pload i,y,d,htan(cos−1(pfload i)) (13) 0≤fgen,↑ i,y,d,h, fgen,↓ i,y,d,h ≤αflex gen,iPgen i,y,d,h (14) pgen i,y,d,h =Pgen i,y,d,h +fgen,↑ i,y,d,h −fgen,↓ i,y,d,h (15) |qgen i,y,d,h| ≤ pgen i,y,d,htan(cos−1(pfgen i)) (16) The impedance and reactance of a line at year ydepend on the upgrading decision variables (zl i,c,y): ri,y =X c∈ΨLR rclizl i,c,y (17) xi,y =X c∈ΨLR xclizl i,c,y (18) Operational constraints for the voltage limits (19) and the line thermal limit (20) are considered: Vmin ≤Vi,y,d,h ≤Vmax (19) I2 i,y,d,h ≤(Smax,L i,y )2(20) Constraints associated with the investment decision variables, indicating that exactly one of the available line types (see Table I) is in place at each line each year: X c∈ΨLR zl i,c,y = 1,∀y, i ∈ΦLR (21) The power flow equations (7)-(9) include bilinear terms due to the multiplication of the resistance and impedance (dependent on the decision variables zl i,c,y) with the squared line current. These bilinearities have been linearized through proper big-M linearizations. Remark. The developed optimization algorithm and the respective application have been extended to include also substation reinforcement and transformers’ upgrade actions in exactly the same way as for the line upgrades (both in costs and constraints formulation). These further equations are omitted here for brevity. V. RESULTS AND DEMONSTRATION The performance of the proposed methodology is applied and demonstrated using a local medium-voltage (MV) distribution network. The distribution system is a 130-bus 20 kV network with 1 substation, 13 load buses, 129 branches and 4 static generator buses (PVs). The planning period is chosen by the applications’ user and it could be 5 or 10 years. Voltage limits are ±10% of the nominal voltage. The interest rate is 1% and the inflation rate 2%. Upward flexibility costs 400 euros/MWh and downward flexibility costs 300 euros/MWh (these prices are forecasts based on current balancing market prices in Greece). Finally, active and reactive power loss cost is 20 euros/MWh. The available line types are shown in Table I. The proposed methodology has been implemented using the Pyomo library of Python with Gurobi as solver. Table I: AVAILABLE CONDUCTOR ALTERNATIVES Conductors Type R (Ω/km) X (Ω/km) Ampacity (A) Cost(euros) 1 1.274 0.417 0.115 10000 2 1.268 0.422 0.16 20000 3 0.576 0.397 0.224 30000 4 0.404 0.386 0.295 36000 A. Future scenarios design In this paper, two scenarios of light and heavy RES penetration are examined. In the light RES case (S1), 3 PVs are installed on buses 44,62 and 76 in years 4,6 and 8, respectively. In the heavy RES case (S2), 8 PVs are installed on buses 44,60,62,70,76,80,90 and 120 in years 4,7,6,6,8,7,7 and 8, respectively. The flexibility rate (being the available flexibility capacity of each asset divided by its nominal power) for both scenarios is set at 10%. The total installed capacity for the light and heavy RES scenario is set at 1.24MW and 3.24MW, respectively. It should be noted that strategic placements (location, year, installed capacity) are designed by the end-user through the User Interface of the application (Fig. 1) and not by the optimization algorithm. Figure 1: Scenarios Builder B. Planning results visualization For each of the simulated scenarios, the user can see what actions are to be taken, which is the year that an action is triggered and the cost of this action (Fig. 2). Actions could be either the request for specific amounts of upward/downward flexibility (from DER/load/batteries) or a decision for a line upgrade at a particular year. For the light RES scenario, the total cost is 8270.23 C with 2 line reinforcements at the second year and no flexibility procurement, since the available flexibility is not enough to compensate for the line reinforcements. On the other hand, for the heavy RES scenario, the total cost is 1486,98 C with no line reinforcements and 3.05 MW purchased flexibility, indicating that adding controllable RES enhances the ADN’s functioning. Figure 2: Planning algorithm outcomes: Flexibility to be purchased per year C. Case Studies To demonstrate the usefulness of the developed tool for a DSO, the following two case studies have been performed. At first, for the two scenarios of PV penetration defined above (Sec. V-A), we consider a varying available flexibility rate both for loads and generators. From Figure 3, we deduce that there is a threshold flexibility rate for each scenario (10% & 8% resp.) after which the DSO can avoid costly investments by purchasing the available flexibility. This study can be used by the DSO to define flexibility procurement targets and incentivize prosumers to invest in flexible assets up to that level. Figure 3: Examining the two scenarios (S1 & S2) of PV penetration varying the available flexibility rate Another major target for DSOs in the era of rapid decarbonization is maximizing the ADNs’ RES hosting capacity while avoiding costly infrastructure upgrades [17]. From Figure 4, we observe that the ADN under study has significant RES hosting capacity perspective, since in absence of local generation the initial cost is high and RES penetration results in decreasing that cost. Moreover, since newly installed assets are considered to be flexible, the well-known U-curve ( [16]) is not apparent even for large penetration, because in hours of high PV production stressing the network the DSO can procure downwards flexibility from these PVs. So, the DSO can motivate RES investments in this network. Figure 4: Examining a scenario (S2) of PV penetration, with constant flexibility rate at 10%, varying the installed capacity VI. CONCLUSIONS In this paper, a novel digital twin and energy application framework for multi-year investment planning is presented. This app is based on the DSO’s data assets available on some private or public EDS and it enables them to evaluate demand and generation growth scenarios and decide on the necessary network reinforcements, considering flexibility procurement as an alternative. VII. ACKNOWLEDGMENT We thank our colleague Manos Zalokostas for his valuable contribution in developing main frontend and backend components of the application in the context of SYNERGIES. REFERENCES [1] Alejandra Tabares, Gregorio Mu˜ noz-Delgado, John F. Franco, Jos´ e M. 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