Optimization-based identification and quantification of demand-side management potential for distributed energy supply systems

Accepted Manuscript Optimization-based identification and quantification of demand-side management potential for distributed energy supply systems Björn Bahl, Matthias Lampe, Philip Voll, André Bardow PII:

S0360-5442(17)31077-0

DOI:

10.1016/j.energy.2017.06.083

Reference:

EGY 11091

To appear in:

Energy

Received Date: 12 April 2016 Revised Date:

30 May 2017

Accepted Date: 13 June 2017

Please cite this article as: Bahl Bjö, Lampe M, Voll P, Bardow André, Optimization-based identification and quantification of demand-side management potential for distributed energy supply systems, Energy (2017), doi: 10.1016/j.energy.2017.06.083. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Optimization-based identification and quantification of demand-side management potential for distributed energy supply systems Björn Bahl, Matthias Lampe, Philip Voll, André Bardow Preprint submitted to Energy

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Title:

Optimization-based identification and quantification of demand-side management potential for distributed energy supply systems

Authors:

Björn Bahla, Matthias Lampea, Philip Volla, André Bardowa*

Affiliations:

a

Keywords:

Demand-Side Management, Optimization, Distributed Energy Supply System, Cogeneration, Trigeneration, Process System.

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Abstract

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A method is presented to identify the potential for demand-side management (DSM) in energy supply systems. Optimization of energy supply systems usually considers energy demands as fixed constraints. Thereby, possible changes on the demand side are neglected. However, demand changes can lead to a better overall solution. Thus, DSM measures should be integrated into the optimization of energy systems. However, integrating optimization of DSM measures generally requires problem-specific process models. To avoid the need for problem-specific process models, we present a generic method applicable to various process domains. The method identifies a merit order of time steps with large potential for DSM and quantifies potential cost savings by DSM. Targets for demand-side measures are provided in a DSM map as guidance for the process engineer. The merits of the novel method are illustrated for an industrial case study. In this study, 9.6% of all time steps are promising for DSM measures since they show a high sensitivity to demand changes. In particular, the method identifies non-intuitive time steps with high cost saving potential through DSM. We identify potential cost savings of more than 10% if DSM measures are implemented.

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1 Introduction

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We consider energy systems which consist of a distributed energy supply system (DESS) and a process system (Figure 1): The DESS converts primary and secondary energy to final energy required by the process system. The process system employs the final energy in technical processes, e.g., manufacturing.

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Today, distributed energy supply system and process system are usually assumed to interact via a fixed interface: The processes demand a fixed amount of final energy in various forms, e.g., heating, cooling, or electricity; the demanded energy flows are provided by the DESS [1]. Fixed demands allow analyzing the distributed energy supply system and process system independently. Independent analysis of both systems is less complex and allows the use of domain-specific tools and case-specific models [2]. In practice, the interface also often represents industrial reality since distributed energy supply system and process system are usually operated by separate divisions in a company (or even two separate companies). However, independent analysis of the DESS and process system neglects any synergies and

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Chair of Technical Thermodynamics, RWTH Aachen University, 52056 Aachen, Germany *[email protected]

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Optimization-based identification and quantification of demand-side management potential for distributed energy supply systems Björn Bahl, Matthias Lampe, Philip Voll, André Bardow Preprint submitted to Energy

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thus usually leads to suboptimal solutions for the overall energy system. Hence, for an optimal overall energy system design, DESS and process system should be considered simultaneously as presented by Papoulias and Grossmann in 1983 for a single operation point [3]. Recently in 2014, Grossmann [4] pointed out the importance of sustainable energy systems in the process industries for enterprise wide optimization. Agha et al. [5] highlighted the benefits of an integrated approach coupling a manufacturing process and the utility system in one mixed-integer linear programming (MILP) model. Energy System Interface Final Energy

Products

Process System Energy Demand

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Distributed Energy Supply System (DESS)

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Figure 1. Energy system with two sub-systems: Distributed energy supply system and process system

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However, integrating the analysis of DESS and process system into one holistic optimization model requires a large and most importantly case-specific model of the overall energy system. Thus, the level of detail in the model is limited and efficient solution strategies are required. Hadera et al. [6] decreased the problem size of the large holistic optimization model with a heuristic two-level approach to solve industrial-size instances. Besides tailor-made solution algorithms, model decomposition can be applied to the integrated problem [7]. Moreover, a discretization approach was recently presented by Tong et al. [8] to solve the MINLP problem of a production process, explicitly accounting for time-sensitive electricity prices and energy resource availability. Apart from numerical complexity of the holistic optimization of DESS and process system, a specific model needs to be developed for each process system. In contrast, the characteristics of the DESS are very similar for a variety of applications.

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To avoid the need of a process specific sub-model, the DESS model usually contains energy storage to (partially) decouple energy demand and energy supply. The storage is located at the interface of the two sub-systems to allow an independent analysis and optimization. The potential for cost savings by employing energy storage was demonstrated for operation optimization problems of large-scale combined heat and power plants [9], trigeneration systems with demand uncertainties [10], residential cogeneration systems [11], optimal operation of industrial production processes with high cooling demand [12] as well as synthesis problems of district heating networks [13]. Facci et al. [14] proposed a graphtheory-based optimization methodology for optimal operation of a trigeneration system with energy storage and [15] proposed a Lagrangian relaxation algorithm to solve an operation problem of a trigeneration system with thermal storage.

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Besides the introduction of energy storage, the overall energy system can be improved by (partial) control of the demand by the supply. Enabling any form of control of the process system by the DESS is commonly referred to as demand-side management (DSM) [16]. The opportunities of DSM are well known and widely discussed in the literature especially for

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Optimization-based identification and quantification of demand-side management potential for distributed energy supply systems Björn Bahl, Matthias Lampe, Philip Voll, André Bardow Preprint submitted to Energy

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electricity markets and (smart) grids as recently reviewed by Siano [17]. Besides electric energy systems, the DSM concept can also be applied to other energy systems such as heating networks or combined heat and power systems: Optimization of energy systems incorporating DSM reveal additional cost savings compared to a separately optimized DESS, e.g., in energy systems accounting for CHPs [18], microCHPs and heat pumps [19] as well as renewable energy resources like wind power [20] and photovoltaics [21]. Moreover, DSM commonly incorporates thermal energy storage in the context of heating demands [22]. Thus, the potential for cost savings by introducing DSM compared to a separately optimized DESS has been demonstrated for several applications and demand types.

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The studies cited above require models of widely varying detail for the demand side of the energy system. Thus, they are intrinsically specific to a single process system. The resulting model cannot be reused for another energy system without detailed modelling the process leading to the demand. Requiring the development of methods for every specific process system hinders the application. A generic method applicable to a variety of energy systems with different process systems (Figure 1) is required. The method ought to provide a systematic identification of cost savings potential for DSM.

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In this paper, we present a generic method simultaneously considering the distributed energy supply system and the process system. The method systematically identifies time steps with large potential for DSM and quantifies possible cost savings by DSM. The presented method is generic and avoids the need for a case-specific process model. The process system is considered on a generic level ensuring reusability of the overall energy system model. In contrast, a detailed model [23] is employed for the DESS as the energy supply system has similar characteristics for most applications. The DESS considered in this work is a complex trigeneration system and the presented method is capable of quantifying DSM potential of all three demands (heating, cooling, and electricity demand).

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The authors briefly introduced the optimization-based method for identification of DSM potential in a conference paper [24]. Here, the method is described in full detail and extended by the so-called DSM map. In Section 2, the proposed method is introduced along with the employed mixed-integer linear program (MILP) model. In Section 3, the method is illustrated for a real-world case-study. Conclusions are drawn in Section 4.

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2 Optimization-based identification and quantification of DSM potential

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The proposed method systematically identifies the potential for more cost efficient energy use through DSM measures. The analysis is based on optimization of the distributed energy supply system – independent from the process system. Thereby, process-specific models are avoided. Thus, the method provides a process engineer with the knowledge about time steps that are valuable to conduct DSM measures from the perspective of the energy supply system. Whether the energy demand can actually be decreased in the process is still subject to the

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evaluation by the process engineer and the presented method only provides information to support this evaluation.

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The method consists of two steps answering two questions (Figure 2): First, at what time is it (most) valuable to reduce the demand? Second, how much energy demand reduction is (most) valuable? These questions are answered from the perspective of the energy supply, i.e., is the current operation state of the supply system efficient or is cost efficiency increased by demand changes. Finally, the results are visualized in the DSM map. The information guides the process engineer towards promising demand-side measures based on information from the energy supply system. The DSM map is based on the demand time series (also often called “load profile”) and concentrates the information on valuable demand-side measures obtained by the presented method.

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Figure 2. Steps of proposed systematic method to assess DSM potential: Identification (Step 1, ‘What time?’), quantification (Step 2, ‘How much?’), result summary (DSM map)

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In Step 1, promising time steps are identified by the sensitivity of the objective function with respect to changes in the energy demand. Time steps with high sensitivity are most promising for DSM measures. Details on the method for identification of promising time steps are described in Section 2.1. The time steps are ordered with decreasing sensitivity in a merit order. In Step 2, improvements of the objective function value are quantified as function of the reduction in the energy demand. Thereby, the optimal size of demand-side measures can be determined. The methodic steps to quantify the cost savings potential are described in Section 2.2. The number of time steps considered for demand reduction in Step 2 is significantly reduced by considering the preselection of promising time steps (Step 1). Thus, the computationally intensive quantification of possible improvements by demand-side measures in Step 2 needs to be performed for the set of most promising time steps only. The proposed method is based on an optimization model of a DESS. The objective function can be economically or ecologically, e.g., total annualized cost, operational costs or CO2 emissions might be used. In the following, we use operational expenditure OPEX as an

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illustrative economic objective function. The presented method is not restricted to a specific DESS optimization model. Thus, we state a compact form including all essential characteristics (the DESS model of the case study is presented in Appendix A):

OPEX∗ (E&t ):= &min OPEX

(1)

Vnt , ,δ n ,t , x

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s.t.

∑V&

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n ,t

= E& t , ∀t ∈ {t1 ,..., tmax }, ∀d ,

(2)

A1V&n ,t + A2δ n ,t + A3 x ≤ b, ∀t ∈ {t1 ,..., t max }, ∀n ∈ {n1 ,..., nmax }

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n xt l V&n ,t ∈ ℝ nmax x tmax , δ n,t ∈ {0,1} max max , x ∈ ℝ × {0,1} .

( )

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The optimization yields the optimal solution OPEX ∗ E& t . To apply the proposed method, the

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model of the DESS has to account for time-varying energy demands E& t (i.e., heating, cooling

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and electricity demands). The energy demand has to be met in every time step t by the output power V&n ,t of the installed energy conversion components (2). The continuous variable V&n ,t

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represents the operational state of component n in time step t . The binary operation variable δ n ,t represents whether the component n is operated in time step t and is used for

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linearization of part-load performance (A.4). Other variables in the optimization problem are summarized in the surrogate variable x , and other constraints of the DESS optimization model are summarized in the surrogate equation (3). The surrogate equation represents both equality and inequality constraints, and the surrogate variables can encompass continuous and binary variables.

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2.1 Step 1: Identification of promising time steps

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Identification of promising time steps is based on the optimal solution OPEX ∗ E& t

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nominal demand E& t , Eq. (1). We investigate the sensitivity of the objective function value

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OPEX ∗ to changes of the energy demand  . This information is generally described by a

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derivative

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the derivative of the objective function with respect to the right hand side of a constraint is contained in the Lagrange multipliers [25]. The Lagrange multipliers are available from the optimization results provided by standard solvers [26]. Thus, at first sight, it seems suitable to use the readily available Lagrange multiplier to identify the DSM potential. However, local information at the optimal solution OPEX ∗ E& of the DESS is not sufficient to identify

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DSM potential in MILP problems. Lagrange multipliers only exist for LP problems. The solver output of MILP problems also contains Lagrange multipliers, however, they are derived from the final LP solve of the solution algorithm [26], i.e., solving the MILP with fixed integer decisions. Thus, the effect of changes of the binary variables (e.g., on/off status of components) is not considered in provided Lagrange multipliers. Moreover, a finite change of the energy demand ∆ E& t can change the active set of constraints [25]. This change of the

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active set leads to changes in the sensitivity of the objective with respect to the demands. Thus, local information (the derivative) is generally insufficient to rigorously identify DSM

with

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In linear programming (LP) problems with linear independent constraints,

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potential in MILP problems. Therefore, sensitivity is identified using the so-called costreduction index ∆OPEX ∗ OPEX ∗ ( E& t + ∆E& t ) − OPEX ∗ ( E& t ) CRIt ,d = = (4) ∀ t, d . ∆E& t ∆E& t For each time step  and demand  , the cost-reduction index CRI t ,d is calculated as forward

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finite difference with a step-width ∆E& t >> 0 . Thus, not only local information is considered

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in the cost-reduction index. The authors recommend ∆ E& t = − 0 . 05 E& t . In minimization

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problems as in Eq. (1), we expect the objective function value to decrease for a demand reduction. Thus, a positive cost-reduction index CRI t ,d indicates improvements of the

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objective function value. The proposed cost-reduction index is a generalization of the steam marginal price used in top-level analysis of energy systems [27]. The introduced costreduction index considers various energy demands  and multiple time steps . Typically, energy demands are changing with time. Thus, the optimization problem is stated for multiple time steps t (1)-(3) and leads to different optimal operating conditions of the energy system for each time step. As a result, demand-side measures have different impacts on the optimal operating conditions depending on the time step in which the measures are applied. Therefore, the cost-reduction index CRI t ,d is calculated for each time step individually (4).

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Improvements of the objective function value by demand reduction represent potential for DSM measures. Thus, time steps t with large positive cost-reduction index CRI t ,d have high

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DSM potential. The most promising time steps are identified by a merit order of all time steps with decreasing cost-reduction index CRI t ,d . The merit order permutes the time series, thus

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we introduce a new index t̃ for time steps in the merit order, i.e., t̃ is the first time step in the merit order, but not the first time step in the time series series: t ≠ t̃ . The set Td of most

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promising time steps for DSM measures is selected from the merit order for each energy demand d . The selection of T d is a trade-off between required computation time for Step 2

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and the gain of information on less promising time steps. The selection can be based on a fixed number of time steps with the highest cost-reduction indices CRI t ,d or a threshold can

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be defined above which all time steps are selected. Otherwise, the user can identify specific characteristics in the merit-order curve (such as decreasing gradient, steps, kinks, etc.) which imply a reasonable selection of the set Td .

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In summary, Step 1 of the proposed method answers the question: At what time is it (most) valuable to manage the demand? Only the preselected promising time steps in Td are

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investigated in Step 2 of the proposed method to quantify improvements of the objective function value and determine the optimal size of demand-side measures.

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2.2 Step 2: Cost savings of promising time steps

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In Step 1, the set Td of promising time steps for demand-side measures has been identified. However, information about the size of the demand-side measure is required. Therefore, Step 2 of the proposed method analyzes the most promising time steps T d in more detail. Relative

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costs OPEX rel indicate how much the energy demand should be reduced. These relative costs

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OPEX rel are the ratio of the objective function values for the reduced energy demand OPEX ∗ ( E& t + ∆ E& t ) and the design point OPEX ∗ ( E& t ) :

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OPEX rel ∆E& t =

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For all time steps t ∈ T d the relative costs OPEX rel are calculated for varying ∆ E& t . The step-

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width ∆ E& t can be defined by the user, the authors recommend a relative definition based on

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the original energy demand E& t (e.g., ∆ E& t = − 0 . 05 E& t ). The amount by which the energy

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demand can be reduced by the process is not limited in this method. In practice, demand reduction would be limited by process constraints (e.g., minimal part-load). These processspecific constraints are not capture by the presented method. If such information is available for a specific process, it could be easily integrated. The potential for cost savings is identified based on the improved efficiency of the energy supply system. This information is concentrated in the DSM map (Section 2.3) to provide the process engineer with targets for cost savings from the energy side which have to be balanced against potential cost increase at the process side. The method is limited to identify the DSM potential based on independent demand changes. In practice, reducing one demand at one time step could result in changes in other demands or at other time steps. These interdependencies are also process specific and not resolved in the presented method which focuses on the energy supply side. Thus, it should be expected that the present analysis provides an upper bound on the DSM potential which could be reduced in practice by process-specific limits and interdependencies of DSM measures. The relative costs OPEX rel (∆ E& t ) provide information about how much energy demand

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reduction ∆ E& t is (most) valuable for the promising time steps. Thereby, OPEX rel indicates

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the economic cost saving potential (in €) by DSM measures as a function of the size of the measure. This is important information as cost reduction by a reduction of the nominal demand does not imply that any further reduction will further reduce cost. Moreover, the relative costs OPEX rel also represent the allowed cost for implementation of DSM measures.

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Cost for employing DSM can result from, e.g., rescheduling or reduction production or investment in storage.

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2.3 DSM map: Targets for process engineers

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The information on valuable demand-side measures obtained by the presented method is visualized in the DSM map. The DSM map is based on the time series of the energy demand given as input for the optimization of the DESS. The demand time series is extended by further information to provide targets of demand-side measures for the process engineer. These targets are the information obtained with the presented method and answer the questions: At what time are demand-side measures valuable (Step 1) and how much should the energy demand be changed (Step 2)? This information is indicated by a color code of the energy demand-profile (Figure 3).

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OPEX ∗ ( E& t + ∆E& t ) , ∀t ∈ Td , ∀d . OPEX ∗ ( E& t )

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Figure 3. Illustrative schematic of the DSM map: Green: DSM is valuable, red: DSM should be avoided, grey: DSM is unfavourable, but has no negative effects.

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For all time steps, the results of Step 1 indicate if demand-side measures are expected to be valuable. This is depicted in a ternary color code (Green, Grey, Red) depending on the value of the cost-reduction index CRI t ,d for each time step (Figure 3). For the promising time steps

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Td , the results of Step 2 quantify the valuable amount of demand-side measure. Thus, for

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promising time steps Td the coloring is further refined by indicating the valuable amount of

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demand reduction (Figure 3). In summary, the ternary color code of the DSM map is as follows: • Green: Promising time steps Td (i.e., high values of cost-reduction index CRI t ,d ) are

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green colored. For promising time steps Td , the green fraction indicates the

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demand reduction ∆ E& t till the minimum of relative costs OPEX Grey:

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grey colored. For promising time steps Td , the grey fraction indicates

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the demand reduction

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OPEX

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Red:

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colored. For promising time steps Td , the red fraction indicates the

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demand reduction ∆ E& t with relative costs OPEX

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Thus, the DSM map summarizes the important information obtained with the presented method in a compact and comprehensive form and provides targets for valuable demand-side measures to the process engineer.

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3 Industrial case study

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In this section the presented method is illustrated by a real-world case study using the MILP model presented in our previous work (for details see Appendix A and [23]). This continuation of our previous work allows us to apply the presented method to a typical example of energy supply system optimization. The model matches the requirement on the DESS model stated in Section 2, Eq. (1)-(3). Moreover, linearized part-load performance curves and minimum part-load are considered in the model (for details see Appendix A). The considered components n in this work are gas-fueled boilers, combined heat and power engines, turbo-compression chillers and absorption chillers. Thus, a complex trigeneration 8

Optimization-based identification and quantification of demand-side management potential for distributed energy supply systems Björn Bahl, Matthias Lampe, Philip Voll, André Bardow Preprint submitted to Energy

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system is considered. However, the proposed method is not limited to this model. Further components and other aspects (e.g., time varying prices or storage) can be incorporated in the DESS model [28]. Demands E& t for cooling, heating and electricity are considered for different buildings (e.g.,

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production, laboratory, facilities, offices). Generally, the solution space for synthesis of DESS is dense [29] and many structures result in similar cost, thus in this case study the optimal structure of the DESS is not the structure from Voll et al. [23] due to a different time-series aggregation. The optimal structure here is a trigeneration system consisting of 3 absorption chillers (AC), 3 compression chillers (CC), 2 boilers (B) and 3 combined heat and power (CHP) engines (Table 1). This study is based on an hourly resolved time period of one month as demand profile (Figure 4).

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Table 1. Technology and nominal thermal power V&nN of the optimal structure for the case

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study (AC – adsorption chiller, CC – compression chiller, B – boiler, CHP – combined heat and power engine)

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B CHP CHP CHP Technology AC AC AC CC CC CC B N & 3.6 1.9 1.9 3.6 2.0 1.2 6.0 0.1 2.3 2.3 2.3 V n / MW 14 12 10 8 6 4 2 0 0

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Figure 4. Energy demand profiles E& t for one month with hourly resolution: cooling (blue,

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dashed-dotted), heating (red, solid) and electricity (green, dashed) demand (color online)

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The objective function OPEX is defined according to our previous work[23] by:

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nmax t max   t max (6) f = OPEX = ∑ ∑ ∆t t p nU& n ,t (δ n ,t ,V&n ,t ) + m n I n  − ∑ ∆t t p el , sell V&t el , sell , n =1  t =1  t =1 where U& n , t is the input energy flow to component n in time step t . The specific cost pn of

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input energy flow U& n of component n represents gas- or electricity prices and ∆t t = 1 h is the

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time interval of time step t . Maintenance costs mn I n are calculated relative to the investment

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cost of the component n according to our previous work [23]. The electricity sold to the grid

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el , sell . We determine the optimal solution, i.e., the V&t el , sell is refunded with the selling price p

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optimal operation V&n ,t for each component n in each time step t , by solving the resulting

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MILP with CPLEX [26].

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3.1 Promising time steps for demand-side measures

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Step 1 of the presented method (Section 2.1) identifies a set of promising time steps Td with

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high DSM potential. For this purpose, we calculate the cost-reduction index CRI t ,d , Eq. (4),

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based on a step-width of ∆ E& t = − 0 .05 E& t . cooling demand

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merit order t˜

merit order t˜

Figure 5. Merit order ̃ of time steps with descending cost-reduction index CRI t ,d for a)

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cooling demand and b) heating demand with sets of promising time steps for cooling demand T c and heating demand T h

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The cost-reduction index CRI t ,d can differ for each time step t. Thus, we put the time steps in

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descending order according to their corresponding cost-reduction index (similar to the construction of a sorted annual load duration curve of an energy demand). Based on the resulting merit order of time steps ̃ (Figure 5), we identify the set of promising time steps Td

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for each demand d . In the first time step of the merit order ̃ , energy cost reduction is higher than in any other time step ̃ ,  > 1. Demand-side measures should consider first the time steps of the merit order with high cost-reduction index (for details see Section 2.1). As expected, the peak heating demand in time step t561 is identified as one of the promising

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cooling demand CRI t ,cooling

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CRI t ,cooling in the merit-order curve are small compared to the cost-reduction index values of

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time steps t561 ∈ Th . However, in the merit order, the time step t561 with the peak heating demand is only at position ̃. Thus, a systematic method is required for the identification of DSM potential as several other, more promising time steps are found. For further discussion on the necessity of Step 1, see Section 3.3 ant the presentation of the visualization in the DSM map. For most time steps, we observe a positive cost-reduction index (Figure 5) indicating cost savings by reducing the energy demand. For time steps with negative cost-reduction index, a demand reduction results in extra cost. Thus, for these time steps, demand reductions have to be avoided. However, these time steps can be considered as a good option for load-shifting: demand could be shifted from one time step to another time step with negative cost-reduction index, if the process allows this load shift. A cooling demand reduction results in cost savings for each time step. According to the proposed method, time steps with high cost-reduction index are selected as most promising time steps for demand-side measures ( T c in Figure 5a). The cost-reduction index of the

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ranges from 0.04 €/kWh to 0.01 €/kWh. The values of

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the heating demand CRI t ,heating (Figure 5b). The cost-reduction index CRI t ,heating ranges from

348 349 350 351

+0.23 €/kWh to −0.06 €/kWh. In the following, we focus on results for the heating demand as it shows higher potential. Further results for the cooling demand are provided in Appendix B and C. For the heating demand, the time steps with highest cost-reduction indices CRI t ,heating are

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selected as most promising time steps ( T h in Figure 5b). We select the first 85 time steps in

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the merit order for further analysis here. The descending gradient of the merit-order curve for ̃ > 85 indicates a reasonable trade-off between required computation time for Step 2 and the gain of information on less promising time steps. For subsequent time steps ̃ ,  > 85 the cost-reduction index is small CRI t ,heating < 0.04 €/kWh, comparable to the CRI t ,cooling of the

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cooling demand for many time steps. Nevertheless, most time steps have a positive costreduction index CRI t ,heating : Reducing the heating demand in these time steps results in cost

359 360 361 362 363 364 365 366

savings. Interestingly, 81 time steps with negative cost-reduction indices are also identified (Figure 5b). For time steps with negative cost-reduction index, a demand reduction immediately results in extra cost. This behavior is counter-intuitive but can result from lower electricity production in cogeneration when reducing the heating demand. Thus, more electricity has to be bought from the grid. The startup of additional adsorption chillers to compensate the heating demand reduction is limited by minimum part-load constraints of the adsorption chillers. For time steps with CRI t ,heating < 0 €/kWh, a demand-side measure leading to

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demand reduction should be prohibited as this demand reduction would result in extra cost. The proposed Step 1 provides valuable information to preselect a set of promising time steps Td for demand-side measures. The promising time steps Td are further analyzed in Step 2 of

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the presented method.

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3.2 Cost savings by demand-side measures

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In Step 2 (Section 2.2) of the presented method, the set of time steps Td with the highest

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DSM potential identified by Step 1 is analyzed to quantify the DSM measures. We quantify how much the energy demand should be reduced by relative costs OPEX rel (∆ E& t ) . The relative

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∆ E& t for the promising time steps t ∈ Td . In this study, the step-width is set to ∆ E& t = − 0 . 05 E& t

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. For illustration of Step 2, the time step with maximum cost-reduction index for the heating demand is discussed in detail here, i.e., the most promising time step ̃ (Figure 6).

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costs OPEX rel (∆ E& t ) , Eq. (5), are calculated as function of the reduction of the energy demand

1 2 ˙ OP EXrel ∆Et /%

375

105 100 95 90 85 -100

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-60

-40

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0

∆E˙ t /% E˙ t

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382 383 384 385 386 387 388 389 390 391

For the most promising time step of the heating demand ̃ , a cost minimum is found at ∆ E& t = − 0 . 65 E& t . Further reduction in the energy demand can reduce cost savings (Figure 6). The potential cost savings are 12.5% of the operational expenditure. These potential savings also represent the limit for cost of employing DSM measures to realize the demand reduction, e.g., change of process scheduling or reduction of production. In time step ̃ , a heating demand reduction results in more use of trigeneration, thus the OPEX decreases. For the optimal reduction found (∆ = 65%), the absorption chillers provide all required cooling demand. Further reduction of the heating demand results in less heat produced by the CHP engine and thus less produced electricity. In turn, this electricity needs to be bought from the grid, which results in less net savings for the overall energy supply for ∆ E& t > − 0 . 65 E& t . Thus,

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Figure 6. Relative costs OPEX rel (∆ E& t ) as function of the energy demand reduction ∆ E& t / E& t for the most promising time step ̃ of the heating demand

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should be limited to the optimal level. Different patterns of relative cost savings OPEX rel (∆ E& t ) have been observed for promising

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time steps t ∈ Td . Three types of pattern have to be distinguished: Besides a monotone

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for time steps with a minimum in OPEX rel (∆ E& t ) , an optimal level of demand reduction exists, here for ̃ at ∆ E& t = − 0 . 65 E& t . If a minimum exists for OPEX rel (∆ E& t ) , demand-side measures

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decreasing OPEX rel (∆ E& t ) (Figure 7a), the dependence can also show a minimum of

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73% are found to have an optimal demand-reduction level. 25% out of this 73% will even lead to extra cost, if the demand is further reduced. The different patterns are observed for promising time steps of both heating and cooling demand. Plots of OPEX rel (∆ E& t ) for the most

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promising time steps of the cooling demand are given in Appendix B.

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105 b

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operational expenditure (Figure 6 and Figure 7b). Thus, in this case, an optimal demandreduction level exists and is identified by the proposed method. Moreover, energy demand reduction beyond the minimum not only reduces cost savings but can even result in extra costs (Figure 7b). 27% of all promising time steps t ∈ Td show the monotone decreasing pattern. The remaining

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95

95

90

90

85 -100

85 -100

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0

∆E˙ t /% E˙ t

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-60

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-20

0

∆E˙ t /% E˙ t

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Figure 7. Patterns of relative costs OPEX rel (∆ E& t ) as function of the energy demand reduction

409

∆ E& t for promising time steps a) 0 ∈ 23 and b) 45 ∈ 23

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The DSM map (Section 2.3) visualizes which time steps are promising for demand side measures and the existence of an optimal demand-reduction. The DSM map for the case study is discussed in the next section.

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3.3 DSM map as target for demand-side measures

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CRI t ,heating (Figure 5). Thus, we show a section of the DSM map for the heating demand

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(Figure 8) for the interval  = 6407 , 77 8. This interval contains the time step t561 with the

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peak heating demand. The complete DSM map of the heating demand and cooling demand is provided in Appendix C. 14 12 non-promising additional cost DSM potential 10 cooling heating electricity 8 6 4 2 0 520 540 560 580 600

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The DSM map (Section 2.3) provides an easy-to-use target for the process engineer showing which demand-side measures should be realized. The DSM map is based on the demand time series (Figure 4) and visualizes the information obtained by Step 1 (Section 3.1) and Step 2 (Section 3.2). As discussed in Section 3.1, the values of the cost-reduction index for cooling CRI t ,cooling in the merit-order curve is small compared to the values of the heating demand

time t / h

Figure 8 DSM map for time interval  = 6407 , 77 8 of the heating demand; Time steps identified as promising time steps t ∈ T h (green), non-promising time steps t ∉ T h (grey),

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negative cost-reduction index (red); optimal demand reduction at minimum of OPEX

427 428

for promising time steps t ∈ T h (limit of green color-bar) The time steps with high cost-reduction index SCR t , heating identified as promising t ∈ T h (Step

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1, Section 3.1) are shown in green. Non-promising time steps are kept in grey and if the costreduction index is negative, the corresponding time step is colored in red (Figure 8). Moreover, for the promising time steps with a minimum of relative costs OPEX rel (∆ E& t ), the

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limit of energy demand reduction is indicated by the size of the green color-bar (Step 2, Section 3.2). If further reduction results in extra costs, e.g. as in Figure 7b, the corresponding part of the demand is colored in red. As mentioned in Section 3.1, the time step t561 with the peak heating demand is identified as

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promising time step t561 ∈ Th . However, several other more promising time steps are found

437

and time step t561 is only at position ̃ = 63 in the merit order. Also counter-intuitive time

438

steps with a local minimum in the energy demand are identified as promising time steps (e.g.,

439

4 , 44 ∈ Th , Figure 8). Moreover, the local maximum can be non-promising. (e.g., 454

440

∉ Th , Figure 8). Thus, the selected promising time steps T h do not simply correspond to

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energy demand of the time steps since the different demand types (heating, cooling and electricity) in the system are connected via trigeneration. Thus, limiting the focus of DSM to

rel

(∆ E& ) t

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peak demands is not sufficient. However, the presented method systematically considers all time steps of all demand time series to provide valuable information for the process engineer based on well-funded optimization results.

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4 Conclusions

447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479

An optimization-based method is presented for the systematic identification of DSM potential in energy systems. The presented method considers simultaneously the two sub-systems of an energy system (distributed energy supply system and process system), but does not require an integrated model of the process system. In contrast, a detailed model of the distributed energy supply system is employed as the supply system is very similar for different applications. Hence, the method is applicable to various energy systems without detailed knowledge of the process. The energy system can be of very different character as long as, the energy demands of the process are available as time series. These potential for cost savings is identified by cost savings on the energy supply side. The energy supply side is represented with a detailed model, allowing for detailed analyzes by the presented method. Thus, cost savings on the energy supply side can also be interpreted as maximum cost allowed for demand side measures. The method is applied to a real-world case study based on a model presented in previous work of the authors [23]. The case study represents a typical example of energy supply system optimization. In the study, 9.6% of all time steps are identified as most promising time steps. The selection of promising time steps is not limited to time steps with demand peaks. Interestingly, also non-intuitive time steps with high cost saving potential through DSM measures are identified. Hence, heuristics focusing on the demand peaks are not sufficient to identify time steps with high DSM potential. For 27% of the promising time steps, the cost decreases monotonically if the demand is reduced. The remaining promising time steps (73%) have an optimal level for demand-side measures. Thus, reducing the energy demand beyond this optimal level reduces cost savings and even can increase cost in 25%.of these time steps. Thus, demand-side measures should be limited to this optimal level of reduction to allow for minimal operation cost. Therefore, the optimal amount of energy demand reduction by DSM measures needs to be determined by a systematic method. For the most promising time steps, the cost could be reduced by more than 10% compared to the optimal solution with the nominal energy demands given in our previous work. The results of the method are summarized in the DSM map, providing the process engineer with information which demand changes are valuable from the perspective of the energy supply system. However, the final decision on the demand-side measure is remaining at the process engineer. The proposed method is generic and can thus be applied to general energy systems optimization models to identify and quantify the system-inherent potential for DSM measures.

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Acknowledgments

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Parts of this study were funded by the German Federal Ministry for Economic Affairs and Energy (ref. no.: 03ET1259A). The support is gratefully acknowledged.

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Nomenclature

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Sets and indices of sets Set of promising time steps 2 − Set of boilers B − Set of CHP engines CHP − Set of compression chillers CC − Set of absorption chillers AC − Index for energy supply components ? − Index for time steps  − Index for merit order time steps − ̂ Index for demand types  − Index of line segments A −

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Variables OPEX E F,G

Continuous: operational expenditure Continuous: operational thermal power

H F,G IJ,KLM EG

kW

Continuous: input power

kW

Continuous: electricity purchased from the grid

EG IJ,NIJJ

kW

Continuous: electricity sold to the grid

x

OF,G EP

− − kW

Continuous/Binary: surrogate variable for compact DESS formulation Binary: operation state Continuous: operational thermal power on line segment

ORF,G,Q

−

ψ n,t

kW

Continuous: variable of nominal power, Glover reformulation

ξ n,t

kW

Continuous: variable of bilinear product, Glover reformulation

A T E S,

E G

TE D

Coefficient matrix of surrogate equation Parameter vector of surrogate equation Nominal thermal power

AC C

b

− − kW

Binary: operation state on line segment

EP

Parameters

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€ kW

F,G,Q

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US VS WS CRI ,Z OPEX[IJ η nN

kW €/kWh % € €/kWh % %

Energy demand specific cost of input power specific maintenance cost Investment cost Cost reduction index Relative cost savings Nominal efficiency

COP nN

%

Nominal coefficient of performance

η N, th

%

Nominal thermal efficiency

η N, el

%

Nominal electric efficiency

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uF,Q

kW

]u ]v n,g

−

Normalized gradient

vaF

%

Relative minimal operation limit

Normalized y-intercept

Appendix A

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This section describes the employed MILP model of the DESS [23] which is used for the illustrative case study in Section 3. In Table A.1., the considered technologies with their nominal coefficient of performance or nominal efficiency are listed.

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Table A.1. The considered technologies (AC – adsorption chiller, CC – compression chiller, B – boiler, CHP – combined heat and power engine) with their nominal coefficient of performance or nominal efficiency. CHP 0.87=η nN, tot

AC 0.67

CC 5.54

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B 0.90

Technology η nN , COP nN / -

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The thermal and electrical nominal efficiency of the CHP engine is a function of the engine size, to capture this behavior, the CHP model is divided into size dependent sub-models:

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▪ Small:

0.5…1.4 MW,

η N,th = 0.460, η N,el = 0.410

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▪ Medium:

1.4…2.3 MW,

η N,th = 0.424, η N,el = 0.446

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▪ Large:

2.3…3.2 MW,

η N,th = 0.388, η N,el = 0.482

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The energy balances for the considered trigeneration system are

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= E& tcooling , ∀t ∈ {t1 ,..., t max },

V& ∑ { }

= E& theating +

n ,t n∈ CC , AC n ,t n∈ B ,CHP

V&t el,buy +

(η ∑ { }

n∈ CHP

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V& ∑ { }

U& ∑ { }

n∈ AC

n ,t

)

U& n,t − V&n,t = E& telectricity +

N,tot n

(A.1)

, ∀t ∈ {t1 ,..., t max } ,

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U& ∑ { }

n∈ CC

(A.2) n ,t

+ V&t el,sell , ∀t ∈ {t1 ,..., t max } .

(A.3)

V&t el ,buy is the electricity bought from the grid and η nN, tot U& n ,t − V&n ,t calculates the electric output

505 506

of the CHP engine. The part-load performance curves are represented by piecewise linear functions: g max  V& N ~ 1  ~  du  (A.4) U& n ,t (δ n ,t , V&nN , V&n ,t ) = ∑  δ n ,t , g ⋅ u n , g ⋅ nN + V&n ,t , g ⋅   ⋅ N , ∀t , ∀n ,  ηn  dv  n , g η n  g =1 

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g max

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~

δ n,t = ∑δ n,t , g ≤ 1, ∀t, ∀n ,

(A.5)

g max ~ V&n,t = ∑V&n,t , g , ∀t , ∀n

(A.6)

g =1

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g =1

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~

~

~

δ n,t , g ⋅V&nN ⋅ vmin ≤ V&n,t , g ≤ δ n,t , g ⋅V&nN , ∀g, ∀t, ∀n . ~ ~ n xt x g V&n,t , g ∈ ℝ n x t x g , δ n,t , g ∈ {0,1} max

max

max

max

max

(A.7)

max

(A.8)

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~

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where V&n,t , g is the continuous degree of freedom representing the output power of segment g

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and δntg is a binary degree of freedom identifying whether the output power is in the

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corresponding segment of the piecewise-linear function. The normalized y-intercept u n , g and

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 du  the normalized gradient   are given as input parameters for all components n and  dv  n, g

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every segment g . The description of the part-load performance of CHP engines is based on

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the thermal output, thus the nominal efficiency η nN needs to be replaced by the nominal

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thermal efficiency η nN, th in Eq. (A.4)-(A.8).

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N The bilinear product δ n,t , g ⋅ V&n in Eq. (A.4) and Eq. (A.7) can be linearized according to

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Petersen [30] and Glover =[31]=[31]. For simplification, this is illustrated for one line-

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segment g = 1 , thus δ n,t , g = δ n,t . The bilinear product is substituted by an auxiliary

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continuous decision variable ξ n,t , therefore a time dependent variable ψ n,t is introduced that

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takes the values of V&nN for all time steps t ψ n ,t = V&nN , ∀t , ∀n ,

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In Eq. (A.1) - (A.7) V&nN is substituted by ψ n,t and the bilinear product δ n,t ⋅ψ n,t is substituted

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by ξ n,t . Two linear constraints are added to guarantee the correct behavior of ξ n,t :

(1 − δ ) ⋅ V& n ,t

N min

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N ≤ ψ n ,t − ξ n ,t ≤ (1 − δ n ,t ) ⋅ V&max , ∀t , ∀n .

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~

EP

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~

AC C

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~

17

(A.9)

(A.8) (A.9)

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Appendix B

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Additionally in this appendix, we provide plots for cooling demand time steps showing similar pattern in Figure B1: 105 a 100 95 90 85 -100

-80

-60

-40

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0

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100 95 90 85 -100

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-40

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0

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SC

∆E˙ t /% E˙ t

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In Section 3.2 we discuss the pattern of relative costs OPEX rel (∆E& t ) for the heating demand.

1 2 ˙ OP EXrel ∆Et /%

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Figure B1. Patterns of relative costs OPEX rel (∆E& t ) as function of the energy demand

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reduction ∆ E& t for promising time steps a)  ∈ 2b and b) 4c ∈ 2b

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Appendix C

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In Figure C1 the full DSM map for the industrial case study of Section 3 is provided. It can be observed that the potential for heating demand changes is larger then for cooling demand changes. In the case study 1 winter month of a trigeneration system for a pharmaceutical industrial site is investigated. We find that the original demand situation is not suitable to operate the trigeneration system in an efficient way in some time steps. By applying DSM measures to the heating demand, the relation between heating-, cooling- and electricity demand is changed toward the best efficiency point of the trigeneration system.

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DSM map

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150

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150

non-promising

additional cost

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heating demand E˙ t / MW

cooling demand E˙ t / MW

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time t / h

Figure C1. DSM map of the complete considered time series for heating demand and cooling demand

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[29] Philip Voll, Mark Jennings, Maike Hennen, Nilay Shah, and André Bardow. The optimum is not enough: A near-optimal solution paradigm for energy systems synthesis. Energy, 82: 446–456, 2015.

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Figure Captions

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Figure 1. Energy system with two sub-systems: Distributed energy supply system and process system

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Figure 2. Steps of proposed systematic method to assess DSM potential: Identification (Step 1, ‘What time?’), quantification (Step 2, ‘How much?’), result summary (DSM map)

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Figure 3. Illustrative schematic of the DSM map: Green: DSM is valuable, Red: DSM should be avoided, gray: DSM is unfavourable, but has no negative effects.

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Figure 4. Energy demand profiles E& t for one month with hourly resolution: cooling (blue,

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dashed-dotted), heating (red, solid) and electricity (green, dashed) demand (color online)

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Figure 5. Merit order ̃ of time steps with descending cost-reduction index for a) cooling demand and b) heating demand with sets of promising time steps for cooling demand T c and

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heating demand T h

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Figure 7. Patterns of relative costs OPEX rel (∆E& t ) as function of the energy demand reduction

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∆ E& t for promising time steps a) 0 ∈ 23 and b) 45 ∈ 23

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Figure 8 DSM map for time interval  = 6407 , 77 8 of the heating demand; Time steps identified as promising time steps t ∈ T h (green), non-promising time steps t ∉ T h (grey),

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negative cost-reduction index (red); optimal demand reduction at minimum of OPEX

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for promising time steps t ∈ T h (limit of green color-bar)

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Figure B1. Patterns of relative costs OPEX rel (∆E& t ) as function of the energy demand

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reduction ∆ E& t for promising time steps a)  ∈ 2b and b) 4c ∈ 2b

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Figure C1. DSM map of the complete considered time series for heating demand and cooling demand

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Figure 6. Relative costs OPEX rel (∆E& t ) as function of the energy demand reduction ∆ E& t / E& t for the most promising time step ̃ of the heating demand

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Tables

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Table 1. Technology and nominal thermal power V&nN of the optimal structure for the case

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study (AC – adsorption chiller, CC – compression chiller, B – boiler, CHP – combined heat and power engine)

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B CHP CHP CHP Technology AC AC AC CC CC CC B N & 3.6 1.9 1.9 3.6 2.0 1.2 6.0 0.1 2.3 2.3 2.3 V n / MW

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ACCEPTED MANUSCRIPT Highlights

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Sensitivity of MILP model solution to demand changes identified High sensitivity indicates potential for demand-side measures Integrated consideration of cooling, heating and electricity Time-resolved targets for demand-side measures shown in ‘DSM map’ Promising time steps for demand-side measures can be intuitive and counter-intuitive

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