Sergeï Agapoff

Mireille Jandon

Thierry Guiot

IMPACT OF A TARIFF BASED HEATING LOAD CONTROL ON ENERGY, COMFORT AND ENVIRONMENT: A PARAMETRIC STUDY IN RESIDENTIAL AND OFFICE BUILDINGS

Keywords: load shedding, energy flexible buildings, performance indicators

In the perspective of systematic deployment of smart meters and smart HVAC systems, energy price is a possible incentive to automatically shift consumption from a constrained time-slot (e.g. around 7:00 pm) to a relaxed one (in the night). Such load shedding mechanisms are already in place in France for domestic hot water usage and are likely to be broadened to heating systems. This paper investigates the impact of an automatic tariff-based heating load control on the energy consumption, load curve, thermal comfort and environmental impact for the end-user. To achieve this study a method has been developed to assess the performance of a control strategy associated with a tariff signal through simulations. This method has been applied to different control strategies and tariff signals for several combinations of buildings and heating control systems. This work focuses on the existing building stock -with its main variations in terms of insulation, typology or heating control under different climatic conditions -while capturing the fundamental of building thermal response with the help of thermal simulation. This paper explains the methodology and the parametric study and shows that load shedding has limited advantages in terms of spared energy and comfort but can have a real effect on the heating load curve. Due to its systematic coverage this work aims at completing the current literature focused either on one technology or on control strategies.

CONTEXT AND OBJECTIVES

Every winter, European power grid operators are focused on weather channels: a single drop in temperature could lead to local or even national blackouts. To avoid these consumption peaks the main solution is to reduce the energy demand during constrained time-slots and shift it to relaxed times, e.g. during the night. Such load shedding mechanisms are already in place in France for domestic hot water usage and are based on a low tariff between 10pm and 6am. However this solution is now widely implemented in the country and is not enough to reduce the energy demand during the day, especially in cold winter evenings. Other techniques are needed and energy providers and flexibility aggregators offer similar solutions adapted to domestic electric heating: either through price incentives to reduce heating during peak days or through load curtailment where the heating power demand is completely turned off. With the deployment of smart meters these solutions become easier to implement and there is a need to assess their efficiency so that the energy industry, control systems manufacturers and consumers can actually work together to reduce peak loads. This paper investigates the impact of an automatic tariff-based heating load control on the energy consumption, load curve, thermal comfort and environmental impact for the enduser. The goal of this work is to provide a methodology to estimate those impacts and to give a feedback to the energy and building communities about how such load shedding solutions perform when they are applied on various buildings in simulation. The proposed methodology considers the association of a tariff signal -when should the building reduce its heating loadand a control strategy -how should the signal be interpreted.

The methodology has been applied to different control strategies and tariff signals for several buildings, which represent the existing building stock -with its main variations in terms of insulation, typology or heating control under different climatic conditions -while capturing the fundamental of building thermal response with the help of thermal simulation. The paper is organized as follows: after a literature review on the subject, we first present the indicators chosen to assess the impact on energy, power, comfort and environment; then the developed methodology is explained; two case studies are presented and their results are discussed; final sections present the conclusions and the perspectives of this work.

LITERATURE REVIEW

Previous studies have focused on energy management optimization at the building level [START_REF] Favre | Application of Dynamic Programming to Study Load Shifting in Buildings[END_REF] or on the assessment of flexibility in an integrated grid model such as buildings equipped with heat-pumps in a modeled electrical grid where flexibility is managed through direct control or dynamic time-of-use pricing [START_REF] Patteeuw | Comparison of Load Shifting Incentives for Low-Energy Buildings with Heat Pumps to Attain Grid Flexibility Benefits[END_REF]. The assessment methodology proposed by Saker is based on the comparison between a simulation with load control and a simulation without, on a stock of 500 buildings [START_REF] Saker | Contribution Au Pilotage de La Charge Pour Accroître La Flexibilité Du Système Électrique[END_REF]. In these simulations the load of electric convectors, domestic hot water tanks and electric vehicles is controlled and optimized to assess the potentialities of Demand Side Management strategies. A building stock approach has also been conducted in [START_REF] Da | Analyse de La Flexibilité Des Usages Électriques Résidentiels[END_REF] to assess the flexibility of domestic electric loads. For this work, variability in the simulated buildings has been introduced through heat transfer coefficients differentiation based on the building construction period.

The approach hereby presented focuses more on developing a generic methodology to assess the performance of load shedding mechanisms from the building point of view. A similar withand-without load control simulation approach is proposed in this work, with a focus on the thermal and electric response at the building level for various building configurations. Simulating at the building level instead of the stock level allows the use of a complex building model and gives an overview of the specific behaviors of each building configuration.

INDICATORS

From the power system point of view, the main incentive for load shedding is the reduction of the power used during the peak period. However it should not be the only indicator to assess the performance of such a mechanism. Acting on the heating load can become a real challenge for the building to maintain a reasonable indoor temperature: the impact on the occupants' comfort should also be assessed. Like many other smart energy mechanisms, load shedding is often presented as a way to reduce the overall consumption and the environmental impact of the building: such indicators are also needed to measure the performance of load shedding. The proposed indicators involve a 𝑟𝑒𝑓 value and a 𝑠ℎ𝑒𝑑 value, the former is obtained when the building is simulated without load shedding while the latter is obtained with load shedding. The global indicators are computed on one year simulated data. For convenience energy and power indicators are normalized to the building surface.

Energy

Because the studied load shedding mechanism acts on the heating load of a dwelling, the indoor temperature will slowly decrease during the load shedding and some of the curtailed energy is very likely to be used after the load shedding period to bring back the dwelling to the temperature set point due to the rebound effect [START_REF] Binswanger | Technological Progress and Sustainable Development: What about the Rebound Effect?[END_REF]. This may actually reduce the energy savings that could be expected. Therefore, to assess the energy performance of load shedding the annual Curtailed Energy (𝑎𝐶𝐸) and the annual Load Shedding Efficiency (𝑎𝐿𝑆𝐸), are proposed and described in equations ( 1) and ( 2).

The Curtailed Energy (𝐶𝐸) of a given load shedding period 𝐿 is the consumption difference between the reference and the load shedding simulations during the load shedding period (between start and end times, denoted 𝑠[𝐿] and 𝑒[𝐿]). It is computed from the cumulated energy consumption 𝐶 𝑟𝑒𝑓/𝑠ℎ𝑒𝑑 𝑡 (at a given time 𝑡) and represents the amount of energy which was not consumed during the period. The sum of this Curtailed Energy over all load shedding periods in an annual simulation forms the annual Curtailed Energy.

{ 𝐶𝐸[𝐿] = (𝐶 𝑟𝑒𝑓 𝑒[𝐿] -𝐶 𝑟𝑒𝑓 𝑠[𝐿] ) -(𝐶 𝑠ℎ𝑒𝑑 𝑒[𝐿] -𝐶 𝑠ℎ𝑒𝑑 𝑠[𝐿] ) 𝑎𝐶𝐸 = ∑ 𝐶𝐸[𝐿] 𝐿 ∈ 𝐿𝑜𝑎𝑑𝑆ℎ𝑒𝑑𝑑𝑖𝑛𝑔𝑠 (1)
The annual Energy Savings (𝑎𝐸𝑆) is calculated as the annual consumption difference between the reference and the load shedding simulations (between the simulation's 𝑠𝑡𝑎𝑟𝑡 and 𝑒𝑛𝑑 times). The annual Load Shedding Efficiency is then calculated as the ratio between the annual Energy Savings and the annual Curtailed Energy.

{ 𝑎𝐸𝑆 = (𝐶 𝑟𝑒𝑓 𝑒𝑛𝑑 -𝐶 𝑟𝑒𝑓 𝑠𝑡𝑎𝑟𝑡 ) -(𝐶 𝑠ℎ𝑒𝑑 𝑒𝑛𝑑 -𝐶 𝑠ℎ𝑒𝑑 𝑠𝑡𝑎𝑟𝑡 ) 𝑎𝐿𝑆𝐸 = 𝑎𝐸𝑆 𝑎𝐶𝐸 ⁄ (2)

Power

To assess the impact of the operation on the load curve, the Maximal Curtailed Power (𝑀𝐶𝑃) is observed for each day where load shedding has occurred. This indicator is defined in equation ( 3) where ∆𝑡 is the simulation time-step and 𝐿𝑆𝑡𝑖𝑚𝑒𝑠[𝑑] represents the load shedding times of the day 𝑑.

𝑀𝐶𝑃[𝑑] = max 𝑡 ∈ 𝐿𝑆𝑡𝑖𝑚𝑒𝑠[𝑑] {(𝐶 𝑟𝑒𝑓 𝑡+1 -𝐶 𝑟𝑒𝑓 𝑡 ) -(𝐶 𝑠ℎ𝑒𝑑 𝑡+1 -𝐶 𝑠ℎ𝑒𝑑 𝑡 )} ∆𝑡 (3)

Comfort

To better understand how occupants perceive indoor temperature the PMV and PPD indicators have been developed [START_REF] Fanger | Thermal Comfort: Analysis and Applications in Environmental Engineering[END_REF] and are now part of a French standard on thermal comfort (AFNOR, 2016). This standard defines comfort zones (I, II, III and IV) related to the level of thermal dissatisfaction of occupants (PPD): this work considers zone II, for which the dissatisfaction should be below 10%. This comfort zone corresponds to a comfort vote (PMV) between -0.5 and +0.5 on a scale from -3 (cold) to +3 (warm).

For a given case (𝑟𝑒𝑓 or 𝑠ℎ𝑒𝑑) and a given time, a cold discomfort (𝐷 𝑐,𝑐𝑎𝑠𝑒

𝑡

) and a warm discomfort (𝐷 𝑤,𝑐𝑎𝑠𝑒 𝑡 ) indicators are described in equations ( 4) and ( 5). Discomfort is only computed when people are in the building and active (i.e. for "active presence" times during the year of study, denoted 𝐴𝑃𝑡𝑖𝑚𝑒𝑠). These indicators mimic the PPD indicator with a saturation to 𝑃𝑃𝐷 𝑙𝑖𝑚 = 10% according to the chosen comfort zone. Then when two cases are both "comfortable" (i.e. their dissatisfaction is below 10%), the difference between indicators is 0.

𝐷 𝑐,𝑐𝑎𝑠𝑒 𝑡 = { 0 if 𝑡 not in 𝐴𝑃𝑡𝑖𝑚𝑒𝑠 𝑃𝑃𝐷 𝑙𝑖𝑚 if 𝑃𝑀𝑉 𝑐𝑎𝑠𝑒 𝑡 ≥ -0.5 𝑃𝑃𝐷 𝑐𝑎𝑠𝑒 𝑡 otherwise (4) 𝐷 𝑤,𝑐𝑎𝑠𝑒 𝑡 = { 0 if 𝑡 not in 𝐴𝑃𝑡𝑖𝑚𝑒𝑠 𝑃𝑃𝐷 𝑙𝑖𝑚 if 𝑃𝑀𝑉 𝑐𝑎𝑠𝑒 𝑡 ≤ 0.5 𝑃𝑃𝐷 𝑐𝑎𝑠𝑒 𝑡 otherwise (5)
The annual Discomfort Variation presented in equation ( 6) is a global indicator of discomfort difference between the 𝑟𝑒𝑓 and the 𝑠ℎ𝑒𝑑 cases. 𝑎𝐷𝑉 𝑐 computes the cold discomfort, the formulation for warm discomfort 𝑎𝐷𝑉 𝑤 is similar.

𝑎𝐷𝑉 𝑐 = ∑ 𝐷 𝑐,𝑠ℎ𝑒𝑑 𝑡 -𝐷 𝑐,𝑟𝑒𝑓 𝑡 𝑡 ∈ 𝐴𝑃𝑡𝑖𝑚𝑒𝑠 ∑ 𝐷 𝑐,𝑟𝑒𝑓 𝑡 𝑡 ∈ 𝐴𝑃𝑡𝑖𝑚𝑒𝑠 (6)

Environment

In this work, the environmental impact of a given consumption is represented by the Global Warming Potential (𝐺𝑊𝑃 in 𝑘𝑔𝐶𝑂2 𝑒𝑞 ) caused by the greenhouse gases emitted to produce and transmit energy. For a case consumption (𝑟𝑒𝑓 or 𝑠ℎ𝑒𝑑) the 𝐺𝑊𝑃 impact (see equation ( 7)) is computed from the production impact 𝐼 𝑝𝑟𝑜𝑑 𝑔𝑤𝑝 of each production source in 𝑝𝑟𝑜𝑑_𝑠𝑜𝑢𝑟𝑐𝑒𝑠 in combination with the energy mix at each time (𝑚𝑖𝑥 𝑗 𝑡 ) and the transmission impact 𝐼 𝑡𝑟 𝑔𝑤𝑝 .

𝐺𝑊𝑃 𝑐𝑎𝑠𝑒 = ∑ (𝐶 𝑐𝑎𝑠𝑒 𝑡+1 -𝐶 𝑐𝑎𝑠𝑒 𝑡 ) ⋅ (𝐼 𝑡𝑟 𝐺𝑊𝑃 + ∑ 𝑚𝑖𝑥 𝑗 𝑡 × 𝐼 𝑝𝑟𝑜𝑑 𝐺𝑊𝑃 [𝑗] 𝑗 ∈ 𝑝𝑟𝑜𝑑_𝑠𝑜𝑢𝑟𝑐𝑒𝑠 ) 𝑠𝑡𝑎𝑟𝑡 ≤ 𝑡 ≤ 𝑒𝑛𝑑-1 (7)
To compare two cases, the Global Warming Potential Variation is proposed (𝐺𝑊𝑃𝑉 in equation ( 8)) between the reference case and the case with load shedding.

𝐺𝑊𝑃𝑉 = 𝐺𝑊𝑃 𝑠ℎ𝑒𝑑 -𝐺𝑊𝑃 𝑟𝑒𝑓 𝐺𝑊𝑃 𝑟𝑒𝑓 (8)

PERFORMANCE ASSESSMENT METHODOLOGY

The method to assess the performance of a load-shedding control system associated with a tariff signal is based on the comparison of 𝑟𝑒𝑓 and 𝑠ℎ𝑒𝑑 simulations as presented in Figure 1.

The starting point of this methodology is to define the tariff signal and the control system.

The tariff signal is the information sent to the building, e.g. through an Energy Management System (EMS), and describes when the heating load should be reduced. The control system represents any regulation system which receives the tariff signal and controls the heating system (e.g. embedded in an EMS, the heating system itself or an external device). Step 1: Identification

The first step of the methodology aims at identifying the response strategy of the control system to the tariff signal. This characterization is needed to properly model how the heating command will be calculated in the simulator. For this work, two types of tariff signal are considered: FIXED signal and MARKET-DRIVEN signal. With a fixed signal, the heating load is reduced on a regular basis (e.g. every working day between 6pm and 8pm) while a marketdriven signal should reduce the heating load when it is the most profitable from a user point of view. Two kinds of response strategies are proposed:

 Load curtailment (LC): during load shedding the whole heating system is turned off ;  Heating set point decrease (HSD): during load shedding the temperature set point is decreased by a fixed or variable value which could be set by the user or the control system's manufacturer.

The LC strategy is easier to implement than HSD and is the most common in the market at the moment. This identification step also includes the characterization of the heating system's physical response to the load shedding strategy: applying an LC strategy to a heat pump is more complex than applying it to electric radiators. To address this challenge, various solutions can be proposed such as (a) expert knowledge, (b) laboratory characterization or (c) in-situ characterization.

Step 2: Parametric study

Once the tariff signal, the control system and its response strategy, the heating system's response model are identified, the second step of the methodology is the parametric study to analyze the behavior of a variety of buildings with or without load shedding. To avoid mixing non-coherent results, the parametric study is limited to a given building sector and a given type of heating system (e.g. electric radiators in residential buildings, heat pump with fan coils in office buildings…). The parameters to study are defined upon using the methodology, it can include usual parameters such as building type, climatic zone, construction period…

The output of such parametric studies is evaluated through the indicators defined to assess the performance of the load shedding with the couple "control system -tariff signal" under various conditions.

CASE STUDIES Electric Convectors in Residential buildings (EC-R)

A main case has been prepared to test the methodology and get results for parametric variations of the building. Laboratory characterization has been carried out to tune the control loop response to LC or HSD strategies. The tariff signal used for this case is a FIXED signal (only on peak-days (22 per year) from 6pm to 8pm) with LC response strategy.

For this case the parametric variations are described in Table 1. The climatic zone variations correspond to three zones related to the French thermal regulation with conventional meteorological data. The normal temperature set point is 21°C and the night setback operated from 10pm to 7am with a temperature set point of 18°C. The building type variations are based on two buildings developed within the HOMES project (Schneider Electric et al., 2012) (see Figure 2). Their model takes into account the heat transfers between rooms and simulates the systems and thermal response of the building on a sub-minute time-step. The building configuration is described in Table 2. This case was simulated for the year 2012, with real meteorological data, which presented a rather cold winter. Several response strategies and signals have been tested such as HSD strategy with various values for temperature set point decrease or MARKET-DRIVEN signals with load shedding periods of maximum 1 hour long or maximum 2 hours long. For the sake of readability only the results for the following "strategy -signal" combinations are presented: The simulated building is a typical building proposed in Task 27 of IEA Solar Heating and Cooling Programme. The simulation model includes two offices (north and south side) and the corridor segment which separates them (see Figure 3). The walls between adjacent offices are considered adiabatic.

 1.

Figure 3. HP-O-exp building representation

Normal temperature set point is 21°C while setback temperature is 16°C on week-ends and from 7pm to 6am on week days.

RESULTS AND DISCUSSION

The Performance Assessment Methodology has been applied to the case studies presented above. Matlab/Simulink tool SIMBAD developed by CSTB [START_REF] Husaunndee | SIMBAD: A Simulation Toolbox for the Design and Test of HVAC Control Systems[END_REF] was used for simulations in EC-R case and the Modelica-based BuildSysPro Library developed by EDF R&D [START_REF] Plessis | BuildSysPro: A Modelica Library for Modelling Buildings and Energy Systems[END_REF] was used for simulations in HP-O-exp case. Two simulators were used in order to illustrate the versatility of the methodology: since 𝑟𝑒𝑓 and 𝑠ℎ𝑒𝑑 simulations are obtained with the same simulation tool within a case, it is reasonable to say that the choice of simulator does not impact significantly the results as long as the simulator is validated in its field of application. However one should be cautious when comparing results obtained with one simulator and results obtained with the other. This section presents and discusses the results.

Electric Convectors in Residential buildings (EC-R)

Given the parametric building variations (Table 1) 36 simulations were run for this case: statistical values (minimum, average and maximum) obtained over all the simulations are presented and kernel density estimation (KDE) was carried out to understand the importance of the different parameters. 3 show that the energy performance is relatively low since the curtailed energy is lower than 3 kWh/m²/year and the actual energy savings are 3% to 20% of this curtailed energy. Load shedding with Load Curtailment strategy means a huge drop in the needed power (up to 107 W/m² in our simulations), which makes it a good candidate in terms of power performance. From the comfort point of view, results show that during load shedding temperatures could decrease with almost 4°C, which is quite high. The increase of temperature (after the end of a load shedding period) is limited to 1°C over the reference simulation, showing that there is a limited overheating in response to the load shedding. Finally, the environmental performance is really low: Global Warming Potential Variation shows a maximal 1.4% decrease in CO 2 emission. The low energy, comfort and environmental performances can be partially explained by the few number of load shedding hours (44 over 8760 in a year) due to the chosen tariff signal. Allowing more load shedding hours could increase the energy and environmental performances. The low comfort performance is also responsible for the low energy performance: the significant temperature decrease during load shedding induces a large compensation when the heating system is turned back on which means a large quantity of energy needed to reach the normal set point temperature. Power performances should be carefully interpreted: load shedding does help in flattening the load curve during load shedding but the rebound effect due to the heating compensation can disturb the local power system.

Aggregated results in Table

Figure 4 presents kernel density estimation graphs to understand the statistical significance of each parameter on the annual Load Shedding Efficiency (𝑎𝐿𝑆𝐸) indicator. It appears that the climatic zone is not really influential but the three other parameters do have an impact:  Building type: a higher 𝑎𝐿𝑆𝐸 value for multiple-dwelling housing simulations is obtained, which can be explained by the simulator hypothesis stating that neighboring dwellings have the same average temperature than the simulated dwelling meaning that the heating needs of this dwelling after load shedding are partially covered by the other dwellings. Therefore the energy savings are slightly higher in this configuration.  Construction period: older buildings present a higher 𝑎𝐿𝑆𝐸 value because they usually have a higher installed heating capacity (to compensate their higher thermal losses) meaning that during load shedding a large amount energy will be curtailed.  Setback: night setback (21°C to 18°C) allows for a higher load shedding efficiency mainly because this setback starts at 10pm and is likely to shrink the heating needs after the end of the load shedding period (8pm). This behavior is strongly related to the time distance between load shedding and setback. The parametric variations of the tariff signal and the response strategy defined for this exploratory case have been run through 7 simulations, whose results are presented in Simulations with a preheating phase (1.4 and 2.3) show high and negative load shedding efficiency (-535% and -77.4%): in those simulations the load shedding operations resulted in consuming much more energy during the year than the reference simulation. The preheating strategy does help in limiting the comfort impact (+0.3% in cold discomfort which is the lowest of all HP-O-exp simulations) but seems not adapted to the heat pump equipped systems.

Looking at the other simulations, it appears that those with a FIXED tariff signal (1.1 to 1.3) show lower 𝑎𝐿𝑆𝐸 values than those with a MARKET-DRIVEN signal (2.1 and 2.2): the total number of load shedding hours (44 for FIXED simulations and 250 for MARKET-DRIVEN) can explain this result. On the other hand, the cold discomfort variation is higher for MARKET-DRIVEN signal simulations (5%) than for FIXED signal ones (0.5%). Because FIXED signal focuses on peak days (usually related to really cold days) the curtailed power is higher in simulations 1.1 to 1.3 than in simulations 2.1 and 2.2. It is noticeable that with a temperature decrease of 0.5°C (simulation 1.1) we obtain a saving of 30Wh/m² (7.9% of the 380Wh/m² curtailed energy), which is higher than all the other simulations. Such a HSD strategy allows for a relatively good energy performance while maintaining the indoor comfort (+0.5% in cold discomfort). However this energy performance is really low compared to the annual energy consumption of the reference simulation (15kWh/m²).

CONCLUSIONS

In this work a framework for the evaluation of load shedding operations has been defined: a set of indicators for Energy, Power, Comfort and Environment performances has been proposed and a Performance Assessment Methodology for load shedding operations has been designed. Starting with the identification of a tariff signal and the response strategy of the control system, this methodology is based on the performance assessment through parametric simulations and the comparison between reference and load shedding simulations. The Performance Assessment Methodology has been applied to two cases: one following the original philosophy of parametric variations in the building configuration and the other exploring variations on the response strategy and the tariff signal for a given building configuration. It appears that the energy and environmental performances are rather low due to the rebound effect which tends to compensate for the lack of heating during load shedding. In the comfort point of view it is possible to limit the cold discomfort increase with the Heating Set point Decrease strategy. On the other hand, the Load Curtailment strategy, a widely used strategy, can seriously damage the indoor comfort during load shedding. The power performance can be satisfying since load shedding can reduce the power used for heating but it should not be independently analyzed as it impacts the comfort and can also have a negative impact on the local power system because of the rebound effect.

In this paper six performance indicators were presented and other indicators can be defined to be used with the methodology. Similarly, the types of tariff signal and response strategy can be extended to meet the user's needs: the main limitation lies in the modeling capabilities of the tool used for energy simulations. The methodology's adaptability is also illustrated through the work presented here where two different energy simulation tools have been used by different research teams to run the simulations.

PERSPECTIVES

On the methodological level, the future work will focus on extending the framework to address the economic performance of such load shedding mechanisms and on proposing an adaptation to buildings and systems in operation. Also an in-depth analysis on the impact of using various simulation tools should be carried on to validate the concept of versatility of the methodology. Other applications could be investigated such as a full parametric study for office buildings or to assess innovative concepts of load shedding which take advantage of the new communication ways with buildings informing aggregators about their load shedding capabilities in real-time. Such a load shedding mechanism would help aggregators schedule shedding periods at the local or even national level while taking into account the buildings needs and limits.

Figure 1 .

 1 Figure 1. Load shedding assessment methodology

Figure 2 .

 2 Figure 2. EC-R buildings representation (left: multiple-dwelling, right: individual) Heat Pump in large Office buildings (HP-O-exp) An exploratory study has been carried out to evaluate the performance of various tariff signals and response strategies on a given building configuration. For this case an Air/Air heat pump model based on expert knowledge is used.

Figure 4 .

 4 Figure 4. aLSE related KDE plots for each parameter for EC-R case (x-axis represents aLSE in %) (Mozart = Individual Housing, Gauguin = Multiple-dwelling housing) Heat Pump in large Office buildings -exploratory (HP-O-exp)

Table 1 . Building variations

 1

	PARAMETER	VARIATIONS
	Building type	Multiple-dwelling housing (95m²)
		Individual Housing (100m²)
	Climatic zone	Nancy
		Rennes
		Nice
	Construction Period 1980-1990
		2000-2005
		After 2012 (BBC)
	Setback	No setback
		Night setback

Table 2 . Building configuration for office exploratory case

 2

	FIXED signal: only on peak-days (22 per year) from 11am to 1pm
	o 1.1. HSD strategy: 0.5°C decrease
	o 1.2 HSD strategy: 2°C decrease
	o 1.3 LC strategy
	o 1.4 LC strategy and overheating 2 hours before load shedding (1°C increase)
	 2. MARKET-DRIVEN signal: 1-2 hours long load shedding slots resulting in 250 hours
	selected on working days between November and Mars based on Critical Peak Pricing
	(2012 EPEX SPOT day-ahead price fixing)
	o 2.1 HSD strategy: 2°C decrease
	o 2.2 LC strategy
	o 2.3 LC strategy and overheating 2 hours before load shedding (1°C increase)
	PARAMETER	CONFIGURATION
	Building type	Office (6470m²)
	Climatic zone	Lyon (2012)
	Construction Period 2000-2005
	Setback	Night & week-end setback

Table 3 . Aggregated simulation results for EC-R case

 3

	INDICATOR		UNIT	MIN AVG MAX
	annual Curtailed Energy		Wh/m²	36	1120 3224
	annual Load Shedding Efficiency	%	2.7	10.3	20
	Maximal Curtailed Power Maximal temperature decrease	1	W/m² °C	2 0.3	43 1.9	107 3.8
	Maximal temperature increase		°C	0	0.2	0.7
	Global Warming Potential Variation	%	-1.4	-0.3	-0.1

Table 4 (

 4 Global Warming Potential indicators were not available for this case).

	INDICATOR	UNIT	1.1	1.2	1.3	1.4	2.1	2.2	2.3
	annual Curtailed Energy	Wh/m²	380 1000 500	58	1088 1080 687
	annual Load Shedding Efficiency	%	7.9	0.1	0.2	-535	9.1	8.8	-77.4
	Maximal Curtailed Power	W/m²	9	14	14	14	7.5	7.3	7.5
	annual Discomfort Variation (cold)	%	0.5	1.0	1.0	0.3	5.1	5.1	0.3
	annual Discomfort Variation (warm)	%	0	0	0	0	0	0	0.3
	Global Warming Potential Variation	%	-	-	-	-	-	-	-

Table 4 . Simulation results for HP-O-exp case

 4

Discomfort indicators were not available for this case, it was replaced by a comparison of the indoor temperature between 𝑟𝑒𝑓 and 𝑠ℎ𝑒𝑑 simulations

ACKNOWLEDGEMENT

This work is part of the project Smart Electric Lyon. This project is supported by the ADEME (The French Environment and Energy Management Agency) and was awarded a €9.7 million grant by the French State within the "Investissements d'Avenir" program ("Investments for the Future").

We would like to thank Denis Covalet and Maya Milliez (EDF R&D) for their work on the "Heat Pump in large Office buildings" exploratory case within the project Smart Electric Lyon.


Bordet Lucile

L ' Intensification En

de corpus de la série américaine How I Met Your Mother », Les Amis du Crelingua, 5-22

The following list of references includes works that are often cited in intensification studies.

Diewald G. (eds.), New Reflections on Grammaticalization, Amsterdam: John Benjamins, 143-161.

MALHEIROS-POULET Maria Eugenia, 1988, « La relativité des expressions d'intensité (exemples en portugais du Brésil) », Annexes des Cahiers de Linguistique Hispanique Médiévale 7, 527-537.

MÉNDEZ-NAYA Belén, 2008, "Special issue on English intensifiers", English Language and Linguistics 12 (2), Cambridge: Cambridge University Press, 213-219.

AUTHOR LUCILE BORDET

Université Jean Moulin -Lyon 3 lucile.bordet@univ-lyon3.fr


Lucile Bordet

Denis Jamet

ARE ENGLISH PREPOSITIONS GRAMMATICAL OR LEXICAL MORPHEMES? 1

Introduction

This article will start from the very traditional assumption that it is necessary to classify prepositions in parts of speech, even if, according to D. Gaatone [2001 : 23] "la notion même de 'préposition' reste aussi controversée que jamais" or, according to A. Borillo [2001 : 141] "le terme de 'préposition' s'applique à des constituants qui diffèrent tant par leur forme que leur mode de fonctionnement ou la spécificité de leur contenu sémantique". Without completely calling the very existence of this traditional class generally called "grammatical" or "syntactic" into question, We aim to reexamine the notion of grammaticality, as it seems most characteristic of prepositions, which are normally placed into the "grammatical" or "syntactic" category.

We will ask ourselves whether it is possible to classify words such as of, instead of, in view of and in ignorance of in examples (1) to (4) in the same category, i.e. the prepositional syntactic class?

(1) EEC 1341 What would be the status of a new document?

(2) A8U 46 Instead of focusing on the narrow agenda of Delors the new Europe should be more forward looking.

(3) HPN 653 In view of the numbers of theses produced by both universities, it seems that the latter hypothesis is the more likely.

(4) CBR 1158 Now that we have the means to observe samples of language which must be fairly close to representative samples, the 1 Many thanks to Lily Cheah, Natalie Mandon-Hunter and Madeleine Wilson for proofreading this paper and their useful comments.

Lucie Bordet & Denis Jamet, "Are English prepositions lexical or grammatical morphemes?", Cercles, Occasional Papers (2010) 1-26. Is it possible to consider the syntactic category of English prepositions as a homogeneous class, or is it better to regard it as a fundamentally heterogeneous class, made up of distinctive elements? Do we not need to posit the existence of a gradient from the more grammatical to the more lexical within the category of English prepositions? Or is it better to posit the existence of a gradient going from the more lexical to the more grammatical, as we will try to demonstrate in this article, especially if we take the evolution of language and the lexicalization process into account?

We will first go back over some definitions of "preposition," as well as the traditional dichotomy between "simple prepositions" and "complex prepositions," so as to highlight the fact that this dichotomy is too restrictive, and, therefore, ineffective. We will finally try and shed new light on the criteria necessary for the establishment of the degrees of what we will refer to as "prepositionality" in English.

I. The traditional approach: some basic landmarks and definitions

Traditionally, there are between 8 and 10 parts of speech, that is to say 8 or 10 syntactic classes. We generally distinguish between lexical morphemes and atical morphemes: gramm Lexical morphemes comprise nouns, verbs, adjectives and adverbs; --Grammatical morphemes include conjunctions, interjections, determiners and prepositions;

-Linguists sometimes add locutions and pronouns to these eight parts of speech. However, these are normally placed into a separate category, because locutions and pronouns function as both lexical and grammatical morphemes.

Following the traditional approach, prepositions therefore fall into the category of grammatical morphemes. However, in this article, we would like to revise the traditional approach by examining not only the processes by which prepositions have been generated, but also the functional role they play in discourse.

Let us now take a closer look at some definitions found in the reference books. The term "preposition" is defined as follows in Dictionnaire de la linguistique by G. [START_REF] Mounin | Dictionnaire de la linguistique. Coll. « Quadrige[END_REF][START_REF] Mounin | Dictionnaire de la linguistique. Coll. « Quadrige[END_REF]: 269]:

Gram. -Ce terme désigne une classe de mots ou de locutions invariables (à, de, par, pour, sur, à cause de, avant de, etc.) For Mounin, prepositions are therefore clearly grammatical morphemes. D. Crystal [1980Crystal [ (1992)): 275] shares this point of view for English prepositions in A Dictionary of Linguistics and Phonetics: J. Dubois et al. [1973: 390] confirm the grammatical status of prepositions in their Dictionnaire de linguistique:

La préposition est un mot invariable qui a pour rôle de relier un constituant de la phrase à un autre constituant ou à la phrase toute entière, en indiquant éventuellement un rapport spatio-temporel. Le mot ou le groupe de mots ainsi reliés sont appelés « régime » ; les prépositions traduisent donc des relations grammaticales et spatiotemporelles.

However, they distinguish between two types of prepositions:

On a distingué des prépositions vides, qui sont de simples outils syntaxiques, et des prépositions pleines, qui, outre l'indication du rapport syntaxique, ont un sens propre.

The definition also then goes on to specify that the term "preposition" is in fact a hypernym for the two following terms: "proper prepositions" and "prepositional locutions". The definition also highlights the close link that binds prepositions and adverbs2 : The tight link that unites prepositions (that supposedly belong to grammatical morphemes) and adverbs (that supposedly belong to lexical morphemes) blurs the distinction between the grammatical and lexical nature of prepositions.

( In A Glossary of English Grammar, G. Leech [2006: 90] makes no mention of the grammatical or lexical nature of prepositions, but merely notes that there are two types of prepositions: "simple" and "complex" prepositions:

Preposition

A word which typically comes in front of a noun phrase, for example of, in, with in of milk, in the building, with all the good intentions I had at the beginning of the year. […] In addition, there are quite a few complex prepositions which are written as more than one word: away from, instead of, in front of, by means of and so on. The meanings of prepositions are very varied, but two important categories are those of place and time relations: at the airport, in the summer and so on.

The same dichotomy is to be found in An Encyclopedic Dictionary of Language and Languages by D. Crystal [1992Crystal [ (1994)): 312]:

Preposition

An item that typically precedes a noun phrase to form a single constituent of structure -a prepositional phrase or prepositional group -often used as an adverbial. […] Constructions of the type in accordance with are sometimes called complex prepositions, because they can be analysed as a sequence of two prepositions surrounding a noun, the whole construction then being used with a following noun phrase: in accordance with your instructions.

Let us now examine the two main types of prepositions in order to determine to what extent this distinction is operative.

II. The two main types of prepositions

The two types of prepositions are generally opposed as follows: "simple" vs. "complex" prepositions.

-In French, simple prepositions are usually referred to as vides (empty), faibles (weak), zéro (zero), légères (light), principales (main), abstraites (abstract), aplaties (flat), incolores (colorless), vraies (true), grammaticales (grammatical), casuelles (case), fonctionnelles (functional) prepositions etc. They are part of a closed class, are in limited number, and are generally made up of only one element. In this category prepositions such as about, above, across, around, as, at, but, by, in, of, on, to, etc. are found, as exemplified in (8), ( 9) and ( 10):

(8) BM1 778 If none of these options are open to you, then shopping at a large supermarket is probably the best solution.

(9) ACW 1145 His hair had been cut very short but only shaved around his ears and towards the back of his neck (10) CEY 3215 To her surprise, Gioella laughed and said, "Really, thatʹs too bad of Ludovico".

-In French, complex prepositions are usually referred to as pleines (contentful), fortes (strong), lourdes (heavy), secondaires (secondary), concrètes (concrete), colorées (colored), fausses (fake), lexicales (lexical), etc. They are part of an almost open class -or at least a class that is less closedwith more members than simple prepositions. Very often, the characteristics of these prepositions are not clearly defined, which raises doubts as to the true prepositional status of some of them. They are often referred to as "complex" prepositions. In this category, prepositions such as according to, except for, apart from, instead of, in front of, etc. are found, as exemplified in (11), ( 12) and ( 13):

(11) BN1 2477 And that first step, according to similar smartarses, is the hardest.

(12) ALS 132 Then there was silence except for the lapping of the rising tide.

(13) ARK 2452 He found himself in front of the main station.

Various issues can be raised, and we would like to shed light on some of these questions:

-Do all complex prepositions necessarily have some semantic content?

Cercles 2010 / 6 -Conversely, are all simple prepositions semantically empty?

Regarding complex prepositions, it is noticeable that they are generally made up of simple prepositions and a noun used as a "prop word" (instead of, in favor of, etc.). The presence of these clearly lexical items and the fact that they retain their lexical meaning (see A. Borillo [2001: 144]) help us detect a relatively strong semantic content in complex prepositions. This enables them to be used as complex prepositions exclusively. Yet, if some simple prepositions are indeed rather "colorless" (just like of in ( 22), which seems to be emblematic of this phenomenon), can we say that simple prepositions such as under, on, above, between etc. in ( 23), ( 24) and ( 25) are devoid of all semantic content? If the main role of prepositions is indeed a functional one, i.e. a relational and subordinating role3 , we think it is inaccurate to say that most simple prepositions are devoid of all semantic content (see D. Gaatone [2001: 26]). According to D. Gaatone, only lexical prepositions (i.e. what he calls "complex prepositions") are relational words, therefore real prepositions. Other "prepositions" are mere link-words ("joncteurs" in French). 4 Our intuition is confirmed by the examples below, with a place indication given in ( 26) and a time indication in ( 27):

(26) GUS 927 A week later Dorian Gray was at his house in the country, where he had invited Lord Henry and several other friends.

(27) EC4 441 Concerts start promptly at 6pm, tickets £2.50

At introduces the NP his house in the country in (5) and 6pm in (6), thus forming prepositional phrases which complement be and start respectively. However, the semantic role, though it may be weak, is almost always present, be it the indication of space (28), time (29), cause (30) etc. Another more fundamental question has to do with the division of prepositions in two different sub-categories, and more particularly with the absence of a zone between the two sub-categories:

-What does the label "complex preposition" really cover? Is there not a gradation in terms of complexity among prepositions belonging to this subclass?

-If there is no doubt that prepositional locutions such as in favor of, according to, in spite of, except for etc. belong to complex prepositions, can we consider more fixed sequences such as because of, into, onto or instead of as part of this subclass, or is it preferable to class them in the category of simple prepositions? Or would these prepositions fall in between the two categories? (see the notion of "cline"). Yet, the etymology of these prepositions indicates that they were originally complex prepositions:

(31) because of (c.1305, bi cause "by cause," modeled on Fr. par cause. Originally a phrase, often followed by a subordinate clause introduced by that or why).

(32) instead of (< OE in stede of 'in place of').

Even prepositions that we would intuitively identify as simple prepositions are historically made up of several elements, be they lexical or grammatical items. We will not discuss the formation of prepositions in this paper as we would wander too far off our point, but an etymological study carried out on etymonline.com confirms this hypothesis5 :

(33) about (O.E. onbutan ʺon the outside of,ʺ from on ʺonʺ + be ʺbyʺ + utan ʺoutside,ʺ from ut (see out)) ( 34) above (O.E. abufan, from on ʺonʺ + bufan ʺover,ʺ compound of be ʺbyʺ + ufan ʺover/high,ʺ), (35) after (O.E. aefter ʺafter, next, following in time,ʺ from O.E. of ʺoffʺ (see apo-) + -ter a comparative suffix), ( 36) behind (O.E. behindan, from bi ʺbyʺ + hindan ʺfrom behindʺ (see hind)), ( 37) beside (O.E. be sidan ʺby the side ofʺ (only as two words), from sidan dative of side (q.v.)), ( 38) between (O.E. betweonum, from bi-ʺbyʺ + tweonum dat. pl. of *tweon ʺtwo eachʺ (cf. Goth. tweih-nai ʺtwo eachʺ)), ( 39) but (O.E. butan, buton ʺunless, without, outside,ʺ from W.Gmc. *be-ʺbyʺ + *utana ʺfrom without.ʺ), ( 40) near (O.E. near ʺcloser, nearer,ʺ comp. of neah, neh ʺnigh.ʺ).

This calls for a redefinition of the categories that are generally admitted. In the third and last section, we would like to propose a more graduated approach that posits not only the absence of clear-cut boundaries, the gradual passing from one category to another, but also degrees of complexity within the sub-categories themselves. We will thus posit a continuum going from the +/-lexical to the +/-grammatical or functional, because we believe that this approach alone can account for the subtleties and specificities of these language realisations.

III. A gradual analysis of prepositions: from the more lexical to the more grammatical

In the last section, we would like to show that there is a cline going from the more lexical to the more grammatical / functional, which corresponds more or less to a cline going from the most discursive uses to the most lexicalized uses. Following A. Mardale's idea, we posit that while some prepositions are closer to the grammatical / functional end of the cline, others are closer to the lexical end, most of them are found in between.

We regard simple prepositions as originating from complex prepositions that have undergone an advanced grammaticalization process, while complex prepositions are still at an intermediary, incomplete stage of the grammaticalization process. We will define "grammaticalization" as follows, taking up J. Kurylowicz's definition [1965: 69]:

Grammaticalization consists in the increase of the range of a morpheme advancing from a lexical to a grammatical or from a less grammatical to a more grammatical status, e.g. from a derivative formant to an inflectional one.

We would like to first of all remind the reader of the difficulty of classifying some occurrences into a specific category because the boundaries of the categories are not clear-cut. It is therefore expected that we should encounter difficulties in determining the boundaries of the "complex preposition category" for they are -initially at least -perceived as prepositional locutions; and we know that locutions pertain both to the lexical and the grammatical uses. We will also try and show that inside a given category, there are degrees of lexicality or grammaticality (for instance, a complex preposition such as in front of is more grammaticalized than up to). We will also try and show that prepositions move along the cline going from the more lexical to the more grammatical uses according to the following pattern:

-Non-lexicalized low-frequency complex "prepositions" -Lexicalized low-frequency prepositions -Complex prepositions perceived as complex -Complex prepositions not perceived as complex -Simple prepositions We would like to examine which criteria enable us to say that a given morpheme (a preposition in our case) is lexical or grammatical, bearing in mind that morphemes always go from the more lexical to the more grammatical. In other words, we would like to show that items which are intuitively perceived as more prepositional are items that have undergone an advanced grammaticalization process. The 9-criterion classification that we put forward is by no means exhaustive; we have not ranked these criteria according to their importance insofar as it is often a difficult task to determine the prevailing criterion/a at work in the grammaticalization of prepositions. Each of these criteria plays a more or less important role according to the stage of the grammaticalization process reached by a given preposition. That is the reason why we have adopted a multicriteria approach, as exemplified below.

1. The prepositions which are closer to the lexical end of the cline belong to an open class ("pas complètement fermée" as S. Oriez would say [2009: 49]), while the prepositions closer to the grammatical end of the cline belong to a closed class (these are fairly easy to list), which is evidence of their advanced grammaticalized status.

2. The prepositions closer to the lexical end of the cline are mostly made up of lexical items (in obedience to, in consideration of, in hope for, in search of) while the prepositions closer to the grammatical end of the cline are only made up of grammatical items or elements whose lexical origin is not -or no longer -perceived6 . Some prepositions fall between those two categories such as in spite of, in front of or in view of, where the lexical item can only be perceived as such by isolating it from the prepositions around it. Otherwise the whole is seen as a lexicalized unit (see criterion 5).

3.

The prepositions closer to the lexical end of the cline have a fairly precise meaning (in contradiction to >> in spite of >> instead of) whereas the meaning of the prepositions closer to the grammatical end of the cline is broader, more vague. The ambiguous meaning is due to the process of desemanticization, a.k.a. semantic bleaching or attrition, which generates various semantic realisations, as exemplified by the following occurrences with the preposition in:

(41) ARM 148 Harlow, in Esse, will also be getting their own indoor mini ramp. (purely spatial) (42) AK9 1407 What eventually appeared in the manifesto was less dramatic. (not spatial geographically speaking) (43) ARS 1287 Getting the cut hay fit to cart or put on tripods may take anything from two days (in ideal conditions) to several weeks. (not spatial at all) (44) AD0 644 There is absolutely no need, on any diet, to stop mixing protein sources in this way. (not spatial at all) This seems to account for the fact that the prepositions closer to the lexical end of the cline may only belong to a single syntactic class, i.e. prepositions, whereas prepositions closer to the grammatical end of the cline may belong to several syntactic classes as the table below shows:

Prépositions Adv Adj N V Conj Interj. Of - - - - - - To + - - - - - In + + + - - - For - - - - + - On + + - - - - With - - - - - - As + - - - + - At - - - - - - By + - + - - - But + - + - + - From - - - - - - Up + + + + - - Out + + + + - + About + + - - - - Into - - - - - - Like + + + + + - Over + + - - - - After + + - - + - Down + + + + - - Between + - - - - - Before + - - - + - 4.
Loss of compositional meaning is noticeable in prepositions that are closer to the grammatical end of the cline; the elements they are originally made up of are scarcely or never retrievable without carrying out an etymological study, as exemplified by between, for which the link with two is not perceived synchronically by any native speaker:

(45) between (O.E. betweonum, from bi-byʺ + tweonum dat. pl. of *tweon ʺtwo eachʺ (cf. Goth. tweih-nai ʺtwo eachʺ))

A phenomenon of morphological and semantic opacification is also to be observed, and it is the loss of compositional meaning that allows for the wide range of meanings of prepositions that are closer to the grammatical end of the cline.

5.

Since the constitutive elements of grammaticalized prepositions, that is to say prepositions that are closer to the grammatical end of the cline, are no longer perceptible, distributional properties are blocked. It implies that basic modifications of the NP become impossible as the tests performed on the complex preposition with the exception of suggest, because the following variations are ungrammatical:

(46) *with the exceptions of / *to the exception of / *with Ø exception of / *with the exception to, etc.

This phenomenon is known as the process of decategorialization and automatization and involves a syntactic reanalysis because the sequence is perceived as a single unit and no longer as a compound structure. Another consequence is the impossibility to split up the elements because complex prepositions are viewed as a whole; therefore the elements they are made up of are not seen as separate units:

( Conversely, except for seems to be less lexicalized, since the insertion of an element between except and for remains possible:

(49) ABS 2126 It's a dictum that largely holds true today, except, of course, for the Pucci tie.

Therefore, the insertion of an element in the middle of a more or less lexicalized unit often remains an option in the case of prepositions that are closer to the lexical end of the cline:

(50) EC3 360 The home currency may appreciate in Ø terms of one currency and yet depreciate in terms of another.

(51) ASY 1016 It is difficult to predict the outcome of changes in the terms of employment of teachers.

(52) FAU 1991 These are usually express, i.e. stated in the terms of the lease, though covenants may also be implied.

(53) EEN 54 In other words, they are unified only through ideological constructs (ʹscriptsʹ in the terms of Gagnon and Simon), and it is these that constitute `sexualityʹ.

(54) ASB 1356 Whereas the ordinary person has a choice whether or not to act, the police officer, in Ø view of his or her status, has a positive obligation to take action.

(55) A8N 440 Neville Southall, whose saves had prevented Forest running away with the game in the first half, gathered the ball and started to think about clearing it but in the view of the referee, George Tyson, he had thought too long.

(56) AKD 201 There is no doubt he will be a dominant figure and in the view of many he is just what is needed to revive a moribund department.

Therefore, it is a legitimate question to ask whether all non lexicalized low frequency complex prepositions that are made up of a PREP + Noun + PREP are real prepositions (i.e. lexicalized, listed in the dictionary) or mere nonlexicalized sequences.

6.

A morphological reduction a.k.a. attrition results from the loss of syntactic autonomy of the elements, which constitute all the prepositions closer to the grammatical end of the cline. Those prepositions, which are very often monosyllabic, are therefore shorter than the prepositions closer to the lexical end of the cline. Consequently, the degree of grammaticalization is expected to be inversely proportional to the morphological length of the preposition.

7.

The most grammaticalized prepositions undergo a process of phonological attrition or erosion as well. This also results from the loss of syntactic autonomy. The preposition of is the most representative of this phenomenon because phonologically, of is usually realised as a weak form:

Of strong form ɒv || ʌv ɑ:v (*), weak form əv -There is also an informal rapid-speech or nonstandard weak form, used before consonants only, ə. (Longman Pronunciation Dictionary de J. Wells).

Of is the only preposition that can be realized as a single phoneme, i.e. a schwa, and it is also the most grammaticalized preposition in English.

8. Lexicalization, and consequently the conventionalization of a preposition, depends on frequency, which means that repetition is a necessary condition for a preposition to lexicalize (see Langacker's concept of entrenchment). In order to be grammaticalized, a non-lexicalized preposition has to appear in discourse first, then has to be used by a certain number of speakers. As mentioned by C. Lehmann [1991: 501]:

The formation of new prepositions through the combination of a (mostly relational) noun with either a preposition or a case suffix is one of the most common grammaticalization processes in the world.

Consequently, the prepositions that are closer to the grammatical end of the cline will have a higher frequency of use than prepositions that are closer to the lexical end because they have reached a higher degree of grammaticalization. A study conducted on the BNC and Google reveals that the five most frequently used prepositions in English are monosyllabic and fully grammaticalized. Interestingly, these studies on two different corpora give identical findings7 . [1973: 145] write:

Prepositions

Most [complex prepositions] are in one of the following categories:

[A] ADVERB or PREP + PREP: along with, as for, away from, out of, up to

[B] VERB/ADJECTIVE/CONJUNCTION/etc + PREP: owing to, due to, because of, etc.

[C] PREP + NOUN + PREP: by means of, in comparison with, in front of, etc.

In [C], which is by far the most numerous category, the noun in some complex prepositions is preceded by a definite or indefinite article.8

This implies various degrees of grammaticalization within the very category of prepositions. If the largest category is PREP + Noun + PREP, it means that this category is more open than that of prepositions and thus less grammaticalized. However, prepositions that belong to the category PREP + Noun + PREP, even if there are more members within this category, are far less frequently used than simple prepositions.

9.

Finally, prepositions that are close to the lexical end of the cline do not undergo a real process of lexicalization, and therefore opacification, which accounts for the possible variations listed in 5. They pertain to more discursive uses, whereas prepositions that are closer to the grammatical end of the cline pertain to lexicalized uses; these are listed in the dictionary. "Grammatical" or "functional" prepositions may be found in "lexical" prepositions but only as inferior ranking constituents (see the recycling of linguistic material). As A. Borillo [2001: 154] English prepositions are thus part of a heterogeneous category, among which prepositions ranging from the least grammaticalized to the most grammaticalized may be classified. We need to bear in mind that these prepositions have lexical origins, which are more or less retrievable according to the type of prepositions. For example, the prepositional status of low-frequency complex prepositions such as for recognition of, by contrast to, in search for, at war with etc. may be questioned: are these real prepositions or merely a preposition + a noun? Moreover, low frequency complex prepositions are perceived as more lexical than high frequency complex prepositions (outside of, instead of, into (with an obvious (ortho)graphic fusion)). High frequency complex prepositions are also more lexical than simple prepositions, for which the process of opacification is complete and synonymous with loss of origin, loss of compositional meaning and morpheme boundaries. Even within this very category that is closer to the grammatical end of the cline, there is a degree going from the most transparent, such as the pair within, without, or towards, to the most grammaticalized, with a higher degree of fusion, like the monosyllabic preposition but, which results from the fusion of three morphemes: < O.E. butan, buton ʺunless, without, outside,ʺ from W.Gmc. *be-ʺbyʺ + *utana ʺfrom withoutʺ.

Conclusion

In conclusion, we would like to remind the reader that it is necessary to qualify the definitions of "preposition" in order to give an accurate picture of the subtleties of the possible linguistic realizations. Rather than opposing lexical and grammatical prepositions at all costs, what matters is to acknowledge that prepositions pertain both to the lexical and to the grammatical. This is certainly the reason why some linguists choose to use the term "semi-lexical", for if lexical means a "certain semantic content" and grammatical "devoid of semantic content", then prepositions, with the noticeable exception of of, (which is the most "colorless" of all) partly function as lexical items. However, prepositions also play a functional role, which can justify their classification as grammatical items.

Consequently, rather than two main categories of prepositions (simple and complex, weak and strong etc.), we posit that there are degrees of "prepositionality", from the more lexical to the more grammatical / functional. The traditional dichotomy between grammatical and lexical is thus questioned and has to be reconsidered. The boundary between the two types is sometimes blurred and this is even more blatant in the case of prepositions, wherever lexicalization processes are at work. against (early 12c., agenes ʺin opposition to,ʺ a southern variant of agen ʺagainʺ), + discursive (no real lexicalization, to be understood as prepositions that are not seen as single units ; Non lexicalized structures, hence possible variations) + lexicalized (lexicalization to be understood as prepositions, which come to be seen as single units and for which there are entries in the dictionary) Bibliography ARRIVÉ, Michel, GADET, Françoise & GALMICHE, Michel. La grammaire d'aujourd'hui : guide alphabétique de linguistique française. Paris : Flammarion, 1986.

along

  : a) We are teaching English in ignorance of a vast amount of basic fact.

)

  H98 1690 Now he stood still, his very appearance drawing the people around him. (preposition grammatical) (6) ACK 1392 I sat up and looked around. (adverb lexical) (7) B3G 236 It also meant that I became much more familiar with the area I lived in and the people around. (adverb lexical)

( 22 )

 22 HLD 2942 The term of the Assembly has been routinely extended, most recently in February 1991 for a period of one year. (23) AE0 3370 You've got terrible shadows under your eyes and you're very pale, my dear.ʹ (24) APT 1823 The balcony above the main door has figures of miners on either side.(25) AM6 930 The balance between a game and reality is a delicate one[…]

( 28 )

 28 ANF 30 I shut him up in my cellar with all he needed for painting and a bottle of cognac, and my maid, who was a very pretty girl, served as his model. (spatial indication) (29) CE7 924 Within six months, however, he had left the Party and set out on the road that led to the formation of the British Union of Fascists in 1932. (temporal indication) (30) FS3 614 But he must kill him, because of his father. (causal indication)

frequent prepositions in the BNC and on Google

  (O.E. andlang ʺalongside of,ʺ from and-ʺopposite, againstʺ (from P.Gmc. *andi-, *anda-from PIE *anti ʺagainst,ʺ locative singular of *ant-ʺfront, forehead;ʺ see ante) + lang ʺlongʺ (see long (adj.))), amid (late 14c., from amidde (c.1200), from O.E. on middan ʺin the middle,ʺ from dative singular of midde ʺmid, middleʺ (see midde)), among (O.E. on gemang ʺin a crowd,ʺ from gemengan ʺto mingleʺ (see mingle). Collective prefix ge-dropped 12c. leaving onmong, amang, among.), except (late 14c., from L. exceptus, pp. of excipere ʺtake out,ʺ from ex-ʺoutʺ + capere ʺto takeʺ (see capable)), for (O.E. for ʺfor, before, on account of,ʺ from P.Gmc. *fura (cf. O.S. furi, Du. voor ʺfor, before;ʺ Ger. für ʺfor;ʺ Dan. for ʺfor,ʺ før ʺbefore;ʺ Goth. faur ʺfor,ʺ faura ʺbeforeʺ)), from (O.E. fram, originally ʺforward movement, advancement,ʺ evolving into sense of ʺmovement away,ʺ from P.Gmc. *fr-(cf. Goth. fram ʺfrom, away,ʺ O.N. fra ʺfrom,ʺ fram ʺforwardʺ), corresponding to PIE *pr-(see pro)), in (O.E. in ʺin,ʺ inne ʺwithin,ʺ from P.Gmc. *in (cf. O.Fris, Du., Ger., Goth. in, O.N. i), from PIE *en-/*n (cf. Gk. en, L. in, O.Ir. in, Welsh yn-, O.C.S. on-)), E. gelic ʺlike, similar,ʺ from P.Gmc. *galikaz ʺhaving the same form,ʺ lit. ʺwith a corresponding bodyʺ (cf. O.S. gilik, O.N. glikr, Du. gelijk, Ger. gleich, Goth. galeiks ʺequally, likeʺ), a compound of *ga-ʺwith, togetherʺ + *likan ʺbodyʺ (cf. O.E. lic ʺbody,ʺ Ger. Leiche ʺcorpse,ʺ Dan. lig, Swed. lik, Du. lijk ʺbody, corpseʺ)), near (O.E. near ʺcloser, nearer,ʺ comp. of neah, neh ʺnigh.ʺ), of (O.E. of, unstressed form of aef (prep., adv.) ʺaway, away from,ʺ from P.Gmc. *af-(cf. O.N. af, O.Fris. af, of ʺof,ʺ Du. af ʺoff, down,ʺ Ger. ab ʺoff, from, downʺ), from PIE *apo-ʺoff, awayʺ (see apo-)), ʺdone with, over,ʺ from pp. of passen ʺgo byʺ (see pass (v.))), round (c.1290, from Anglo-Fr. rounde, O.Fr. roont, probably originally *redond, from V.L. *retundus (cf. Prov. redon, Sp. redondo, O.It. ritondo), from L. rotundus ʺlike a wheel, circular, round,ʺ related to rota ʺwheelʺ (see rotary)), since (c.1450, synnes, from sithenes ʺsince,ʺ from sithen (plus adverbial genitive -es), from O.E. siððan ʺthen, later, after that,ʺ originally sið ðan ʺafter that,ʺ from sið ʺafterʺ + ðan, weakened form of ðam, dative of ðaet (see that)), to (O.E. to ʺin the direction of, for the purpose of, furthermore,ʺ from W.Gmc. *to (cf. O.S., O.Fris. to, Du. too, O.H.G. zuo, Ger. zu ʺtoʺ), from PIE pronomial base *do-ʺto, toward, upwardʺ (cf. L. donec ʺas long as,ʺ O.C.S. do ʺas far as, to,ʺ Gk. suffix -de ʺto, toward,ʺ O.Ir. do, Lith. da-)), Goth. iup ʺup, upward,ʺ uf ʺon, upon, under;ʺ OHG oba, Ger. ob ʺover, above, on, uponʺ), from PIE base *upo ʺup from belowʺ (cf. Skt. upa ʺnear, under, up to, on,ʺ Gk. hypo ʺunder, below,ʺ L. sub ʺunder;ʺ see sub-)), upon (1121, from up + on, probably influenced by O.N. upp a. Distinct from O.E. uppan which merely meant ʺup.ʺ), via (1779, from L. via ʺby way of,ʺ ablative form of via ʺway, road, channel, course,ʺ of uncertain origin), except for (late 14c., from L. exceptus, pp. of excipere ʺtake out,ʺ from ex-ʺoutʺ + capere ʺto takeʺ (see capable). Adjectival function led to use as a preposition, conjunction.), inside of (1392, ynneside ʺinterior of the body,ʺ compound of inne (adv.) + side. inside of, in ref. to time, is from 1839.), in front of (c.1290, from O.Fr. front ʺforehead, brow,ʺ from L. frontem (nom. frons) ʺforehead,ʺ perhaps lit. ʺthat which projects,ʺ from PIE *bhront-, from base *bhren-ʺto project, stand out.ʺ), ahte) ʺto have, own,ʺ from P.Gmc. *aiganan ʺto possessʺ (cf. O.Fris. aga, O.N. eiga, O.H.G. eigan, Goth. aigan ʺto possess, haveʺ), from PIE *aik-ʺto be master of, possessʺ (cf. Skt. ise ʺhe owns,ʺ isah ʺowner, lord, ruler;ʺ Avestan is-ʺriches,ʺ isvan-ʺwell-off, richʺ). Sense of ʺto have to repayʺ began in late O.E. with the phrase agan to geldanne lit. ʺto own to yield,ʺ which was used to translate L. debere (earlier in O.E. this would have been sceal ʺshallʺ); by c.1175 the phrase had been shortened to simply agan, and own (v.) took over this wordʹs original sense. An original Gmc. preterite-present verb (cf. can, dare, may, etc.). New past tense form owed arose 15c. to replace oughte, which developed into ought (1).), such as (O.E. swylc, swilc from a P.Gmc. compound *swalikaz ʺso formedʺ (cf. O.S. sulik, O.N. slikr, O.Fris. selik, M.Du. selc, Du. zulk, O.H.G. sulih, Ger. solch, Goth. swaleiks), from swa ʺsoʺ (see so) + *likan ʺform,ʺ source of O.E. gelic ʺsimilarʺ (see like).), thanks to (O.E. þancian ʺto give thanks,ʺ from P.Gmc. *thankojan (cf. O.S. thancon, O.N. þakka, Dan. takke, O.Fris. thankia, M.Du., Ger. danken ʺto thankʺ), from *thankoz ʺthought, gratitude,ʺ from PIE base *tong-ʺto think, feel.ʺ For sense evolution, cf. related O.E. noun þanc, þonc, originally ʺthought,ʺ but by c.1000 ʺgood thoughts, gratitude.ʺ The whole group is from the same root as think (q.v.).), up to (O.E. up, uppe, from P.Gmc. *upp-ʺupʺ (cf. O.Fris. up; O.N. upp; Dan., Du. op; O.H.G. uf, Ger. auf ʺupʺ; Goth. iup ʺup, upward,ʺ uf ʺon, upon, under;ʺ OHG oba, Ger. ob ʺover, above, on, uponʺ), from PIE base *upo ʺup from belowʺ (cf. Skt. upa ʺnear, under, up to, on,ʺ Gk. hypo ʺunder, below,ʺ L. sub ʺunder;ʺ see sub-).

	despite (c.1300, from O.Fr. despit, from L. despectus ʺa looking down on,ʺ from despicere (see despise)), onto (1581, as on to, from on + to), unlike (c.1200, ʺNot resembling,ʺ from un-(1) ʺnotʺ + like. Cf. O.E. ungelic, O.Fris. unlik, O.N. ulikr, M.Da. ulige. Unlikely ʺnot likely to occurʺ is + lexical + grammatical
	opposite (1391, ʺplaced on the other side of (something),ʺ from O.Fr. oposite attested from late 14c. (cf. O.N. ulikligr, M.Da. uligelig)), down (O.E. ofdune ʺdownwards,ʺ from dune ʺfrom the hill,ʺ dat. of dun ʺhillʺ (see down (n.2))), (13c.), from L. oppositus, pp. of opponere ʺset againstʺ (see opponent)), up (O.E. up, uppe, from P.Gmc. *upp-ʺupʺ (cf. O.Fris. up; O.N. upp; Dan., Open class Closed class
	by (O.E. be (unstressed) or bi (stressed), from P.Gmc. *bi ʺaround, aboutʺ (cf. during (late 14c., prp. of obsolete verb duren ʺto last, endureʺ (late 13c.), from O.Fr. durer, from L. durare ʺendure.ʺ), inside (1392, ynneside ʺinterior of the body,ʺ compound of inne (adv.) + side), into (O.E. into, originally in to), like (ʺhaving the same characteristics or qualitiesʺ (as another), M.E. shortening of O.off (by c.1200 as an emphatic form of O.E. of (see of), employed in the adverbial use of that word), outside (1505 (n.), ʺouter side,ʺ from out + side (q.v.)), over (O.E. ofer, from P.Gmc. *uberi (cf. O.S. obar, O.Fris. over, O.N. yfir, O.H.G. ubar, Ger. über, Goth. ufar ʺover, aboveʺ), from PIE *uper (see super-)), past (c.1300, through (c.1300, metathesis of O.E. þurh, from W.Gmc. *thurkh (cf. O.S. thuru, O.Fris. thruch, M.Du. dore, Du. door, O.H.G. thuruh, Ger. durch, Goth. þairh ʺthroughʺ), from PIE base *tr-ʺthroughʺ (cf. Skt. tirah, Avestan taro ʺthrough, beyond,ʺ L. trans ʺbeyond,ʺ O.Ir. tre, Welsh tra ʺthroughʺ)), toward(s) (O.E. toweard ʺin the direction of,ʺ prepositional use of toweard (adj.) ʺcoming, approaching,ʺ from to (see to) + -weard, from P.Gmc. *-warth, from PIE *wert ʺturnʺ (see -ward)), under (O.E. under, from P.Gmc. *under-(cf. O.Fris. under, Du. onder, O.H.G. untar, Ger. unter, O.N. undir, Goth. undar), from PIE *ndhero-ʺlowerʺ (cf. Skt. adhah ʺbelow;ʺ Avestan athara-ʺlower;ʺ L. infernus ʺlower,ʺ infra ʺbelowʺ)), phrase, often followed by a subordinate clause introduced by that or Most Prépositions BNC Prépositions Google Of 3049246 In 25360000000 To 2599205 Of 25360000000 In 1931797 To 25360000000 For 880702 For 25320000000 With 659799 By 24240000000 As 653137 With 16600000000 At 522790 From 16000000000 By 513362 At 15940000000 But 446614 As 15730000000 From 425917 About 13210000000 More lexical, hence a more semantic role More grammatical(ized), hence a more functional role and therefore more specific roles (e.g. verbs governing a given preposition) Fairly specific meaning Fairly ill-defined, vague, broad meaning, (see desemanticization, semantic bleaching, semantic attrition) Perceptibility of the compositional meaning Loss of the compositional meaning Morphologically long items Morphologically short items Some flexibility in the use of complex prepositions. Therefore, it remains possible to insert elements, hence the possibility to separate or alter the elements. Distributional properties are blocked, hence impossibility to separate or alter elements. (see process of decategorialization and automatization due to syntactic reanalysis. The structure is perceived as a single unit and not made up of several distinct elements). Strong forms Phonological attrition or erosion Low frequency High frequency (process of Du. op; O.H.G. uf, Ger. auf ʺupʺ; because of (c.1305, bi cause ʺby cause,ʺ modeled on Fr. par cause. Originally a On 731142 On 25230000000 generalization)
	Du. bij, Ger. bei ʺby, at, nearʺ), from *umbi, (cognate with second element in PIE *ambhi ʺaround,ʺ cf. Skt. abhi ʺtoward, to,ʺ Gk. amphi-ʺaround, underneath (O.E. underneoðan, from under + neoðan ʺbelowʺ (see why.) Up 207709 Up 12730000000 on (O.E. on, unstressed variant of an ʺin, on, into,ʺ from P.Gmc. (cf. Du. aan, Ger. an, Goth. ana ʺon, uponʺ), from PIE base *ano ʺonʺ (cf. Avestan ana beneath)), due to (mid-14c., from O.Fr. deu, pp. of devoir ʺto owe,ʺ from L. debere ʺto Out 197273 Over 3080000000 aboutʺ)), ʺon,ʺ Gk. ana ʺon, upon,ʺ L. an-, O.C.S. na, Lith. nuo ʺdown fromʺ). Also oweʺ (see debt)), About 192000 Out 2750000000
	used in O.E. in many places where we would now use in.)

around (c.1300, from phrase on round), as (late 12c., worn-down form of O.E. alswa ʺquite soʺ (see also)), at (O.E. aet, common P.Gmc. (cf. O.N., Goth. at, O.Fris. et, O.H.G. az), from PIE *ad-ʺto, near, atʺ (cf. L. ad ʺto, towardʺ Skt. adhi ʺnearʺ)), before (O.E. beforan, from P.Gmc. *bi-ʺbyʺ + *forana ʺfrom the front,ʺ adv. derivative of *fora (see for)), behind (O.E. behindan, from bi ʺbyʺ + hindan ʺfrom behindʺ (see hind)), below (early 14c., biloogh, from be-ʺbyʺ + logh, lou, lowe ʺlow.ʺ Apparently a variant of earlier a-lowe (influenced by other advs. in be-, cf. before)), beneath (O.E. be ʺbyʺ + neoðan ʺbelow,ʺ originally ʺfrom below,ʺ from P.Gmc. *niþar ʺlower, farther down, downʺ (see nether)), beside (O.E. be sidan ʺby the side ofʺ (only as two words), from sidan dative of side (q.v.)), between (O.E. betweonum, from bi-ʺbyʺ + tweonum dat. pl. of *tweon ʺtwo eachʺ (cf. Goth. tweih-nai ʺtwo eachʺ)), beyond (O.E. begeondan ʺfrom the farther side,ʺ from be ʺbyʺ + geond ʺyonderʺ (prep.), from P.Gmc. *jandana), but (O.E. butan, buton ʺunless, without, outside,ʺ from W.Gmc. *be-ʺbyʺ + *utana ʺfrom without.ʺ), with (O.E. wið ʺagainst, opposite, toward,ʺ a shortened form related to wiðer, from P.Gmc. *withro-ʺagainstʺ (cf. O.S. withar ʺagainst,ʺ O.N. viðr ʺagainst, with, toward, at,ʺ M.Du., Du. weder, Du. weer ʺagain,ʺ Goth. wiþra ʺagainst, oppositeʺ), from PIE *wi-tero-, lit. ʺmore apart,ʺ from base *wi-ʺseparationʺ (cf. Skt. vi, Avestan vi-ʺasunder,ʺ Skt. vitaram ʺfurther, farther,ʺ O.C.S. vutoru ʺother, secondʺ)), within (O.E. wiðinnan, lit. ʺagainst the inside,ʺ see with + in), without (O.E. wiðutan, lit. ʺagainst the outsideʺ (opposite of within), see with + out) Complex prepositions according to (late 14c., ʺagreeing,ʺ pp. adj. and adv. from accord (q.v.). According to, lit. ʺin a manner agreeing withʺ is attested from mid-15c.), apart (late 14c., from O.Fr. à part ʺto the side,ʺ from L. ad ʺtoʺ + partem accusative of pars ʺa sideʺ), from (O.E. fram, originally ʺforward movement, advancement,ʺ evolving into sense of ʺmovement away,ʺ from P.Gmc. *fr-(cf. Goth. fram ʺfrom, away,ʺ O.N. fra ʺfrom,ʺ fram ʺforwardʺ), corresponding to PIE *pr-), in spite of (c.1300, shortened form of despit ʺmaliceʺ (see despite). Corresponding to M.Du. spijt, M.L.G. spyt, M.Swed. spit. Commonly spelled spight c.1575-1700. The verb is attested from c.1400. Phrase in spite of is recorded from c.1400.), instead of (< OE in stede of 'in place of'), near to (O.E. near ʺcloser, nearer,ʺ comp. of neah, neh ʺnigh.ʺ Influenced by O.N. naer ʺnear,ʺ it came to be used as a positive form c.1250, and new comp. nearer developed 1500s (see nigh). Originally an adv., but now supplanted in most such senses by nearly; it has in turn supplanted correct nigh as an adjective. out of (O.E. ut, common Gmc. (cf. O.N., O.Fris., Goth. ut, Du. uit, Ger. aus), from PIE base *ud-ʺup, up awayʺ (cf. Skt. ut ʺup, out,ʺ uttarah ʺhigher, upper, later, northern;ʺ Avestan uz-ʺup, out,ʺ O.Ir. ud-ʺout,ʺ L. usque ʺall the way to, without interruption,ʺ Gk. hysteros ʺthe latter,ʺ Rus. vy-ʺoutʺ)., outside of (1505 (n.), ʺouter side,ʺ from out + side (q.v.). The adj. is attested from 1634; the prep. from 1826; the adv. from 1813.), owing to (O.E. agan (pt.

See Camille Debras's article for further details.

This role will not be dealt with in this article.

A "joncteur" is a kind of purely syntactic link-word, without any semantic content, a preposition that is almost empty because of its use rather than because of its meaning.

We will only mention what appeared to us as the most relevant examples, but the reader may find the etymology of simple and complex prepositions in the appendix.

See the diachronic remarks on simple prepositions in the first part, such as about << abutan, on the outskirts of.

A more comprehensive list is to be found in the appendix.

Our emphasis.

Appendix