Uncertainties in the design and operation of distributed energy resources: The case of micro-CHP systems

ARTICLE IN PRESS Energy 33 (2008) 1518–1536

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Uncertainties in the design and operation of distributed energy resources: The case of micro-CHP systems Michiel Houwing a,, Austin N. Ajah a,b, Petra W. Heijnen a, Ivo Bouwmans a, Paulien M. Herder a a b

Faculty of Technology, Policy and Management, Energy and Industry Department, Delft University of Technology, Jaffalaan 5, 2628 BX Delft, The Netherlands Product and Process Engineering, Faculty of Applied Science, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands

a r t i c l e in f o

a b s t r a c t

Article history: Received 3 October 2007

Large-scale diffusion of distributed energy resources (DERs) will have a profound impact on electricity infrastructure functioning: it will bring radical changes to the traditional model of generation and supply as well as to the business model of the energy industry. DERs comprise distributed power generators, distributed energy storages and controllable loads. There are, however, many uncertainties that influence the design and operation of DERs. This paper clarifies these uncertainties by proposing and applying a comprehensive framework for uncertainty analysis. We thereby adopt an integrated approach that considers not only the technical, but also the economic and institutional uncertainties. A delineation of the work is a focus on residential DERs and on micro-CHP systems specifically. After the proposed framework for uncertainty analysis is explained the uncertainties pertaining to the design and operation of residential DERs and micro-CHP systems are identified. In a case study system a selection of the uncertainties are quantitatively analysed. The case study system consists of a household that intelligently applies a micro-CHP unit in conjunction with energy storages and that interacts with its energy supplier. With a sensitivity analysis of the system model the salient impacts of the uncertainties on system behaviour and performance are enunciated. & 2008 Elsevier Ltd. All rights reserved.

Keywords: Demand response Distributed energy resources Energy efficiency Micro-combined heat and power Model predictive control Residential electricity usage Uncertainty analysis

1. Introduction 1.1. Distributed energy resources (DERs) DERs are expected to play a significant role in the future electricity supply [1]. This concept of DERs comprises three subconcepts, namely: distributed generation of electricity (DG), distributed energy storage and controllable energy loads (load management). The penetration of DG at medium and low voltages, both in utility networks and downstream behind customer meters, is increasing in developed countries worldwide [1]. A wide body of literature states that DG has a good chance of pervading the electricity infrastructure in the future (e.g. [2,3]). Examples of DG technologies are photo-voltaic systems, small wind turbines, micro-combined heat and power plants (mCHP), and other small systems using renewable energy sources (e.g. biogas digesters). Drivers for DG are the environmental benefits (reduction of carbon emissions due to the use of renewable energy sources and the

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E-mail address: [email protected] (M. Houwing). 0360-5442/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2008.07.003

efficient use of fossil fuels), reduced investment risks, fuel diversification and energy autonomy, and increased energy efficiency (less line losses, co-generation options). In addition, the presence of generation close to demand can increase the power quality and reliability of delivered electricity. Other benefits, such as grid expansion deferral, are also often discussed [1]. Furthermore, several small-scale electricity storage technologies are under development (e.g. lithium-ion batteries, plug-in hybrid electric vehicles [4]) and more extensive load management schemes are foreseen for distributed power systems [5,6]. Drivers for DERs in general are the generation and sale of electricity and its accompanying attributes (e.g. CO2 credits, white and green certificates) on several markets. Besides these economic drivers for DERs there are technical drivers in the provision of ancillary services to network operators. DERs can thus play a crucial role in supporting key policy objectives as market liberalisation, mitigating climate change, increasing the amount of electricity generated from renewable sources, and enhancing energy saving. Large-scale diffusion of DERs will have a profound impact on electricity infrastructure functioning: it will bring radical changes to the traditional model of generation and supply as well as to the business model of the energy industry. Actors’ performance and decision-making will be

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Nomenclature

Subscrips

c es ec eext f1 f2 f g h1 h2 hc hc_DHW hc_SH hs iext k m N n pf pi,ext pe,ext Pmax

c c_DHW c_SH down e ext f i k m max min o part s SH th tot up

r si so tdown tup DT

specific heat capacity, kJ/kg K electricity stored in battery, kWh residential electricity consumption, kW electricity exported from household to supplier, kW natural gas flow to Stirling engine, kW natural gas flow to auxiliary gas burner, kW total natural gas flow to household, kW electricity generated by Stirling engine, kW heat generated by Stirling engine, kW heat generated by auxiliary burner, kW residential heat consumption, kW domestic hot water consumption, kW space heating consumption, kW heat contained in the hot water storage, kWh electricity imported by household from supplier, kW simulation time step volume of water contained in the hot water storage, l prediction horizon length, number of time steps variable used for up-time fuel price, h/kWh electricity import price, h/kWh electricity feed-in price, h/kWh maximum capacity of power line to/from household, kW variable used for down-time electricity inflow to the battery, kW electricity outflow of the battery, kW down-time of Stirling engine, simulation time steps up-time of Stirling engine, simulation time steps temperature difference, 1C

Binary variables u v x1 xi xe

deciding the start-up or shut-down of a conversion technology for a certain time step deciding if a conversion technology is in operation for a certain time step deciding on part or full load operation of Stirling engine deciding on electricity import from supplier deciding on electricity export to supplier

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consumption domestic hot water consumption space heating consumption shutting down of a conversion technology electric, export from/to external energy supplier fuel inflow, import simulation time step subinterval of prediction horizon maximum or full load minimal load outflow part load storage space heating thermal total starting up of a conversion technology

Superscripts CHP aux

combined heat and power auxiliary burner

Abbreviations CHP mCHP DER(s) DG DR EMS ESCO ICT MPC ORC TSO RES-E RTP UoS VPP

combined heat and power micro-combined heat and power distributed energy resources distributed generation (of electricity) demand response energy management system energy service company information and communication technology model predictive control organic rankine cycle transmission system operator electricity from renewable energy sources real-time pricing use of system charges virtual power plant

Greek symbols

m Z

micro efficiency

affected due to changing technical and social dynamics within the infrastructure [7].

1.2. Residential energy use, micro-combined heat and power technology and ICT developments In this paper, we focus on residential, or micro (m) DERs. Households consume energy in the form of electricity and heat (and to a smaller extent in the form of cold). In The Netherlands, space heating and domestic hot water are mainly produced inside the house via the conversion of natural gas in boilers. District heating networks, heat pumps and solar boilers are still only marginally used. In 2006 the domestic sector was responsible for

about 25% of the Dutch electricity consumption and 41% of the Dutch natural gas consumption [8,9]. Applying DG at customer sites has key economic and environmental potentials. Specific potential lies in the opportunity to locally utilise the waste heat from the conversion of primary fuels into electricity by combined heat and power systems (CHP). This could lead to more efficient energy use and thus to cost savings and carbon emission reductions [10]. Consequently, there has been significant progress toward developing small CHP applications (kW-scale), so-called micro-CHP or mCHP systems, based on Stirling engine, internal combustion engine, gas turbine, or fuel cell conversion technology [1,3,11]. Stirling mCHP systems are expected to pervade the Dutch market substantially in the short- to mid-term [12]. These Stirling

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systems target the housing market segment of system replacements and are probably not meant for newly built houses as these have too little heat demand. The matured Dutch market is expected to comprise of 400,000 units per year [13]. In this paper, we only consider mCHP DG systems. Another development in the electricity infrastructures is the incorporation of more information and communication technology (ICT). Novel ICT systems facilitate the intelligent control of networks and DER technologies, and enable a more active incorporation of end users in electricity and ancillary services markets. An increase in DERs combined with more ICT enables smarter power systems, more active and intelligent network management, and demand response options at the consumer level. The increased system complexity due to DER application is described in detail in [7,14]. Households applying DERs could operate more independently of energy suppliers, they can devise new contractual arrangements with suppliers or network managers, and they might even trade energy among each other. Households thereby become so-called ‘prosumers’ (producers and consumers at the same time), and value webs rather than value chains are formed. However, in the design and application of (residential) DERs there are still many uncertainties about the impacts on the electricity system. Which types of DERs and accompanying technologies are suitable for which households? How to design suitable DER technologies and control systems to meet economic and environmental objectives? What retail market designs (e.g. pricing schemes) can benefit the operation of DERs? How should contractual arrangements between operators and owners of DERs be devised? For the efficient utilisation of DER technologies the various uncertainties that might plague them during their entire lifespan ought to be identified and accommodated during their design and operation. 1.3. Paper objective and layout The place of DERs in the energy landscape is getting brighter as research efforts are being intensified. However, there are still myriads of uncertainties that ultimately besiege the design and operation of (residential) DERs. These uncertainties will impact both the short- and long-term performance of DERs if they are not considered, analysed and accommodated in the early phase of the design. So, the impacts of the application of DERs on the electricity system and its actors are unsure. The objective of this paper is to clarify part of these impacts by proposing and applying a comprehensive framework for uncertainty analysis. In Section 2 the proposed framework for uncertainty analysis is explained. In Section 3 we identify and explicate the economic, technical and regulatory uncertainties pertaining to the design and operation of residential DERs and mCHP systems. This involves the first stage of the framework. In Section 4, the further stages of the framework are applied in a case study: a selection of the uncertainties described in Section 3 is projected onto a specific sub-system and are quantitatively analysed. The case system consists of a household that applies a mCHP unit in conjunction with energy storages and that interacts with its energy supplier. Section 5 presents the outcomes of the sensitivity analysis where we assessed the impacts of the uncertainties on system behaviour. In Section 6 conclusions and recommendations for further research are given.

2. Proposed framework for uncertainty analysis In Section 1.3, it has been conjectured that myriads of uncertainties can affect the design and operation of (residential)

DERs. By uncertainty, we mean the general lack of technical, economic, institutional and/or politico-social knowledge about how the future will unfold. Uncertainties do interact, and if they are not completely identified and handled at the early part of the DERs design process, they may not only negatively affect the operation of DERs but may also lower their profitability. As a decision support tool for the designers and DERs operators, a generic framework for uncertainty identification and analysis has been proposed in this section. The first step in the proposed framework (depicted in Fig. 1), the first step in the proposed framework for uncertainty analysis is the identification and classification of the envisaged uncertainties in the system under analysis. This is either the total system or the set of its building blocks. The set of building blocks is the totality of the physical and non-physical components, units or sub-systems making up the system. At this step, the identification should be comprehensive and should span the economic, the technical as well as the institutional or regulatory spheres of the system. In Section 3 we apply this step to the electricity infrastructure system in which DERs are applied. The second stage of the framework is the analysis of the impacts of the identified uncertainties on both the short- and long-term performance of the system. In this step, a behavioural model of the system is constructed and used for the analysis of the system behaviour, assuming that specified uncertainties influence the system. Such a mathematical or behavioural model produces the state attributes of the system as output. At the evaluation stage, a comparison is made of the system behaviour or outputs relative to some given performance targets. The output of the evaluation stage forms the basis for the judgment of the impacts that the analysed uncertainty has on the system. If the impacts of the uncertainty are strong, a mitigation or optimisation step is initiated. At this stage, options that will cushion the effects of the analysed uncertainty are designed into the system. In Sections 4 and 5, the impact analysis and evaluation stages are applied in the case study sub-system. With the evaluation we provide recommendations to designers and operators of the sub-system. In Fig. 1, the inputs of the framework are all the employed models (mental and mathematical) as well as the parameters and variables used in the uncertainty analysis. The main body of the framework—the plan of action intended to accomplish the specific goal of comprehensively analysing and accommodating uncertainties into the system—is denoted as the ‘strategy’. The outputs of the framework are the goals or final products of each stage of the strategy.

3. Identification of design and operational uncertainties pertaining to residential DERs This section identifies and classifies the various uncertainties (economic, technical and institutional/regulatory) related to domestic DERs and their application in the electricity system. This is the first step of our framework. Most design cases still lack an integrated approach that considers not only the technical constraints or uncertainties, but also the economic and institutional constraints. We think that the first step towards design for flexibility is the identification and consideration of uncertainties in an integrated form: all constraints and uncertainties that could manifest themselves at any time. To provide insight into the functioning of an electricity system with DERs the technical and economic interactions in such a system are conceptualised first. Subsequently we discuss the economic, technical and institutional uncertainties in designing and operating DERs.

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Set of Building Blocks

System

Identify &Classify Uncertainties

Behavioural Models

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Uncertianties

Analyse Impacts System Behaviour

Evaluate

Performance Model

System Performance

Mitigation Models

Mitigate (Optimise)

Input

Strategy

Optimized Performance Output

Fig. 1. Framework for addressing uncertainties in the design and operation of DERs.

Fig. 2. Socio-technical system of the electricity infrastructure with the application of DERs (thick arrows depict power flows and electricity sales. The thin arrows show the control authority the transmission and distribution system operators could have).

3.1. Electricity infrastructure with distributed energy resources In [7] we discussed the socio-technical impacts of the introduction of DERs on critical actors in the electricity infra-

structure. In this paper, we explain these issues in more detail. An electricity infrastructure system incorporating DERs is shown conceptually in Fig. 2. The figure is an elaboration on work described in [15]. In the figure the thick arrows represent power

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flows and electricity sales, and the thin arrows show the control authority that the transmission and distribution system operators may have. This conceptual overview can apply to DERs in general and is not limited to residential DERs. In the physical sub-system electricity from large generators reaches the loads via the transmission and distribution networks (a–b–c). Distributed generators can produce power directly for loads (d) or their electricity can be stored in an appropriate storage system (f). In this way, loads could be served with electricity from these storage systems (h). Storages can also be filled with electricity from the external distribution network (g). Electricity from DG and storages can also flow up into the distribution network (e, i) and possibly into the transmission network (j). The transmission network manager guards against congestion, maintains reliability of transmission services and provides ancillary services for electricity transport. For the distribution network these tasks are done by the distribution system operator. Ancillary services are all services necessary for the operation of a transmission or distribution system. The system operator maintains system stability and manages the energy balance within a control zone. A second task is to provide (or contract) sufficient black-start power. The transmission network manager and the system operator together form the transmission system operator (TSO). The TSO works together with the distribution system operator in fulfilling its tasks. The economic sub-system represents the Dutch market design which has a decentralised structure (i.e. the TSO only has technical and no financial information about the system) and involves wholesale and retail competition. Large producers can sell electricity directly to the several markets (1). Market types are the bilateral market (including ‘over-the-counter’ transactions), the power exchanges, the TSO-run interconnection capacity auction, and the balancing market (which is included in the ‘ancillary services market’). We have not shown the capacity market and markets for electricity attributes as green certificates and CO2 credits. Operators of DERs may sell electricity directly to the market (2), but as market participation costs are relatively high, this will most probably not happen in practice. DERs can deliver power directly to (residential) consumers (3). These could also be other households than households owning and/or operating DERs, thus creating an internal market amongst households. Large consumers can obtain electricity directly from the market (4). Smaller consumers acquire electricity via their energy supplier (5,6). Furthermore, power from DERs can be traded through an aggregating body that trades for clusters of households on the different markets (7,5). The aggregating function can be fulfilled by several actors. Possible aggregators are energy suppliers, producers (generators), integrated utilities, or other independent aggregators such as energy service companies (ESCOs) or housing corporations. Large producers, TSOs and DSOs are currently responsible for providing ancillary services. DERs, however, could provide ancillary services as well, possibly via ancillary services markets in the future [16]. The DSO (possibly in cooperation with the supplier) could function as aggregator in trading on ancillary services markets. In principle, apart from households only energy suppliers end DSOs are authorised to set operating parameters for DERs. Several actors could operate and manage the ICT infrastructure in the distribution network, possibly in conjunction with each other. The DSO, however, is expected to own the required ICT infrastructure and necessary power electronic equipment (e.g. intelligent meters). Other important actors relating to the system of Fig. 2 are metering companies, ESCOs, traders and brokers. Metering

companies can be new actors or existing suppliers. They ‘own’ and possibly trade metering data. The metering company has full access to data but has no authority to set parameters of DERs [17]. It is expected that suppliers will fulfil the role as metering entity once intelligent meters are widely used [17]. An ESCO provides added-value services, possibly with the metering data that have been received after authorisation by household customers. Traders trade the power; they match supply and demand of electricity as efficiently as possible. Some suppliers and producers have their own trading floors, others contract trading out to external parties. Brokers act as intermediary between demand and supply on behalf of market parties. Contrary to traders they have no actual position in the market. All actors operating in the electricity infrastructure will be confronted with changing circumstances due to the introduction and application of DERs. The technical and economic sub-systems are linked by bi-directional flows of information on: prices, power flows, capacity restrictions, dispatch instructions, etc. Through aggregation of DER electricity and its attributes, the value of DERs can be enhanced. The aggregating activity may include, for example, collection of DER parameters and market information, submission of bids and offers to market players, and making optimal power trading decisions to maximise the benefits for households and the aggregator. As mentioned before, the aggregation process can be conducted by several actors. Aggregators can be program responsible parties themselves (for enabling access to electricity markets), or they can be part of a separate program responsible party. The aggregator either deals with DERs directly on behalf of his residential clients, or deals through a large intermediary with direct access to relevant markets. 3.2. Economic uncertainties The success or failure of implementing a new technology in the electricity infrastructure is affected to a high degree by electricity market design and its development. Therefore we pay particular attention to the market uncertainties and possible future market developments. As described, the electricity infrastructure becomes a more complex system due to the introduction and application of DERs and the accompanying ICT infrastructure. The operational activities and economic decision-making of almost all actors is influenced and resulting economic impacts are uncertain. An example is the possible need for different forecast models of residential electricity consumption, taking into account residential power exports during certain moments of a day. We do not go into detail regarding the complex build-up of revenues and costs for all actors and how items might change in a future with significant adoption of DERs. Costs for actors include, for example, feed-in revenues for households and balancing costs for energy suppliers. Also, gas and electricity sales will change substantially for suppliers if households apply mCHP units. For DSOs costs include, for example, network reinforcement costs needed to mitigate technical problems associated with integrating DG into distribution networks. On the other hand, distribution losses decrease and DG could release network capacity that can be used to accommodate future loads [18]. More economic uncertainties are the following:

 The ownership of DERs can take several forms; besides 

households owning mCHPs, energy suppliers or ESCOs could lease out mCHP units to households. Aggregators could trade electricity from DERs on several different markets as shown in Fig. 2. Further, there are different

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regimes to economically coordinate clusters of residential DERs [19] (e.g. via microgrids or virtual power plants (VPPs)). For households operating DERs there is a lot of uncertainty on the investment and operational costs of mCHP systems. Also the costs of electricity storage technologies are uncertain. It is unclear what the regime will be regarding electricity feedin. Will net-metering be implemented, or will the feed-in tariff be lower than electricity import prices? Furthermore, tariffs can be based on more real-time pricing (RTP). A household should not pay tax on the natural gas that fuels its mCHP if the excess electricity that it exports is subject to energy tax when it is used by another consumer. If such double-taxation is not treated properly through legislation this will negatively affect the adoption of mCHP technologies. Investment costs of mCHP systems are expected to be significant. Present-day high-efficiency condensing boilers cost around h2400 [20]. Stirling mCHP systems that are expected to enter the Dutch market in 2008 are estimated to cost around h6500 [20], which is significantly higher. It is uncertain if governments will provide investment subsidies or mandate lower gas tariffs for households with mCHPs. It is important to note that mCHP systems are one of a group of competing heating technologies for the domestic sector. Besides condensing boilers, options are heat pumps, heat networks, and solar boilers. Developments—technical, economic, or regulatory—in these other technologies will indirectly determine the economic attractiveness of mCHP systems. We would like to note that there is quite a deficiency in the literature on investment and operational costs of the ICT infrastructure and systems to facilitate effective integration of DERs (e.g. intelligent meters, intelligent controllers, in-house domotics, communication lines). Some indications can be found (e.g. [21,22]), but publicly accessible studies and data are scarce. Therefore, it is difficult to arrive at generic cost figures for smart power system components. A last category of economic uncertainties relate to the implementation of demand response measures (DR). DR refers to a set of strategies that can be used in competitive electricity markets to increase the participation of the demand side, or end-use customers, in setting prices and clearing the market [23]. There are several DR implementation types, which could also apply to residential customers. Options include price differentiation (or dynamic pricing), interruptible loads, and specific emergency programs [23,24]. Furthermore, there are different types of pricing in price differentiation programs. Examples are flat rates, time-of-use pricing, real-time tariffs (RTP), and critical peak prices [25]. It is uncertain which DR implementation and accompanying pricing types will be offered to households via contractual arrangements with energy suppliers and network operators.

3.3. Technical uncertainties In [26] a good overview is given of important technical challenges for power networks accompanying an increased penetration of DG. The main challenges are voltage rise effects, transient variations, harmonic distortions, power quality aspects, and protection and stability issues. Positive network effects are decreased energy losses and investment deferral. The authors of [26] also state that active network management can significantly mitigate negative network impacts of applying DERs and can increase the amount of DG to be connected to the existing network. Additional to the challenges in [26] (which can be seen as challenges for the broader concept of DERs, besides just DG),

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we identify these additional technical challenges and uncertainties for DERs in general and mCHP systems in particular:

 Different conversion technologies are possible for mCHP



             

systems: Stirling engines, internal combustion engines, fuel cells, microturbines, organic rankine cycles (ORCs), and steam cells [3]. Which technology will be adopted will mostly depend on costs. The financial attractiveness of a technology will to a large extent be based on the household type in which the technology will operate (number of residents, age of the building, free-standing or not, degree of isolation, etc.) and the climate in which the household is located. Each household type will have different electricity and heat demand profiles. This in turn determines the amount of running hours of each technology and subsequent operational cost savings. The fuel type for a mCHP system. Stirling engines, for example, are external combustion engines and can run on different fuels. High temperature SOFC fuel cells can also operate on several different fuels such as hydrogen, natural gas and methanol. Part-load options for mCHP prime movers. Some manufacturers, for example, build Stirling engines of which power output cannot be modulated and others build engines that can. Future development of thermal and electric efficiencies and resulting heat-to-power ratios of mCHP prime movers (different heat-to-power ratios suit different household types). Overhaul times of mCHP systems. mCHP system component lifetimes. Allowable number of start-stops for mCHP prime movers. Start-up and cool-down characteristics of mCHP prime movers. Emissions of greenhouse gases (e.g. CO2) and pollutants from mCHP systems. Future developments of residential electricity and heat demand. This is important for the dimensioning of DER technologies. In-house heating system configuration: opportunities for storing heat from the mCHP system in the form of hot water. The possibility of small-scale electricity storage. Local control modes of mCHP systems, e.g. heat-led, loadfollowing, or cost-minimising. Control criterion: cost only, or multiple criteria such as costs and emissions. Possibilities for central or distributed control of clusters of DERs in microgrids and VPPs. Finally, the degree of intelligence of ICT systems that could enter the market (such as DER controllers and metering equipment) is uncertain.

3.4. Institutional uncertainties The institutional uncertainties concern aspects of the social, political, regulatory and legal uncertainties that may affect DERs. In [26] it is said that with the absence of a clear policy and associated regulatory instruments on the treatment of DG, it is very unlikely that this type of power generation is going to thrive. The reasons for this are given to be partly historical and related to the way distribution networks have been developed and operated as passive networks. In order to foster the required changes, there is a clear need to develop and articulate appropriate policies that support the integration of DG into distribution networks [26]. The expected CO2 emission reduction levels from residential energy use due to mCHP application, the changing incomes from VAT and energy taxes, and the costs of possible subsidy schemes to support renewable electricity are uncertain for the government. Below we

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state the main institutional uncertainties regarding the design and operation of DERs:

 Legislation regarding investment subsidies for mCHPs, feed-in

 





  

tariffs, net-metering, double-taxation prevention, and gas tariffs for mCHP households (as described under the economic uncertainties). The electricity from renewable energy sources (RES-E) subsidy scheme in place, e.g. feed-in premiums/tariffs, quota obligations, tax incentives. CO2 emission policy. This policy could determine the economic attractiveness of fuel-efficient mCHP systems. For example, the domestic sector could fall under emission trading schemes or utilities could invest in and operate VPPs earning them CO2 credits to trade with on CO2 credit markets. Regulation on DG connection charges (deep, shallow, shallowish) and the design of time- and space-varying use of system charges (UoS) (network tariffs) pertaining to DER operation. With varying UoS charges, system operation could be steered. The degree of unbundling and liberalisation of the electricity sector. A more liberalised sector will incentivise new contractual arrangements between, for example, ESCOs and DER households; Behaviour of all involved actors. Individual and general public perception of DER technologies. Experience of fitters in installing mCHP systems due to the novelty of the technologies.

4. Case study Now that the uncertainties in the design and operation of DERs have been identified we apply the impact analysis and evaluation stages of our framework to a specific case study system. This case study system is a sub-system of the total socio-technical system of Section 3. We quantitatively analyse the impacts of a set of uncertainties via a sensitivity analysis of a model of the system. First the system will be described. Then the uncertainties of which the impact on system performance have been analysed are discussed. Finally, the modelling assumptions and the mathematical model of the system are presented. 4.1. System description The analysis focuses on the system as shown in Fig. 3. In the system a household interacts with its energy supplier. The supplier functions as aggregator for the household. Energy flows are present between the household and the supplier as shown. The household has full control over its DERs and there is no interaction with other households regarding electricity trade. We chose this specific system because in our research we focus on the socio-technical or techno-economic impacts of DER application for households specifically and on the technical functioning of their installed DERs. Furthermore, regarding the level of observation of system effects and phenomena we do not adopt a very small time scale. Therefore, electro-technical aspects of DER technologies and power electronics fall outside the scope of our work. The adopted time scale will be discussed further in Section 5.1. Fig. 3 shows that households fulfil their electricity and heat consumption requirements through several alternative supply means. The mCHP unit consists of a Stirling engine prime mover (conversion 1) and an auxiliary burner (conversion 2), which can provide additional thermal power. The Stirling engine converts natural gas (f1) into electricity (g) and heat (h1). The heat in the flue gases is supplied to the heat storage in the

Fig. 3. Conceptual overview of the household-supplier system.

form of hot water (hs). The auxiliary burner also converts natural gas (f2) and provides additional heat (h2). All heat consumption (hc) is taken from the heat storage. Different configurations of a mCHP unit in relation to possible hot water storage systems can be thought of. There are two classes of heat demand: domestic hot water and space heating. There could be storage of domestic hot water only, or there could be no possibility for hot water storage at all (for possible configurations see [27,28]). As a base case we envisage one large heat storage from which all heat, for domestic hot water as well as for space heating purposes, can be extracted. This system is being marketed by a manufacturer in the UK (see [29]). One storage allows us to combine space heating and domestic hot water demand, which is more convenient for the modelling. Electricity can be stored in a battery (es). Electricity can flow to and from the battery, represented in Fig. 3 by (si) and (so), respectively. Locally generated electricity can thus be used directly by the household (ec), it can be stored or it can be sold to the supplier (eext). Electricity can also be imported from the supplier (iext). The supplier thus sells primary fuel (f ¼ f1+f2) for fuelling the mCHP unit as well as additionally required import electricity for households. The supplier could buy the electricity that is produced by households in excess of their own consumption. We do not consider thermal and electric load shift options.

4.2. Analysed system uncertainties The household-supplier system is shown in Fig. 4 again. Additionally, external factors working on the system, system uncertainties and system performance are shown. External factors in the form of Dutch and European legislation work on the system and can be regarded as fixed. The system delivers a performance in terms of outcomes of interests for certain stakeholders. The outcomes we are interested in are the costs of residential electricity and gas consumption, the supplier’s revenues from gas and electricity sales to the household, CO2 emissions from residential energy use and economic feasibility of DER systems for the government, and technical aspects of mCHP

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Fig. 4. System consisting of a DER household in interaction with its energy supplier. External factors work on the system and the system delivers a performance in terms of outcomes of interests for stakeholders. The system contains uncertainties of which the impact on system performance is researched.

units for DER developers. The system uncertainties of which the impact on system performance have been researched here are shown at the top of the figure. Gaining insight in the sensitivity of the performance to system uncertainties could provide valuable information for the proper judgement and evaluation of DERs and mCHPs by different actors. The objective of this case is to identify a first set of interesting interactions between uncertainties in the household-supplier system and the performance of that system. The uncertainties we look into are categorised in DER technology characteristics, economic parameters and seasonal residential electricity and heat consumption profiles. The following technology characteristics were studied:

 the presence and the absence of an electricity storage;  different configurations for residential hot water storage;  the influence of different minimal up-times of the Stirling engine;

 the capacity of heat and electricity storages;  least-cost model predictive control (MPC) specificities. The final technical characteristic that was studied (i.e. leastcost MPC specificities) needs some clarification. First we note that different control modes can be adopted in mCHP operation. Examples are heat-led (also called thermal-led) or load-following control. The unit then switches on whenever there is a heat or electricity requirement in the household (see, for example, [10] for the different functioning of these control modes). Another possible control mode is least-cost control, in which the main objective is to fulfil energy needs at least cost. In such least-cost control, information on future parameter values can be included. This is what is meant by least-cost MPC. Furthermore, this control mode is more open in the sense that the actuation of prime movers is less strictly controlled than in thermal-led control. This leaves more room for flexibility in the operation of the DERs. In this case study we assume local DER control to be of the least cost, model predictive type. The influence of two aspects of this control

mode, namely the length of the prediction horizon and the priority in prime mover and auxiliary heating activation, were studied in the sensitivity analysis. A detailed description of the control mode and on the meaning of the terms ‘prediction horizon’ and ‘priority setting’ is given in Section 4.5. A first set of uncertain economic parameter in the system are the build-up of electricity import and feed-in tariffs. The influence of fixed and more real-time, varying, tariffs was researched. Further, the influence of a prevention of double-taxation on energy for households and of lower gas tariffs for households with mCHPs were looked into. Lastly, the influence of seasonal differences in residential electricity and heat demand profiles is investigated. This uncertainty type is related to the possible climates in which mCHPs could be functioning. Some climates are less suitable for Stirling mCHPs, in terms of number of running hours, than others (see also [3]). 4.3. Modelling assumptions Before presenting the system model, this section gives the most important modelling assumptions. More model parameters are given in the description of the model input in Section 5.1. We note that assumptions denoted with (*) correspond specifically to the Dutch situation.

 Produced heat cannot be dumped; all heat should be used usefully.

 The mCHP unit comprises a Stirling engine and an auxiliary



burner. The WhisperGens and the Microgens mCHP systems are taken as a basis for our system model [30,31]. The Stirling engine is assumed to have a full load electric power output of 1.1 kWe, which is similar to values mentioned in [3,30,31]. If part-load operation is possible (this may be an option for the Microgens engine), part-load capacity is assumed at 0.55 kWe. Auxiliary burner capacity is assumed to lie between 0 and 20 kWth.

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 The electric efficiencies (Ze) of current state-of-the-art Stirling 



  



      

engines lay around 15% [12]. In [12] average values for current annual domestic heating needs are given. Domestic hot water demand is stated to be some 9 GJ and space heating between 30 and 50 GJ. We assume a final annual energy demand of 45 GJ ( ¼ 12,500 kWh) [12] (*). Also in [12] an energetic efficiency value of 105% is mentioned for space heating systems. All efficiency values are based on fuel (i.e. natural gas) lower heating value (LHV). Values for domestic hot water heating systems are mentioned between 75% in 2006 and 89% in 2015. The authors in [12] conclude that they will take 83% for domestic hot water heating in the period before 2010. In [32] an average domestic natural gas consumption of 1736 m3 per year is given: 1300 for space heating, 300 for domestic hot water, and the rest for cooking. For the total efficiency (Ztot) of a conventional high-efficiency condensing boiler, a Stirling engine and an auxiliary burner, we therefore assume a value of: (13/16)  105%+(3/16)  83% ¼ 100.875%. We thus also assume that the proportion between domestic hot water and space heating is constant throughout each day and for each season (*). Efficiency values are independent of power output level and of season. There are no energy losses in the conversion and storage systems. Combustion in the mCHP unit and in conventional high-efficiency boilers is complete. Different Stirling engines are known to have different start and stop characteristics. Microgens Stirling engines have a warmup and cool-down-time of around 3 min [13]. As our simulation time step represents 15 min periods (explained further in Section 5.1), we therefore neglect these warm-up and cooldown periods. Stirling engines cannot be subjected to too many start/stop cycles as this limits the engine’s lifetime. As starting values, a minimal up-time of half an hour and a minimal down-time of 15 min are therefore assumed for the Stirling engine, which is reasonable for Microgens engines according to [13]. Water temperature in the heat storage should lie between 55 and 80 1C. The Stirling engine gets priority over the auxiliary burner in heating up water. Natural gas consists of about 85 vol% of CH4 and has a LHV of 31.65 MJ/m3 [33] (*). Parasitic load from balance of plant equipment (e.g. pumps) is neglected. The power flow in the physical power lines connecting the household with the external network is limited by a maximum capacity of 8 kW [34] (*). Average CO2 emissions of centrally generated power: 600 g/ kWh [12] (*). Intelligent metering is present in the household and prices can be conveyed by the supplier to the household.

and auxiliary burner are in operation at a specific time step k. The CHP aux aux binary variables uCHP up;k , udown;k , uup;k , udown;k are start-up and shutdown indicator for the mCHP prime mover and auxiliary burner at time step k. An electricity balance should be satisfied relating the power output of conversion unit 1, the input and output power flows of the electricity storage, the electricity consumption, and electricity exchanged with the energy supplier. This power balance is given by g k þ iext;k þ so;k  eext;k  si;k  ec;k ¼ 0,

(1)

where g k ¼ Ze f 1;k , with Ze the electric efficiency of the Stirling engine. For the Stirling engine, part load and full load operation is modelled by f 1;k ¼ vCHP f 1;part þ x1;k ðf 1;max  f 1;part Þ, k

(2)

, x1;k pvCHP k

(3)

where x1,k is a binary variable deciding whether the Stirling engine operates at full or part load. The constraint that forces the prime mover to stay in operation until the up-time is reached is CHP vCHP kþn Xuup;k ;

n ¼ 0; . . . ; t up  1.

(4)

The constraint that forces the prime mover to stay out of operation during down-time is CHP 1  vCHP kþr Xudown;k ;

r ¼ 0; . . . ; t down  1.

(5)

The auxiliary burner operation is modelled by aux vaux k f 2;min pf 2;k pvk f 2;max .

(6)

As the main advantage of mCHP systems is the efficient cogeneration of heat and power, we ensure as a starting-point that the Stirling engine gets priority over the auxiliary burner in providing heat to the heat storage. The constraint taking care of this is modelled by CHP vaux . k pvk

(7)

The amounts of electricity and heat stored should be between minimum and maximum values: es;min pes;k pes;max ,

(8)

hs;min phs;k phs;max .

(9)

The electricity flows to and from the battery are limited by minimum and maximum values: so;min pso;k pso;max ,

(10)

si;min psi;k psi;max .

(11)

Every time step k there can only be either electricity import from or export to the external network. Constraints on the import and export power flows are therefore:

4.4. Mathematical system model formulation

eext;k pZe f 1;k þ so;k ,

(12)

The mathematical model with which we quantify the impacts of the system uncertainties is an elaboration of the model we described in [35]. A substantial part of our mathematical model is based on the work of Handschin et al. [36]. Our model differs, however, in that we consider the mCHP unit as a combination of a prime mover and an auxiliary burner. Further, we incorporate an electricity storage and we also consider varying electricity import prices. Analogous to [36] we first define the following binary variables. vCHP and vaux indicate whether the mCHP prime mover k k

eext;k pxe;k P max ,

(13)

iext;k pec;k þ si;k ,

(14)

iext;k pxi;k P max ,

(15)

xi;k þ xe;k p1,

(16)

where Pmax is the maximum power flow (8 kW) through the physical connection between the household and the external network.

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The binary variables v and u have to be linked. This is modelled by CHP CHP vCHP  vCHP k k1 ¼ uup;k  udown;k ,

(17)

aux aux  vaux vaux k k1 ¼ uup;k  udown;k ,

(18)

CHP uCHP up;k þ udown;k p1,

(19)

aux uaux up;k þ udown;k p1.

(20)

The heat in the heat storage is modelled by hs;kþ1 ¼ hs;k þ h1;k þ h2;k  hcp;k ,

(21)

where h1;k ¼ ðZtot  Ze Þf 1;k ; h2;k ¼ Ztot f 2;k and Ztot is the total efficiency of the mCHP unit. The electricity in the electricity storage is modelled by es;kþ1 ¼ es;k þ si;k  so;k .

(22)

1527

controller consists of N time steps, i.e. predictions are made from k until k+N1. A subinterval of the horizon is denoted by m, m ¼ 0, y, N1. The prediction model the controller uses is similar to the mathematical system model as described in Section 4.4 (i.e. the controller uses a perfect model). The mixed-integer, linear programming, problem to be solved by the controller at each time step k involves minimising (23) subject to the equality and inequality constraints (1)–(22) in the prediction horizon N. At each k the controller uses system measurement data and (predicted) future data on prices and energy consumption in making its control decision. The problem is classified as linear because all relations (1)–(23) are linear and as mixed-integer because the problem involves real and binary variables. At each k the outputs of the first prediction step are sent as input to the system. Regarding the size of the optimisation problem, with a prediction horizon N of four steps, for example, the optimisation problem involves around 100 equations and 40 variables.

4.5. Local energy management and DER control The DERs in the household are assumed to be controlled in the previously mentioned least-cost, model predictive, control mode. MPC is based on solving an optimisation problem at each control step, over a prediction horizon N which is subject to system dynamics, an objective function, and constraints on states, actions, and outputs [37]. At each control step the optimisation yields a sequence of actions optimising expected system behaviour in the horizon. Actions are implemented by the system until the next control step, after which the procedure is repeated with new system measurements. Due to the prediction horizon an MPC controller can take benefit of knowledge about the future, e.g. forecasted energy demand, possibly inferred from historical data of energy consumption. The system model therefore incorporates a sophisticated local MPC controller. The controller automatically determines which actions to take in order to minimise the operational costs of fulfilling residential electricity and heat requirements subject to the operational constraints. The controller uses the MPC strategy to take into account the decision freedom of self-generation of power, of choosing between electricity imports and exports, and of storing electricity and heat. Furthermore, the MPC controller incorporates models of the dynamics and constraints of the installed mCHP unit and energy storages and it can incorporate predictions on market prices and residential electricity and heat demands. The residential MPC controller is connected to the mCHP unit and storage systems via in-house domotics and can control all the power and heat flows. It can receive information from the energy supplier via an installed intelligent meter. The controller and the domotics can in fact be seen as a local energy management system (EMS). 4.5.1. MPC formulation The objective of the MPC controller is to minimise the daily operational costs of residential energy use. These energy costs depend on the price pf for fuel (i.e. natural gas), the price pi,ext for importing electricity and the price pe,ext at which electricity is fedin. The cost function for control or simulation step k, with a prediction horizon of N, is therefore defined as Cost ¼

N 1 X

ððf 1;kþm þ f 2;kþm Þpf þ iext;kþm pi;ext;kþm  eext;kþm pe;ext Þ.

m¼0

(23) The decision variables in the optimisation are f1,k+m, f2,k+m, iext,k+m, and eext,k+m. The prediction horizon considered by the MPC

5. Simulation results In this section, we quantitatively analyse the impacts of the chosen uncertainties via a sensitivity analysis of the system model. We note that in this sensitivity analysis no complete parameter distributions are considered. For each of the identified uncertainties, we have investigated their sensitivities to the variations in some parameter values sampled out of the total possible parameter spaces. Simulation outcomes from the system model are also compared with outcomes from a model of a ‘conventional’ household applying just a high-efficiency condensing boiler. 5.1. Simulation input First, we describe further input data for the simulations (next to data already stated in the modelling assumptions in Section 4.3). 5.1.1. Energy demand patterns Residential daily electricity and heat demand profiles have been created from 2006 data obtained from EnergieNed, the Dutch Federation of Energy Companies. EnergieNed annually determines so-called ‘profile fractions’ with which market parties can construct aggregate load profiles of groups of residential customers. This is done by multiplying these fractions by the annual average consumption of a specific group of customers. In creating the residential electricity profiles we used an average annual consumption of one household of 3400 kWh (given by the official informative website of the Energy Research Centre of the Netherlands [9] for 2006). Heat profiles have been created using the average residential heat consumption of 12,500 kWh. The obtained energy demand profiles for a single household are thus average residential profiles, and we did not use specific profiles that could have been constructed via detailed thermal models of households and via aggregating the electricity consumption of individual appliances. We are aware of the fact that real-life residential electricity demand is highly intermittent and that therefore the use of average profiles does not fully correspond with reality. However, aggregating real-life demand data into patterns with a time resolution of, for example, 15 min filters out demand spikes and will lead to smoother demand curves that will correspond to a larger extent to the profiles constructed by us for our simulations.

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Domestic heat demand follows a much smoother pattern and therefore the used heat profiles in the models are relatively realistic. Further, it should be noted that the use of a large hot water storage system from which the heat demand is taken will act as a buffer between final heat demand and heat supply by the mCHP system. The heat that needs to be supplied by the mCHP system then does not have to follow the intermittent heat demand exactly, due to the buffer function of the storage. We have selected the demand profiles of three different days in 2006 as simulation input, namely the 21 January (winter, weekend day), the 22 November (autumn, week day) and the 19 July (summer, week day). These days have been chosen as they are all in different seasons and each show substantially different demand patterns. Furthermore, the variable electricity prices that we used in several simulations also differ substantially in these days. The electricity and heat demands of the winter, autumn, and summer day are, respectively: 11.5 and 56.2 kWh, 10.4 and 54.4 kWh, and 7.6 and 7.9 kWh.

electricity demand [kW]

0.75

21 january 22 november 19 july

0.60

0.45

0.30

0.15 1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103 Fig. 6. Electricity demand data for average Dutch household on three different days in 2006.

4.00 3.50 heat demand [kW]

5.1.2. Price data In [8] a total gas tariff for small consumers of 552 h/1000 m3 is given (for consumer class: 2000 m3). According to [9], 91% of the gas tariff is variable (including taxes). This leads to a value of 0.502 h/m3. With a LHV of 31.65 MJ/m3 this becomes 0.057 h/kWh. The variable, more real-time, electricity import/feed-in tariffs have been constructed as follows. The Dutch central bureau of statistics states a total electricity tariff for small consumers for 2006 of 194 h/MWh [8] (household class: single tariff, 3000 kWh). The variable part of the total tariff (including energy and VAT taxes) is around 90% of the total tariff [9], so this becomes 0.1746 h/kWh. The variable supply part of the total tariff accounts for 32% of the total tariff [9]. For this variable supply part we have substituted Dutch power exchange prices. We took Amsterdam Power Exchange data for the mentioned days. In our simulations we mainly use time-varying tariffs. This is due to the fact that MPC control will only lead to cost benefits in a situation with variable prices (otherwise anticipation on changing prices is impossible). As reference we also show results for situations in which the import or (and) feed-in tariff price is (are) fixed in time. In simulations with a fixed electricity import tariff we take the value of 0.1746 h/kWh. The fixed feed-in tariff is constructed as follows. From EnergieNed we obtained the average commercial feed-in tariff for 2006 of 0.0601 h/kWh. We further compensated for all the energy taxes and the VAT that is raised over the variable part of the tariff. A total tax compensation of 0.065 h/kWh is thereby arrived upon. This compensation leads to a fixed feed-in tariff of 0.0601+0.065 ¼ 0.125h/kWh. Possible pricing structures of electricity import and feed-in tariffs are shown in Fig. 5. The feed-in tariff could be equal to a fixed or variable import tariff, it could be 0, or it could be a fixed commercial tariff set by private energy companies. In principle, the feed-in tariff could be variable while the import tariff is fixed. This could happen when an aggregator would like to actively influence the operation of residential DERs by setting price tariffs. During stand-alone DER operation, however, this combination is unlikely to occur. If the feed-in tariff is equal to the import price, double-taxation is automatically prevented. With the other feedin tariff structures this prevention could be excluded, however. In our simulations we thus consider a selection of the pricing structures of Fig. 5. Heat profiles have a resolution of 1 h (equal to the resolution of the gas profiles), electricity profiles of 15 min and price profiles of 1 h (equal to the power exchange price variability). Figs. 6 and 7 show the energy demand profiles. The devised variable electricity prices are shown in Figs. 8 and 9. We also show data for a part of

Fig. 5. Possible pricing structure of electricity import and feed-in tariffs.

3.00 2.50 2.00 1.50

21 january 22 november 19 july

1.00 0.50 0.00 1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103 Fig. 7. Heat demand data for average Dutch household on three different days in 2006.

the next day as the decision made by the MPC controller (the prediction horizon) at the end of a day incorporates data from the next day.

5.1.3. Chosen time scale The simulation time interval is 15 min. Modelling the performance of mCHP systems is highly dependent on the temporal

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The starting values for the simulations with the system model are, for k ¼ 1:

electricity price [C/kWh]

0.37

0.32

CHP aux aux vCHP ¼ vaux ¼ uCHP 1 1 up;1 ¼ udown;1 ¼ uup;1 ¼ udown;1 ¼ 0,

21 january 19 july

es;1 ¼ es;min ¼ 0 kWh;

0.27

hs;1 ¼ hs;min ¼ mc DT ¼ 100  4:18ð55  20Þ ¼ 14; 630 kJ ¼ 4:06 kWh:

0.22

0.17

In calculating hs,1 we have used the heat storage volume, m, of 100 l, an environmental temperature of 20 1C and the specific heat capacity of water, c, of 4.18 kJ/kg K.

0.12

5.2. mCHP vs. conventional heating: the influence of electricity prices and seasonal differences

1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103 Fig. 8. Variable electricity import or feed-inn tariff for 2 days in 2006.

0.92 electricity price [C/kWh]

1529

0.82 22 november

0.72 0.62 0.52 0.42 0.32 0.22 0.12 1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103

Fig. 9. Variable electricity import or feed-inn tariff for 22 November 2006.

precision with which both the thermal and electrical demand is considered. For instance, the environmental outcomes of mCHP deployment have been reported to vary by up to 40% depending on the temporal resolution of the analysis [38]. In [38] a relatively small difference in outcomes was observed for demand data precisions between 5 and 10 min. Results varied more significantly with 30-min precision data. A 15-min temporal precision was shown to produce accurate economic and environmental results in (optimisation) modelling of mCHP systems. In [38] it was concluded that demand data in 10-min blocks were sufficient to obtain results that reflected the assumed constraints on the mCHP model. We therefore assume that 15 min time intervals will lead to reliable simulation outcomes. 5.1.4. Initial values Because power exchange prices are known a day in advance to market parties, the electricity price, when being variable, is also known to the household controller on forehand. The information is then assumed to have been conveyed to the household by the supplier via the intelligent meter. Further, as a first step we have taken the predicted residential heat and electricity demand for prediction horizon N with which the MPC controller works as being equal to the actual demand in that horizon. The initial value for the capacity of the hot water storage is 100 l. The battery has a minimum and maximum storage capacity of 0 kWh (es,min) and 2 kWh (es,max), respectively. Lithium-ion batteries can be fully charged and discharged four times per hour [39]. Therefore we assume so,max ¼ si,max ¼ es,max ¼ 2 kWh (per 15 min time step).

The settings of parameters in the base case system model are as described in the sections on the modelling assumptions (4.3) and simulation input (5.1). Here we compare the base case system to a conventional system under different electricity pricing regimes. The conventional system is based on a household employing a high-efficiency condensing boiler. This boiler is modelled similar to the auxiliary burner (Eq. (6)) and has a total efficiency equal to that of the Stirling engine and the auxiliary burner (i.e. 100.875%). The conventional system is further the same as the base case system. The used variable electricity import and feed-in tariffs are equal to each other. As said before, the fixed feed-in tariff of 0.125 h/kWh, which is used in some simulations, includes double-taxation prevention. We further look into the influence of a zero feed-in tariff and of a fixed import tariff. This fixed import tariff is 0.1746 h/kWh, as previously described. We have implemented the mathematical simulation model in the MapleTM software. We obtained system outcomes per time step k for a full day period, for prediction horizon lengths of N ¼ 1 and 6. As the dynamics of important system parameters (i.e. energy demand and varying electricity tariffs) have a time period of a day, we should in fact do simulation studies with N values up to 96 in order to observe for which N the best system outcomes are found. Due to computation time limitations, we could, however, not simulate with higher N values than 6. We explicitly note that the focus of this paper is not the functioning of the MPC controller in terms of finding the optimal prediction horizon length and adopted time resolution in that horizon. With a prediction horizon length of 6 steps, each step having a time length of 15 min, we can already observe very interesting system outcomes. For N ¼ 6 the optimisation solver gave slightly different results for repeated simulation runs, showing that the solver finds local minima of the objective function (Eq. (24)). The results given here are the ones representing the lowest daily costs. The daily performances of the base case system and the conventional system for the different seasonal days and pricing regimes are shown in Tables 1–3. Results are given for N ¼ 1 and 6 and are separated by a ‘/’ symbol. Beside relevant energy flows (i.e. electricity production, import and export, and gas use for the Stirling engine and the auxiliary burner), we show the daily energy costs from Eq. (23) and the CO2 emissions from residential energy use. The amount of CO2 emissions is calculated as follows. We multiply the net electricity import ( ¼ impexp) with the average CO2 emissions of centrally generated power. This value is reported in [12] as being 0.6 kg/kWh and represents the emissions from burning the average fuel mix in the Netherlands. We further add to that the emissions from burning natural gas in the Stirling engine and the auxiliary burner. Emissions from burning gas in these units are calculated by us to be 0.19 kg CO2/kWh.

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Table 1 Daily system model simulation outcomes: autumn, week day System

Feed-in tariff (h/kWh)

Costs (h)

CO2 (kg)

prod (kWh)

Base case

0 0.125 Var.

4.14/4.02 4.00/4.14a 3.67/2.00

12.7/13.3 12.7/12.8 12.7/12.9

9.6/8.5 9.6/8.9 9.6/9.4

Conventional

0 0.125 Var.

5.74/5.19 5.19, N ¼ 6 4.09, N ¼ 6

16.5/16.7 16.6 16.6

– – –

Base case, fixed el. import tariff

0 0.125

4.06 3.92

12.7 12.7

9.6 9.6

Conventional, fixed el. import tariff

Fixed, oimport 4.90

16.5

–

imp (kWh)

exp (kWh)

2.1/2.0 3.0/2.4 3.0/19.8

1.4/0.1 2.2/0.9 2.2/18.8

10.4/10.4 10.4 29.2

Gas for Stirling (kWh) 64.2/56.8 64.2/59.6 64.2/62.3

0.0/0.0 0.0 18.8

– – –

2.1 2.8

1.4 2.0

64.2 64.2

10.4

0.0

–

Gas for aux. burner (kWh) 0.4/7.3 0.2/3.2 0.2/2.3 54.0/54.8 54.8 54.5 0.4 0.4 54.0

‘prod’ is produced electricity, ‘imp’ is imported electricity, ‘exp’ is exported electricity. Results for N ¼ 1 and 6 are separated by a ‘/’ symbol. a Daily energy costs are higher for N ¼ 6 than for N ¼ 1 due to a substantial increase in energy content (and thus gas use) of the heat storage during the day. These gas costs amount to approximately 0.14h.

Table 2 Daily system model simulation outcomes: winter, weekend day System

Feed-in tariff (h/kWh)

Costs (h)

CO2 (kg)

prod (kWh)

Base case

0 0.125 Var.

4.24/4.19 4.13/4.12 4.10/3.59

13.6/14.0 13.6/13.8 13.6/13.7

9.8/8.8 9.8/9.2 9.8/9.4

Conventional

0 0.125 Var.

5.20/5.13 5.08, N ¼ 6 4.82, N ¼ 6

17.5/17.8 17.6 17.7

– – –

Base case, fixed el. import tariff

0 0.125

4.24 4.14

13.6 13.6

9.8 9.8

Conventional, fixed el. import tariff

Fixed, oimport 5.19

17.5

imp (kWh)

exp (kWh)

2.6/2.9 2.9/3.0 2.9/22.2

0.9/0.2 1.2/0.7 1.2/20.0

11.5/11.9 11.9 34.3

0.0/0.0 0.4 22.8

Gas for Stirling (kWh) 65.1/58.7 65.1/61.4 65.1/62.3 – – –

2.6 2.9

0.9 1.2

65.1 65.1

–

11.5

0.0

–

imp (kWh)

exp (kWh)

6.7/6.2 6.8/6.2 6.8/19.7

0.5/0.0 0.5/0.2 0.5/13.8

Gas for aux. burner (kWh) 1.0/6.5 1.0/3.9 1.0/2.9 55.7/56.2 56.2 56.9 1.0 1.0 55.7

Table 3 Daily system model simulation outcomes; summer, week day System

Feed-in tariff (h/kWh)

Costs (h)

CO2 (kg)

prod (kWh)

Base case

0 0.125 Var.

2.05/1.85 2.00/1.89 1.93/1.43

5.5/5.5 5.5/5.6 5.5/5.7

1.4/1.4 1.4/1.5 1.4/1.7

Conventional

0 0.125 Var.

2.19/2.09 2.09, N ¼ 6 1.66, N ¼ 6

6.0/6.1 6.0 6.0

– – –

Base case, fixed el. import tariff

0 0.125

1.69 1.64

5.5 5.5

1.4 1.4

6.7 6.8

Conventional, fixed el. import tariff

Fixed, oimport 1.77

6.0

–

7.6

We therefore used the above-mentioned electric and thermal efficiencies and assumed perfect combustion of the gas. For the conventional system all feed-in tariff structures lead to similar system outcomes for N ¼ 1. We therefore only present the outcomes for N ¼ 1 with the feed-in tariff of 0 h/kWh. With a fixed electricity import tariff in the conventional system it does not make a difference if the feed-in tariff is 0 or 0.125. As

7.6/7.6 7.6 28.0

Gas for Stirling (kWh)

Gas for aux. burner (kWh)

9.2/9.2 9.2/10.1 9.2/11.0

0.0/0.0 0.0/0.0 0.0/0.0

– – –

7.8/8.0 8.0 8.0

0.5 0.5

9.2 9.2

0.0 0.0

0.0

–

7.8

0.0/0.0 0.0 20.4

long as the fixed feed-in tariff is lower than the import tariff results are similar, as no use will be made of the battery then. We note that the outcomes from simulations with a conventional system without a battery are equal to outcomes for the conventional system for N ¼ 1. In the undertaken simulations having a fixed electricity import tariff the feed-in tariff was also fixed. Therefore, in that case, a prediction horizon larger than 1

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1.80 1.60 1.40 f_1, f_2 [kWh]

will not make any difference in simulation outcomes. The results from simulations with a fixed import tariff are therefore only shown for N ¼ 1. Further, the electricity balance (prod+imp ¼ cons+exp) is not always met due to the fact that at the end of the day there is sometimes still some electricity contained in the battery. In the cost calculation we multiply this remaining amount of electricity with the average feed-in tariff of that day. For the CO2 emission calculations this remaining electricity is considered as additional export. Also, at the end of a day there could be more thermal energy contained in the hot water storage compared to the beginning of that day. This results in somewhat higher gas consumption and consequently higher costs. In most calculations these costs are negligible (at most 0.05 h per day), but for the base case system, with a fixed feed-in tariff, during autumn, however, this effect is substantial (i.e. 0.14 h). From Tables 1–3 the following main conclusions are inferred:

1531

f_1 f_2

1.20 1.00 0.80 0.60 0.40 0.20 0.00 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93

7.00









6.50

h_s h_s_MAX h_s_MIN

6.00 5.50 5.00 4.50 4.00 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97

2.00 electricity imp and exp [kWh]



base case mCHP system leads to significantly lower costs, less imported electricity, more gas consumption and less CO2 emissions when compared to the conventional system. Due to the relatively low heat demand in summer, however, these cost and CO2 emission savings are less for the summer day. This shows that in relatively mild climates a Stirling mCHP system could lead to unacceptable returns on investments for a household. This conclusion is in line with other studies on mCHP systems (see [3]). For N ¼ 1, for the base case system and in each seasonal day, the energy costs are lower when a feed-in tariff is present instead of it being 0. Further, the variable feed-in tariff gives higher cost savings compared to the conventional system than the fixed, non-zero, tariff. For N ¼ 6 this trend is also observed, for the conventional as well as for the base case system. With a variable feed-in tariff, for both the base case as the conventional system, going from N ¼ 1 to 6, much more use is made of the battery. This can be seen in the larger numbers for ‘imp’ and ‘exp’. The usage of the battery enables the achievement of lower costs. The net difference between daily imported and exported electricity, however, remains relatively the same. Figs. 10 and 11 show the simulation results for the base case system, for the autumn week day, for N ¼ 1 and 6, respectively. Comparing the results for N ¼ 1 and 6 we see that for N ¼ 6 much more use is made of the heat and electricity storages. Also the electricity import and export flows are much more volatile for N ¼ 6. The operational cost savings with larger N values, due to the application of the battery, should cover the investments in both the battery itself as in the MPC control unit and the required in-house domotics. From the above results it can be seen that daily savings due to the application of a battery in conjunction with MPC control can provide cost savings from almost 0 up to 1.67 h per day, depending on the feed-in tariff regime and on season. These savings could thus, under suitable circumstances, provide acceptable returns on investment. In Figs. 10 and 11 it can be further seen that the daily number of start-ups for the Stirling engine is substantial (13 and 17 start-ups for N ¼ 1 and 6, respectively). The yearly amount of start-ups should not be much more than 2000 for a free piston Stirling engine [13]. From our results it can be seen that this number might be met within a period of a year. In the summer day, however, the number of start-ups was much lower (around 5). For the fixed as well as for the variable feed-in tariff, the base case system and the conventional system give relatively

heat in storage [kWh]

 For N ¼ 1, in each seasonal day and for each pricing regime, the

1.50

i_ext e_ext

1.00

0.50

0.00 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 Fig. 10. Simulation results for autumn week day, N ¼ 1: (a) gas supply to Stirling engine (f1) and auxiliary burner (f2) [kWh] per simulation step, (b) energy level in the heat storage [kWh] and (c) electricity import and export [kWh] per simulation step.



similar costs savings when going from N ¼ 1 to 6. Each season, however, these savings resulting from the increase in N are different. This result is clearer for the variable feed-in tariff than for the fixed feed-in tariff. For example, for the autumn day the base case system gives cost savings of 1.67 h (3.67–2.00) and the conventional system 1.65 h (5.74–4.09). For the base case as well as the conventional system, it depends on the daily build-up of the variable import tariff, if, for fixed feed-in tariffs, a variable import tariff leads to an increase in costs compared to a fixed import tariff. These cost differences are of course the result of our specific way of constructing the variable from the fixed import tariff and of the chosen days to include in our simulation studies.

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 During the autumn and winter days, for the base case system 1.80 1.60

f_1 f_2

f_1, f_2 [kWh]

1.40 1.20 1.00



0.80 0.60 0.40 0.20 0.00 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93

with a variable electricity import tariff, there was a shift from gas use by the Stirling to gas use by the auxiliary burner when going to higher N values. This results in less self-generated electricity and lower total gas consumption. These effects are independent of feed-in tariff regime. During the summer day, however, these effects were not observed. With the conventional system we have also obtained simulation results for N ¼ 10 for the autumn day. Costs were then 4.14 h for a variable feed-in tariff and 5.08 h for a fixed feed-in tariff of 0.125 h. We thus see that a larger N value thus does not necessarily have to result in lower costs. Unfortunately, due to computation time constraints it was impossible to obtain simulation results for larger N values to see which value would be optimal.

5.3. Influence of double-taxation prevention and lower gas tariffs

heat in storage [kWh]

7.00 6.50

In this section, the influence of double-taxation prevention and of lower gas tariffs for households with mCHPs is presented. Table 4 gives the daily performances of the base case system for the autumn day. Results are given for N ¼ 1 and 6 and are separated by a ‘/’ symbol. Main conclusions following from Tables 1 and 4 are:

h_s h_s_MAX h_s_MIN

6.00 5.50 5.00

 Double-taxation of energy for households applying mCHP 4.50 4.00 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97

electricity imp and exp [kWh]

2.00

1.50

i_ext e_ext

1.00

5.4. DER technology characteristics

0.50

0.00 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93

electricity in storage [kWh]

2.00

1.50



systems results in a significant increase in operational energy costs for these households. Granting households that apply mCHP systems lower gas tariffs can result in more than proportional total daily cost savings. For the base case system, for example, we get the following picture. With a fixed feed-in tariff and N ¼ 1 the expected savings solely resulting from lower gas tariffs would be: (64.4 * 0.057)–(64.3 * 0.029) ¼ 1.84 h. The actual savings are, however, 4.00–2.05 ¼ 1.95 h. For N ¼ 6 the expected and actual savings are 1.74 and 2.14 h, respectively. With a variable feed-in tariff N ¼ 1 gives lower actual than expected savings, however. For N ¼ 6 the actual savings are again larger than the expected savings.

e_s

1.00

0.50

0.00 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 Fig. 11. Simulation results for autumn week day, N ¼ 6: (a) gas supply to Stirling engine (f1) and auxiliary burner (f2) [kWh] per simulation step; (b) level of thermal energy in the heat storage [kWh], (c) electricity import and export [kWh] per simulation step and (d) energy level of the battery [kWh].

In this section, we present the results from simulations with models in which the technology characteristics mentioned in Section 4.2 were varied. Before discussing the results we should first explain what is meant by a system with an ‘other configuration’ (as mentioned in Table 5) and how such a system was modelled. One of the characteristics of Section 4.2 was a different configuration for residential hot water storage. Besides the base case configuration of Fig. 3 we have modelled a system, which only incorporates storage of domestic hot water (DHW) and not for space heating (SH). Fig. 12 gives a conceptual overview of such a system. There is a seeming resemblance between Figs. 3 and 12, nonetheless Fig. 3 differs from Fig. 12 in that the heat demand in this figure is split up into separate space heating and domestic hot water demand and that there is now only hot water storage for domestic hot water. Instead of all the residential heat consumption being taken from one central heat storage, now only domestic hot water is taken from a storage (hc_DHW). Water for space heating (hc_SH) is coming directly from the mCHP system. For simulation purposes we have therefore split the autumn day heat demand curve into two curves using the previously described proportion between

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Table 4 Outcomes from system model simulations with varying economic parameters; autumn, week day System

Feed-in tariff (h/kWh)

Costs (h)

CO2 (kg)

prod (kWh)

Base case

0.125 Var.

4.00/4.14 3.67/2.00

12.7/12.8 12.7/12.9

9.6/8.9 9.6/9.4

Base case, half gas price

0.125 Var.

2.05/2.00 2.10/0.09

12.7/12.7 12.6/12.7

9.6/9.7 9.6/9.8

Conventional, half gas price

Var.

4.20/2.55

16.5/16.6

–

Base case, no tax compensation

0.06

4.18/4.01

12.7/13.2

9.6/8.8

imp (kWh)

exp (kWh)

Gas for Stirling (kWh)

3.0/2.4 3.0/19.8

2.2/0.9 2.2/18.8

64.2/59.6 64.2/62.3

0.2/3.2 0.2/2.3

2.8/1.7 3.2/21.1

2.0/1.0 2.5/20.5

64.3/64.6 64.2/65.1

0.0/0.0 0.0/0.0

10.4/29.4

0.0/19.0

2.9/2.0

2.2/0.4

– 64.2/58.7

Gas for aux. burner (kWh)

54.0/54.8 0.4/5.9

‘prod’ is produced electricity, ‘imp’ is imported electricity, ‘exp’ is exported electricity. Results for N ¼ 1 and 6 are separated by a ‘/’ symbol.

Table 5 Outcomes from system model simulations with varying technology characteristics: autumn, week day System

Costs (h)

CO2 (kg)

prod (kWh)

imp (kWh)

exp (kWh)

Gas for Stirling Gas for aux. (kWh) burner (kWh)

Base case Base case, el. storage ¼ 3.0 kWh Base case, el. storage ¼ 1.0 kWh Base case, el. storage ¼ 0.5 kWh Base case, no el. storagea (N ¼ 1 & 5) Base case, heat storage ¼ 70 l Base case, heat storage ¼ 130 l, N ¼ 1 onlyb Base case, Stirling up-time ¼ 1 Base case, no priority Base case, no el. storage, no priority Base case, no el. storage, no heat storage, no priority Other configuration, N ¼ 6 only Other configuration, no priority, N ¼ 1 only Other configuration, no heat storage, no priority, N ¼ 1 only Other configuration, no el. storage, N ¼ 1 only

3.67/2.00 3.67/1.19 3.67/2.84 3.67/3.26 3.67/3.69 3.79/2.11 3.84 3.67/2.01 4.80/2.06 3.81/3.66 4.80/4.79 1.88 3.73 4.82 3.58

12.7/12.9 12.7/13.0 12.7/12.9 12.7/12.9 12.7/12.9 12.7/12.9 12.8 12.7/12.9 15.1/13.2 13.3/12.9 15.1/15.0 12.9 13.3 15.2 12.7

9.6/9.4 9.6/9.2 9.6/9.4 9.6/9.4 9.6/9.4 9.6/9.5 9.9 9.6/9.5 3.3/8.4 7.8/8.8 3.3/3.0 9.2 7.8 3.3 9.6

3.0/19.8 3.0/19.6 3.0/13.5 3.0/8.3 3.0/4.3 3.0/21.9 6.0 3.0/15.7 7.5/23.1 4.2/5.0 7.5/7.7 17.9 4.2 7.5 3.1

2.2/18.8 2.3/18.4 2.3/12.5 2.3/7.3 2.3/3.2 2.2/21.0 5.5 2.3/14.8 0.4/21.1 1.6/3.4 0.4/0.4 16.7 1.7 0.4 2.3

64.2/62.3 64.2/61.4 64.2/62.3 64.2/62.3 64.2/62.3 64.2/63.3 66.0 64.2/63.3 22.0/55.9 52.3/58.7 22.0/20.2 61.4 52.3 22.0 64.2

0.2/2.3 0.2/3.1 0.2/2.3 0.2/2.3 0.2/2.2 0.4/1.7 0.0 0.2/2.0 35.2/7.1 9.5/4.0 35.2/35.8 2.5 9.6 35.6 0.2

‘prod’ is produced electricity, ‘imp’ is imported electricity, ‘exp’ is exported electricity. Results for N ¼ 1 and 6 are separated by a ‘/’ symbol. a No results were obtained for N ¼ 6. b Daily energy costs are higher for N ¼ 1 compared to the base case due to a substantial increase in energy content (and thus gas use) of the heat storage during the day.

DHW and SH of 3:13 (see Section 4.3). We thereby assume that the ration between DHW and SH demand is equal during the day. The following equations should be incorporated in the mathematical model describing the system of Fig. 12. The first energy balance is h3;k ¼ h1;k þ h2;k ,

(24)

where h1;k ¼ ðZtot  Ze Þf 1;k ; h2;k ¼ Ztot f 2;k and Ztot is the total efficiency of the mCHP unit. This total efficiency is now assumed to be equal to the space heating efficiency of 105%. Further, h3;k ¼ h4;k þ hc_SH;k , should hold. Eq. (21) now changes to:   83  hc_DHW;k . hs;kþ1 ¼ hs;k þ h4;k 105

(25)

(26)

Because the efficiency of providing DHW is 83%, we have incorporated the ratio of 83/105 in Eq. (26). The above equations can be combined to give  83  (27) hs;kþ1 ¼ hs;k þ ðh1;k þ h2;k  hc_SH;k Þ 105  hc_DHW;k ,

Fig. 12. Conceptual overview of the household-supplier system. This figure differs from Fig. 3 in that the heat demand is split-up into separate space heating and domestic hot water demand and that there is now only hot water storage for domestic hot water.

where h1;k ¼ ðZtot  Ze Þf 1;k ; h2;k ¼ Ztot f 2;k . The linear optimisation solver of MapleTM could not find feasible solutions for all of our intended simulations. With lower heat storage capacities than 70 l in the base case system, for example, no feasible solutions could be found. Also, in the simulations with the other hot water storage configuration no

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feasible solutions could be found for N ¼ 1; we only obtained results for N ¼ 6. The omission of the priority constraint on the activation of the Stirling engine over the auxiliary burner often resulted in feasible solutions, however. Enough interesting outcomes could still be obtained and they are shown in Table 5. The base case system used variable import and feed-in tariffs. Main conclusions following from Table 5 are:

 When the priority constraint on the activation of the Stirling

 The battery capacity determines to a large extent the possible









cost savings in MPC applied to our base case system. Daily costs for N ¼ 6 decrease substantially with increasing battery capacities. Interesting to see is that the total amount of daily electricity import and export remain almost the same when going from a storage capacity of 2–3 kWh. Although these total amounts remain equal, the power flows in and out of the battery show very different daily patterns in both cases. So, with a larger electricity storage capacity stronger price anticipative behaviour is possible. Without a battery in the base case system no price anticipative behaviour was observed when going from N ¼ 1 to 6. With the possibility of storing heat in the storage, this could be expected to some extent, however. Simulations with substantially larger N values should be done to research this issue further. The battery is thus a crucial part of the system. In Section 5.2 it could be seen that the conventional and the base case system, with a variable feed-in tariff, gave rather similar cost savings when adopting a longer prediction horizon of N ¼ 6 (savings were 1.65 and 1.67 h, respectively). We think the relatively high price of generating electricity from gas with the mCHP system makes that having such a system instead of a condensing boiler, in conjunction with a battery, does not contribute to substantial additional cost savings when employing a longer prediction horizon. Generating 1 kWh of electricity with the mCHP system when there is no heat needed from the mCHP system results in self-generated electricity costs of roughly seven times the gas costs. This is always higher than the electricity import and feed-in tariff. Still, due to the fact that heat should be supplied by the mCHP system at certain moments (and then the self-generated electricity becomes cheap, i.e. 1/7 part of the gas price!), heat can be stored and because the generated power flow is linked to all other power flows in the system, a substantially longer prediction horizon than N ¼ 6 might lead to larger cost savings compared to the conventional system due to this additional degree of flexibility in the base case. This issue should be researched further. We conjectured that a lower gas tariff might lead to additional cost savings for the base case system compared to the conventional system when going from N ¼ 1 to 6. As a test we therefore simulated both the base case as the conventional system with half gas prices (see Table 4). Our hypothesis was confirmed: the base case system gave cost savings of 2.01 h (2.10–0.09) and the conventional system savings of 1.65 h (4.20–2.55). Apparently, with a lower gas tariff the additional degree of freedom of the base case system is utilised more in the system control. Heat storage capacity seems to have a moderate influence on daily energy costs. The higher costs for a capacity of 130 l can be attributed to an increase in energy content in the heat storage over the day, however. With a content of 70 l this effect was not observed and costs increased with this decrease in storage capacity. Further research should strengthen the conjecture that a smaller storage capacity results in higher costs. A minimal up-time of the Stirling engine of 1 simulation time step instead of 2 had no significant influence on simulation outcomes.

 







engine over the auxiliary burner is omitted from the model we see that, for N ¼ 1, much higher costs are the result. Also much higher CO2 emissions can be observed, which is due to the fact that relatively more heat is then generated by the auxiliary burner compared to the Stirling engine and more ‘dirty’ electricity is imported. With N ¼ 6 costs and emissions drop significantly due to a shift towards heat generation by the Stirling engine instead of the auxiliary burner. Without the priority constraint the MPC controller achieves significantly higher cost reductions when going from N ¼ 1 to 6 as compared to the base case. For the base case system without the priority constraint, the cost advantage of a battery is also clear when comparing the results with the same system having no electricity storage. For the system without a battery, without the priority constraint and without a heat storage it was possible to find solutions for simulations with N ¼ 1 till N ¼ 6. The system without a heat storage shows higher electricity imports, less self-generated power and a relatively large amount of gas used by the auxiliary burner. When comparing the results with results from a similar system with a heat storage the value of having the heat storage is evident. Daily costs and CO2 emissions are significantly lower for the system with a heat storage. With the system model incorporating the other hot water storage configuration feasible solution were only obtained for N ¼ 6 (with the priority constraint still incorporated in the model). Results show somewhat lower costs as compared to the base case system for N ¼ 6. When the battery was omitted from the model, and with the priority setting included, solutions could be found for N ¼ 1. The model with the other configuration, without a heat storage, without priority in activation of the Stirling engine and the auxiliary burner, gives similar results for N ¼ 1 as a similar system that additionally has no electricity storage. The results from simulations with the model with the other configuration are almost the same as results with the base case system (for N ¼ 1). Except for the model with the other configuration having no battery; in that case substantially lower costs were obtained than with the base case system having no battery.

5.5. Error analysis The results from model simulations will always differ from real-life system operation. Here, the developed mathematical system models and model input data lead to simulation outcomes that cannot yet be validated with real-life data. Stirling mCHP systems are still in the development phase with several pilot projects running at this moment worldwide. Information from these field trials is not publicly available. Further, MPC controllers are at present not commercially available for residential energy management purposes. Also real-time electricity pricing is not yet being offered to residential customers. We therefore limit this section to a description of the possible errors that our modelling work might contain. Regarding the model input data we have already discussed the level of correspondence between the used residential energy demand profiles and real-life profiles in Section 5.1. The development and use of more realistic demand patterns in the simulations is recommended for future research. Further we have not done stochastic simulations with multiple households that all have slightly different energy demand obtained from normal distributions over the average values. The purpose of this work

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was not to show the spread in simulation outcomes with respect to different energy demand inputs, but to show the potential savings of one average household. Due to the fact that we assumed a perfect prediction of the energy demand data the results will probably be on the positive side in terms of economic savings. Simulating with different predicted and real energy demand profiles is important future research. Here we used a perfect prediction in order to show the maximum possible savings that can be achieved. Regarding the computational methods we note that, with the use of the linear optimisation solver of MapleTM, simulations took extremely long (for N ¼ 6, simulating 1 day took several hours on a regular personal computer). The performance of MPC controllers therefore is very dependent on solver quality and future research should focus on simplifying the optimisation problem or using better solvers. With this work we have thus wanted to show the maximum possible savings with residential MPC control and we acknowledge that the results presented here could be refined to better reflect the real-life system and should definitely be validated with real-life experiments in the future.

6. Conclusions and future research We have proposed and applied a comprehensive framework for uncertainty analysis. We thereby adopted an integrated approach that considers not only the technical, but also the economic and institutional uncertainties. We applied the framework to an electricity infrastructure in which residential DERs were employed. The main uncertainties pertaining to the design and operation of residential DERs and mCHP systems were thereby identified. In a case study system a selection of the uncertainties was quantitatively analysed. The case study system consisted of a household that applies a mCHP unit in conjunction with energy storages and that interacts with its energy supplier. The uncertainties we looked into were a set of specific DER technology characteristics, different electricity and gas pricing regimes and seasonal differences in residential electricity and heat demand. The sensitivity analysis of the system model showed that with the adopted least-cost control strategy the highest cost savings can be realised with variable electricity import and feed-in tariffs. The cost savings in applying a mCHP system are further significantly higher in the colder seasons. Further salient results were that a battery can already provide substantial benefit for households that receive real-time prices, which they can anticipate. For lower gas tariffs a mCHP system, in conjunction with energy storage systems, instead of a conventional high-efficiency condensing boiler provides significant additional financial benefits on top of the savings from using the battery. With our broad uncertainty analysis and the obtained quantitative simulation outcomes from the case study a first set of insights has been created for designers of not only DER technologies, but also of the institutions, economic policies and policy instruments affecting the economic feasibility and environmental potential of DERs. Interesting options for further research include the following:

 The influence of a longer prediction horizon adopted by the



MPC controller in the base case system. We should therefore find other optimisation solvers that can more effectively and efficiently find solutions for the extensive optimisation problems at hand. More thorough analysis on the impact of a different heating configuration on the system performance. Why the costs are











1535

influenced by a different configuration should be more clearly understood. Uncertainties that could be further investigated for the base case system as presented in this paper are only full load operation for the Stirling engine and longer minimal up-times. The current model was not capable yet to investigate those uncertainties. Other uncertainties for the household-supplier system could be researched. Options are other mCHP conversion technologies as fuel cells and internal combustion engines, different Stirling engine conversion efficiencies, and future energy demands. The use of more realistic residential energy demand patterns. In deriving individual residential energy demand profiles from aggregate profiles effort should be made to let these generated profiles correspond to real-life profiles as good as possible. Sources that mention real-life residential demand profiles should therefore be consulted as a benchmark. In the MPC controller predictions on residential energy demand could be simulated to be different from the actual values. The influence of non-perfect predictions can then be researched. Also, the influence of a non-perfect prediction model used by the MPC controller, as opposed to the system model in the simulation, could be looked into. Another interesting further addition to the study would be multi-criteria system control, including, beside cost minimisation, the minimisation of CO2 emissions from residential energy use.

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