Joël Agnus

Nicolas Chaillet

Cédric Clévy

Sounkalo Dembélé

Michaël Gauthier

Yassine Haddab

Guillaume J Laurent

Philippe Lutz
email: philippe.lutz@femto-st.fr

Nadine Le Fort-Piat

Kanty Rabenorosoa

N Piat

M Rakotondrabe

B Tamadazte

Robotic microassembly and micromanipulation at FEMTO-ST

Keywords: Microgrippers, Microassembly, Micromanipulation, Microrobotic automation, MEMS assembly

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Introduction

Until now, miniaturization was driven by a general diminution of the volume of the product (e.g. cell phones). Currently, the major objective of the miniaturization is to increase the number of functionalities in a product whose volume is mostly constant (e.g. smart phone). In the future, the functions realized using micro or nanotechnologies would be assembled and packaged in order to build integrated multifunctional products or even intelligent products. The hybridization of technologies in micronanosystems is consequently a major stake for the next ten years.The application fields of these future products are typically the networks of sensors for environmental monitoring or the diagnostic and drug delivery done by intelligent systems embedded in human body. Industrial robotics at this scale should be especially studied in order to propose handling, positioning solutions for automatic assembly of these new generation systems. Since 1995, the research team from Besanc ¸on, France, has performed significant research activities in the field of micro and nano robotics. These activities were started since in the LAB-laboratory (Laboratoire d'Automatique de Besanc ¸on) and are being continued at FEMTO-ST, where the LAB is integrated in 2008 as the AS2M department (Automatic Control and Micro-Mechatronic Systems Department).

FEMTO-ST/AS2M activities deal with the micromanipulation and microassembly issues. More precisely, FEMTO-ST robotic motions, perception, control and manipulation at the microscale and also new activities at the nanoscale. It corresponds to various and multidisciplinary scientific issues:

-Microrobotic and adaptronic systems: systems for feeding, carrying, gripping, micrometer size and microfabricated robotics, strategies for microassembly. Some examples are in [START_REF] Chen | Microfabricated bistable module for digital microrobotics[END_REF][START_REF] Lopez-Walle | Principle of a submerged freeze gripper for micro-assembly[END_REF][START_REF] Rakotondrabe | Development, modeling, and control of a micro-/nanopositioning 2-DOF stickslip device[END_REF], -Advanced control of dynamic and complex systems: modelling and control of microactuators microsystems, and smart materials, of discrete or continuous distributed systems, control by exteroceptive sensors notably by vision. Some examples of our works are given in [START_REF] Boudaoud | Modeling and optimal force control of a nonlinear electrostatic microgripper[END_REF][START_REF] Delettre | Robust control of a planar manipulator for flexible and contactless handling[END_REF][START_REF] Gauthier | Original hybrid control for robotic structures using magnetic shape memory alloys actuators[END_REF][START_REF] Grossard | Modeling and robust control strategy for a control-optimized piezoelectric microgripper[END_REF][START_REF] Khadraoui | Interval modeling and robust control of piezoelectric microactuators[END_REF][START_REF] Kharboutly | Predictive control of a micro bead's trajectory in a dielectrophoresis-based device[END_REF][START_REF] Rakotondrabe | Force control in piezoelectric microactuators using self scheduled HINF technique[END_REF][START_REF] Rakotondrabe | Quadrilateral modelling and robust control of a nonlinear piezoelectric cantilever[END_REF][START_REF] Rakotondrabe | Complete open loop control of hysteretic, creeped and oscillating piezoelectric cantilever[END_REF][START_REF] Rakotondrabe | Dynamic displacement self-sensing and robust control of cantilevered piezoelectric actuators dedicated to microassembly tasks[END_REF][START_REF] Rakotondrabe | Robust feedforward-feedback control of a nonlinear and oscillating 2-DOF piezocantilever[END_REF], -Micromanipulation and microassembly: characterization of the interactions in the microworld, strategies for microhandling based on physical principles relevant at this scale (the case of the liquid environment has been particularly studied) [START_REF] Dong | A novel integrated micro-force measurement system for plane-plane contact research[END_REF][START_REF] Gauthier | Capillary force disturbances on a partially submerged cylindrical micromanipulator[END_REF][START_REF] Gauthier | Forces analysis for micromanipulations in dry and liquid media[END_REF][START_REF] Rabenorosoa | Measurement of pull-off force for planar contact at the microscale[END_REF], -Perception and measurement: measure of microforces and artificial vision [START_REF] Abadie | Modeling and experimentation of a passive low frequency nanoforce sensor based on diamagnetic levitation[END_REF][START_REF] Dembele | A trifocal transfer based virtual microscope for robotic manipulation of MEMS components[END_REF][START_REF] Tamadazte | A multicale calibration of a photon video microscope for visual servo control[END_REF][START_REF] Tamadazte | Cad model based tracking and 3d visual-based control for MEMS microassembly[END_REF].

Figure 1 summarizes the major addressed issues studied at FEMTO-ST/AS2M. This paper summarizes the activities of the French institute FEMTO-ST in micromanipulation and micro-assembly. First section is devoted to present some tools for micromanipulation and microassembly which have been developed. In the following section is presented automatic 3D assembly using visual servoing on 400 microns objects. An other way to assemble automatically microparts is to use force control as presented in Section 4. Teleoperation of the assembly of 40 microns objects are detailed in Section 5 before a presentation of the future challenges in micronanoassembly.

Tools for micromanipulation and microassembly

Microgrippers made at FEMTO-ST

The microgrippers, developed at FEMTO-ST [START_REF] Lit | A four-degree-offreedom microprehensile microrobot on chip[END_REF], are based on two degrees of freedom (DOF) bimorphs that allow open-and-close motion as well as up-and-down motion (Fig. 2). Each finger is able to move independently from the other in two orthogonal directions. This microgripper, named MMOC (Microprehensile Microrobot On Chip) has therefore 4 DOF and is able to grip, hold and Fig. 2 Mobilities of the microgripper release submillimetric-sized objects up to several micrometers. The up-and down motion can be useful for fine motion, for release strategies of objects by crossing the fingers or for insertion of microparts and is particularly convenient to align the finger-tips if they are misaligned after the microfabrication processes and assembly.

The principle of one finger is based on a piezoelectric cantilever with local electrode [START_REF] Lit | The constitutive equations of a piezoelectric duo-bimorph[END_REF], named duo-bimorph (Fig. 3). Such a microgripper presents at the end of the finger tips for ±100 V a 320 µm stroke for open/close motion and a 200 µm stroke for up/down motion.

Several packaging have been designed from 2002 to 2012 (Fig. 4): the first one, built to illustrate the 'Microrobot on chip' concept (Fig. 4a) has rapidly given way to a more robust plug-and-use microgripper integrated in a LEMO ® connector (Fig. 4b) for micromanipulation of objects which dimensions are between 100 µm and 1 mm. The version given in Fig. 4c has been designed for compactness reasons to embed the microgripper on a KLEINDIECK's robot (MM3) for micromanipulation in a Scanning Electron Microscope (SEM). The last version (Fig. 3d) allows several developments, including finger-tips improvement and integration of position and force sensors. It is able to manipulate objects which sizes are between 10 and 100 µm.

Beyond its performances and its four degrees of freedom that make this FEMTO-ST microgripper particularly efficient, the success of a micromanipulation is often conditioned by the end-effectors. In most of the microgrippers, actuators and end-effectors are both made on the Author'spersonal copy Fig. 4 FEMTO-ST microgrippers along the years same element. The microgripper developed at FEMTO-ST is composed of an actuator and a connection system to fix end-effectors. The two piezoelectric actuators have two spatulas (Fig. 3) where different kinds of finger-tips can be fixed. An automated fixing system, with removable thermal glue has already been studied [START_REF] Agnus | Silicon end-effectors for microgripping task[END_REF]. This microgripper is then particularly flexible to support any end-effector design.

Indeed, the size, the shape, the materials in contact and the environment conditions are some important parameters to achieve a good micromanipulation. These parameters must be adapted to the objects manipulated. The finger-tips material must be also choice for the expected application (conductive finger-tips, transparent, biocompatible, etc.).

We designed several end-effectors to match each application. For instance, the first prototypes were equipped with Nickel finger-tips with 200 µm in thickness microfabricated by a LIGA-UV process. Figure 5 shows different shapes. They allowed to easily handle objects between 100 µm and more. The environment conditions are also critical at this scale because of the complex force gradients due to adhesion forces (surface tension forces, electrostatic forces and Van der Waals atomic forces). Below 100 µm, many problems arise, especially during the release phase, due to the surface forces between the end-effectors and the manipulated object. Specific silicon end-effectors able to grasp objects between 10 and 100 µm have been designed (Fig. 6) [START_REF] Agnus | Silicon end-effectors for microgripping task[END_REF]. They were microfabricated mainly with DRIE process on SOI wafer with 10 µm for the handle thickness. The gap and the alignment of the tips are provided by breakable-parts broke after gluing the pair of fingers on the spatulas of the actuators (Fig. 6a andb). Figure 6d ande show respectively the manipulation of a 20-µm silicate grain and 100-µm glass sphere. Several research activities in the field of microgripping tools are currently under development concerning in particular some sensorized finger-tips based on piezoresitive effect. It measures grasping forces and enables the control in force and/or position of the fingers, based on self-sensing technique [START_REF] Ivan | Current integration force and displacement self-sensing method for cantilevered piezoelectric actuators[END_REF][START_REF] Ivan | Quasi-static displacement self-sensing method for cantilevered piezoelectric actuators[END_REF]. The presented FEMTO-ST microgripper is now commercially available for purchase at the start-up PERCIPIO ROBOTICS (http://www.percipio-robotics.com) end of the research team. The so-called PiTweez (Fig. 7) is able to mechanically grasp micro parts between 100 µm and 1 mm. PERCIPIO-ROBOTICS proposes various options with high resolution sensors to increase the accuracy of finger positioning or can design any fingers on demand with a great range of materials according to the user needs. For instance, Fig. 8 shows polymer finger-tips designed by PERCIPIO-ROBOTICS to manipulate objects measuring a few tens of micrometers.

The 2 DOF high stroke and high resolution microrobot: TRING-module

The manipulation and assembly of small components and MEMS may require a system that is able to perform a long distance and a high resolution/precision at the same time. Picking a small component from one location, transporting and placing it in another location for assembly needs that the transportation system have micrometric or submicrometric precision and often more than a ten of millimeters of distance to cover. A way to reach such performances is the use of stepper microrobots often based on stick-slip motion principle. In this section, we present the TRING-module stick-slip microrobot and its use for pick-and-place tasks in microassembly of MEMS at FEMTO-ST.

Kinematic and principle of motion of the TRING-module

The TRING-module is a microrobot that has 2 DOF: linear motion along the axis of its support and angular motion about the same axis (Fig. 9). The axis that supports the microrobot is a cylindrical glass. A cantilever is placed at the extremity of the TRING-module and is used as endeffector that facilitates the handling of the manipulated objects. Developed in the previous work [START_REF] Rakotondrabe | Development, modeling, and control of a micro-/nanopositioning 2-DOF stickslip device[END_REF], its principle of movement is based on the stick-slip functioning and uses piezoelectric microactuators described in [START_REF] Bergander | Monolithic piezoelectric push-pull actuators for inertial drives[END_REF]. The main features of the TRING-module are its theoretical unlimited stroke both in rotation and in translation, the high resolution that it can offer and its good dexterity (rotation and translation).

Performances of the TRING-module

As a stick-slip microrobot, the TRING-module can perform the high stroke motion by step-by-step. This is obtained by applying a sawtooth voltage to the piezoelectric microactuators. The speed of the microrobot is proportional to both the frequency f ss and the amplitude U ss of the voltage, while the step-magnitude depends principally on the amplitude [START_REF] Rakotondrabe | Voltage/frequency proportional control of stick-slip microsystems[END_REF]. The high stroke motion is usually employed for a coarse positioning in a large distance. It is also possible to work within a step (sub-step). This sub-step motion, usually employed for fine positioning, is obtained by applying a voltage with limited slope to the microactuators. In substep motion, the resolution of the TRING-module is greatly amplified, although the limited range of motion. The stepby-step motion and the sub-step motion can be managed and switched automatically by using the closed-loop control law developed in [START_REF] Rakotondrabe | Voltage/frequency proportional control of stick-slip microsystems[END_REF]. The principal advantage of the latter control law is the obtention of high speed and high precision at the same time without manual reconfiguration of the controller. 1 summarizes the performances of the TRINGmodule alone without closed-loop control [START_REF] Rakotondrabe | Voltage/frequency proportional control of stick-slip microsystems[END_REF][START_REF] Rakotondrabe | Development, modeling, and control of a micro-/nanopositioning 2-DOF stickslip device[END_REF]. It clearly shows the high performances, in particular in term of resolution and stroke, of the microrobot that are well suited to the requirement in microassembly in general.

Author'spersonal copy

Pick-and-place tasks based on two TRING-modules

To perform pick-and-place tasks in microassembly, the TRING-module can be used in different ways. One of the main interesting ways is to employ two TRING-modules in the same axis. As pictured in Fig. 10, the two microrobots form a microgripper with variable gap between their endeffectors. This scheme allows the manipulation of microobjects and objects of various sizes. Additionally to that, the transport in large distance and with a high resolution is possible thanks to the performances of the microrobots.

In the configuration pictured in Fig. 10, we have proposed to control on force the first TRING-module and to control on position the second one. The main advantage is that additionally to the precise positioning, the manipulation force and the insertion force (during the assembly) are also commanded in such a way that the destruction of the objects is avoided. It also enables the good gripping of the objects. A pick-and-place task for microassembly based on the two TRING-modules can be splitted into several sub-tasks. The Fig. 10 Two TRING-modules used for pick-and-place tasks in microassembly objective of splitting into sub-tasks is to facilitate the control of the two microrobots. They are as follows.

-Approach: the two microrobots approach near the object to be manipulated. They are both controlled on position in this sub-task. -Picking: when the microrobots are near the object, one of the two TRING-modules is switched into force control such that its approach is stopped until a given reference force. When this reference force (also called manipulation force) is reached, the picking sub-task is finished. -Transport: after the picking, the object is transported by the two TRING-modules from its initial location to another location. The microrobot controlled on position has as reference input the final location while the microrobot controlled on force has as reference input the manipulation force. -Place: when reaching the final location, the force reference given to the microrobot controlled on force is set to zero. The aim is to release slowly the object. -Moving away: finally, the two microrobots move away from the object in order to completely release the latter. For that, they are controlled on position and their reference inputs correspond to their initial positions.

In Fig. 11a, we present the positions of the two TRINGmodules performing a pick-and-place task, x g being the position of the left microrobot while x d that of the right one. All along the task, the left microrobot is controlled on position. On the other hand, the right microrobot is controlled on force between the picking sub-task and the place sub-task.

Author'spersonal copy

The different experimental results demonstrated the interesting advantages that bring the TRING-module microrobot in microassembly of small objects. In particular, different sizes of objects can be manipulated, their transport from a location to another one for assembly is large and can be done very precisely, and the manipulation force can be controlled in order to avoid the objects destruction and to obtain a good gripping. Finally, the high dexterity (2 DOF) of the microrobot can also be very benefit for pick-andplace and manipulation in the space, instead of only in the plane.

Smart surface

The manipulation without contact is the best way to manipulate clean or delicate objects such as silicon wafers, glass sheets, solar cell or flat foodstuffs. A new principle of aerodynamic traction using induced air flow is proposed to transport and position objects without contact [START_REF] Delettre | 2-DOF contactless distributed manipulation using superposition of induced air flows[END_REF]35]. The induced air flow surface is a 120 mm × 120 mm square surface drilled by two kinds of holes (cf. Fig. 12). The object is maintained in constant levitation thanks to the air cushion created by the airflow that comes through a common air inlet. The novelty is that the object can be moved on the table by generating strong vertical air jets through specific holes of the surface. Theses vertical air jets create an induced air flow in the surrounding fluid that pulls the object towards the nozzle (cf. Fig. 12. Each nozzle is driven by an independent solenoid valve. Thus an object can be transported by opening successively the appropriate valves.

The experimental setup for the induced air flow surface is composed of pressurized air supply, two pressure regulators, the set of 56 solenoid valves and its control system, Fig. 12 The induced air flow surface and a computer for vision processing. Figure 13 describes the complete hardware configuration. The induced air flow surface is put on a mechanical platform to adjust its equilibrium position. Default settings for operating pressures are 15 kPa for levitation and 500 kPa for traction. The valves are independently actuated through a multi-channel digital output board (NI USB-6509) and a 5 V/ 24 V amplifier circuit. A camera is used to grab video frames of the surface of the manipulator. The image processing is done by a computer at the rate of 60 frames per second (the software is cvLink).

2 DOF position control

A control architecture based on two PID controllers is proposed (see Fig. 14). One PID controls the x-position of the object and the other one controls its y-position. The controllers give respectively the number of y-directed and x-directed lines of air jets to enable and their position(s) relative to the object.

The PID controllers are tuned with the same coefficients, as the distance between two nozzles along the two directions is the same (16 mm). The "X pattern" and "Y pattern" blocks calculate the distribution map of the 56 traction nozzles on the surface. They give the position of the nozzles to open depending on the number of y-oriented lines and x-oriented lines to enable and the position of the object. The OR block combines the two patterns using the logical or operator in order to send a unique pattern to the system corresponding to the air jets to enable. The proportional, integral and derivative coefficients of both PID controllers are respectively: KP = 2, KI = 0.15 and KD = 1. They have been tuned by trial-and-error in previous work [START_REF] Delettre | 2-DOF contactless distributed manipulation using superposition of induced air flows[END_REF].

Experimental results

Results are shown in Fig. 15. The measured position of the object is compared to the simulated one. The experimental settling time is about 1.5 s. Small overshoot (less than 5 %) appears sometimes because of the discretization of the control signal and the minimal distance of 8 mm between the edge of the object and the nearest sink. The final position of the object varies in a maximal range of 100 µm. We have also experienced tracking: results are shown in Fig. 16. The performances are quite good, but we can note a tracking error of less than 2 mm for a speed motion value of 5.03 mm/s. Performances in tracking could be improved adapting controller to this aim. The PID controllers robustness has been evaluated using other objects: the system is stable and gives good performances for different objects.

Conclusion and future works on the smart surface

The described new contactless transport system for delicate and clean products may be implemented in several industrial production processes, such as semiconductor manufacturing, solar cell production or food industry. The manipulation and object position control have been experimented on the [START_REF] Dejeu | Reducing the adhesion between surfaces using surface structuring with PS latex particle[END_REF] Target 3D structure at macroscale device and gives good performances. Robust controllers has been also implemented on the system to guaranty the stability of the closed loop, to deal with the non linearity of the system and with the different shapes of objects [START_REF] Delettre | Robust control of a planar manipulator for flexible and contactless handling[END_REF]. In the future, more complex tasks could be achieved such as 3-DOF positioning, trajectory following, part sorting, etc. We also prospect to miniaturize the device in order to adapt the manipulation principle to millimeter-sized objects (useful in pharmaceutical or watchmaker industries).

3D microassembly using visual servoing

Application

The application studied is the assembly of five parts by their U-grooves to get stables 3D structures without any use of glue (Fig. 17). The parts and their grooves measure 400 µm × 400 µm × 100 µm ± 1.5 µm and 100 µm× 100 µm × 100 µm ± 1.5 µm respectively leading to an Fig. [START_REF] Delettre | 2-DOF contactless distributed manipulation using superposition of induced air flows[END_REF] Target 3D structure at macroscale Author'spersonal copy assembly clearance ranging from -3 and 3 µm. It is a test structure that highlights most of the problems of 3D assembly, notably the need of precision in the control of robot dedicated to the application. This is nothing but the generalization of the assembly of two parts, A and B for example. The objective is then to automatically insert a groove of B into a groove of A by means of visual servoing. That objective may be divided into three basic tasks that should be performed in the following sequence: positioning of A at the assembly place (task#1), positioning of B at the insertion place (task#2) and vertical insertion of B into A (task#3) (Fig. 18).

The setup used is positioned inside a controlled environment on a vibration-free table (Fig. 19). It comprises a 5 DOF robotic systems distributed into two robots: a xyα robot and a zϕ robot. The former system (positioning table) is equipped with a compliant support and enables positioning of parts in horizontal plane. The latter system (manipulator) supports the gripper and enables vertical and spatial orientation of microparts. The microhandling system is a 2-finger gripper with 4 DOF (2 per finger) as described in [START_REF] Agnus | Overview of microgrippers and design of a micromanipulation station based on MMOC microgripper[END_REF]. The imaging system comprises two photon videomicroscopes, but only the one positioned at an angle of π/ 4 rad from horizontal plane is used in order to ensure the best perspective view during the assembly tasks. According to the references [START_REF] Ammi | Haptically generated paths of an AFM-based nanomanipulator using potential fields[END_REF][START_REF] Figl | A fully automated calibration method for an optical see-through head-mounted operating microscope with variable zoom and focus[END_REF][START_REF] Tamadazte | A multiscale calibration of a photon video microscope for visual servo control: application to micromanipulation[END_REF][START_REF] Zhou | Calibration of a parametric model of an optical microscope[END_REF] it can be described by the linear perspective model whose parameters are determined using a 2D calibration rig.

Developed solution

Let R c , R A , R A * , R B , R B * 1 and R B * 2 be the frame attached to the camera (i.e. the videomicroscope), the current and final frames of the micropart A, the current, insertion and

Author'spersonal copy

They are obtained either in tele-operated mode (using a joystick) or directly from the CAD model. Let R F be the base frame of the workcell. The homogeneous transformation between the camera frame R c and the workcell frame R F is noted F M A and is computed for each object pose.

For each task the regulation to zero of the error e defined from i M * i consists of choosing s = ( F t i , θu) as the current 3D pose and s * = ( F t i * , 0) as the desired pose of the micropart i, respectively:

e = F t i -F t i * θu (1)
The corresponding control law defined by the exponential decrease of the error is then:

v ω F = -λ I 3x3 0 3x3 0 3x3 J -1 ω (s -s * ) = -λ F t i -F t i * F R i θu (2)
The task 1 involves the control of the xyα table as:

⎛ ⎜ ⎝ v x v y ω α ⎞ ⎟ ⎠ F = -λ 1 ⎛ ⎜ ⎝ F t x -F t x * F t y -F t y * F R A θu α ⎞ ⎟ ⎠ (3)
The task 2 involves the control of the xyα table as: The task 3 involves the control of the zϕ manipulator as:

⎛ ⎜ ⎝ v x v y ω α ⎞ ⎟ F = -λ 2 ⎛ ⎜ ⎝ F t x -F t x * F t y -F t y * F R B θu α ⎞ ⎟ ⎠ (4)
v z ω ϕ F = -λ 3 F t z -F t z * F R A θu ϕ ( 5
)
The terms λ, λ 1 , λ 2 and λ 3 are the gains enabling the modulation of the decrease speed.

Results and discussions

Figure 21 shows some SEM (scanning electron microscope) images of the final assembly. The obtained mechanical play is about 3 µm showing the relevance of the tracking to deliver high quality pose measurement compatible with microassembly. The final positioning and orientation errors are 3.5 µm and 0.3 × 10 -2 rad, respectively.

The approach works despite partial occlusions of parts and blurred images (because of the small depth of field of the microscope).

The assembly is performed successively 10 times, it takes an average of 41 s with a standard deviation of 3 s.

Figure 22 shows some images of the final assembly of five parts and some steps: a right and stable structure is obtained without any use of solidaring effect.

Microassembly of MOEMS using force control

Force guided micro-assembly tasks based on active gripping

Using force control to achieve micro-assembly processes is a relevant but complex approach. On the one hand, force Fig. 23 Guiding task: a micro-object is held between two fingers of a microgripper and guided in the rail sensing brings high dexterity which is all the more important at the micro scale than macro one: Indeed micro scale assembling suffers from surface force predominance, difficulties of other sensing alternatives (vision are huge sensors for example) but also lack of knowledge. On the second hand, force sensors have to be very small to be closely integrated to the contacts (handled micro-object and fingers of the microgripper example) to ensure good quality of measurement and to measure forces of some hundreds of Micro-Newtons. Very few technologies are today available to enable such sensors development.

Based on those statements, two force sensors from femtotools (Switzerland) were integrated to form a microgripper (Fig. 23). This microgripper thus provides the measured contact force between finger 1 and the components but also between finger 2 and the same component. Such a microgripper can be used to perform automated cycles including pick, motions and place tasks. Figure 23 displays the experimental set-up used to perform a guiding task (guiding of the micro-object along a rail). During such a task, contacts between the micro-object and the rail happen when moving the microgripper along the rail axis (X). Contact forces can be estimated through force sensors and a behavioral model of the whole microgripper (force sensors, microobject subjected to a lateral (Y) force) [START_REF] Rabenorosoa | Study of forces during micro-assembly tasks using two-sensingfinger grippers[END_REF]. Based on these estimations, the force control along Y is ensured [START_REF] Rabenorosoa | Active force control for robotic micro-assembly: application to guiding tasks[END_REF]. Figure 24 displays the forces and positions during such a guiding task. Based on this principle, automated guiding tasks based on force control were ensured for the first time with good stability and robustness [START_REF] Rabenorosoa | Hybrid force/position control applied to automated guiding tasks at the microscale[END_REF][START_REF] Rabenorosoa | Active force control for robotic micro-assembly: application to guiding tasks[END_REF].

Assembled micro-optical benches

Micro-assembly enables to combine in the plane or out of plane several chips issued from different and incompatible microfabrication processes. This approach is particularly interesting in the field of MOEMS because it enables to combine basic optical components issued from dedicated microfabrication processes and then conducts to a product with good optical properties. 1) is the estimated contact force between micro-object and rail and ( 3) is the positioning of the micro-object along the rail the present case, active (based on piezoelectric material) microgripping is used which is an extremely interesting approach because it enables to adapt the relative position of two components during the assembly process (through accurate control) but also to ensure high contact forces in a reversible way. A micro-assembly station has been developed (Fig. 25) to ensure the assembly of RFS-MOB (Reconfigurable Free Space Micro-Optical Bench). RFS-MOB is composed of a set of several kinds of Silicon components that have been designed to be easily and accurately Fig. 26 Assembled RFS-MOB: b Every holder possesses one optical functionality and is assembled onto a substrate. Its positioning accuracy is ensured thanks to a V-groove system whereas its holding is done by springs. a Such elementary assemblies can be combined onto the substrate to achieve various and complex optical functionalities manipulated and assembled onto a baseplate [START_REF] Bargiel | Towards micro-assembly of hybrid MOEMS components on a reconfigurable silicon free-space micro-optical bench[END_REF] (Fig. 26). Each holder possesses one optical property (some are micromirrors, others have ball lens or beam splitter for example). Assembly of each holder onto the substrate is done using an active (piezo driven) microgripper. Figure 27 Displays one example assembled RFS-MOB comprising 3 holders assembled onto a substrate [42].

Positioning accuracy achieved

Previous sections shown that complex micro-assemblies can be performed. Nevertheless, obtaining good and suitable positioning accuracy is at the same time a important challenge and requires information from an optical performances point of view. To ensure the best positioning accuracy, a specific V-Groove design has been proposed. Each holder has two male V-grooves perfectly fitting with female V-rails fabricated into the baseplate (Fig. 26b). A system based on small springs then enables to hold the holder onto the baseplate once micro-assembly performed.

To characterize the positioning accuracy of one holder relative to substrate, a laser based scanning is performed after micro-assembling (Fig. 28) [42]. The gripping principle used being based on active gripping, it is then possible to adapt the position of the holder to improve its positioning accuracy. Several sets of micro-assembling processes were performed [START_REF] Bargiel | Technology platform for hybrid integration of MOEMS on reconfigurable silicon micro-optical table[END_REF]. During each set, ten different positioning were performed and shown that a positioning accuracy better than the micron (along X) and better than 0.1 • around Y and Z can be ensured.

Teleoperated assembly of 40 microns objects

The last category of works deals with smaller object whose size is between 10 to 100 microns. At that scale adhesion cannot be neglected and should be taken into account in the design of handling strategies. We are proposing a new reliable and reversible method to position micro-object on a substrate. The principle is an hybrid strategy between adhesion manipulation and gripping. It is based on a hierarchy of forces. In one hand, to guarantee object's release, the adhesion force between object and substrate must be higher than the adhesion force between object and gripper along the normal vector n of the substrate (see in Fig. 29a):

F adhesion object-substrate
F adhesion object-gripper [START_REF] Bargiel | Technology platform for hybrid integration of MOEMS on reconfigurable silicon micro-optical table[END_REF] To reduce the impact of external perturbations, F adhesion object-gripper must be lower as possible and F adhesion object-substrate must be higher possible. The major drawback of this release method is the difficulties to grasp the object on the substrate [START_REF] Haliyo | Manipulation of micro-objects using adhesion forces and dynamical effects[END_REF]. A reliable grasping cannot be obtained by using only the adhesion force of the gripper. This method is a good way to release the object but not for grasping.

In other hand, to grasp the object, a gripping force higher than the adhesion force between substrate and object along the direction n is required (see in Fig. 29b): F gripping object-gripper F adhesion object-substrate [START_REF] Bergander | Monolithic piezoelectric push-pull actuators for inertial drives[END_REF] One of the best technological solution is to use gripper with two fingers where the gripping force could be easily higher than adhesion between the object and the substrate.

Our hybrid method uses advantages of both adhesion manipulation and gripping. It induces a reliable release and grasping of micro-object. To guarantee, the conditions ( 6) and [START_REF] Bergander | Monolithic piezoelectric push-pull actuators for inertial drives[END_REF], the gripper must have a high ratio between its gripping force and the adhesion force 'object-gripper'.

As presented in Fig. 29, two ways have been chosen to guarantee first object's manipulation: increase adhesion forces between the substrate and the object and decrease adhesion force between the object and the gripper.

We choose to use as substrate a transparent gel film wellknown in microelectronics: Gel-Pak. This material is in fact transparent and softly adhesive, it consequently allows accurate pick and place tasks. Moreover, the low mechanical stiffness of this polymer induces natural compliance of the substrate required for micro-assembly. In a second time, Fig. 30 End-effectors' shape in SEM view. Scalloping is visible in lower picture efforts have been made on end-effectors shaping. First, surface in contact with the micro-object has been reduced by using end-effectors with a small thickness. In second time, the fabrication process called DRIE have been used to give the gripping surface a specific texture. Etching anisotropy of this process is made by a short succession of isotropic etching/protection cycles. These cycles create a phenomenon called scalloping illustrated in Fig. 30. In this way, contact shape between object and end-effectors is a succession of microscopic contact points. The roughness induced by DRIE is able to highly reduce pull-off force. As presented in Fig. 31, nanostructurations or chemical functionalisations can also be used to reduce the adhesion on the gripper end-effectors [START_REF] Dejeu | Adhesion forces controlled by chemical self-assembly and PH , application to robotic microhandling[END_REF][START_REF] Dejeu | Reduction of micro-object's using chemical functionalisation[END_REF][START_REF] Dejeu | Robotic microhandling controlled by chemical self-assembly[END_REF][START_REF] Dejeu | Reducing the adhesion between surfaces using surface structuring with PS latex particle[END_REF].

Experimental set-up

The experimental set-up is based on the piezoelectric gripper presented above. Several kind of finger tips can be glued Fig. [START_REF] Ivan | Current integration force and displacement self-sensing method for cantilevered piezoelectric actuators[END_REF] Nanostructuration of end-effectors' shape (collaborative works between FEMTO-ST and EMPA Institute, Thun, Switzerland) [START_REF] Dejeu | Reducing the adhesion between surfaces using surface structuring with PS latex particle[END_REF] Author'spersonal copy on this piezoelectric actuator. The finger tips [START_REF] Agnus | Silicon end-effectors for microgripping task[END_REF]29] used for micro-assembly have been designed to handle microscopic objects. They are build in single crystal silicon SOI wafer by a well-known microfabrication process: DRIE. These endeffectors have a long and thin beam (12 designed to handle objects from 5 µm to few hundred micrometers.

Testing micro-assembly needs micro-objects that could be mechanically fastened to the others. Thus, micro-objects have been designed with mechanical fastener structures already studied in [START_REF] Dechev | Mechanical fastener designs for use in the microassembly of 3d microstructures[END_REF]. To supply a challenging benchmark, objects' shape are squares of 40 µm sides with a thickness of 5 µm. SOI wafers of 5 µm device layer thickness and DRIE process have been used to build these microparts [START_REF] Hériban | Mechanical detethering technique for silicon MEMS etched with dried process[END_REF]. Many shapes, fastener designs and sizes were tested (Fig. 32). Two kind of parts are presented in this article: the first one is 40 µm square puzzle parts, with four notches of µm. The second one is a mechanical plug device between two 40 µm squares. The male part have a key which is able to lock the female part after assembly as proposed by Dechev [START_REF] Dechev | Mechanical fastener designs for use in the microassembly of 3d microstructures[END_REF].

Results

This approach has been tested in teleoperate mode to assemble benchmark micro-objects. Two kind of mechanical assembly have been tried to make a three-dimensional microproduct. The first one is made by an insertion of two identical puzzle parts. The second one is a reversible assembly of two different parts.

Insertion

Each puzzle piece has four notches, close to 5 µm width and 10 µm long. As part's thickness is 5 µm, assembly of two requires to insert perpendicularly (Fig. 33). The first part is gripped and place vertically on the substrate. The second part is taken vertically too perpendicularly to the first one (step 1). Then two puzzle pieces are ready to be assembled. Then the second part is gripped, Assembly clearance is very small and evaluated to 200 nm by SEM measurement and accuracy can be made up by substrate compliance. Indeed, compliance of adhesive substrate allows small rotative motion of the first part thus insertion is easily performed without any fine orientation of the gripper (step 3). When insertion is complete, microgripper is opened to release assembled part (step 4). This last operation can failed when adhesive effects between gripper and puzzle piece are stronger than between both puzzle pieces. In fact, the part stay sticked on the end-effector and opening the gripper disassemble the micro-product. Consequently, the trajectory proposed in Fig. 33 is used to induce a reliable release.

Reversible assembly

The second assembly benchmark requires more steps and more accuracy. Both mechanical parts are different but have the same square shape of 40 µm side. The first part have a small key joint with a T shape on one side. The second part have a T shaped imprint in center of the square (Fig. 34). To perform assembly, the key must be inserted in the imprint and then a lateral motion of the second part locks the assembly. This benchmark is inspired from Dechev et al. [START_REF] Dechev | Mechanical fastener designs for use in the microassembly of 3d microstructures[END_REF].

Fig. 34 Lock joint design

This benchmark has been tested with our robotic structure (Fig. 35). Parts' orientation is very important, especially for the relative orientation between both micro-objects. The first part is set vertically on the substrate. The gripper is used to grip and align the second part above the key (step 1). When the key is in the imprint (visible on the vertical view), a vertical motion the key in the hole (step 2). Finally a lateral motion locks the key and the assembly is performed (step 3).

After locking motion, the 3D microproduct realized can be extracted from the substrate and moved to another place (step 4). Moreover the major interest of this kind of assembly is the possibility to disassemble it. To perform it, motions are repeated on opposite way: a lateral motion to unlock the key (step 5) and a vertical motion to disengage the key from the imprint (step 6). Several cycles of assembly-disassembly have been tested.

Analysis of the reliability

In order to show the reliability of our method, numerous pick and place operations have been performed in teleoperation and in an automatic cycle. The tests have been done on a silicon micro-objects whose dimensions are 5×10×20 µm 3 . The objective of the pick and place operation is to grasp the object placed on the substrate, to move it along 100 µm and to release it on the substrate. To evaluate the reliability, the success rate of the pick and place operations and the time cycle have been measured.

First, tests have been done in teleoperation. The operator see the lateral view and the vertical view on two screens. He controls the trajectories and the gripper movements with a joystick without force feedback. Sixty operations have been done. The time cycle stays always between 3 and 4 s. Secondly, tests have been done in an automatic cycle without force and position feedback. The pick and place trajectory was repeated 60 times and the time cycle was 1.8 s.

Fig. 35 Reversible assembly

In both tests, the reliability reaches 100 %. As only some articles in the literature quote the reliability of micromanipulation methods, it is quite difficult to compare this value with other works. However, tests of the reliability of microhandling strategies have been presented in [START_REF] Dafflon | A micromanipulation setup for comparative tests of microgrippers[END_REF][START_REF] Gauthier | Comparison between micro-objects manipulations in dry and liquid mediums[END_REF]. Both tests have been done on polystyrene spheres whose diameter is 50 µm. The success rate was between 51 and 67 % on around 100 tests in [START_REF] Gauthier | Comparison between micro-objects manipulations in dry and liquid mediums[END_REF] and was between 74 and 95 % on 60 tests in [START_REF] Dafflon | A micromanipulation setup for comparative tests of microgrippers[END_REF]. Consequently, our method allows a higher reliability on smaller objects which represents a significant contribution.

Conclusion

This paper has drawn an overview of the scientific works of FEMTO-ST institute in the automation of 'microassembly' and 'micromanipulation' based on robotic means. We gave three major proposals for microrobotics means which have been developed during the last decade: a piezoelectric microgripper that can move finely grasped objects in two directions and rotation (an industrial version of this microgripper is now on the market), a 2 DOF modules, named TRING-module that can move objet on a long coarse in translation and rotation, and the smart surface we currently studied. The paper proposed several method for the automation of out of plane assembly of objects whose typical size is from 10 to 400 microns. Closed loop control based on micro-vision has been studied and applied on the fully automatic assembly of several 400 microns objects. Force control has been also analyzed and is used for optical Microsystems assembly. At least, open loop trajectories of 40 microns objects with a throughput of 1,800 unit per hour have been achieved. Scientific and technological aspects and industrial relevance have been presented. The research group is now continuing its work on the assembly and manipulation of components and processes of smaller objects. We focus on challenges of assembling components of less than 10 µm up to hundreds of nanometers. For this, we develop new strategies to manipulate, new manipulation tools, new methods of control of high precision (integrating the noises for example), integrated microfabricated sensors, ... Micromanipulation and micro-assembly around the micrometer is a key step in the packaging of nanotechnologies and is thus a bottleneck for the advent of nanotechnological products.

Fig. 1

 1 Fig. 1 Major adressed issues studied at FEMTO-ST/AS2M

Fig. 3

 3 Fig. 3 Piezoelectric actuators of the FEMTO-ST microgripper

Fig. 5 Fig. 6

 56 Fig. 5 Nickel finger-tips (200 µm thick)

Fig. 7 a

 7 Fig. 7 a PiTweez from PERCIPIO-ROBOTICS, b micromanipulation of a silicon micro part 40 µm × 40 µm × 5 µm, c polymer microcow to demonstrate micro-assembly (500 µm long, smallest nose part is 50 µm × 50 µm × 5 µm), d fiber, 7 µm diameter, e silicon parts assembly, 7 µm width

Fig. 8 aFig. 9 A

 89 Fig. 8 a PiezoTweeze prototype, b and c details of polymer finger-tips

Fig. 11

 11 Fig. 11 Evolution of the two TRING-modules performing a pick-andplace task for microassembly

Fig. 13 Fig. 14

 1314 Fig. 13 Overview of the experimental setup

  Fig. 15 Experimental results

Fig. 18

 18 Fig. 18 Objective of the work: insertion of two microparts by their groove

Fig. 19 Fig. 20

 1920 Fig. 19 Assembly setup

Fig. 21 Fig. 22

 2122 Fig. 21 Some images of the assembled structure from a scanning electron microscope

Fig. 24

 24 Fig. 24 Forces acting during a guiding task: (2) measured contact forces between micro-object and fingers 1 and 2 (1) is the estimated contact force between micro-object and rail and (3) is the positioning of the micro-object along the rail

Fig. 27

 27 Fig. 27 Assembled RFS-MOB composed of three holders all being aligned along one optical path

Fig. 28

 28 Fig. 28 Laser based scanning of a holder to characterize its positioning accuracy relative to the substrate

  Fig. 29 of the Release and Grasping of the objects

Fig. 32

 32 Fig. 32 Micro-objects designed for assembly

Fig. 33

 33 Fig. 33 Insertion assembly

Table 1

 1 Performances of the TRING-module

	Motion	Step	Max speed	Stroke
	Linear Angular	70 nm → 200 nm 17 µrad → 44 µrad	2 mm/s 2.4 rpm	Unlimited Unlimited

Table

Micro-assembly cell comprising one 4 DOF piezoelectric microgripper, two robotized arms split onto 9 DOF (micropositionner and nanopositionner), one vacuum gripper and two high magnification cameras

Acknowledgments These works have been supported by the French National Agency (ANR) under NANOROL contract ANR-07-ROBO-0003: Nanoanalyse for micromanipulate, PRONOMIA Contract ANR No. 05-BLAN-0325-01 and SMART BLOCKS contract ANR-2011-BS03-005, the European Union under EUPASS contract IST-NMP-1-507978-2: Evolvable Ultra Precision Assembly Systems: Next Generation Technologies for Rapid Deployment of Distributed Ultra Precision Assembly Services for Manufacture of Micro-and Author'spersonal copy J Micro-Bio Robot (2013) 8:91-106 105 Nano-scale Products, HYDROMEL contract NMP2-CT-2006-026622: Hybrid ultra precision manufacturing process based on positionaland self-assembly for complex micro-products, FAB2ASM contract FoF.NMP.2012-3: Efficient and Precise 3D Integration of Heterogeneous Microsystems from Fabrication to Assembly, and by the Franche-Comté region under the MIAAMI and MIOP Projects and NEMO/Marie-Curie. Authors would like to thank C. Gorecki and S. Bargiel, from the MN2S Department of FEMTO-ST for their contribution on MOEMS assembly.


Oskar Lecuyer

Ruben Bibas

Combining climate and energy policies: synergies or antagonisms?

Keywords: Renewable energy, energy efficiency, energy policy, climate policy, policy interaction. JEL Classification: Q28, Q41, Q48, Q58

The European Union plans to include an energy efficiency binding target in addition to the renewables and CO2 targets. In this paper, we develop a requisite framework to study interactions arising from the combination of instruments aiming at reducing emissions, promoting renewables and energy efficiency. The model allows the exact assessment of the instruments interactions for quantities and prices. All instruments lead to emissions reductions and the carbon price gives the right incentives for renewable and energy efficiency. Contrary to these expected positive outcomes, we find that the combination of more than two instruments creates significant antagonisms regarding major policy objectives.

Introduction

The European Union (EU) has developed a climate and energy strategy with multiple objectives. Energy supply plays a central role in this strategy, not only for energy security concerns but mainly because it represents the largest opportunity for greenhouse gases (GHG) emissions mitigation. According to UNFCCC data UNFCCC (2011), the combustion of fossil fuels makes up for 88 % of total EU GHG emissions.

The EU implemented in 2009 the Climate and Energy Package (CEP), aiming at (i) cutting GHG emissions by 20 % compared to 1990 levels, (ii) producing 20 % of its energy from renewable sources by 2020 UE (2009a,b,c) and (iii) increasing energy efficiency by 20%. This last objective is not binding. Therefore, the EU plans to release a Directive on energy efficiency including binding measures for energy consumption reductions, among others UE (2011a,b). The CEP strengthens the European Emissions Trading Scheme (ETS), designed to share emissions reduction efforts among member states. For renewable energy, objectives are set at the state level, and most member states use a feed-in-tariff to reach it. Energy efficiency legislation is sector-oriented, due to the scattered nature of energy savings. Current legislation focuses on energy-intensive sectors such as buildings, manufacturing, energy transformation and transport.

Given the high degree of interdependency between emissions, various energy production sources and energy consumption reductions, interactions between those policies are inevitably significant. A wide range of research papers has investigated rationales, scope and conditions for efficient and effective policies to reduce GHG emissions, apart or in combination. A number of effects have been listed and characterized, but no formal definition of interactions has yet been formulated and microeconomic analysis of interactions between the objectives of the European Climate and Energy Package are still scarce.

This paper aims at helping bridging this gap. Its objective is to disentangle the role interactions can play in the performance of a policy combination by giving formal definition of interaction terms and quantifying them. We develop therefore a simple model of supplies and demand in the energy sector including the policy instruments of the CEP: a price on CO 2 emissions, a renewable energy subsidy and various demand reduction instruments. In various policy combination scenarios we derive interaction terms between instruments.

Section 3 presents the model framework and analyzes interaction terms arising from the combination of several climate and energy policy instruments in several policy mix scenarii. Sections 4 and 5 discuss the results and conclude.

Interactions and rationales for overlapping policies

The study of instrument combination is of particular interest in the energy sector. Regardless of the reason invoked for their implementation, climate and energy policy instruments affect energy-related goods that are highly substituable, emphasizing the importance ofinteractions and indirect effects of specific policies. In a very general sense, interactions can affect expected outcomes at any level: scope, objectives, implementation, operation or timing of a specific policy [START_REF] Sorrell | Carbon trading in the policy mix[END_REF].

While each of these aspects is worth investigating for further insight in policy design, we will focus on a microeconomic perspective. This section discusses some issues in the economic study of climate and energy policy interactions and reviews some of the approaches adopted in the literature. For an exhaustive review of interaction studies and a general framework to assess potential effects of interaction between two instruments or two policy schemes, see for instance [START_REF] Oikonomou | A framework on interactions of climate and energy policy instruments[END_REF].

Rationales for overlapping policies

According to basic economic theory, a single CO 2 price across the whole economy is the most efficient policy for mitigating emissions, because it allows for a first best allocation of resources. However this first-best regime refers to an ideal situation, because of several shortcomings in the emissions allowance market. Market failures, technological failures and externalities prevent the carbon market from reaching the right equilibrium. In the short term, the absence of transmission of CO 2 price effects to end-users, imperfect foresight and bounded rationality can limit the efficiency and relevance of the emissions market. In the mid-term, security of supply concerns, imperfect competition and liquidity constraints can hinder the proper evolution of the permit price trajectory. In the long term, innovation failures, market power and market barriers limit the emergence of low carbon technologies.

Correcting each of these externalities or market failures is an objective as such. The so-called Tinbergen rule [START_REF] Tinbergen | On the Theory of Economic Policy[END_REF] states that policy-makers should carry out an instrument for each one of its objective to avoid a trade-off that would favor one objective over another. Besides parallel achievement of different objectives, the joint implementation of policy instruments has been justified on several grounds:

• Induced technical change may be higher for some options than for others, justifying specific support [START_REF] Philibert | Interactions of policies for renewable energy and climate[END_REF].

• The combination of inertia in technology deployment and imperfect foresight can justify implementing more costly options before the full potential for cheaper options is exhausted [START_REF] Ha-Duong | Influence of socioeconomic inertia and uncertainty on optimal co2-emission abatement[END_REF].

• Some market failures, regulatory failures or behavioural failures may reduce the economic efficiency of market-based instruments, justifying additional instruments to tackle them [START_REF] Gillingham | Comparing and combining energy saving policies: Will proposed residential sector policies meet french official targets[END_REF].

Regarding the CEP, the overlapping of policy instruments is supported by two alternative arguments. The first one places the climate mitigation objective as the main driver of economic changes, and other instruments are aimed at tackling the European ETS market failures. In this view, energy efficiency and renewable energy policies reduce knowledge-based and technology-based failures of specific low-carbon technologies. In the second view, several objectives are considered simultaneously. Reaching 20 % of renewable energy production and 20 % of energy consumption reductions are important as such because of additional benefits they bring along (e.g. local employment or the alleviation of energy security concerns). Yet, regardless of the adopted view, the interactions between European climate and energy policies are inevitably significant, given the high degree of interdependence between emissions, energy production sources and energy consumption reductions.

Interactions resulting from policy overlapping

There are several approaches in the literature on climate an energy policy interaction. Some authors classify interactions in different manners, mostly on the basis of effect on expected outcomes, scope and governance [START_REF] Sorrell | Carbon trading in the policy mix[END_REF], Sorrell et al., 2003). Other analyze and sometimes quantify those effects, using analytical or numerical models [START_REF] Abrell | The interaction of emissions trading and renewable energy promotion[END_REF][START_REF] Skytte | Interplay between environmental regulation and power markets[END_REF][START_REF] Sorrell | White certificate schemes: Economic analysis and interactions with the EU ETS[END_REF]. A last category of papers uses a sectoral approach to highlight interaction, mainly in the electricity generation sector [START_REF] Fischer | Combining policies for renewable energy: Is the whole less than the sum of its parts?[END_REF]Preonas, 2010, Traber and[START_REF] Traber | Impacts of the german support for renewable energy on electricity prices, emissions, and firms[END_REF].

As defined by [START_REF] Sorrell | Carbon trading in the policy mix[END_REF], a relevant distinction between direct and indirect interactions can be based upon the difference between affected and targeted groups. Direct interactions occur when groups targeted by two policy instruments overlap in some way. An indirect interaction takes place between two policy instruments when a target group is indirectly affected by one of the instruments, as when a renewable obligation on electricity producers and a tax on downstream electricity consumption both raise electricity price for end-users.

The INTERACT project report [START_REF] Sorrell | Project INTERACT: Interaction in EU climate policy[END_REF] makes further distinctions between internal and external interactions, and between vertical and horizontal interactions. Internal interactions refer to interactions between two or more climate policy instruments whereas external interactions refer to interactions between climate and non-climate policy instruments. Horizontal interactions refer to the same level of governance (the European level for instance) while vertical interactions refer to different levels. The report also defines trade policy interactions as the influence of one policy instrument on another by the exchange of an environmental trading commodity.

Analyzing mechanisms behind interactions, [START_REF] Skytte | Interplay between environmental regulation and power markets[END_REF] as well as [START_REF] Sorrell | White certificate schemes: Economic analysis and interactions with the EU ETS[END_REF] develop graphical equilibrium analysis frameworks to separate effects in each considered market (environmental commodity, electricity or energy efficiency goods) and to distinguish effects on demand curve from effects on supply curve. They show in a graphical way that the promotion of one type of energy displaces demand and supply curves for all types of commodities, having an ambiguous effects on prices. [START_REF] Abrell | The interaction of emissions trading and renewable energy promotion[END_REF] develop a static computable general equilibrium model of Germany with differentiated renewable technologies to test the effects of an emissions trading scheme and renewable support mechanisms on each other. Their study shows that adding an instrument promoting renewables to an ETS decreases environmental effectiveness by letting the carbon price drop to zero in some cases. This addition also decreases total welfare due to the additional financing needs of the renewable support scheme. This additional cost is highly sensitive on the learning rate assumptions for low carbon technologies. Numerical sectoral approaches, as developed by [START_REF] Traber | Impacts of the german support for renewable energy on electricity prices, emissions, and firms[END_REF] allow a more specific discussion on supply technologies and a quantification of synergies between instruments. They show two frequently counteracting effects when combining an European ETS and national renewable promotion schemes: a substitution effect and a permit price effect. The latter occurs when substituting renewables to emitting fossil production. Increased renewable production then reduces total emissions, thus reducing the price of emissions permits and the end-user price. But promoting renewables substitutes to fossil energy a more expensive energy, increasing therefore the final price and leading to the substitution effect.

Fischer and Preonas (2010) develop a static partial equilibrium analytical framework enabling to analyze variations in quantities and prices when various policies are combined. Applying it to the American electricity production sector, they discuss perverse effects of the addition of an emissions cap or a renewable quota to a set of price-instruments (carbon tax, renewable subsidy or fossil fuel tax). The first major result is that overlapping price-instruments with an emissions cap can lead to the development of relative dirty technologies. When an emissions cap is in place, instruments raising the emissions permit price discourage dirty technologies, whereas instruments that lower the emissions price allow dirty technologies to displace cleaner ones4 . In other terms, "when emissions are capped, none of the overlapping policies can simultaneously disadvantage both kinds of fossil generation" (Fischer and Preonas, 2010, p. 16). This meritorder effect has been previously described by [START_REF] Böhringer | Green serves the dirtiest. on the interaction between black and green quotas[END_REF]. The second major result is that when price instruments are combined to a renewable portfolio standard (RPS), any additional taxation of fossil energy will lower generation from renewable sources because of the market share constraint of the RPS.

Motivation and contributions

Most approaches tend to focus on graphical or qualitative approaches, or on specific interactions between two instruments, often the EU-ETS and an instrument promoting renewable energy. A comprehensive microeconomic approach of interactions between three objectives and three instruments is still lacking. This paper helps bridging the gap by analyzing interactions between all objectives of the Climate and Energy Package. We complement the previous approaches, more governance-oriented, by giving formal microeconomic definitions and analytical demonstrations of interaction effects. While simple on purpose, as it focuses on a deterministic, static partial equilibrium framework, we believe our methodology is a valuable tool to compare and assess effects of multiple instruments of the European climate and energy policy, in a context where binding targets may be voted for energy consumption reductions.

A minimal microeconomic framework to analyze policy interactions

This section presents the simple model developed to analyze interactions between climate and energy policies. The first subsection introduces the general framework and following subsections examine the different policy mix scenarii considered. Table 1 describes all four scenarii and the policy instruments included in each. Annex A lists all variables used in the model.

Model framework

Two fully substituable energies are combined to satisfy an exogenous demand in energy (D): the energy from fossil fuels (f ) and the energy from renewable sources (r). This energy (in Joules or in MWh), is assumed to be consumed through a non-specified energetic vector, for instance electricity, in order to satisfy a service such as lighting, transportation or heating. The demand can be reduced by an amount e through energy efficiency investments. This reduction refers to the production of the same energy service with a different efficiency. For instance, it can be the electricity savings following a switch to energy savings bulbs or a switch to an A+ labeled appliance. These reductions do not refer to sufficiency behaviors, where end-users adapt their consumption to price or specific programs. For a detailed discussion on the differences between efficiency and sufficiency, see Giraudet et al. (2011a,b). Sufficiency is represented by the decreasing slope of the net demand function. It represents all energy savings behavior components unrelated to technological improvement and which cannot be easily subsidized. Gross demand D is defined by a function decreasing with the wholesale price p (thus D (p) ≤ 0). Demand is met according to following equation:

f + r = D(p) -e (1)
The cost of producing energy from the two different sources (C f and C r ) is assumed to be in both cases growing and convex (C

f (f ) ≥ 0, C f (f ) > 0 and C r (r) ≥ 0, C r (r) > 0, where C i = ∂Ci(i) ∂i and C i (i) = ∂ 2 Ci(i) (∂i) 2 )
. Decreasing returns can be justified by the adopted static framework. With a given technology mix and production capacity, each energy producer uses first the most efficient installations and moves gradually to costlier ones, according to merit order. Energy savings are provided by investments in energy efficiency, assumed to have also decreasing returns with respect to the energy savings, so for the same reason C e (e) ≥ 0 and C e (e) > 0.

We consider four policy mix scenarii (cf. Table 1), including an instrument promoting energy efficiency, an instrument limiting GHG emissions and a renewable energy subsidy (ρ) (for instance a feed-in tariff). Energy efficiency promoting instruments include a subsidy (ε) and a quantitative energy efficiency target (A) as in the French white certificate scheme, where participants must provide a certain amount of certificate at the end of each period. The white certificate are issued for each unit of energy saved compared to a baseline scenario. The future European directive under discussion considers to force the implementation of such a scheme in all member states. As further explained

Scenario

Policy instruments T-S EE subsidy Carbon tax Renewable subsidy

T-Q EE quota C-S EE subsidy Emission cap C-Q EE quota
Table 1: Policy instruments included in the scenarii in section 3.3, ε then becomes analogous to dual variable and can be used as a proxy for the price of white certificates used on the energy efficiency market associated to the constraint. GHG limiting instruments include a carbon tax (φ) and a cap-and-trade system . As we model a perfect market in a world without uncertainty, this latter is equivalent to a tax equal to the price of emissions permits. We therefore limit our study of scenarii including a cap-and-trade system to the interactions between renewable energy and energy efficiency instruments with the certificate price.

The two energies and the energy-efficient good to reduce demand are produced by representative producers, assumed to be price-takers and satisfying the following symmetric profit-maximization programs:

max f π f = (p -φ) • f -C f (f ) for production from fossil source (2) max r π r = (p + ρ) • r -C r (r)
for production from renewable source ( 3)

max e π e = (p + ε) • e -C e (e)
for energy savings from efficient goods (4) with f, r, e ≥ 0 and p the wholesale price. In this setting, the price is the wholesale market price. It comprises neither price instruments nor the public cost of the policy. For simplicity, we consider energy efficiency as an energy good. It means that we only consider the final savings of efficient goods and tune the cost curve accordingly.

When replacing an old refrigerator for example, the choice is between taking an average-rated one or a more efficient one. The cost difference between both can be here seen as an energy efficiency investment. This investment leads to a saving corresponding to the consumption difference between both appliances during a given time. Considering energy efficiency in this way allows the development of a quasi-symmetric framework useful to apprehend interaction effects. The cost function C e (e) thus gives the portion of the total cost of a given efficient good corresponding to the energy savings.

Scenario T-S: carbon tax and energy efficiency subsidy

We compute the total differentials of the market equilibrium equations derived from the first-order conditions of the profit-maximization programs (2), (3), (4) and the demand constraint (1). It results in following system allowing us to study instantaneous and infinitesimal variations of wholesale price, energy quantities and energy savings around the equilibrium: System 1 (Price and quantity differentials in scenario T-S).

dp = (df + dr + de) /D (p) (5) df = (dp -dφ) /C f (f ) (6) dr = (dp + dρ) /C r (r) (7) de = (dp + dε) /C e (e) (8)
Solving this system for df , dr, de and dp, gives following equations, describing variations in wholesale price, energy quantities and energy savings as a function of the various policy changes:

Result 1 (Differentials with respect to instrument levels in scenario T-S).

df = -dφ • (η f η r + η f η e + η f η D ) -dρ • η f η r -dε • η f η e η f + η r + η e + η D (9) dr = dρ • (η r η f + η r η e + η r η D ) + dφ • η r η f -dε • η r η e η f + η r + η e + η D (10) de = dε • (η e η f + η e η r + η e η D ) + dφ • η e η f -dρ • η e η r η f + η r + η e + η D (11) dp = dφ • η f -dρ • η r -dε • η e η f + η r + η e + η D ( 12
)
where η i ( with i ∈ {f, r, e}) is defined as

η i = 1 C i
≥ 0 and corresponds to the derivative of the inverse supply function with respect to price η i = 1/C i (q) = (C -1 i ) (p + α i ) for both energy types and the energy savings, with α i referring to price instruments (α i ≤ 0 for taxes and α i ≥ 0 for subsidies). The inverse supply function corresponds to the marginal cost curve if we consider a pure competition framework with price-taking producers. η D is defined as η D = -D (q) ≥ 0 in order to have a positive variable and facilitate the comparison with marginal cost curve derivatives.

In ( 9), ( 10), ( 11) and ( 12), the coefficient of policy variables dφ, dρ and dε corresponds to the partial derivatives of respective quantity or price variables with respect to corresponding policy variable. For instance, in (9), the coefficient of dφ corresponds to the partial derivative of fossil production with respect to carbon tax, ∂f ∂φ =

-(η f ηr+η f ηe+η f η D ) η f +ηr+ηe+η D
. It corresponds to the variation of fossil production when the carbon tax is changing.

In this example, the partial derivative is negative, meaning that increasing the carbon tax reduces energy production from fossil fuel at equilibrium. This is due to several effects. Increasing the tax increases the marginal cost of producing energy from fossil fuel. This increase shifts the supply curve C -1 f (p -φ) downwards (because it is an increasing function), raising the price at equilibrium. This shift is characterized by expression -η f η D in (9), corresponding to the product of fossil energy supply curve and the opposite demand curve. An increase in φ will also have an effect on η f itself, indirectly changing the slope of the supply curve. If C f is increasing with respect to production, the partial derivative of the fossil energy supply curve with respect to carbon tax is negative:

∂C -1 f (p-φ) ∂φ = -1 C f (C -1 f (p-φ)) ≤ 0.
The decreasing slope of the supply curve adds up to the downward shift.

df dr de dp dφ -+ + + dρ -+ -dε --+ -Table 2: Signs of the partial derivatives of both energy types (f, r), energy savings (e) and market price (p) with respect to the policy instrument levels (φ, ρ and ε) in scenario T-S.

An increase in φ also reduces the relative cost of renewable energy and energy savings compared to energy from fossil fuel. The change in relative costs induces a substitution between fossil energy and the two other energy options, renewable energy and energy efficiency. This substitution is characterized by expressions -η f η r and -η f η e in (9). The analogous expressions can be found in ( 10) and (11). All above effects are tempered by the sum of all supply curves and the demand curve. The substitutions and this tempering can be seen as a first effect of instrument combination.

Table 2 summarizes the signs of the partial derivatives of both energy types (f, r), energy savings (e) and market price (p) with respect to the policy instrument levels (φ, ρ and ε). For instance, asign on the intersection of column df and line dφ means that ∂f ∂φ is negative, an increase in φ comes with a decrease in f at equilibrium. The rate of variation of the market price is negative with respect to subsidies ρ and ε because we do not consider the funding of those policy instruments.

Equations ( 9), ( 10), ( 11) and ( 12) can also be interpreted as a whole, interpreting the effect on price or production of a combined change of two separate instrument levels. A simultaneous increase of φ, ρ and ε will have negative effects on fossil energy production that add up. Similarly, an increase in both φ and ε will have two positive effects on energy savings that add up. By contrast, an increase in both ρ and ε will have an ambiguous effect on renewable production, as the two effects have opposite signs. In this framework, we can give following definitions: Definition 1 (synergy). Two policy instruments are in synergy with respect to a given variable (like production or price) when the partial derivative of this variable with respect to the policy instruments have the same sign.

Definition 2 (antagonism). Two policy instruments are in synergy with respect to a given variable (like production or price) when the partial derivative of this variable with respect to the policy instruments have opposite sign.

Here, subsidies for renewable energy and energy savings are antagonistic for renewable production and energy savings. A simultaneous increase in the level of the subsidies will result in an ambiguous effect on renewable production and on savings resulting from energy efficiency. Similarly, the carbon tax and the subsidy for either renewable production or energy savings are in synergy for respectively either renewable production and emissions reductions or energy savings and emissions reductions. They are antagonistic for respectively either energy savings and emissions reductions or renewable production and emissions reductions. Table 2 shows also that subsidies for renewable production and energy savings are in synergy with respect to the wholesale price, as both tend to reduce it, whereas there is an antagonism between those instruments and the carbon tax with repsect to the wholesale price. This is due to the fact that for simplicity we did not consider the impact of price instruments on the public finances.

Scenario T-Q: carbon tax and energy efficiency target

In this scenario, the subsidy on energy efficiency is replaced by a quantitative target. To represent an energy efficiency target, we assume that all accountable reductions are made through energy efficiency investments. This is true for instance for the French white certificate scheme, where certificate are issued on the basis of standard procedures such as the replacement of an appliance. Additional consumption reduction can be the result of sufficiency behaviors. Those reductions are however difficult to account for. In the present setting, they are captured by the decreasing slope of the demand curve, or a possible shift to the left. Change in the energy price resulting from various policies can also lead to a rebound effect. A demand reduction will induce a price drop that itself lead to an demand increase.

For simplicity, we therefore display an energy efficiency target as a demand reduction requirement e , corresponding to a certain percentage of total consumption. Global energy demand has to be lowered by a certain percentage A compared to the business-as-usual scenario. We moreover assume that the quota is binding. By doing so, we simply assume C e is bigger than C r and C f : other energy types are cheaper. This seems reasonable, otherwise promotion of energy efficiency would be unnecessary.

In the equations, all goods are linked by the quota constraint : e = A D(p) = A(f + r + e). Totally differentiating this constraint, system (1) becomes: System 2 (Price and quantity differentials in scenario T-Q).

dp = (df + dr + de) /D (p) (13) df = (dp -dφ) /C f (f ) (14) dr = (dp + dρ) /C r (r) (15) de = A 1 -A (df + dr) + dA 1 -A (f + r + e) ( 16
)
The system is resolved with following outcome:

Result 2 (Differentials with respect to instrument levels in scenario T-Q).

df = -dφ • (η f η r + η f (1 -A)η D ) -dρ • η f η r -dA • η f • D(p) η f + η r + (1 -A)η D (17) dr = -dρ • (η r η f + η r (1 -A)η D ) -dφ • η f η r -dA • η r • D(p) η f + η r + (1 -A)η D (18) de = dφ • A η f η D -dρ • A η r η D + dA • D(p) • (η f + η r + η D ) (1 -A)η D + η f + η r ( 19
)
df dr de dp dε

dφ -+ + + - dρ -+ --+ dA --+ -+
Table 3: Signs of partial derivatives of variables (f, r, e, p) and certificate shadow price (ε) with respect to instrument levels (φ, ρ and A) in scenario T-Q.

dp = dφ • η f -dρ • η r -dA • D(p) η f + η r + (1 -A)η D ( 20
)
This result can be analyzed in the same way as the previous one. In ( 17), ( 18), ( 19) and ( 20), the coefficients of dφ, dρ and dA correspond to the partial derivatives of price and quantities with respect to the policy instrument. Compared to scenario T-S, the addition of a consumption reduction quota simplifies the system by removing some of the substitutions. This is due to the additional constraint, linking the energy savings to total demand, and reducing the number of variables in the system. With this binding constraint, the variations of e are due to the variation of the global energy demand, and can be seen as a shift along the demand curve (expressions (A η f η D ) and (-A η r η D ) in ( 19)). This effect is tempered by some substitutions between e and r, and between e and f , at a level depending on the relative slopes of inverse demand functions. Equations ( 17) and ( 18) thus display only one substitution term, similar to the corresponding one in (19).

The addition of a consumption reduction quota affects the slope of the demand curve. The quota permanently reduces the demand and η D is replaced by (1 -A)η D . This change of the demand curve slope has an effect on energy production when the quota A is moving. An increase in the quota level rises the energy savings compared to renewable and fossil energy productions ( ∂f ∂A ≤ 0 and ∂r ∂A ≤ 0). The effect on the wholesale price follows this move of the demand curve and decreases too, at a rate proportional to BAU demand (i.e. the demand without the savings).

Table 3 summarizes the signs of rates of variations of both energy types (f, r), energy savings (e), market price (p) and certificate shadow price (ε) with respect to policy instrument levels (φ, ρ and A). The certificate shadow price is defined in the next section. Results are comparable as those presented in Table 2. The effects of a small change in the quota A have the same sign than the effects of a change in energy savings subsidy in the previous section. The magnitude of these effects changes however, depending this time on the absolute level of demand. In addition to antagonisms and synergies highlighted in Table 2, we show here the counteracting effects of respectively renewable subsidy and carbon tax or energy savings subsidy and carbon tax on the certificate price ε (as described in section 3.4).

Scenario T-Q: effects on the energy efficiency certificate price (ε)

With a consumption reduction quota, ε becomes a shadow price, that is an indication of the price of a white certificate if the consumption reduction quota is backed by a certificate market. It can be seen as an addition to the wholesale price for the energy savings, in order to help them become competitive compared to energy production. Formally, it corresponds to the spread between the wholesale price p and the marginal cost of energy savings C e . Replacing de, df, dr in the quota constraint ( 16) and solving for dε gives:

Result 3 (Certificate price differential in scenario T-Q). dε = dρ • (η r (η e + Aη D )) -dφ • (η f (η e + Aη D )) + dA • D(p) (η e + η f + η r + η D ) η f η e + η r η e + (1 -A)η e η D ( 21
)
Changes in the carbon tax or the renewable subsidy will cause some substitutions between fossil and renewable energy, and move the equilibrium price. An increase in renewable subsidy dρ will raise the certificate price, by increasing the spread between wholesale price and marginal cost of energy savings. On the contrary, the carbon tax, by raising the wholesale price p decreases this spread and causes the certificate price to fall.

A change in the quota level dA first moves the demand curve, causing the wholesale price to drop, and consequently the certificate price to raise. Second, it causes the relative share of the energy savings to raise compared to renewable and fossil energy, leading to an increase of the marginal cost of energy savings, and thus an increase in ε. It is noteworthy that when an energy efficiency quota is in place, the energy savings cost curve has no impact on the equilibrium any more.

Scenarii C-S and C-Q: addition of energy efficiency instruments to a CO 2 cap

This framework also allows to analyze impacts of instrument combination on the ETS permit price. In order to do so, we assume the cap is binding, and thus emissions and fossil production are fixed: df = 0. In this setting, φ becomes the shadow price of the emissions constraint, equal to the absolute value of the spread between market price and the marginal cost of producing energy from a fossil fuel. φ can be interpreted as a proxy of the ETS permit price. The effect of changes in renewables and energy efficiency instruments on the permit price is summarized in Table 4.

Scenario C-S: CO 2 cap and EE subsidy

By substituting df from (9) and resolving for dφ, we obtain:

Result 4 (emissions permit price differential in scenario C-S).

dφ = -dρ η r η r + η e + η D -dε η e η r + η e + η D ( 22
)
dρ dε dA dφ ---Table 4: Signs of rate of variations of CO 2 permit price (φ) with respect to policy instrument levels (ε, ρ and A) in scenarii C-S and C-Q.

We see that an increase in either the renewable or the energy savings subsidy has a negative impact on the emissions permit price, weighted by a ratio denoting the substitution between fossil energy and alternatives to fossil energy when they are subsidized. When for instance renewable energy is subsidized, it increases its market share compared to fossil energy. This reduces the burden on fossil energy producers, it is less costly to comply with the emissions quota and the permit price drops. This result illustrates the recent debate about the necessity to "set aside" some of the emissions permits in parallel of implementing energy-efficiency measures, in order to prevent the carbon price to collapse. An increased objective on renewable energy production or energy savings would put a downward pressure on carbon price, weakening the price signal given to the whole economy.

Scenario C-Q: CO 2 cap and EE quota

With an energy savings quota, dφ can be derived from ( 17), giving following equation:

Result 5 (emissions permit price differential in scenario C-Q). dφ = -dρ η r η r + (1 -A)η D -dA D(p) η r + (1 -A)η D ( 23
)
The results are comparable to the situation with only price instruments. An increase in the energy savings quota will have a negative influence on the emissions permit price. This time only, the magnitude of the influence is proportional to total demand and not the slope of the curve, resulting in a potentially larger effect on permit price.

Summary of results and discussion

Regarding the primary objective of the European climate and energy strategy, namely the reduction of GHG emissions, the model shows that all the instruments considered unequivocally reduce fossil energy consumption and therefore associated GHG emissions (see Tables 2 and3). The impact of the different instruments on the wholesale price is however variable. If the impact on public finance is overlooked and no charge is put on end-users, a carbon tax will raise the price with the emissions reductions whereas renewable and energy savings subsidies lower it.

The interaction between emissions permit price and subsidies for renewable energy production or energy savings is shown to be negative. At equilibrium, the two subsidies reduce the emissions permit price. If the existence of a significant emissions price is considered an objective in itself, this could lead to a serious loss of global efficiency for the policy package on the long term. The perspective of a strengthening of the renewable production objective or the energy efficiency target has already had a negative impact on the forward ETS price. As widely discussed in the press and the economic literature, a set-aside of some of the emissions permits would be a way to keep the market under pressure and would help reduce regulatory uncertainty about future levels of CO 2 price.

Regarding all objectives of the Climate and Energy Package, the model shows that a carbon tax promotes at the same time the reduction of fossil energy consumption, the development of renewable energy and consumption reductions through energy efficiency investments. In the presence of substantial objectives for renewables and energy savings, this instrument may however not be sufficient. It only ensures renewable energy and consumption reductions evolve in the right direction, not that they will reach a specified target. Instruments specifically promoting renewables and energy efficiency have to be added to the system to ensure renewable production is above and energy consumption below targeted levels. When they are implemented together, the two subsidies have however opposite effects on productions and tend to reduce the absolute level of each other.

We give a formal definition of synergistic and antagonistic effects in the model. Two policy instruments have antagonistic effects with respect to a given variable (like production or price) when their partial derivative with respect to this variable have opposite signs. Two policy instruments are in synergy when those partial derivatives have the same sign. When they are implemented together, a carbon tax, a renewable subsidy and an energy savings subsidy have antagonistic effects with respect to market price. The two subsidies are antagonists with respect to renewable production and energy savings. The promotion of renewables comes at the expense of energy savings promotion and conversely.

According to the model, the addition of a consumption reduction quota or a white certificate scheme has, as one could expect, positive effects on the demand, by reducing the net demand curve and reducing its slope. By reducing the net demand, the energy savings quota reduces the need for fossil energy (and thus GHG emissions) and reduces the market price. Moeover an energy efficiency quota reduces the slope of the net demand curve. But energy efficiency investments are in competition with renewables and in the model, an increase of the quota comes with a decrease in renewable production at equilibrium. Furthermore, an increase of the consumption reduction quota is followed by a decrease in carbon price. This decrease is proportional to total demand, resulting in a potentially large effect on permit price.

Since the model is static, it overlooks important dynamic effects such as inertia or technical change. Yet, in the energy sector, a static analysis makes sense for several reasons. First, the capital-intensive nature of the energy sector, coupled with the imperfections in investors' expectations stresses the importance of short-term signals for investment decisions. Regulatory uncertainty is perceived as a major risk for investors, thus un-derstanding interaction between those signals at the investors' time scale is crucial. Moreover, long-term signals emerge from the interactions of short-term effects, and most analysis dealing with optimal mix of energy sources implicitly assume that short-term marginal costs equal long-term maginal costs.

Another major assumption of the model is the perfect subsituability between renewable energy and energy efficiency. This is true with regards to some objectives, such as meeting the energy demand , the reduction of fossil fuel consumption or the reduction of GHG emissions. Being in the top-priority list of the EU strategy, linking those policies and the targets associated stands to reason. To be fully effective, policies such as the improvement of energy security or the fight against climate change should consider all antagonistic effects of a simultaneous promotion of energy efficiency and renewable energy or develop a single instrument to reach its objective with less risks and less uncertainty.

However, in many other aspects, renewable energy and energy efficiency are rather complementary. Renewables are supply-side oriented whereas energy efficiency has a huge potential on the end-user side. Energy savings often min-gle technology-based energy efficiency improvements with behavioral-based energy sufficiency improvements. While both tend to save energy, their promotion is obviously very differ-ent in nature, involving information campaigns and indirect incentives in the latter case. The promotion of technology-based energy efficiency can also take many forms, ranging from R&D subsidies to training programs for building sector workers or cross-incentive reductions.

Conclusion

In order to analyze interaction effects between instruments of the European Climate and Energy Package, we develop in this paper a stylized analytical framework of the energy sector. This framework allows to compare and quantify interactions of various nature on prices and quantities. We use it to give a formal definition of synergistic and antagonist interaction effects. We discuss the potential effects of future mandatory instruments of the draft Energy Efficiency Directive. We show that regarding the objective of GHG emissions reductions all instruments are effective, but that major antagonisms arise when several objectives are considered concerning wholesale power price and emissions allowance price as well as renewable energy production and energy savings levels.

In a very broad sense, one instrument allows to control the absolute production of one energy type, but it only ensures that alternative energy types evolve in the right direction. Additional instruments are needed to control the absolute production from several energy sources at the same time, but at the expense of possible antagonisms between instruments. With three constraints, as considered in this model, it is possible to control the absolute production from three energy sources. The absolute level of price can be controlled, but at the expense of loosing the control on the production level from one energy source. In the existence of an objective on the energy price level (for distributional or political purpose for example) or on the carbon price, an additional constraint is necessary, but is likely to have a significant effect on welfare.

In our model, a single carbon price allows the reduction of fossil fuels. Additional measures are necessary to ensure renewable energy and energy consump-tion reductions are above targeted levels. Those additional measures reduce the efficiency of any instrument taken independently. Setting a price on renewable energy or energy efficiency promotion reduces the carbon price, and thus the incentive of carbon-free economy-wide investments (other than those promoted by the policies considered). The joint promotion of renewable energy and energy efficiency has antagonist effects by substituting renewables to energy savings and conversely. This corroborates current concerns about a future carbon price drop following the tightening of renewable or energy efficiency development objectives.

We also model the introduction of a quantitative binding consumption reduction target. We show that by reducing the net demand, the energy efficiency quota reduces GHG emissions and reduces the market price. This leads however again to antagonistic effects with instruments promoting renewables. Despite having several positive effects on its own (like lower dependency on energy imports, lower future capital-intensive investment needs and additional positive externalities such as local employment), a demand reduction instrument may not be compatible with other instruments in the Climate and Energy Package.

The existence of these interactions suggests the need for an integrated approach of climate and energy policy definition. The objectives have to be tuned together, and instrument levels have to be defined taking into account all other instruments. Put in other words, when adding a binding instrument to the existing climate and energy instrument pool, those existing instruments should be assessed and reviewed accordingly. If considered important, the price reduction objective, a European priority not so long ago (along with the energy markets liberalization), should also be integrated into the policy design process and should be adressed with a specific instrument.

Bearing in mind that the devils is in the details and that a detailed assessment of specific instruments have to be done, one should consider our methodology for assessing climate and energy policy packages at a macroeconomic level. UE (2009a). Decision on the effort of member states to reduce their greenhouse gas emissions to meet the community's greenhouse gas emission reduction commitments up to 2020.

of variables List of variables

  Decision 406/2009/EC, European Parliament and Council. UE (2009b). Directive amending directive 2003/87/ec so as to improve and extend the greenhouse gas emission allowance trading scheme of the community. Directive 2009/29/EC, European Parliament and Council. UE (2009c). Directive on the promotion of the use of energy from renewable sources and amending and subsequently repealing directives 2001/77/ec and 2003/30/ec. Directive 2009/28/EC, European Parliament and Council. UE (2011a). Energy efficiency plan 2011. Communication from the Commission COM(2011) 109 final, European Commission. UE (2011b). Proposal for a directive on energy efficiency and repealing directives 2004/8/ec and 2006/32/ec. Proposal COM(2011) 370 final, European Parliament and Council. UNFCCC (2011). Greenhouse gas inventory data. http://unfccc.int/ghg_data/ items/3800.php. Cost curve for energetic good i C i Marginal cost curve for good i C i Marginal cost curve variation for i η i Slope of the supply curve of good i η D Opposite of the demand curve slope

	f	Fossil energy
	r	Renewable energy
	e	Energy savings
	p	Wholesale price
	D	Energy demand
	C i φ	Carbon tax
	ρ	Renewable energy subsidy
		Energy savings subsidy
	A	Consumption reduction quota
	dα	Small variations of variable α

A List

But this displacement is only a second order effect. It does not affect the global amount of emissions.

Acknowledgments

We thank Philippe Quirion and Adrien Vogt-Schilb for their useful comments and suggestions. This work as benefited from presentation feedbacks from participants at the 23rd International Climate Policy Workshop in the University of Malta, at the annual conference of the French Association of Energy Economists 2011, at internal seminars at EDF R&D energy economics department (EDF R&D EFESE) and at internal seminars at CIRED. Funding for this project was provided by EDF R&D and the CIRED.