Evaluating the role of waste-to-energy and cogeneration units in district heatings and electricity markets

This paper investigates the activity of a multi-utility that uses Waste-to-Energy (WtE) and cogeneration (COG) plants to provide services in the heat and in the electricity markets. We assume that it employs WtE and COG units to participate in the day-ahead and real-time electricity markets and, with the support of heat-only units, it satisfies the heat demand of local district heating areas (DHAs). We use stochastic programming to develop three linked problems that describe the sequence of the decision process regarding the operation of WtE and COG facilities: (i) the first problem considers the point of view of the multi-utility that defines the day-ahead and the real-time heat scheduling of its plants and the maximum amount of electricity that WtE and COG units can offer in the day-ahead electricity market, taking into account the uncertainty of the real-time heat demand; (ii) the second problem models the day-ahead electricity market cleared by the Power Exchange, where the electricity dispatch of WtE and COG units is limited by the maximum power offers defined in step (i); and (iii) given the heat and power schedules respectively determined in steps (i) and (ii), the last problem describes the activity of theTransmission System Operator that re-dispatches WtE and COG outputs and decides their participation in the reserves and the real-time electricity markets, incorporating uncertain electricity demand and renewable power generation. Italian data are taken to investigate the operation of the WtE and COG plants under different assumptions. A reference analysis shows that these facilities obtain stable revenues from the heating market, but those from the electricity markets are very variable and mainly derives from reserve procurement. In addition, we perform two sensitivity analyses: in the first one, where we consider high natural gas and CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document} prices, the use of WtE and COG units increases to substitute gas-fueled plants with a consequent increase of their profits; in the second one, which describes an electricity market with a high renewable penetration, the activity of these facilities becomes more irregular because of the augmented penetration of intermitted renewable generation.


Introduction
The European Green Deal is a new growth strategy that aims to guide Europe towards carbon neutrality (see European Commission (2019)).It defines a roadmap that boosts the efficient use of resources by moving to a clean and circular economy where biodiversity is restored and pollution is reduced.Among its targets, there is the so-called "Fit-for-55" benchmark that imposes a reduction of the European greenhouse gas (GHG) emissions by at least 55% by 2030 compared to 1990 levels (see European Commission (2020a)).As far as energy production is concerned, the European Green Deal proposes to reach the binding target of 40% of renewable sources in the energy mix by 2030.The decarbonisation goal established by the European Green Deal also includes actions to strengthen the sustainability of the production processes and of the supply of raw materials, with the final scope of limiting waste generation.
Waste management is becoming a global challenge that involves different environmental, social, and economic aspects.This is due the fact that the production of solid waste has increased exponentially across the world in last years and it is expected to double in large and medium-sized cities and triple in the emerging countries by 2050, where it may not be properly treated due to the lack of recycling, landfill and incineration facilities (see IEG (2022)).In the past, waste was considered as the useless outcome of a linear economy model, based on a "take, make and dispose" principle, where raw materials were collected and transformed into products that were used until they were finally discarded as waste.
Europe has recently recognized that this economic model is no longer adequate and in 2015 launched its first Circular Economy Action Plan that has been renewed in 2020 in the framework of the Green Deal (see European Commission (2020b)).Both circular economy packages consider "reducing, reusing and recycling" as the three pillars for guaranteeing raw material and energy savings, waste recycling and carbon emission reduction (see European Commission (2015) and Genovese et al. (2017)).The European Commission has also issued a guidance on the production of energy from waste that can be considered as an efficient way to increase electricity and heat provision and to reduce GHG emissions from the waste sector, as well as, the utilization of landfills (see European Commission (2017)).In particular, Waste-to-Energy (WtE) technology, together with cogeneration (COG) units, can be simultaneously employed for covering the heat demand in a district heating (DH) and supply electricity.This implies a coupling of the heating and the electricity systems, which guarantees a higher flexibility needed to balance intermittent renewable power production.

Literature review
In the literature, the management of heat and power production through COG units and the development of the WtE technology in DHAs are usually analysed separately.In the following, we refer to the most recent papers that tackle these topics.
Considering the modelling of heat and power systems, Mitridati et al. (2020) propose a hierarchical optimization problem under uncertainty to define the optimal coordination of heat and power systems.Their modeling approach is based on a sequential solution of three optimization problems: the first one describes the participation of combined heat and power (CHP), heat-pumps and heat-only units in the day-ahead heat market, taking into account the forecasts on the uncertain wind power and power demand and the bids of the competitors; the second one describes the day-ahead electricity market clearing given a certain realization of the uncertainty; the third one is devoted to the intraday heat re-dispatch.These models consider the point of view of the System Operators of the heat and the electricity market and are solved using a Benders decomposition approach.
A different analysis is conducted by Kumbartzky et al. (2017).After providing a detailed literature review of these topics, Kumbartzky et al. (2017) develops a multistage stochastic mixed-integer linear programming (MILP) model to simultaneously optimise the operation of a CHP plant with heat storage.It is assumed that this plant bids in reserves, day-ahead and balancing electricity markets and price uncertainty is modelled through stochastic processes.The proposed model is applied to a gas turbine CHP plant with heat storage that is controlled by a German municipal energy supply company, which has to guarantee a secure supply of power and heat to a DHA.
The role of CHP plants in electricity markets is also investigated in Hellmers et al. (2016), but with a different approach.In particular, this paper analyses the portfolio effects of a set of technologies, including a wind farm and a CHP system that accounts for incinerators, gas and steam turbines, and heat storage units.Both day-ahead and balancing electricity markets are considered.The model proposed is deterministic but includes the heat demand and the spot price of electricity as uncertain parameters.The case study is based on the CHP-wind system located in Denmark.
Focusing on the role assumed by WtE units, Malinauskaite et al. (2017) provide a deep review of national municipal waste management systems and WtE development in selected European countries and analyse them as key elements of the circular economy.From a modelling point of view, Istrate et al. (2021) apply a material flow analysis to quantify the energy recovery potential of municipal solid waste under possible scenarios for 2030.These scenarios describe the structural changes that can affect the energy recovery potential, such as the increase in the separate collection rates and the implementation of more efficient material recovery facilities.The case study is calibrate to the city of Madrid in Spain.Hu et al. (2020) proposes a two-stage distributionally robust optimization model where electricity prices, waste supply, and district heating demand are assumed to be uncertain.In the first stage, the amount of electricity offered to the day-ahead market on an hourly basis is determined.The second-stage defines the municipal solid waste storage level in the bunker and the schedule of the power and the heat to be delivered to consumers.The Northern European facilities are considered for constructing the case study.In Ju et al. (2022), a virtual power plant including wind and solar power plants, gas-power plant carbon capture, power-to-gas, and waste incineration is analysed.First, information gap 5 Page 4 of 49 decision theory and fuzzy satisfaction method are used to construct an almost decarbonised optimal operation model, where uncertain variables are wind and solar power production and consumers' demand.The objectives of this first model are the maximization of the revenues and the minimization of carbon emissions.Secondly, to optimize the subdivision of the cooperative operation revenues among the entities operating in the virtual power plant, a Nash negotiation-based benefit allocation strategy is introduced.The case study analysed is inspired by Lankao rural energy revolution pilot program in China.

Paper contributions and research questions
Overall, all the above analyses motivate us to investigate these issues in a unified framework and we focus on the operation of a Multi-Utility (MU) that uses heat-only (HO), WtE, and gas-fired COG plants to satisfy the heat demand of local district heating areas (DHAs).In addition, it participates in the day-ahead and real-time electricity markets to sell the power produced with WtE and COG units.These facilities are also assumed to procure reserve capacity.The main novelties of this study are summarized as follows.
Differently from the aforementioned papers, this analysis is conducted considering the viewpoint of the MU that evaluates whether supplying heat to DHAs and participating in the electricity markets with WtE and COG plants is profitable.Our attention is mainly concentrated on the role assumed by WtE units.Moreover, to the best of our knowledge, it is the first time that a paper proposes a complete modelling of the operation of the WtE stations both in the heat and in the energy and reserve markets.In addition, we also models the utilization of waste in the WtE plants and the pollutant generated from its combustion that are normally controlled by national regulations.We also investigate the operation of the WtE and COG units under different assumptions.In addition to a Reference case, we assess two sensitivity analyses to account for two important issues that are currently discussed at European level: (1) the energy crisis due to the increase of the natural gas price and the parallel augment of the CO 2 cost; (2) the decarbonization targets imposed by the European Commissions.
Therefore, this paper aims at answering the following research questions RQ, with a particular focus on WtE units: • RQ1: How will the WtE and COG units be used in the heat and in the electricity markets?• RQ2: Will be the employment of WtE stations for the provision of heat and power profitable for the MU? • RQ3: How much will the application of a high carbon price combined with the increase of the natural gas cost modify the operation of WtE units?• RQ4: How will the WtE operation be affected in an energy market with a high penetration of renewable energy sources?

Methodology and modelling enhacements
From a methodological point of view, the use of stochastic programming to develop three integrated subsequent problems allows us to model, considering uncertainty, sequential levels of decisions taken on the operation of WtE and COG plants in DHAs and electricity markets both in day ahead and in real time (see Kunz (2013), Mitridati et al. (2020), andRintämki et al. (2016) for similar modelling methods).
Our approach takes inspiration from that proposed by Mitridati et al. (2020), but our analysis is different because, first, we consider the point of the MU instead of that the System Operators and, second, we perform a deeper study of the electricity markets.In the following, we denote the developed problems as Problem 1, Problem 2, and Problem 3, respectively.More specifically, Problem 1 examines the decision process of the MU that defines the day-ahead and the real-time heat scheduling of the DHAs and the maximum amount of power that WtE and COG units can offer in the day-ahead electricity market, taking into account the uncertainty of the realtime heat demand.These maximum power offers of the WtE and COG units enter as an input in Problem 2 that considers the point of view of the Power Exchange (PX), which clears the day-ahead electricity market and determines the power schedules of WtE and COG plants together with those of the other generating units participating in this market.In Problem 3, taking as reference the heat schedules of WtE and COG units defined in Problem 1 and the electricity schedules of these and of the other power generating units determined in Problem 2 by the PX, the Transmission System Operator (TSO) re-dispatches all these plants and decides their participation in the reserve and in the real-time balancing market assuming uncertain realtime demand and renewable power output.Notice that, to have consistent results on the outcomes of the electricity markets in Problem 2 and Problem 3, we need to consider the participation of all the other generating units available in the power system.However, this is only instrumental to the scope of our analysis because we do not investigate the impacts of WtE and COG facilities on the functioning of the whole power system.On the contrary, our goal is to evaluate the activity of WtE and COG units in a given electricity market.For these reasons, we just individualise the WtE and COG units of a single MU and not all the cogeneration participating in the power system.

Policy insights
The numerical study is conducted on the Italian power system and accounts for DHAs located in the Italian Northern area to analyse RQ1.We first consider a Reference case that illustrates the standard operation of WtE and COG units in the heat and power markets and we then propose two sensitivity analyses.Sensitivity analysis 1 addresses RQ3 and investigates the role played by the WtE and COG stations in these markets under the assumption of a significant increase in the natural gas and CO 2 prices.Sensitivity analysis 2 assesses RQ4 and studies how the WtE and COG plants may modify their heat and power output and their reserve provision 5 Page 6 of 49 in a power system with a high penetration of renewable energy units.As for RQ1, our analysis shows that the supply of heat remains quite regular in all cases, the COG units actively participate in all markets, while the production of power and the provision of reserves of WtE plants depend on the assumptions made on electricity markets.In the Reference case, WtE stations are considered too expensive and are excluded from the clearing of day-ahead electricity market, but they are employed by TSO to procure power and reserves.The situation changes in the two sensitivity analyses where WtE units are used in all markets, even though with different intensity.In assessing RQ3, we show that WtE plants become more competitive when the natural gas prices increase and they are deployed to substitute gas-fired power stations in the electricity and in the reserve markets.In addressing RQ4, we find that the services of WtE plants in an almost decarbonised power system are affected by the variability of renewable energy production.As for RQ2, we observe that the participation of the WtE in the heat and power markets is profitable, especially under the assumptions of Sensitivity analysis 1.
The rest of the paper is organized as follows.Section 2 describes the approach proposed and presents the formulation of the three optimization problems developed.Section 3 explains the case study and provides the input data used.Section 4 illustrates the results obtained in the reference case and in the two sensitivity analyses.Section 5 concludes the paper with final remarks.Finally, Appendices A and B report the notation used in the formulation of the three problems and the input data related to the scenarios used in the case study, respectively.

Mathematical formulation of the three optimization problems
This section describes the proposed approach and the mathematical formulation of three subsequent optimization problems developed.Fig. 1 illustrates the structure of the three optimization problems, the sequence of the decisions taken and the information transferred from one problem to another.In the upper part of Fig. 1, we summarize the formulation of each optimization problem, indicating the goal, the objective function, a synthetic list of the constraints, and the sources of uncertainty modelled with scenarios.In the lower part of Fig. 1, the arrows show which outcomes of a problem enter as inputs in the subsequent ones.The sequence of the operation of the MU, PX and TSO is partially influenced by the case study that is focused on the Italian electricity market, where the TSO's activities are concentrated after the closure of the day-ahead electricity market cleared by the PX.However, without loss of generality, the analysis can be easily adequate for the power market design of the Central-Western European countries, where the reverse procurement is done before the clearing of the day-ahead electricity market (see Domínguez et al. (2019) for more details).
We consider two geographical levels: the reliability electricity zones, in which the electricity market is subdivided, and the DHAs for the local supply of heat (see Fig. 2).In the zonal representation of the power system adopted in Problem 2 and Problem 3, we assume that there is one bus per zone to which the corresponding generating technologies are connected.These bidding zones are linked by transmission lines with limited transfer capacity.
This simplified network configuration is based on the approach of the reliability zones.This does not account for loop flows but it reflects the Available Transfer Capacity model that is still used in some of the European countries, such as Italy, participating in the Price Coupling of Regions used to clear the European day-ahead electricity markets in a coordinated way with the EUPHEMIA algorithm (see NEMO Committee (2020) and Price Coupling of Regions ( 2022)).In Fig. 2, the reliability zones of the electricity markets are denoted as Zones A, B, C, D. The DHAs that the MU supplies are heat islands grouped together in one of the reliability zones of the electricity market (Zone A in Fig. 2).This implies that DHAs are isolated and there aren't heat pipelines among them.The MU owns different HO, COG and WtE units in each of the DHA that are sufficient to satisfy the local demand of heat.We do not model a heat market.In the following, we present the formulation of the three problems developed.The notations of the three models are reported in Appendix A.

Problem 1: Heat and electricity self-dispatch of the MU's WtE, COG and HO units
Problem 1 is a mixed-integer two-stage stochastic programming problem that describes the operation of a MU company supplying heat to independent local DHAs and defining the maximum amount of power produced with WtE and COG units to be sold in the day-ahead electricity market.The final objective of the MU is to maximize its profits deriving from its participation in these markets.The problem is mainly focused on the heat provision: the first stage defines the scheduling of the day-ahead heat output of HO, COG and WtE units that satisfy the local DHAs demand and the second stage determines the corresponding real-time heat supply.In addition, the maximum power offers of WtE and COG plants destined to the day-ahead electricity market are decided.
The uncertainty related to the heat demand of DHAs is modeled through a set of scenarios that represent the variation of the day-ahead heat demand prediction with respect to the actual demand in real time.The heat and the electricity prices are assumed to be known and defined according to historical data.Finally, the self-electricity consumption of the HO units is not considered.The formulation of Problem 1 is presented below. s.t. (1) Heat demand balances: Heat production limits: Electricity production limits: Binary variables: Ramping and other operation limits: (2) Non-negativity constraints: The objective function (1) corresponds to the total expected profit of the MU that are given by the difference between the income deriving from selling heat to DHAs (15) ) ∑ t∈T W ri ( e ⋅ q eDA i,t + h (q hDA i,t + q hB+ i,t,s − q hB− i,t,s )) ≤ E r ∀i ∈ WtE(i), ∀r, ∀s ) q hB− i,t,s ≥ 0, ∀i, ∀t, ∀s (26) w i,t,s ≥ 0, ∀i ∈ WtE(i), ∀t, ∀s and power in the day-ahead electricity market, and the operating costs of the HO, COG and WtE units together with the penalization charges imposed to the real-time heat deviations of HO and COG stations.
The problem is subject to the following constraints.Constraints (2) enforce the day-ahead heat balance in each DHA and hour.Constraints (3) define the heat balance of each DHA in the real-time operation per each hour and scenario, taking into account the deviations between the day-ahead prediction and the actual heat demand.These constraints are introduced because the MU must counteract the possible positive (higher demand than expected) or negative (lower demand than expected) heat deviations using its plants.Constraints (4) limit the heat production of unit i in each hour and scenario, while conditions (5) impose the minimum heat output, considering the possible negative deviation in the real-time operation.Constraints (6) establish that the minimum electricity production from COG or WtE units depends on the heat generation, whereas (7) enforce the upper limit of the electricity production considering the maximum electricity production (capacity of the turbine) and the heat generation in each scenario.Constraints (8) introduce the binary variable u i,t used to describe the operation of the different units.Constraints (9) and (10) limit the ramping capability of the HO and COG units in each hour and scenario.Constraints (11) determine the amount of waste used by each WtE plant to produce heat and power in each hour and scenario.Constraints (12) limit the quantity of waste that each WtE unit can manage in each hour and scenario, while conditions ( 13) and ( 14) impose the ramping limits of WtE units through the waste used in each hour and scenario.Minimum up/down times are enforced to all units i through conditions ( 15)-( 20).This formulation is based on the approach proposed in Carrión and Arroyo (2006).The binary variables u i,t indicate the on/off status of units i.In conditions ( 15)-( 20), L i and M i represent the number of initial hours in which plant i must be online and offline, respectively, at the beginning of the planning horizon.L i and M i are defined as follows: Note that U i,0 is the initial commitment status (time 0) of heat unit i (for more details, see Carrión and Arroyo (2006)).As specified in the legislation (see Warringa ( 2021)), WtE units are not actually involved in the EU Emission Trading System (EU-ETS).However, the combustion of waste generates a set of pollutants that can be subject to restrictions at national level.In Italy, for instance, the regulation imposes a cap on the emissions of specific contaminants generated by incinerators and WtE plants (see ARPA-Agenzia Regionale per la Protezione dell'Ambiente (2017) and Cernuschi et al. (2020)).In particular, these contaminants are: SO 2 , NO X , CO, COT, NH 3 , HCI, and particles.Therefore, constraints ( 21) are here introduced to account for possible national environmental policies applied to WtE units and impose limits on the emissions of monitored contaminants.Finally, are the non-negativity constraints of the variables used in the model.
From the solution of Problem 1, we get the values of the maximum power offers of WtE and COG units ( q eDA i,t ) that could be submitted to the day-ahead electricity market and the on/off status of these units in each hour ( u i,t ).These results enter into Problem 2 as input data.The following equations define the relationship between the values assumed by these variables of Problem 1 and the corresponding parameters Q eDA i,t and U i,t introduced in Problem 2: Moreover, the heat production q hDA i,t schedules of the WtE and COG units in the day ahead and their maximum up deviation q hB+ i,t,s and the minimum down deviation q hB− i,t,s in the real-time operation, as obtained from the solution of Problem 1, are input to Problem 3 that describes the operation of the TSO.Therefore, we introduce these conditions: Finally, conditions (28) related to on/off status of the WtE and COG stations are also included in Problem 3.

Problem 2: Clearing of the day-ahead electricity market
Problem 2 is a deterministic model that analyzes the participation of the MU's WtE and the COG units in the day-ahead electricity market that is cleared by the PX taking into account a forecast of the possible real-time realization of the intermittent renewable power generation and of the consumers' demand.This simulates the approach adopted in EUPHEMIA.We recall that, in addition to the MU's WtE and the COG plants, all the other generating technologies available in the whole power system (i.e.coal, gas turbine, biomass, geothermal, hydro, wind and solar PV units) are considered in Problem 2. As already explained in the Introduction, this assumption is needed to determine the equilibrium of the electricity market.The model formulation is as follows. Minimize Electricity market balances: Power generation constraints: Power flow limits: Unserved demand limits: The objective function (32) represents the total cost of operating the power system, which has to be minimized.The terms included are in order: the cost of unserved demand; the operating costs of all electricity generating units; the carbon emission, the start-up and the shut-down costs of the fossil-fuel power plants; the power production and the CO 2 costs of the MU's COG units; and, finally, the power production costs of the MU's WtE plants.The costs C O i,t and C OW i,t associated with MU's COG and WtE stations are computed using the exergy approach proposed in Nuorkivi (2010).We also account for the carbon charges applied to the MU's COG units and to the generating technologies g that are involved in the EU-ETS.As explained in (33) As already explained, the market is cleared at zonal level and the power exchanged between reliability zones is constrained by pipelines with limited transfer capacity.The zonal market balances are enforced by conditions (33).The zonal power supply identified by these conditions accounts for the electricity p DA z,g,t produced by the generating technologies available in the zone, the power p eDA i,t offered by the MU's COG and WtE units when considering the zone where they are located, and the flows exchanged between zones.This has to satisfy the zonal demand netted by the potential unserved demand.Notice that, the power output p eDA i,t of MU's stations is a variable in the balance constraints (33).However, the amount of electricity effectively offered by the MU's WTE and COG units in the day-ahead electricity market cannot exceed the maximum power offers defined in Problem 1.This is essential to guarantee the respect of the heat supply constraints of Problem 1.Therefore, we impose constraints (40) on variable p eDA i,t that is strictly related to conditions ( 27) and ( 28).Constraints (34) impose the lower bounds and the capacity limits on the generation of fossil-fuel power plants.These conditions account for the on/off status of these units thanks to the binary variables u G z,g,t that are defined in (43).These binary variables are also used to determine the effective start-up and shut-down costs of fossil-fuel power plant as indicated in constraints ( 35) and ( 36), respectively.Constraints (37) enforce the power production limits of not-fossil power plants.The use of the availability factors F DA z,g,t takes into consideration the intermittency of renewable power production.Constraints ( 38) and ( 39) establish the intertemporal up and down ramping limits imposed on dispatchable units, respectively.Constraints (41) correspond to the limits on the power exchanged between reliability zones, and, finally, conditions (42) determine the cap on unserved demand.
The power schedules of generating technologies g, their on/off status, and the power scheduled for the WtE and COG units resulting from the solution of Problem 2 are input to Problem 3. The following equations establish the link between the variables of Problem 2 and the associated parameters of Problem 3:

Problem 3: Unit re-dispatch, reserve procurement and balance of the real-time electricity market
Problem 3 describes the activities of the TSO, which operates after the clearing of the day-ahead electricity market.The problem is formulated as a twostage stochastic programming model where, at the first stage, the TSO tests the (44) P DA z,g,t = p DA z,g,t , ∀z, ∀g, ∀t technical feasibility of the units' schedules defined by the PX in Problem 2 and performs the required re-dispatch of the generating units and of the MU's WtE and COG plants.This is done in the day ahead, immediately after the closure of the day-ahead electricity market.Notice that the schedules defined for the WtE, the COG and the other generating units in Problem 2 are considered as input data to this problem (see conditions (44-46)).In addition, minimum up/down spinning reserve needs are settled based on the prediction of the net demand (consumption minus intermittent renewable power) in each bidding zone.At the second stage, representing the real time, the balancing market is executed to determine the use of spinning reserve according to the actual realization of the electricity demand and of the intermittent renewable power generation.The uncertainty of these parameters is modeled through a set of scenarios.
The TSO requires that all dispatchable units among the generating technologies g available in the power system, together with the MU's WtE and COG stations, provide reserve services.To ensure that WtE and COG units work respecting both their relationship between heat and electricity output and the possible deviations occurring in their real-time heat supply as defined in Problem 1 must be taken into account.Therefore, we account for conditions (28-31) that establish the links between Problem 1 and Problem 3. Finally, as in Problem 2 we consider a zonal representation of the electricity market.The complete formulation of Problem 3 is as follows: 5 Page 16 of 49 Power balances: Reserve requirements: Fossil fuel generating technologies operation: Not fossil-fuel generating technologies operation: (48) Deployed reserve limits: COG and WtE plants operation: Power flow limits: Unserved demand limits: Additional non-negativity constraints: The objective function (47) minimizes the TSO's operating costs.It comprises the following terms: the cost of re-dispatching the generating technologies g in each zone and their reserve capacity procurement costs in the day ahead; the expected cost of deploying up/down reserve provided by generating technologies g in the balancing market; similar costs for the MU's COG and WtE units; and the expected penalization cost of the unserved demand in day ahead and in real time.Constraints ( 48) and (49) impose the power balance in the day-head and in the balancing market in each zone and hour, respectively.In particular, constraints (49) consider the reserve deployment in real time needed to counteract the forecast error of the intermittent renewable power generation and electricity demand with respect to the prediction made in the day ahead.Constraints ( 50) and ( 51) establish the minimum up/down reserve capacity, respectively, required by the TSO in each zone and hour in the day-ahead market.Generically, we assume that all generating units can provide reserve capacity, as well as the COG and WtE plants of the MU.Constraints (52-56) define the operation of fossil-fuel generating technologies g ∈ GF(g) taking into account their on/off status determined in Problem 2. In particular, condition (52, 53) impose the maximum and minimum production of these units, on the basis of the redispatched power schedules and the requirement on reserve provision defined in day ahead Constraints (54) define the power production in real time accounting for reserve deployment.Conditions (55) and (56) impose the ramping limits in real time.Constraints (57-62) refer to not fossil-fuel technologies g ∈ GNF(g) , whose main characteristic is the uncertainty in the power availability.Constraints (57) establish that the power re-dispatch and the up reserve capacity can not be higher than the available power, while constraints (58) impose that the power re-dispatch minus the down reserve capacity must be greater or equal than zero.Constraints ( 59) and ( 60) impose a limit on the up/down reserve capacity, respectively, that can be offered considering both a limit on the reserve capacity that can be offered (represented by factor F R g ) and the available power predicted in the day ahead (represented by F DA z,g,t ⋅ P z,g ).This condition is imposed to take into account the technical restric- tions that non-dispatchable technologies, such as wind and solar PV units, may have to meet the quality requirements of the reserve service.Constraints (61) and ( 62) limit the reserve deployed in the balancing market considering the redispatch power scheduled in the day ahead and the power available in each real-time scenario.Constraints ( 63) and ( 64) hold for all generating technologies and establish that the reserve deployed by the generating technologies in each scenario cannot exceed the reserve capacity scheduled in the day ahead.Constraints (65-76) describe the operation of COG and WtE power plants.These constraints are equivalent to those included in Problem 1, but, in this case, the reserve capacity scheduled and deployed must be considered in the generation limits.Notice that (67) and ( 68) limit the positive/negative heat deviation in the balancing market according to the maximum heat deviation found in Problem 1, as previously explained.As with the non-dispatchable technologies, constraints ( 69) and ( 70) impose a limit on the reserve capacity that these power plants can offer based on the power scheduled in the day-ahead market and a technical factor ( F HR i ) that ensures the quality of the service.Constraints ( 77) and ( 78) set the limits on the power exchange between zones, whereas (79) and ( 80) limit the unserved demand in the day-ahead and balancing markets.

WtE units' profits
Considering our focus on WtE units and the RQ2 listed in the Introduction, we introduce the following expression to compute the expected total profit of these plants: According to the planning horizon considered in this paper, the profit of the MU's WtE units results from the sum of the following terms: (i) the income received for the heat supply to part of he MU's customers as defined in Problem 1, (ii) the income coming from selling electricity in the day-ahead energy market as obtained in Problem 2, (iii) the income/expenses resulting from the electricity re-dispatch made by the TSO in the day ahead (stage one) in Problem 3, (iv) the income attained from the reserve capacity provided as determined in Problem 3, (v) the expected ( 84) 5 Page 20 of 49 income/expenses due to the deployment of up/down reserve in Problem 3, and (vi) the expected cost of the waste used considering the final heat and power generated resulting from Problem 3.These profits are computed ex-post after the solution of three subsequent problems.In term (ii), the electricity prices eDA−P2 z,t correspond to the dual variables of energy balances (33) of Problem 2.Moreover, in the amount of electricity sold p eDA i,t we have that i ∈ I C (z) (see ( 33)).Similarly, in term (iii), the electricity prices eDA−P3 z,t are the dual variables of the energy balance constraints (48) of Problem 3. Again, in q eDAt i,t − P eDA i,t we have that i ∈ I C (z).

Case study
The case study focuses on the Italian electricity market and on three DHAs located in Lombardy that is a region in the Northern area of Italy (see AIRU-Associazione Italiana Riscaldamento Urbano ( 2022)).We first analyse a Reference case and then we implement two sensitivity analyses.Sensitivity analysis 1 aims at assessing the impacts of the increase of the natural gas cost and of the CO 2 price on the power system and on the operation of the WTE units, since the Reference case is based on pre-pandemic data.Sensitivity analysis 2 investigates the integration of WtE units in a power systems with a significant penetration of renewable energy sources.The problems described above have been solved using CPLEX IBM CPLEX (2022) under GAMS GAMS Development Corp (2022) in an Intel CORE i7 with 16 GB of RAM.This section presents the input data used in the Reference case.The modified data needed to run the sensitivity analyses are directly reported in Sects.4.2 and 4.3, respectively.

Multi-utility and heat demand
In this case study, we consider a MU company that supplies heat to three independent DHAs located in the Lombardy region in the North of Italy, using HO, gas-fired COG and WtE units.We suppose that these DHAs are not integrated because, as explained in European Commission (2022), the Italian heat market is not regulated at national level and DHs are usually regulated through public-private partnerships.
We assume that the MU totally owns 30 units subdivided into 3 WtE, 6 COG, and 21 HO plants, respectively.Table 1 provides the location in the three DHAs, the type, the electricity and heat capacity, the ramping capability, and the operating cost of each of these units.The total heat capacity in DHA1, DHA2 and DHA3 is 130.6 MWh-t, 525 MWh-t, and 693.4 MWh-t, respectively; whereas the total electricity capacity per DHA is 12.2 MWh-e, 159.4 MWh-e, and 257.8 MWh-e, respectively.The power to heat ratio ( ) of COG plants is equal to 0.6.For the WtE units, the efficiency rate considered for the electricity generation is equal to 20% ( e = 1∕0.20 tonne waste per MWh-e), while for the heat gen- eration is equal to 50% ( h = 1∕0.50tonne waste per MWh-t) according to Chen  et al. (2020), Istrate et al. (2021), Weber et al. (2020).Additionally, the minimum working time for HO units is 3 hours, whereas for COG and WtE units is 5 hours.We consider all units offline in the hour prior to the planning horizon.The minimum heat production is not considered for any unit.The operating costs of the WtE units located in DHA1, DHA2 and DHA3 are 15 €/tonne waste-h, 16 €/ tonne waste-h, and 17 €/tonne waste-h, respectively (see Beretta and Consonni (2018), Xin-gang et al. (2016)).If transformed in €/MWh using the efficiency rate for the power generation previously mentioned, these become 75 €/MWh, 80 €/MWh, and 85 €/MWh, respectively.The cost imposed to the real-time heat deviations is 1.1 and 0.9 times the operating cost of the unit for the up and down deviation, respectively.The planning horizon of this numerical analysis corresponds to one week.In particular, we consider historical data from January 14, 2019 to January 20, 2019, which have been collected from ENTSO-E (see ENTSO-E ( 2022)).The prediction of the day-ahead electricity prices used by the MU in Problem 1 for its self day-ahead scheduling is indicated in Fig. 3.These prices correspond to the actual prices resulting from the market clearing in the week under study.
The heat price applied to consumers in Problem 1 is set equal to 70 €/MWh, based on the average price found in Italy and Germany for the district heating (see Werner (2016)).This is considered fixed in advance.The hourly heat demand in each DHA has been generated using the data provided in the project Heat Roadmap Europe (see Lund et al. (2017)).From this project, we have extracted the 168 hourly data of the period January 14-20, 2019 referred to Italy.These data have been normalized by first dividing them by the maximum demand value of the year and then multiplying the obtained values by the heat capacity of each DHA considered in Problem 1.These are used to estimate the day-ahead heat demand prediction considered by the MU.Then, five real-time heat scenarios per DHA are randomly generated considering a forecast error of 3%.We assume that the scenarios are equiprobable.Fig. 4 represents the day-ahead prediction of the heat demand, the real-time scenarios of the heat demand, and the heat production capacity of each DHA.
Finally, the emission rates associated with the pollutants produced by waste combustion in the WtE units are based on the information provided in ARPA-Agenzia Regionale per la Protezione dell'Ambiente (2017) and Cernuschi et al. (2020), and take the following values (g per tonne of waste): SO 2 = 12.9, NO X = 379.9,CO = 70.1,COT = 2.2, NH 3 = 12.6, HCI = 26.6,particles = 1.2.The limits on the emissions of those pollutants are also taken from these reports.

Italian power system
In Problem 2 and Problem 3, we consider the zonal representation adopted by the Italian power system to participate in the day-ahead electricity market cleared by EUPHEMIA (see NEMO Committee (2020), Price Coupling of Regions ( 2022) and Valori dei limiti di transito tra le zone di mercato ( 2019)).This configuration accounts for six main bidding zones: North, Center-North, Center-South, Sardinia, South, and Sicily that, in the following, are denoted as NORD, CNOR, CSUD, SARD, SUD, SICI, respectively (see Fig. 5).The MU's HO, WtE and COG units are located in the NORD bidding zone.In the analysis, we also account for the energy flows exchanged with the foreign zones connected with Italy, which are: Austria (AUST), Slovenia (SLOV), Switzerland (SWIT), France (FRAN), Corsica (CORS), Greece (GREE), and Malta (MALT).
Table 2 provides the origin, destination and maximum power flow allowed among the Italian bidding zones and the foreign countries.For the power exchanges with the foreign countries, we assume that these are scheduled and agreed prior to the clearing of the day-ahead electricity market Price Coupling of Regions (2022).These power flows are estimated using the historical data of the scheduled power flow between Italy and the neighbouring countries for the week under study provided by ENTSO-E (see ENTSO-E (2022)).Therefore, their values enter as input data in Problem 2 and Problem 3 (see Fig. 17 in Appendix B).
The generating technologies g ∈ G included in Problem 2 and Problem 3 in addi- tion to MU's WtE and COG units are: coal, gas turbine (gast), hydroelectric (hydr), wind, solar photovoltaic (soPV), biomass (biom), and geothermal (geot) power The capacity per technology and zone is indicated in Table 3, corresponding to the available capacity by the end of 2018 in Italy, as provided by Italian TSO Terna.1 Notice that we account for all types of hydroelectric power plants used in Italy for electricity production that we, then, aggregate per bidding zone as a unique power station.In our analysis, we assimilate the total hydroelectric capacity to a thermal unit with a given availability factor.Based on the historical data on hydro availability provided by GSE,2 we assume that the availability factor of the hydroelectric capacity for every hour is 40%.The total generating capacity considered amounts to 120.77 GW.
The minimum power output of coal and gas turbine units is considered 10% of the capacity, whereas they are assumed to be at half capacity the hour prior to the planning horizon.The ramping capability is 50% for coal, 60% for gas turbine, 60% for biomass, and 90% for geothermal units.The reserve capacity requirement in each hour corresponds to 10% of the day-ahead electricity demand in each zone.Only solar PV units can not provide reserve capacity, whereas wind units can procure up to 20% of the available power in each hour.
Table 4 indicates the operating cost of each generating technology.Since the data of the hydroelectric power plants are aggregated per type and per zone, we assume that their operating costs are close to those of the thermal units in order to guarantee a limit in their use (see Carrión et al. (2018) and Domínguez and Vitali (2021) for similar applications).For both coal and gas turbine units, the start-up and shut-down costs are equivalent to those got from generating electricity at full capacity for 12 hours, i.e., the cost is obtained by multiplying the operating cost of Table 4 times the capacity indicated in Table 3 times 12 hours.The cost of scheduling up/down reserve capacity is 20% of the operating cost, while the cost of deploying up/down reserve is 10% higher and 10% lower than the operating cost, respectively.
The carbon footprint of coal and natural gas-based plants is taken from University of Oxford Our World in Data (2022), adopting the values 380 and 201.96 kgCO2-e/ MWh, respectively.The carbon price for every hour of the considered week in 2019 is 23.27 €/tCO2-e SENDECO2 (2022).As already specified, WtE units are not actually involved in the EU-ETS system (see Warringa (2021)).To estimate the hourly availability factors of intermittent renewable sources, namely wind and solar PV power, we take the historical data of the day-ahead prediction and the actual generation provided by ENTSO-E (see ENTSO-E ( 2022)) for each Italian bidding zone.With those data, scenarios for the real-time power availability are generated considering a forecast error of 5% and 3% for the wind and solar PV power, respectively.The scenarios per bidding zone are depicted in Figs.18 and 19 in Appendix B. In a similar way, the data needed to determine the hourly electricity demand in each bidding zone for the day-ahead and real-time operation are collected from ENTSO-E ENTSO-E (2022).Fig. 20 in Appendix B represents the day-ahead electricity demand and the real-time scenarios.In total, 45 scenarios equiprobable are considered.Finally, unserved demand is priced at 10,000 €/MWh.

Results
This section presents the results obtained from solving the developed models under the assumptions described in Sect.3. We first illustrate the outcomes of the Reference case and, then, those of the two sensitivity analyses, mainly fo.Our goal is to answer the research questions reported in the Introduction.

Reference case
Considering our research question RQ1, we show the operation of the WtE and the COG units in the heat and the electricity markets through the analysis of the results obtained from the solution of the three subsequent problems.First, we analyse the outcome of the self-scheduling performed by the MU with Problem 1. Fig. 6 depicts the heat scheduled by each technology in the day ahead in each DHA to supply the heat demand predicted.Fig. 7 represents the power to be generated by COG and WtE units in each DHA according to the prediction of the market electricity prices considered by the planner.As it can be observed, most of the heat demand is supplied by HO units, while COG and WtE units are mainly used to generate electricity.In general, the higher the electricity prices, the higher the maximum power offers that the COG facilities are ready to submit to the day-ahead electricity market.Fig. 8 shows the waste used by each WtE unit in each heat-demand scenario.From the comparison of Figs. 7 and 8, we observe that the use of waste directly depends on the electricity generation of those facilities.
Second, we provide the results of the participation of MU's WtE and COG stations in the day-ahead electricity market cleared by PX as proposed in Problem 2. Figs.9-11 show the power scheduled by each technology in each Italian bidding zone, as well as the scheduled power interchanged with the foreign countries in all the hours of the considered week.
The bidding zone NORD is the one with the highest demand.More specifically, the demand of this region is higher than the total demand of the rest of the country.From Fig. 9, we can observe that a large part of the electricity demand of the Northern part of Italy is supplied by gas, hydro, and biomass power plants.
In the bidding zone NORD, it is also remarkable the power imported from foreign countries, mainly France and Switzerland.It is important to highlight the comparatively low generation from solar or wind resources and a slight amount of electricity exported to Slovenia.The power demand in the CNOR zone is also mainly covered by gas-fired plants even though, in the energy mix, there is a significant utilization of the geothermal capacity, which is available only in this zone.Again, wind and solar power plants are not significantly used.Moreover, a small part of the electricity produced is exported to Corsica (CORS).The energy mix changes in zone CSUD, where the use of coal power units substitute part of the gas-based power stations.The energy supply of wind and solar plants is larger and, in particular, it increases as long as the production of fossil-fuel plants decreases (see Fig. 10).In Sardinia (SARD), the renewable resources are predominant and are able to supply most of the demand.
In Fig. 11, we observe that the renewable resources in the South of Italy and in Sicily are quite abundant, but still there is a high generation from coal and gas power plants.In the bidding zone SUD, from the third day of the week, the coal and gas power plants are working at minimum capacity, which must be due to the high start-up and shut-down costs of these facilities.In Sicily, the wind generation makes the operation of coal and gas power plants comparatively much more variable than in other zones.As already explained, the MU operates in the NORD zone only.In Fig. 9, the schedules defined by the PX for the WtE and the COG stations are labeled with "MU".Focusing on the WtE units, we observe that they do not sell electricity, while COG units do but for a very small amount compared with that of the other generating technologies.For this reason, it is difficult to observe in Fig. 9.This happens because the prediction of the electricity prices made by the MU for the self-dispatching (Problem 1) are in many hours higher than the prices obtained by solving the PX's problem (Problem 2).In other words, the WtE technology is too expensive comparing to others participating in the clearing of the day-ahead electricity market and, therefore, it is excluded from the equilibrium schedules of the PX.However, the situation changes in Problem 3 where the electricity generation of the MU becomes more similar to that resulting from Problem 1 (see Fig. 12).This depends on the fact that, in Problem 3 part of the generation capacity is needed by the TSO to satisfy the reserve requirement, and therefore, also these technologies of the MU are re-considered for providing both electricity and reserve services.
Thirdly, the outcomes of Problem 3, which correspond to the re-schedule of power outputs made by the TSO to satisfy the reserve requirements and to account for the more updated information on electricity demand and renewable-based power in real time, are explained.In the following, we report some of the results obtained, especially for the WtE and COG units to give more insights on the use of these technologies.Fig. 12 compares the electricity scheduled by the TSO for the WtE units, after the re-dispatch that occurs in the day-ahead market of Problem 3 (see upper plot) with the schedule resulting from the self-scheduling of these units operated by the MU in Problem 1 (see lower plot).As already said, in Problem 3, the electricity schedules of the COG and WtE units of the MU can be modified by the TSO depending on power and reserve needs that it has to accomplish.Considering the power schedules of the WtE units resulting from the day-ahead re-dispatching activities of the TSO in Problem 3, their electricity generation is higher compared to that obtained in the day-ahead self-scheduling of the MU in Problem 1, specially for WtE unit 3.In addition, in Problem 3, it is also observed more variability in the electricity generation, which is related to the provision of reserve services.In fact, the reserve capacity procured by both COG and WtE is significant as highlighted by Fig. 13.Fig. 14 represents the use of waste of the three WtE units in the real-time balancing market for each scenario (light blue) considered in Problem 3 and its expected value (dark blue).The comparison between the use of waste in Problem 1 and in Problem 3 highlights a lower use of waste results for WtE unit 3 (see Fig. 8 and 14, respectively), which is due to the deployment of down reserve in the real-time operation.
Fig. 15 provides a general overview on the whole Italian power system and shows the day-ahead energy schedule in Italy after the re-dispatch performed by the TSO (upper plot) and the up/down reserve capacity (lower plot) provided by the different generating technologies g ∈ G .We observe a very high generation from gas power plants, followed by hydro and biomass units.As expected, under the circumstances of this Reference case, the provision of reserve capacity is mainly done by coal and gas power plants.
Table 5 gives the aggregated economic outcomes of the WtE units along the whole period considered for this decision-making process.Notice that the label "P1", "P2" and "P3" used in this table refer to Problem 1, Problem 2, and Problem 3, respectively.Specifically, Table 5 reports the income coming from the heat production scheduled in the day ahead resulting from Problem 1 (see column 2), the income of the electricity offered in the day-ahead electricity market cleared by the  PX in Problem 2 (see column 3), the revenues/costs depending on the day-ahead redispatch performed by the TSO for the energy supply that is the difference between the energy scheduled in Problem 3 and in Problem 2 (see column 4), the revenues for providing reserve capacity (column 5), and the revenues/costs for the reserve deployed in the real-time operation, coming from Problem 3 (column 6).Column 7 indicates the cost of the waste used considering the heat and electricity finally supplied, as determined in Problem 3. Column 8 reports the final profit considering the total income and the cost.This is done for each day of the week, the total amounts achieved along the week, and the average of the 7 days.It gives us some insights to answer our research question RQ2.
Along the considered week, the WtE units obtain profits in all days.We can highlight that the income received from supplying heat is very stable along the week, while that from the participation in the electricity markets is comparatively more variable.These units do not get any revenues from the day-ahead electricity market of the PX since their schedules are not included in the final equilibrium.As already observed, WtE plants are restored by the TSO in Problem 3 both for the electricity and the reserve services.They are remunerated for the power produced and the reserve capacity provided.However, these plants are used by the TSO to mainly regulate down reserves that imply costs (a negative income in Table 5).Both the reserve procurement and their deployment are very dependent on the electricity market conditions of the corresponding day.This also affects the cost of waste used by WtE units for the production of heat and power.The total profits of these units is 974.4 k€ with a daily average of 139.2 k€.Finally, the daily emissions of the WtE units are reported in Table 6.These values are very much below the daily limits imposed by the Italian regulator as reported in ARPA-Agenzia Regionale per la Protezione dell'Ambiente (2017) and Cernuschi et al. (2020).

Sensitivity analysis 1: increase of the gas cost and the CO 2 price
To answer our research question RQ3, we conduct this sensitivity analysis with the scope of evaluating the impacts of the increase of the natural gas costs combined with an increment of the CO 2 allowance price on the operation of the MU's WtE and COG units and of the entire power system.In particular, we assume that the operating cost for running gas-based plants increases by 50%, 100% and 150% compared to its reference value provided in Table 4, becoming equal to 87 €/MWh, 116 €/MWh, and 145 €/MWh in the three cases, respectively.In addition, we set the carbon price equal to 93.08 €/tonne CO 2 , namely four times higher than the value applied in the Reference case.The other input data remain unchanged with respect to the Reference case (see Section 3).With these assumptions, we aim at modelling the energy crisis that the European electricity market is currently facing.Table 7 indicates the expected power generated along the week under study by each technology, the CO 2 emissions of the system, and the total expected costs in each case.These results are the final outcomes obtained from Problem 3. From Table 7, we observe that the electricity generation from gas power plants decreases with respect to the reference case as long as the natural gas price increases.This progressive cut in the gas-based electricity production is compensated by coal units and WtE plants, whose utilization increases in terms of GWh generated and waste use, respectively.The total power production of not-fossil fuel technologies remains stable along the three cases considered and corresponds to their maximum expected output.The more intense utilization of highly pollutant coal plants is due to the fact gas-fired power units become more expensive, implying a shift in the merit order of these technologies. 3Notice that this new production mix resulting from the assumptions of this sensitivity analysis leads to a decrement of the total amount of CO 2 emissions generated.However, this outcome could be biased by the fact that WtE are not yet included in the EU-ETS.Finally, it is registered a progressive growth of the total expected cost of the system in Problem 3 that is proportional to the augments of the emission allowance price and of the operating charges of gasfired units.Finally, in all cases, demand is fully served.Table 8 summarizes the economic outcomes obtained by the WtE units along the whole week in each case of this sensitivity analysis.As for question RQ2, we can observe that the increase of the operating costs of the gas units has a negative impact on the equilibrium electricity prices, which significantly raise compared to the Reference case, but it makes WtE technologies more competitive.As a consequence, WtE units generate more heat and power and, in addition, participate more actively in the day-ahead market cleared by the PX.In addition, differently from what observed in the Reference case, WtE units are mainly used to procure up reserves.The combination of these effects is translated into augmented revenues that more than compensate the increased costs for the use of waste which are doubled compared to the Reference case.This is also evident from their profits that, in the three cases of Sensitivity analysis 1, result to be 187%, 308%, 483% higher than in the Reference case, respectively.

Sensitivity analysis 2: future power system
The aim of this sensitivity analysis is to answer our research question RQ4.In other words, we aim at investigating the operation of the WtE units in an electricity market with a higher level of renewable integration, a higher cost of the CO 2 emissions, a lower fossil-fuel capacity, and a higher capacity of interconnection compared to the Reference case.Taking into account the regulatory framework and the future scenarios foreseen by the European Commission to achieve decarbonised energy systems (see European Commission (2012), European Commission (2020c) and European Commission ( 2021)), we introduce the following assumptions, adapted for the Italian power system, with respect to the Reference case: • The wind and solar PV capacity is doubled and the biomass capacity is 30% higher; • The capacity of coal and gas-fired power plants reduces by 50% and by 10%, respectively; • The carbon price is equal to 93.08 €/tonne CO 2 as in Sensitivity analysis 1; • The electricity demand grows by 5%; • The interconnecting capacity among the Italian zones is 50% higher.
The other input data remain as in the Reference case (see Section 3).Notice that, to make the outcomes of this analysis comparable with those of the Reference case, we do not account for the investment costs needed for this transformation of the energy mix and the transmission service and we assume that these costs have already been amortized.From now on, we refer to the outcomes of Sensitivity analysis 2 as Future.
Again, we mainly focus on the findings for the WtE units.Fig. 16 shows the final use of waste per scenario (light blue) and in expectation (dark blue) from Problem 3, as a result of applying the assumptions of Sensitivity analysis 2. Comparing this figure with Fig. 14 of the Reference case, a much higher variability in the operation  of the WtE units is observed.This is due to the fact that there is an increase in the generation of intermittent renewable units, which entails higher reserve deployment.
To show the operation of this modified power system, Table 9 compares the power generated by each technology along the considered week, the use of waste by the WtE units, the total CO 2 emissions, and the total expected cost in the Reference and in the so-called Future cases.A remarkable result is that there is a huge reduction in the comparatively more pollutant coal generation that is recovered by the increase in the generation from gas, wind, solar PV, biomass, and WtE units.Notice that, as expected, in Future case the priority is given to renewable and not-emitting power plants.In other words, geothermal, wind, solar PV and biomass are used at full capacity.The WtE plants face an increase in their exploitation, but it is lower than the one registered in the cases of Sensitivity analysis 1.This derives from the fact that, under the Future assumptions, the availability of the cheaper and clean renewable-based plants is larger.This modification of the generation mix, driven by the assumptions of the case under analysis, implies a 20% decrease in the amount of CO 2 emitted with respect to the Reference case.It is highly noticeable the increase in the total expected costs registered in Problem 3 under the Future case assumptions.This significant increment depends on the higher CO 2 price and on the augmented management of reserves that are needed to compensate for the variability caused by the huge penetration of wind and solar power production.In addition, let us clarify that the total cost indicated in Table 9 for the Future case does not account for the penalization cost of the unserved demand that is registered in the CNOR zone in some real time hours of Problem 3 for a total of about 1081 MWh, representing 0.16% of the total demand along the week.This load shedding occurs even though it is assumed an enlargement of the transmission capacity.It is also true that the models proposed in this paper are a simplification of the actual operation of a power system and, hence, in reality the TSO counts on mechanisms to avoid this type of situations.However, this represents a signal of the fact that the intermittency of wind and solar power production stresses the whole system.This implies that an adequate transmission system and a sufficient reserve capacity are needed to accommodate the large penetration of renewable energy sources, otherwise the system could face very high operating costs.
Finally, Table 10 provides the economic outcomes of the WtE units along the week in the Reference and Future cases to give some additional insights for research question RQ2.In general, we observe an increment of the WtE units' incomes with respect to the Reference case, due to the increase of both the heat and power generation and the electricity prices.This implies that, in the Future case, the WtE's profits are 24% higher than in the Reference case (see Table 10).However, they remain significantly lower than those obtained under the assumptions of Sensitivity analysis 1 (compare Tables 8 and 10).This is not surprising since their utilization in the Future case is similar to that observed in the Reference case, where WtE's are employed by the TSO to produce electricity and provide down reserves.In the Future case, the unique difference is that WtE plants actively participate in the PX's market.

Conclusions
In this paper, we study the operation of a MU that satisfies the heat demand of local DHAs and participates in the electricity and reserve markets with its COG and WtE facilities.The analysis is conducted by developing and solving three sequential optimization problems.The proposed approach has been applied to a case study based on the Italian power system and DHAs.Considering our research questions presented in the Introduction, we can draw the following conclusions: • RQ1: The MU mainly covers the heat demand of the DHAs with HO so that it can use WtE and COG units to generate electricity to sell in the power markets.On the basis of our assumptions and input data, we find that PX accepts the power offers of COG units, but those of the WtE are taken into consideration only when economically convenient on the basis of the plant merit order.For instance, in the Reference case, WtE stations result to be too expensive compared to the other generating technologies available in market and therefore their schedules are excluded from the equilibrium.Instead, both in Sensitivity analysis 1 and Sensitivity analysis 2, PX includes their power supply in the clearing of the market.Considering the TSO's activities, in all cases, both the COG and WtE units are called to produce electricity and provide relatively high level of reserve capacity as results from the solution of Problem 3.Moreover, the electricity output of these plants is influenced by the level of integration of renewable power generation.Finally, the production of heat of WtE and COG units is quite stable, even though in Sensitivity analysis 1 and, especially, in Sensitivity analysis 2 it is larger than in the Reference case.These outcomes are line with the more active role played by these plants under the market conditions described by the two sensitivity analyses.• RQ2: Our analysis shows that, in all cases, the WtE units can get profits from their participation in the heat and electricity market.The profits vary according to the market conditions and the level of renewable power generation.• RQ3: Sensitivity analysis 1 shows that the combined increase of the natural gas costs and carbon price leads to a cut in the gas-power production that is com-5 Page 40 of 49 pensated by the coal and WtE units that become more competitive.The WtE's power schedules resulting from Problem 2 are significant and, moreover, differently from Reference case, these stations are use to provide up reserves and a minimal part of down reserves.This changed trend in the deployment of these units is reflected in their profits that are higher than those obtained in the Reference case and in Sensitivity analysis 2. • RQ4: In the Sensitivity analysis 2, the higher level of intermittent renewable energy production increases the variability of the WtE units' operation.Their electricity production increases with respect to the Reference case but is lower than in the Sensitivity analysis 1 since, in the Future case the priority is given to the renewable power plants.Moreover, as in the Reference case, WtE units are used to mainly procure down reserves.
An additional remark regards the operation of the Italian power system, where it is noticeable the different energy mix of each bidding zone that depends on the availability of renewable energy sources and gas-fired power plants.Moreover, we highlight that, in both sensitivity analyses, the the total expected costs of the power system operation significantly augments compared to the Reference case.This especially holds for the Sensitivity analysis 2 where there a load shedding is also registered.
Finally, this work could be extended by: (i) analysing the operation of the WtE units along the year considering the waste availability and the energy density of that waste; (iii) solving a sensitivity analysis on the WtE capacity, (iii) performing a sensitivity analysis on the heat-to-power efficiency ( ) of the COG units, (iv) including a risk measure in Problem 1 to evaluate its impacts on the expected profits of the MU.

Appendix B: Additional input data
In this Appendix, we report additional information related to the input data described in Sect.3. Fig. 17 depicts the scheduled power flows between the geographical and the foreign zones with which the Italian power system is connected.Figs. 18,19,20 show the scenarios considered in the case study to represent the real-time variability in Problem 3. In particular, Fig. 18 represents the wind

Fig. 1 Fig. 2
Fig. 1 Structure of the three subsequent problems Page 14 of 49 the description of Problem 1, WtE plants are not yet subject to this environmental regulation.

Fig. 5
Fig. 5 Zonal representation of the Italian electricity market

Fig. 6
Fig. 6 MU self-dispatch: heat scheduled by each technology in the day ahead of delivery in each DHA (Problem 1) (color figure online)

Fig. 7 5
Fig. 7 MU self-dispatch: electricity scheduled in the day ahead of delivery by COG and WtE units in each DHA and prediction of the electricity price (Problem 1) (color figure online)

Fig. 14
Fig. 14 Day-ahead re-scheduling market (TSO): waste used on average (dark blue) and per scenario (light blue) by the three WtE units resulting from Problem 3 (color figure online)

Fig. 16
Fig. 16 Day-ahead re-scheduling market (TSO): waste used on average (dark blue) and per scenario (light blue) by the three WtE units resulting from Problem 3 under the Future assumptions (color figure online)

Fig. 17 5
Fig. 17 Scheduled power flow between Italian and foreign zones

Table 1
Characteristics of the HO, COG, and WtE units

Table 2
Problem 3, coal and gas turbine are considered as fossil-fuel power plants.The rest of technologies is labelled as not-fossil fuel generating units.

Table 5
Economic outcomes for the WtE units in each day and in total (k€)

Table 6
Daily emissions of the WtE units (tonne)

Table 7
Expected power generated per technology along the week, CO 2 emissions, and total expected cost of Problem 3 for each case

Table 8
Economic outcomes for the WtE units along the week in each case (k€)

Table 9
Expected power generated per technology along the week, CO 2 emissions, and total expected cost of Problem 3 for each case

Table 10
Economic outcomes for the WtE units along the week in each case (k€) Heat demand in the day ahead of delivery in area a and in hour t (MWh-t) Heat demand of area a, in hour t and scenario s (MWh-t) Heat scheduled by plant i in the day-ahead dispatch in hour t (MWh-t) Up/down deviation in the balancing of the heat dispatch of unit i, in hour t and scenario s (MWh-t) Electricity scheduled by unit i ∈ I C (i) in the day-ahead market in hour t (MWh-e) u i,t Binary variable indicating the on/off status of unit i in hour t w i,t,s Waste use of unit i ∈ WtE(i) in hour t and scenario s (tonne) It is reported the notation used in Problem 2. The sets already included in Problem 1 are not indicated.Subset of WtE and COG plants, among units i ∈ I C (i) , located in zone z Operating cost of generating technology g in hour t (€/MWh) Cost of electricity production of unit i ∈ COG(i) of the MU in hour t (€/MWh) Cost of electricity production of unit i ∈ WtE(i) of the MU in hour t (€/tonne waste-h) Electricity demand in the day-ahead market in zone z and time t (MWh) Prediction of the renewable source availability factor in the day-ahead market in zone z, generating technology g and hour t (p.u.) Minimum generation level of generating technology g located in zone z (MWh) P z,g Generation capacity of technology g located in zone z (MW) Maximum power offer of unit i ∈ I C (i) in hour t, as defined in Problem 1 (MWh) CO 2 emission factor corresponding to fossil-fuel technology g or COG units i ∈ COG(i) (tonne CO 2 /MWh) U i,t On/off status of plant i, in hour t, as defined in Problem 1. Start-up cost of fossil-fuel unit g in the day-ahead electricity market in zone z and hour t (€) Shut-down cost of fossil-fuel unit g in the day-ahead electricity market in zone z and hour t (€) Involuntary unserved demand in the day-ahead electricity market in zone z and hour t (MWh) p DA z,g,t Electricity scheduled in the day-ahead market by generating technology g in zone z for each hour t (MWh) Electricity scheduled in the day-ahead market by plant i ∈ I C (i) in hour t (MWh) Power flow in the day-ahead market through link , in hour t (MWh) Binary variable defining the on/off status of fossil-fuel technology g of zone z in hour t This list reports the notation of Problem 3 that has not been used in the former two models.Cost of reserve procurement from plant i ∈ I C (i) (€/MWh) Cost of deploying up/down reserves of generating technology g in hour t (€/MWh) Cost of deploying up/down reserves of plant i ∈ I C (i) (€/MWh) Zonal requirement of up/down reserves in zone z in hour t (MWh) Factor limiting the reserve capacity offered by generating technology g Electricity demand in the balancing market in zone z, in hour t and scenario (MWh) Intermittent renewable power availability in the balancing market of technology g, in zone z, hour t and scenario (p.u.) Involuntary unserved demand in the balancing market in zone z, hour t and scenario (MWh) Energy re-scheduled in the day-ahead market by generating technology g of zone z, in hour t (MWh) Energy generated in the balancing market by generating technology g of zone z, in hour t and scenario (MWh) Power flow re-scheduled in the day ahead through link , in hour t (MWh) Power flow in the balancing market through link , in hour t and scenario (MWh) Energy re-scheduled in the day-ahead market by unit i ∈ I C , in hour t (MWh) Up/down heat deviation in the balancing market of r plant i ∈ I C , in hour t and scenario (MWh-t) Up/Down reserve capacity scheduled in the day-ahead market by generating technology g of zone z, in hour t (MWh) Up/Down reserve deployed in the balancing market by generating technology g of zone z, in hour t and scenario (MWh) Up/Down reserve capacity scheduled in the day-ahead market by unit i ∈ I C in hour t (MWh) Up/Down reserve deployed in the balancing market by unit i ∈ I C , in hour t and scenario (MWh) Waste used by unit i ∈ WtE(i) in hour t and scenario (tonne) i Down ramp limit of plant i (MWh/h) ramp up i Up ramp limit of plant i (MWh/h) T on∕off i Number of hours that plant i has been online/offline prior to the scheduling horizon (h) T U∕Dmin i Minimum up/down time of plant i (h) W i Maximum waste that plant i ∈ WtE(i) can use (tonne waste) W i Minimum waste that plant i can use, with i ∈ WtE(i) (tonne waste) h t Heat price in hour t (€/MWh-t) eDA t Electricity price in hour t (€/MWh-e) W ri Emission factor of pollutant type r for unit i (tonne-pollutant/tonne-fuel) s Probability of scenario s Power to heat relationship of COG and WtE plants (MWh-e/MWh-t) e Fuel consumption per electricity unit (tonne/MWh-e) h Fuel consumption per heat unit (tonne/MWh-t)