Optimal Industrial Clusters: Flex4Fact Summer Research Report

Project Report Optimal Industrial Clusters Flex4Fact Summer Research Report Author(s) Madeline Kitch, Mikael Støen, Miguel Muñoz, Thiago Silva, Marc Juanpera, Pau Fisco-Compte Report Number 2024:00958 — Unrestricted Client(s) Internal Technology for a better society SINTEF Industry Address: P.O. Box 4760 Torgarden, NO-7465 Trondheim Telephone: +47 40005100 [email protected] Enterprise Number: 919 303 808 KEYWORDS: Flexible industry, Optimal Scheduling, Industrial Cluster, Renewables Project Report Optimal Industrial Clusters Flex4Fact Summer Research Report VERSION 1.3 DATE 3rd September 2024 AUTHOR(S) Madeline Kitch, Mikael Støen, Miguel Muñoz, Thiago Silva, Marc Juanpera, Pau Fisco-Compte CLIENT(S) Internal CLIENT’S REFERENCE PROJECT NUMBER 102027880 NUMBER OF PAGES AND ATTACHMENTS 26 ABSTRACT We study the integration of digitization, smart scheduling, local renewable energy production, and variable energy prices in different industrial companies to make an optimization entity for industrial cluster energy use. We discuss two energy optimization approaches: a centralized choice for all energy consumption and local-level trading of energy surplus and develop a graph-based package to implement these mechanisms given mixed-integer programming models for each of the firms. Testing our modeling package with data from the EU project Flex4Fact, we show that clustering decreases aggregate costs due to the lack of sell-back penalties, and the relative benefit among firms depends on internal prices. PREPARED BY Miguel Muñoz Ortiz SIGNATURE CHECKED BY Lars Hellemo SIGNATURE APPROVED BY Frode Rømo SIGNATURE REPORT NUMBER 2024:00958 ISBN 978-82-14-07014-9 CLASSIFICATION Unrestricted CLASSIFICATION THIS PAGE Unrestricted 1 of 26 Miguel Muñoz Ortiz (Sep 3, 2024 14:52 GMT+2) Lars Hellemo (Sep 3, 2024 14:55 GMT+2) Document History VERSION DATE VERSION DESCRIPTION 1.0 16.08.2023 Final version after Summer Researcher’s stay at SINTEF 1.1 12.04.2024 Revised version sent to QA 1.2 05.07.2024 Final version with QA 1.3 03.09.2024 Final version with small corrections before signature PROJECT NUMBER 102027880 REPORT NUMBER 2024:00958 VERSION 1.3 2 of 26 Contents 1 Introduction 4 2 Conceptual Framework 6 2.1 Theoretical results ......................................... 7 2.2 Market Models .......................................... 8 2.3 Mechanism 1: Automatic Trading ................................. 9 2.4 Mechanism 2: Centralized choice ................................. 10 3 Problem Formulation of Industrial Clusters 11 3.1 Factory Scheduling ........................................ 11 3.1.1 Problem Formulation ................................... 11 3.1.2 Objective Function .................................... 12 3.1.3 Constraints ........................................ 12 3.1.4 Implementation ...................................... 14 3.1.5 Performance improvements ............................... 14 3.2 Aggregator Implementation .................................... 14 3.3 Practical Challenges ........................................ 17 4 Case studies 18 4.1 Main assumptions and data .................................... 18 4.2 Production Scheduling in the Factories .............................. 18 4.3 Energy Aggregator for Industrial Cluster ............................. 18 4.3.1 Effect of r= 0.5 ...................................... 20 4.3.2 Effect of r= 0.2 ...................................... 21 5 Conclusions and next steps 24 PROJECT NUMBER 102027880 REPORT NUMBER 2024:00958 VERSION 1.3 3 of 26 Chapter 1 Introduction The electricity system depends on a delicate balance between supply and demand. As storing energy is costly, when expected demand exceeds supply, the grid will often tap into high-price suppliers or shut down end-users entirely. Traditional generation sources such as natural gas and coal are dependable and (relatively) adaptable to demand profiles, reducing the potential scale of this problem. However, as the generation share of variable renewable energies such as solar and wind grows, so will the need for stronger market mechanisms to mitigate potential imbalances. Flex4Fact (Grant agreement ID: 101058657, DOI: 10.3030/101058657), a project funded by the European Union and coordinated by SINTEF Manufacturing AS, seeks to address how a specific but important group of electricity consumers—industrial manufacturers—can thoughtfully engage in the transitioning energy market. Industrial users consume large amounts of total electricity but have particular challenges in adaptation to energy prices and availability. Since industrial processes are so complex, even formulating a set of options can be difficult, often requiring the digitalization of factory processes. The task of the Flex4Fact is both to work on the development of new market models and methods of engagement between manufacturers and the grid and develop a computational infrastructure that will facilitate their inclusion; to create an “end-to-end ecosystem... to enable flexible manufacturing... in energy intensive industrial sectors” [5]. Our work relates to the market design and computational modeling of a subset of this larger market: industrial clusters. Industrial clusters are communities of manufacturers concentrated in a small geographic area. Many industrial firms have started producing energy locally, a phenomenon known as prosuming [9]. Prosuming can take the form of on-site Photovoltaic (PV) solar panels, nearby wind turbines, or replacing natural gas with hydrogen [4]. Yet, the electricity market is presently ill-suited to deal with their supply. As such, prosumers face steep sell-back rates should they have surplus energy, presenting a natural marketplace for energy exchange among firms within a cluster. Firms with extra energy can sell theirs locally for an intermediate rate to others consuming energy, generating a Pareto improvement. Caprara et al. [2], a previous Flex4Fact study, documented this Pareto improvement in a case study of rubber production, showing potentially significant energy cost and emissions savings from making a centralized cluster decision. Inspired by Caprara et al. [2], we study and model in detail the problem of local-level energy sharing and optimization industrial clusters, viewing them as a microcosm of the challenges a larger “end-to-end ecosystem” might face—from incentive compatibility constraints to the linkage of digital twins. We formalize the set-up in the language of mechanism design, showing that a perfect (direct) mechanism is unattainable, and, given this, offer two potential approaches: participation-based centralized choice and automatic trading that are simple and transparent. Second, we present a mixed-integer problem formulation and abstract graph-based computational package for both factory-scheduling and energy aggregation suited to the essential needs of clusters. We test this model on Flex4Fact data and show that costs decrease, and the relative benefit of different firms is sensitive to our choice of the internal discount rate or sell-back penalty. The remainder of this report is structured as follows. Chapter 2provides a thorough description of the conceptual framework, business models, and theoretical results. Chapter 3presents mixed-integer formulaPROJECT NUMBER 102027880 REPORT NUMBER 2024:00958 VERSION 1.3 4 of 26 tions of factory production scheduling and a market (aggregator) platform. Chapter 4presents case studies and their sensitivity to the choice of internal discount rates. Chapter 5concludes. PROJECT NUMBER 102027880 REPORT NUMBER 2024:00958 VERSION 1.3 5 of 26 Chapter 2 Conceptual Framework This chapter discusses the mechanism design set-up for industrial cluster energy sharing. The high-level structure is as follows: We define firms as the sum of energy management and factory scheduling systems. The energy management (EM) system administrates the energy balance at the factory, taking into account energy flows from their own renewable sources, between other firms in the cluster, and with the grid. The factory scheduling (FS) system optimizes the factory’s production profiles based on demand and system constraints. We model the factories individually (business as usual or BAU) and in a centralized cluster. The key difference is that in the cluster case, there is an intermediary entity, the aggregator, between the firms and the grid. The aggregator uses price information and the relative cost of firm’s production options to pick the lowest-cost choice for the cluster. A diagram of the two options (individual factories and clusters) are shown in fig. 2.1. To make this problem tractable, a set of simplifying assumptions in line with [2] are needed. First, energy costs are assumed known and linear. This means that firms are able to pick when they want to produce given the prices of the system and that consuming twice as much costs twice as much. Second, it is assumed that different firms have the ability to coordinate energy use profiles. A leading example would be collective weekly scheduling: Each firm would like to make a fixed amount of the good over the period but may present alternative options for when that production would occur. Third, a zero transaction cost or energy loss are assumed when transporting electricity across firms, which is a reasonable assumption considering the low cost and limited loss for short distances. Firm’s Problem. In the simplest model, firms make a fixed amount of goods for a given strategic period but can decide when and how they would like to produce over the shorter intermediate time steps. Each firm also has a local (renewable) energy source which they may use at some cost. Lastly, the firm can decide if they would like to opt into a larger Aggregator system. Below the language used in assignment or allocation problems [1] is presented. Formally, let Ibe the set of firms (agents) and J=ℝ𝑇the set of possible energy demand vectors to the Aggregator at each of the 𝑇operational periods (objects). The notation  𝑗(𝑖)={𝑗𝑖,1,…,𝑗𝑖,𝑇}means that firm 𝑖is consuming 𝑗𝑖,𝑡energy units from the grid at times 1≤𝑡≤𝑇. Furthermore, each firm has a set of energy vectors 𝑆(𝑖)for which they are able to meet the product demand. Thus if 𝑗∉𝑆(𝑖), demand will not be met. When firms chose among 𝑀profiles as in [2], ‖𝑆(𝑖)‖=𝑀. Each firm has preferences 𝜋𝑖over the possible consumption bundles, defined over the set 𝑆(𝑖)⊂J 𝜋𝑖∶J|𝑆(𝑖)→ℝ These preferences 𝜋𝑖(𝑗𝑖)account for the costs independent of non-local energy use or supply. They tell us how different energy consumption profiles cost to implement, excluding those costs associated with acquiring or selling energy through the Aggregator. Examples of components of these preferences include wages to workers, start-up and stopping costs, and material costs. PROJECT NUMBER 102027880 REPORT NUMBER 2024:00958 VERSION 1.3 6 of 26 Figure 2.1: Cluster and benchmark definition Benchmark. The status-quo environment is modeled as one where firms face price 𝑝𝑡for an energy unit at time 𝑡and sell back energy to the grid at a lower price than the grid prices 𝑟∈(0,1)where 𝑟is the sell-back penalty. Firms pick a profile 𝑗𝑖and face total cost 𝐶𝐵𝐴𝑈 𝐶𝐵𝐴𝑈(𝑖)=𝜋𝑖(𝑗𝑖)+ 𝑇 ∑ 𝑡=1[𝕀𝑖,𝑡𝑗𝑖,𝑡𝑝𝑡+(1−𝕀𝑖,𝑡)𝑟𝑝𝑡𝑗𝑖,𝑡] where 𝕀𝑖,𝑡an indicator for positive energy demand (i.e. 𝑗𝑖,𝑡>0). Aggregator. The Aggregator is a central entity that can help facilitate the decision of energy use and shared costs. The objective is to minimize the sum of individual objectives while still meeting individual incentivecompatibility constraints. Formally, it can pick options on allocations and subsidies which map the set of firms to their received allotments. We define 𝜇∶I→Jbe the allocation function so that 𝜇(𝑖)=𝑗𝑖, and 𝑡∶I→ℝ|I| be the subsidy function compensating the losers (those made worse-off by their Aggregator assignments). Objective. The Aggregator’s objective is 𝑇𝐶𝐴𝑔𝑔=∑ I𝜋𝑖(𝜇(𝑖))+ 𝑇 ∑ 𝑡=1[𝕀𝑡𝑝𝑡∑ I𝜇(𝑖)𝑡+(1−𝕀𝑡)𝑟𝑝𝑡∑ I𝜇(𝑖)𝑡] where 𝕀𝑡is the indicator for positive net demand at time 𝑡. The allocations 𝜇(I)must satisfy the condition of the firms on being part of the cluster (𝑡(𝑖)≤𝐶𝐵𝐴𝑈(𝑖)) and feasibility for meeting needed production quota (𝑗𝑖∈J|𝑆(𝑖)). 2.1 Theoretical results We present here two theoretical results: (1) clustering energy choice and use will always weakly decrease total costs, and (2) even in a simple case, a direct mechanism cannot exist. PROJECT NUMBER 102027880 REPORT NUMBER 2024:00958 VERSION 1.3 7 of 26 A clustered system, no matter the mechanism, is guaranteed to at least weakly decrease total costs if reporting is truthful. The decrease in cost is due to the fact that internal trading will always save money due to the difference between the purchase and sell-back costs. Lemma 1. Under a clustered system, each profile set results in weakly lower costs with inequality when any two firms would individually buy and sell at the same time. Formally for profile choices 𝜇∗(I)={𝑗1,…,𝑗𝑁}, ∃𝑡∈𝑇and (𝑖1,𝑖2)∈I2s.t. 𝕀𝑖1,𝑡≠𝕀𝑖2,𝑡. The profile fixed costs are independent of energy aggregation, hence we will focus on the power costs. If all firms buy or sell at time 𝑡, then we can factor out the indicators to yield identical costs. ∑ I𝜋𝑖(𝑗𝑖)+ 𝑇 ∑ 𝑡=1[𝕀𝑡𝑝𝑡∑ I𝑗𝑖,𝑡+(1−𝕀𝑡)𝑟𝑝𝑡∑ I𝑗𝑖,𝑡]=∑ I𝜋𝑖(𝑗𝑖)+ 𝑇 ∑ 𝑡=1[𝕀𝑡𝑝𝑡∑ I𝑗𝑖,𝑡+(1−𝕀𝑡)𝑟𝑝𝑡∑ I𝑗𝑖,𝑡] If not, they differ by ∑ 𝕀𝑖,𝑡≠𝕀𝑡(𝕀𝑡−𝕀𝑛,𝑡)𝑗𝑖,𝑡𝑟𝑝𝑡−(𝕀𝑡−𝕀𝑖,𝑡)𝑗𝑖,𝑡𝑝𝑡 =−(1−𝑟)𝑝𝑡∑ 𝕀𝑖,𝑡≠𝕀𝑡(𝕀𝑡−𝕀𝑖,𝑡)𝑗𝑖,𝑡 =−Sign(𝑗𝑖,𝑡)(𝕀𝑡−𝕀𝑖,𝑡)(1−𝑟)𝑝𝑡∑ 𝕀𝑖,𝑡≠𝕀𝐴𝑔𝑔|𝑗𝑖,𝑡| =−(1−𝑟)𝑝𝑡∑ 𝕀𝑖,𝑡≠𝕀𝑡|𝑗𝑛,𝑡|<0 Since 𝑟∈(0,1), the Aggregator cost less the benchmark cost is negative; aggregation weakly saves costs for all options and at all time steps. The second result is that there is unlikely to be a direct mechanism for achieving the optimal outcome, or fairly redistributing the surplus. Theorem 2. (Direct Mechanism Impossibility). Assume an alternative profile decreases the cost of one firm and increases the cost of another, and both firms have probabilistic knowledge of the other’s preferences, which are continuous on a bounded and overlapping region. Then no truthful, efficient, budget balanced mechanism exists which will always decrease firm costs. Our negative result is an exact application of the Meyerson-Satterwaite Theorem where one firm is the “buyer” and the other is a “seller.” Given the impossibility result for a very simple setting, we therefore cannot rule out the fact that firm face incentives to leave out options or artificially alter their preferences should choice be centralized. Consider the case when factory scheduling happens weekly, and all firms made worse off by the new system will receive subsidies. A firm already knowing their likely allocation may then report higher non-energy costs in order to get additional money from the aggregator. In addition, if they know that another option is preferable for them, they may leave out that energy profile from their option set entirely. Therefore, even though the Aggregator can always lower costs, the scale of benefit and the fairness of the cost-sharing is critically dependent on the system implementation, the relative preferences of the firms, and the degree of information-sharing. 2.2 Market Models The best system design is likely to be a function of the frequency of aggregation, and relative size of the firms. Below we discuss two types of market systems and heuristics as to when both of them may be beneficial. PROJECT NUMBER 102027880 REPORT NUMBER 2024:00958 VERSION 1.3 8 of 26 Figure 3.1: Cluster and benchmark definition constraints, and objectives. The edges are link constraints, expressions relating variables in different models (nodes). Lastly, groups of nodes can form subgraphs. When modelling the firms with Plasmo, they are represented by a subgraph with three nodes: a factory scheduling (FS) node, an energy management (EM) node, and a messenger node. We create factory scheduling and energy management JuMP models in separate packages. Alternatively, the user can specify their own JuMP model. These are then attached to their respective nodes and—along with the specified factory name—define a factory structure. The messenger node takes in constraints from the FS and EM models to define the feasible set for each firm. This node, re-labeled with the name of the firm, is the point of contact with the Aggregator. The Aggregator need not have knowledge of the specific inputs or needs given rise to the given domain and preferences. A diagram of the informational flow in the Plasmo model is represented in fig. 3.1. The node connecting all firms represents the cluster or aggregator, and it is defined as "main". Below the different equations of this node will be presented for its implementation in Plasmo. As the node "main" is an optimization model as well as the other nodes, several variables and constraints are defined. Table 3.3: Parameters of the aggregator or "main" node Parameter Description 𝑃𝑟𝑖𝑐𝑒𝑝𝑜𝑤𝑒𝑟 𝑡Float, power price at time 𝑡 𝑀Integer, big number 𝑟Float in (0,1), discount rate. At time 𝑡the grid sell-back price is thus 𝑟𝑃𝑟𝑖𝑐𝑒𝑝𝑜𝑤𝑒𝑟 𝑡. The power balances at main are defined in eq. (3.18), eq. (3.19) and eq. (3.20). 𝑃𝑏𝑜𝑢𝑔ℎ𝑡,𝑎𝑔𝑔 𝑡≤𝑀⋅𝐼𝑡∀𝑡∈𝑇(3.18) 𝑃𝑠𝑜𝑙𝑑,𝑎𝑔𝑔 𝑡≤𝑀⋅(1−𝐼𝑡) ∀𝑡∈𝑇(3.19) 𝑃𝑏𝑜𝑢𝑔ℎ𝑡,𝑎𝑔𝑔 𝑡−𝑃𝑠𝑜𝑙𝑑,𝑎𝑔𝑔 𝑡=𝑃𝑎𝑔𝑔 𝑡∀𝑡∈𝑇(3.20) The total power of the aggregator, 𝑃𝑎𝑔𝑔 𝑡, is based on the power balances of the other energy management and factory nodes, and thus a linking constraint represented in eq. (3.21). The variable 𝑃𝑏𝑎𝑙 𝑛,𝑡 is the power balance of each of the energy management and factory nodes: 𝑃𝑏𝑎𝑙 𝑛,𝑡 =𝑃𝐸𝑀𝑆 𝑛,𝑡 −𝑃𝑓𝑎𝑐𝑡𝑜𝑟𝑦 𝑛,𝑡 ∀𝑡∈𝑇,𝑛∈𝑁(3.21) PROJECT NUMBER 102027880 REPORT NUMBER 2024:00958 VERSION 1.3 15 of 26 Table 3.4: Decision variables related to the aggregator or "main" node Decision Variables Description 𝑃𝑏𝑎𝑙 𝑛,𝑡 Power balance of each firm 𝑛at time 𝑡 𝑃𝐸𝑀𝑆 𝑛,𝑡 Power from the energy management system of each firm 𝑛at time 𝑡 𝑃𝑓𝑎𝑐𝑡𝑜𝑟𝑦 𝑛,𝑡 Power demand of the factory for each firm 𝑛at time 𝑡 𝐶𝑚𝑜𝑑𝑒𝑙 𝑚,𝑛 Total non-power cost of each model 𝑚used for each firm 𝑛 𝑃𝑎𝑔𝑔 𝑡Float, the aggregator’s power at time 𝑡 𝐶𝑎𝑔𝑔 Float, the aggregator’s cost 𝐶𝑡𝑜𝑡𝑎𝑙,𝑎𝑔𝑔 Float, the aggregator’s total cost 𝐶𝑝𝑜𝑤𝑒𝑟,𝑎𝑔𝑔 Float, the aggregator’s power cost 𝐼𝑡Binary, it defines power sold and bought for the constraints at time 𝑡 𝑃𝑏𝑜𝑢𝑔ℎ𝑡,𝑎𝑔𝑔 𝑡Float, bought power by the aggregator at time 𝑡 𝑃𝑠𝑜𝑙𝑑,𝑎𝑔𝑔 𝑡Float, sold power by the aggregator at time 𝑡 𝑃𝑓𝑎𝑐𝑡𝑜𝑟𝑦 𝑛,𝑡 and 𝑃𝐸𝑀𝑆 𝑛,𝑡 are the power demand at the factory and from the energy management system (for example power from PV or a battery) respectively for firm 𝑛and time 𝑡. These variables are created in practice in the respective scheduling and energy management system optimization models, and they are linked together at the energy management system node for that factory 𝑛, using what Plasmo defines a linking constraint, which is a constraint that involves variables from different optimization models. 𝑃𝑓𝑎𝑐𝑡𝑜𝑟𝑦 𝑛,𝑡 uses in this case the formulation in eq. (3.22) for the case of a scheduling model explained in section section 3.1. However, the power demand formulation will depend on the specific scheduling model used for that specific factory. 𝑃𝑓𝑎𝑐𝑡𝑜𝑟𝑦 𝑛𝑠𝑐ℎ,𝑡 =𝑃𝑝𝑟𝑜𝑑 𝑡+𝑃𝑠𝑡𝑎𝑟𝑡 𝑡+𝑃𝑐ℎ𝑎𝑛𝑔𝑒 𝑡,∀𝑡∈𝑇(3.22) Where 𝑛𝑠𝑐ℎrepresents a factory that models their scheduling using the description in section section 3.1,𝑃𝑝𝑟𝑜𝑑 𝑡 is the power consumed by the manufacturing of the products, 𝑃𝑠𝑡𝑎𝑟𝑡 𝑡is the power consumption caused by starting producing a product, and 𝑃𝑐ℎ𝑎𝑛𝑔𝑒 𝑡is the power consumption originated when changing from one product to the other in the line, as described in eqs. (3.23) to (3.25) respectively. 𝑃𝑝𝑟𝑜𝑑 𝑡=∑ 𝑙∈𝐿∑ 𝑝∈𝑃[𝑝𝑟𝑙,𝑝,𝑡⋅𝐶𝐸 𝑝]𝑡=∆𝑇𝑆𝑇 𝑝,...,𝑇 (3.23) 𝑃𝑠𝑡𝑎𝑟𝑡 𝑡+𝑡′−1=∑ 𝑙∈𝐿∑ 𝑝∈𝑃[𝑠𝑡𝑙,𝑝,𝑡⋅𝐶𝐸𝑆𝑇 𝑝,𝑡′−𝑡]𝑡=1,...,𝑇−∆𝑇𝑆𝑇 𝑝,𝑡′=𝑡,...,𝑡+∆𝑇𝑆𝑇 𝑝|𝑡′≤𝑇(3.24) 𝑃𝑐ℎ𝑎𝑛𝑔𝑒 𝑡+𝑡′−1 =∑ 𝑙∈𝐿∑ 𝑝∈𝑃[∑ 𝑝′∈𝑃|𝑝′≠𝑝𝑐ℎ𝑙,𝑝,𝑝′,𝑡⋅𝐶𝐸𝐶𝐻 𝑝,𝑝′,𝑡′−𝑡]𝑡=∆𝑇𝑆𝑇 𝑝,...,𝑇−∆𝑇𝐶𝐻 𝑝,𝑝′,𝑡′=𝑡,...,𝑡+𝑡+∆𝑇𝐶𝐻 𝑝,𝑝′|𝑡′≤𝑇 (3.25) On the other hand, 𝑃𝐸𝑀𝑆 𝑛,𝑡 is the power coming from the EMS. In the case studies it represents a very simple model with a fixed normalized PV profile multiplied by a fixed, installed PV capacity, as shown in eq. (3.26). 𝑃𝐸𝑀𝑆 𝑛,𝑡 =𝑝𝑃𝑉 𝑡⋅𝑐𝑎𝑝𝑝𝑣 𝑛∀𝑛∈𝑁,𝑡∈𝑇(3.26) Where 𝑝𝑃𝑉 𝑡is a normalized profile of PV production for time 𝑡, which is scaled up with the fixed installed PV capacity 𝑐𝑎𝑝𝑝𝑣 𝑛at firm 𝑛. However, this 𝑃𝐸𝑀𝑆 𝑛,𝑡 can belong to a more complex energy management models, PROJECT NUMBER 102027880 REPORT NUMBER 2024:00958 VERSION 1.3 16 of 26 including batteries, investments etc. Future analyses will use the model EnergyModelsX [6] for this purpose. Next, the power balance at the aggregator is represented in eq. (3.27), and it is again a liking constraint. As mentioned above each energy management system at a firm 𝑛has a variable 𝑃𝑏𝑎𝑙 𝑛,𝑡, containing the balance between the energy flows from the energy management system models (e.g. PV produced) and the power demand at the factory, defined in the specific scheduling models. The sum of all the 𝑃𝑏𝑎𝑙 𝑛,𝑡 from all firms is linked to the power balance of the aggregator, defined as a variable in the aggregator optimization model in "main". 𝑃𝑎𝑔𝑔 𝑡=∑ 𝑛∈𝑁𝑃𝑏𝑎𝑙 𝑛,𝑡 (3.27) The power costs of the aggregator are calculated as follows, in eq. (3.28). 𝐶𝑝𝑜𝑤𝑒𝑟,𝑎𝑔𝑔=∑ 𝑡∈𝑇𝑃𝑏𝑜𝑢𝑔ℎ𝑡,𝑎𝑔𝑔 𝑡⋅𝑃𝑟𝑖𝑐𝑒𝑝𝑜𝑤𝑒𝑟 𝑡−𝑃𝑠𝑜𝑙𝑑,𝑎𝑔𝑔 𝑡⋅𝑃𝑟𝑖𝑐𝑒𝑝𝑜𝑤𝑒𝑟 𝑡⋅𝑟(3.28) The other non-power costs of the aggregator depend on the costs from the energy management and firm nodes, as described in eq. (3.29), and depending on the model use. For the analyses presented in this report, none of these extra costs were considered, but they can represent investments, material costs, maintenance costs, labour costs etc. This is again a linking constraint that connects the different optimization models used through cost variables in this case. 𝐶𝑎𝑔𝑔=∑ 𝑛∈𝑁,𝑚∈𝑀𝑜𝑑𝑒𝑙𝑠𝐶𝑚𝑜𝑑𝑒𝑙 𝑚,𝑛 (3.29) Finally, the total costs of the aggregator, which equates the objective function of the aggregator consists on the sum of the non-power and power costs, as described in eq. (3.30). 𝐶𝑡𝑜𝑡𝑎𝑙,𝑎𝑔𝑔=𝐶𝑎𝑔𝑔+𝐶𝑝𝑜𝑤𝑒𝑟,𝑎𝑔𝑔 (3.30) 3.3 Practical Challenges The main challenges from the modelling implementation came from attaching models to JuMP nodes and synchronizing link constraints in TimeStruct in the case of iterating through the time periods. Plasmo does not allow for referencing a node by a string (ie “Firm 1”), meaning that to find the node, we have to search over the labels attached to all nodes in the graph. While tedious from a coding set-up vantage point, there is no performance loss since the messenger nodes must only be found once. In addition, Plasmo doesn’t allow for the same model to attach to more than one node. Thus, in constructing graphs, the instance models must be re-defined before assigning them to the FS/EM nodes. Following work in the project has made it easier to navigate through the different nodes and models by among others, using standard naming of nodes and models. For TimeStruct, it seems important to be careful in referencing time steps as the solving is done for integer time 1≤𝑡≤𝑇. Using collect(T)or setting an iterator was a useful workaround. A last note is that many of these errors would occur silently. Printing out link constraints, and testing simple cases is therefore very important. Based on these challenges, TimeStruct has been updated to make it easy to iterate through operational periods in future implementations. PROJECT NUMBER 102027880 REPORT NUMBER 2024:00958 VERSION 1.3 17 of 26 Chapter 4 Case studies This chapter presents a test analysis performed for a generic industrial cluster, with the main purpose of testing the framework and its potential. The main focus will be on the scheduling and the industrial cluster presented in the previous chapter. For each of these models, the setup, main assumptions and results will be presented. 4.1 Main assumptions and data There are two main parameters that are obtained from real data. The first one is electricity prices, obtained for 120 hours (in the period 3rd-11th of March 2023 and hourly resolution) of Spanish1spot prices. For the PV profiles for the different countries, a profile PVGIS2is used. This profile is from a generic PV system in northern Spain, normalized with its maximum capacity. The profile will be then scaled up for each firm that has its own PV system based on the installed capacity. The profiles are shown in fig. 4.1. The rest of the values are defined as dummy values. 4.2 Production Scheduling in the Factories The scheduling test is applied on a single factory, compared to a baseline factory without an optimized schedule. The case regards a factory with 3 products and two lines. The products p1 and p2 can be produced on the same line (l1) while p3 is the only product produced at its own line (l2). p1 and p3 require one worker while p2 requires three. The energy consumption profiles are rather similar for the three products. There are available workers throughout the entire temporal horizon, but the numbers are reduced for the night shift all week (5 workers on daytime and 3 in the nighttime), so this will effect the production at nighttime since if we produce p2 we are unable to produce anything on the other line. Electricity prices vary with time, following the profile mentioned in section 4.1. The difference between baseline and smart scheduling is two constraints. For the baseline case each product can only have one startup for the whole period and the model is unable to change between products. One limitation of this approach is that the problem might be infeasible, e.g. if they reduce the number of workers at night, then they might not be able to produce the required product amounts. 4.3 Energy Aggregator for Industrial Cluster The Aggregation system is tested on a simulated cluster. This cluster is composed of three firms (in the Wizarding World): Honeydukes, Ollivanders, and Hogshead. These three firms have a scheduling model of the one 1Downloaded from https://www.ree.es/ 2https://re.jrc.ec.europa.eu/pvg_tools/en/ PROJECT NUMBER 102027880 REPORT NUMBER 2024:00958 VERSION 1.3 18 of 26 Figure 4.1: Normalized PV profile and electricity prices used for the case studies. Table 4.1: Input data used in the analyses Honeydukes Olivanders Hogshead Products p1, p2, p3 p1, p2 p1 Demand per product (units) 1000, 3000, 4000 2000, 2000 2000 Workers needed per product 1, 4, 1 1, 5 1 Production per hour and product (units) 50, 50, 50 50, 50 50 Energy use (kWh) per hour and per product 10, 10, 10 10, 10 10 Start-up energy profile (all products, kWh/h) [20, 30] [20, 20] [40, 20] Lines and products they can produce l1 (p3), l2 (p1, p2) l1 (p1, p2) l1 (p1) Energy profile in each line to change a product (kWh/h) [20, 20] [20, 20] — Installed PV capacity (kW) 0 20 10 presented above, in section 3.1 and section 4.2. Honeydukes makes three products on two lines. Line 1 can only make the third product, and line 2 can pick between products 2 and 3. Ollivanders makes two products on 1 line. Hogshead makes one product on one line. They all face a set demand per product which they can meet using the available lines and workers. They have a fixed amount of time and energy use to begin production. Once in steady-state, they produce a fixed amount of the product with a fixed energy consumption. When switching, they are have set time and energy costs for transitioning between steady states. These switching values can depend on the set of products that are being moved between. In addition, each product requires some number of workers to produce. This is the same for starting, switching and steady-state for a given product. The input data used for the analyses is presented in section 4.3 On the energy management side, Honeydukes has no local supply and must always purchase electricity from the grid or the Aggregator. Ollivanders and Hogshead can use their own PV cells. Data for the profile of PV production is scaled from the nominalized profile described in section 4.1 above depending on the installed capacity of these two firms that has PV. The optimization will be over one strategic period (120 hours) using electricity spot prices from Spain described in section 4.1. Prices peak during times of higher demand (often midday) and generally are decreasing PROJECT NUMBER 102027880 REPORT NUMBER 2024:00958 VERSION 1.3 19 of 26 Figure 4.2: Energy profiles of the case BAU and 𝑟=0.5. They represent the energy balance of each firm, also showing a profile with only the factory demand without PV as a dashed line, and the total energy balance of all firms in a black, dotted line. later in the week. The analysed cases are built based on the comparison between the Benchmark (individual optimization) and Centralized Choice algorithms. Apart from these two main scenarios, the analysis is complemented by sensitivities to the sell-back discount rate 𝑟. In order to calculate the cost for each individual firms energy use we use 𝑟=0.7to calculate the internal prices described in 2. 4.3.1 Effect of r= 0.5 Recall that when 𝑟=0.5(a value aligning with [2]), firms selling energy to the grid by the firms will receive 50% of the price. We discuss this in Section 2.4. So the if the price is 2Euros, they would get 1Euro. In the Benchmark case for 𝑟=0.5, firms do not have enough demand to require continuous production. As such, they are able to save money by postponing production to the end of the week and selling back excess on the earlier days. fig. 4.2 shows both the net energy use from the firms and the energy use relating to the firm’s factory. The grey line shows the total power demand to the grid from the Aggregator assuming a Monday - Friday work-week (hours 0 to 120). As seen in fig. 4.1, electricity prices decrease for the last days of the week, and this will promote the main part of the production to happen during these days. In addition, there is a considerable amount of PV production except for the second half of the third day. This allows production and energy exchange during the day of most days. We can see these effects of the PV-production and electricity price profiles in the results below. Under Centralized Choice, shown in fig. 4.3, since they can make gains from inter-firm selling we see that in the middle of the week, some factories begin production, boosted by the ability for Ollivanders and Hogshead to supply discounted energy. Suppliers (Ollivanders and Hogshead) can sell surplus energy from PVs at a higher price. Energy users (Honeydukes and Ollivanders) can buy energy at a cheaper rate than later in the week. Like in benchmark case, all firms take advance of the cheap end of week prices for which there is a large aggregate spike in energy demand from the grid. PROJECT NUMBER 102027880 REPORT NUMBER 2024:00958 VERSION 1.3 20 of 26 Figure 4.3: Energy profiles of the Cluster case and 𝑟=0.5. They represent the energy balance of each firm, also showing a profile with only the factory demand without PV as a dashed line, and the total energy balance of all firms in a black, dotted line. Lastly, we plot the difference in benchmark versus cluster costs for the firms in fig. 4.3. These are created by re-defining internal prices for the buying and selling of the energy as discussed in for Centralized Choice. We see here that all firms benefit, and that Honeydukes benefits the most. As we will see, this is a natural result of the relative prices on internal and external exchange. Since the baseline difference between 𝑟,𝑟is pretty small, the mark-up benefit to the internal sellers is minimal compared to that of internal buyers. This favors the non-producer (Honeydukes). 4.3.2 Effect of r= 0.2 As we raise the external selling discount, this increases the incentive for the energy to be used internally. In the benchmark case this implies that the firm should prioritize use of its PV production. The new benchmark results are plotted in fig. 4.5 and Cluster results in fig. 4.6. As we imagine theoretically, in both cases there is higher demand in the high-price start of the week since the loss from external trading is more costly. Since Honeydukes has no cheap PV energy to use, it still starts at the end of the week. Ollivanders begins much earlier in the week and Hogshead, which has less demand to fulfill, continues to postpone production. In the Cluster case, this result is amplified. Since Honeydukes has cheap energy it can now also take from the other firms, it begins production on Tuesday. Likewise, Ollivanders takes from Hogshead to start on Monday. As we use post-processing to evaluate cost savings, there is now clear benefit of clustering given to the energy producers (Ollivanders and Hogshead), reversing the earlier trend. The values are presented in fig. 4.7. PROJECT NUMBER 102027880 REPORT NUMBER 2024:00958 VERSION 1.3 21 of 26 Figure 4.4: Cost savings for each firm when the cluster case is compared to the benchmark case, r=0.5 Figure 4.5: Energy profiles of the benchmark case and r=0.2. They represent the energy balance of each firm, also showing a profile with only the factory demand without PV as a dashed line, and the total energy balance of all firms in a black, dotted line. PROJECT NUMBER 102027880 REPORT NUMBER 2024:00958 VERSION 1.3 22 of 26 Figure 4.6: Energy profiles of the Cluster case and r=0.2. They represent the energy balance of each firm, also showing a profile with only the factory demand without PV as a dashed line, and the total energy balance of all firms in a black, dotted line. Figure 4.7: Cost savings for each firm when the cluster case is compared to the BAU case, r=0.2 PROJECT NUMBER 102027880 REPORT NUMBER 2024:00958 VERSION 1.3 23 of 26 Chapter 5 Conclusions and next steps Our project worked to model ways for firms in a cluster to jointly optimize and, in so doing, save costs and best use local energy availability. Going about this required careful attention to how factories made energy-use decisions and how one can link them in a simple computational model. From a market-design side, clustering saves money even if firms pick the same production and renewable energy profiles as before because of the benefit to local selling. Yet, how to pick the best option and share the benefits is an open question. Centralized decision-making has high cost-saving value, but is impractical if firms have different objectives and would like to have control of their production. Automatic trading may offer a promising alternative since it allows firms to operate as they are now with the added bonus of exchanging energy with other firms should they have extra. The presented modelling framework is suitable for a wide variety of uses. Firms could trade options where they give money to not produce in order to go about factory maintenance. We can also easily adapt the case to include emissions for firms seeking to meet emissions quotas or account for a carbon price. Our next steps on the Aggregator model are as follows: •Incorporating computationally-tractable ways to share firm information with the aggregator. •Including emissions into the Aggregation analysis. •Considering renewable energy investments. For the production scheduling side, it is important to add more functionalities to model different industrial processes, such as improving workforce constraints (not only number of workers, but also requirements in specialized tasks), more demand fulfilling options or implement material flow, waste and recycling etc. On the theory side, it is important to better understand concrete cases when industrial energy sharing would happen. Using this, we can offer tailored ideas about how one may properly run a local industrial cluster market. Future analyses will be built on more detailed data from the use cases in Flex4Fact, to actually measure the benefits of a industrial cluster in real life situations. Beyond the scope of this paper is including an Aggregator in short-term Demand Response (DR) markets. Characteristics depend on the time scale of demand response, but our general advice is to make pricing scheduling and options as transparent as possible to all cluster participants. This will help lessen any efficiency loss in having a two-level (aggregator, DR) approach to energy costs. Most of all, we hope that our work can be used as a basis for the some of more complex technological and economic questions the Flex4Fact project will seek to address, and others looking at the construction of new business models and digital systems to help facilitate and mitigate the economic impact of the energy transition. PROJECT NUMBER 102027880 REPORT NUMBER 2024:00958 VERSION 1.3 24 of 26