Clementine Straub
email: clementine.straub@centralesupelec.fr

Sorin Olaru
email: sorin.olaru@centralesupelec.fr

Jean Maeght

Patrick Panciatici

Zonal congestion management mixing large battery storage systems and generation curtailment

The French transmission system operator (RTE) needs to face a significant congestion increase in specific zones of the electrical network due to high integration of renewable energies. Network reconfiguration and renewable energy curtailment are currently employed to manage congestion and guarantee the system security and stability. In sensitive zones, however, stronger levers need to be developed. Large battery storage systems are receiving an increasing interest for their potential in congestion management. In this paper, a model for local congestion management mixing batteries and renewable generation curtailment is developed. Subsequently, an energy management approach relying on the principles of Model Predictive Control is presented. Results of simulations on RTE data sets are presented for the analysis of the degrees of freedom and sensitive parameters of the design.

I. INTRODUCTION

A. Motivations

The renewable energy sector is fast-growing world-wide and the latest reports confirm such an increase in renewable energy generation on the French territory [START_REF]Electricte (RTE) France. Generation adequacy report on the electricity supply-demand balance in France[END_REF]. Consequently, an increase of transits in fragile zones of the electrical transportation network is foreseen. As demand is expected to stagnate, the French Transmission System Operator policy is to investigate new exploitation methods of the existing electrical installations and favour their optimal operation in the renewed context instead of developing new installations. Congestion management is a sensitive aspect in the current operation that will become critical in the future. Two means have been identified as possible technological approaches to deal with this problem: renewable generation curtailments and operation of large battery storage systems. Generation curtailment is already applied with simple strategies. For example, policies for curtailing all or half of the generation are currently implemented. These strategies are not optimal and finding the right amount to curtail, as well as the concomitant use of storage, opens the way to energy and economic savings. From a control theoretic point of view, curtailment and storage are control actions presenting delays. Their impact cannot be neglected, as the estimated delay value for curtailment is 45 seconds. In this time-delay control context [START_REF] Olaru | Predictive control for linear systems with delayed input subject to constraints[END_REF], the exploitation of the installation is facing a considerable complexity. Overloads can be allowed on some electrical lines, but are strictly regulated. The same action can clear an overload on a line and worsen flows on neighbour lines. The human operators in charge of the operation and supervision need to be assisted by an automatic policy selection for the optimal use of the new levers which, while offering new solutions to congestion problems also increase the complexity of the decision-making. An online optimization-based strategy is needed to determine what the most appropriate action is, taking into consideration the time-delay levers system, the permissible overload remaining duration and more generally network constraints.

Curtailment and storage have already been studied in several papers. For instance, [START_REF] Gu | Fast sensitivity analysis approach to assessing congestion induced wind curtailment[END_REF] and [START_REF] Daniel | Factors influencing wind energy curtailment[END_REF] are investigating wind curtailment as a consequence of congested transportation networks. Taking into account that the prediction mechanism is the natural counterpart for delays [START_REF] Camacho | Dead-time compensators: A survey[END_REF], the work reported in [START_REF] Li | MPC for reducing energy storage requirement of wind power systems[END_REF] presents a model predictive control (MPC) approach using battery energy systems to mitigate wind power intermittencies. The authors of [START_REF] Parisio | A model predictive control approach to microgrid operation optimization[END_REF] propose a model and optimization of microgrids bringing into account energy storage, disturbance on renewable energy generation, and curtailment schedule. However the latter articles are focused on balancing generation and load, and are not taking into account power grid limitations. The approach in [START_REF] Biegel | Model predictive control for power flows in networks with limited capacity[END_REF] designs a controller for ensuring balance between power consumption and generation as well as taking into account grid capacities and thereby reducing congestion problems. The controller, though, does not take into account long delays that can occur when using curtailment and more importantly, the model is designed for tree networks. The French electrical transportation network under consideration is a mesh network. The aim of the present paper is to develop a new congestion management method designed for mesh networks that combines in a generic recedinghorizon optimization problem the different levers (storage and generation curtailment) while considering their timedelay characteristics.

It should be noted that closed-loop systems appear in the power systems literature [START_REF] Tang | Real-time Optimal Power Flow[END_REF] [START_REF] Bolognani | Distributed reactive power feedback control for voltage regulation and loss minimization[END_REF] for applications that operate on short timescales or information lacking context. The presented method needs a feedback mechanism of the system for both reasons. The controller can only have access to local measurements and needs to act fast (an action taken every two seconds). The method relies on the receding-horizon principle to reach a feedback formulation and benefits from its intrinsic prediction mechanism to deal with the time-delay in the control actions.

The main contribution of the problem is to reformulate the congestion problem in a dynamical state-space description including the operational constraints, suitable for a Model Predictive Control formulation [START_REF] Eduardo | Model predictive control[END_REF] [18] [START_REF] David Q Mayne | Constrained model predictive control: Stability and optimality[END_REF]. It will be shown that the structure of the constraints is imposing a time-varying receding-horizon optimization. The feasibility in enforced by means of a constraint softening approach and the performances are studied in a series of simulations scenarios for a representative test zone.

Notations

We first define some notations.

• Z N odes is the set of nodes in the zone considered ; n N is its cardinal. • Z Batt ⊂ Z N odes is the set of nodes where a battery is installed ; n B is its cardinal. • Z Curt ⊂ Z N odes is the set of nodes where the generation can be curtailed ; n C its cardinal.

• Z Lines ⊂ {(i, j) ∈ {1..N } 2 }

A. Definition of a Zone

The French transmission electrical network is a 6000 nodes network with voltage levels from 63 to 400 kV [START_REF] Josz | AC power flow data in MATPOWER and QCQP format: iTesla, RTE snapshots, and PEGASE[END_REF]. The model considered in the present work deals with a small zone with less than 30 nodes (Fig. 3). Variations in flows are represented by a linearization, based on report coefficient called PTDF (Power Transfer Distribution Factor). A short description is given above and a complete definition can be found in [START_REF] Šošić | Features of power transfer distribution coefficients in power system networks[END_REF]. PTDF are commonly used in power systems network modeling and analysis. They are relatively easy to compute and often very useful in congestion modeling [START_REF] Liu | Effectiveness of the distribution factor approximations used in congestion modeling[END_REF], [START_REF] Bart | Network modelling for congestion management: zonal representation versus nodal representation[END_REF].

B. Principle

The system is modelled with the following linear representation of the power flow equations by the mean of PTDF:

F ij = F 0 ij + n∈Z N odes P T DF (ij, n) • ∆P inj n (1)
F 0 ij is the measured power flow on line ij before any system operation and F ij the power flow on line ij after an operation. System operations considered in this article (generation curtailment and battery operation) are both injection modifications. ∆P inj n represents the injection modification at bus n. Equation (1) allows us to determine the new power flow resulting from an operation in a set of buses.

For the sake of illustration of the PTDF notion the 8 nodes benchmark network described in Fig. 1 will be used.

In order to define PTDF, a slack bus needs to be introduced in the formalism. The slack node can be any of the 8 nodes, but can not be changed along the real-time operation and in particular in the optimization-based decision making. A Fig. 1. Example of PTDF on a small network PTDF shows the linearized impact on a line of a transfer of power between a bus of the network and the slack bus. PTDF(ij, n) is the oriented flow between i and j when the node n produced 1 MW and the slack bus consumes 1 MW. In the example of Fig. 1, P T DF (ij, n) = 0.8 (in red). A definition of a PTDF is:

P T DF (ij, n) = ∆F ij ∆P n
with ∆F ij the variation in power through branch ij due to the transaction from bus n to the slack bus and ∆P n the power of transaction from bus n to the slack bus. Generation curtailment and battery actions at a specific bus are modelled as a transfer of power between this bus and the slack bus. PTDF enable us to determine the fraction of power transfers flowing over each line of the zone. They are computed on the complete network with the slack bus chosen far from the zone. In a real case, F 0 are available via real-time measurements, while in a simulator, they are computed using the model of the complete network. PTDF and F 0 contain implicitly the interactions between the zone considered and the rest of the network. It may be noted that the flows representation with PTDF is equivalent to the DC modeling [START_REF] Zimmerman | Matpower: Steady-state operations, planning, and analysis tools for power systems research and education[END_REF].

C. System dynamics

The system dynamics can be represented with the help of PTDF to determine the influence of levers on flows on each line. The system outputs are curtailment and battery orders. The system presents delays between the decision-making and the order realization. The delay is τ curt = 45s for generation curtailment and τ batt = 1s for batteries action. The state is composed of power flows, battery charge, battery power injections and curtailments. Orders given at each time step are modifications of curtailment and power injections in the battery, respectively ∆P curt and ∆P batt . Power injections are not constant on all time steps, they evolve according to ∆P evol representing the difference between two consecutive time steps injections (changes in production or load not related to orders).

The system dynamics contains [START_REF] Ld Arya | Line switching for alleviating overloads under line outage condition taking bus voltage limits into account[END_REF] with

∆P inj = ∆P curt + ∆P batt + ∆P evol
The dynamical model has to include the evolution of battery charges E, battery power injections P batt and curtailment P curt , described at each discrete-time step k using a sampling of ∆t on the continuous-time scale:

E k+1 b = E k b + ∆t • P batt,k+1 b , ∀b ∈ Z Batt P batt,k+1 b = P batt,k b + ∆P batt b , ∀b ∈ Z Batt P curt,k+1 n = P curt,k n + ∆P curt n , ∀n ∈ Z Curt
The aggregated state dynamics can be written in the form:

x k+1 = Ax k +B curt .u k-dcurt curt +B batt .u k-d batt batt +B w w k (2)
with x k a vector containing power flows for each line of the zone, batteries energy, amounts of curtailed generation, and power injections in batteries:

x k =     (F k ij ) (E k b ) (P curt,k p ) (P batt,k b )     ∈ R n and n = n L + n B + n C + n B .
The discrete-time delay is related to the sampling time:

d curt = τ curt ∆t -1; d batt = τ batt ∆t - 1
u k curt is a vector containing orders on curtailment modifications and u k batt is a vector containing orders on modifications of power injections in batteries. w k is a vector representing disturbances in power injections. w k can be measured at time k, but w k+t for t ∈ {1..N } is unknown.

The assumption made in section IV for predictions purposes is w k+t = w k for t ∈ {0..N -1} with N the length of the prediction window.

u k curt = (∆P curt,k n ) ∈ R n C , u k batt = (∆P batt,k n ) ∈ R n B , w k = (∆P evol,k n ) ∈ R n N The matrices B curt ∈ R n×n C , B batt ∈ R n×n B and B w ∈ R n×n N
are defined as follows.

B curt =     M curt 0 n B ×n C 1 n C ×n C 0 n B ×n C     , B Batt =     M batt ∆t * 1 n B ×n B 0 n C ×n B 1 n B ×n B     B w = M w 0 (n-n L )×n B
M curt , M batt and M w contains the PTDF, such that the k th line in these matrices corresponds to the PTDF of the k th line of (F ij ) at nodes where generation can be curtailed, at nodes where a battery is installed or at nodes where the injections may vary.

All states are considered to be measured along the operation and can be initialized accordingly. Delay on the controls u curt and u batt are known on time windows [0, d curt ] and [0, d batt ]. The system dynamics are thus well-defined in terms of forward trajectories.

D. Constraints

The electrical lines temperatures should stay within predefined limit values [START_REF]Reseau de Transport d'Electricte (RTE) France[END_REF]. They depend on power flow (by means of the Joule effect) and weather conditions and are defined to avoid an excessive heating and dilatation. Flows must satisfy these thermal limitations. Congestion appears whenever the limit of a line is exceeded. Overloads can be tolerated for a limited time. Fig. 2 illustrates an example of permitted overloads, where a 15 MW overload can be tolerated for a 1 minute period. However these overloads are allowed only when an incident occurs on the network (failure of a power plant or an electric line...) and thus should be considered as event triggered. In a normal situation, power flows must stay within the thermal limit. As power flows are constantly evolving, a margin is taken with this limit to avoid crossing it. Assuming that control can be applied every ∆t = 2s, the margin must represent the maximum of the variations during a ∆t period in normal situation.

When imposing the constraints to the system, it is necessary to distinguish between these two cases : normal situation and incident situation. Model constraints on power flow are:

|F k+t ij | ≤ L k+t ij , t ∈ N (3)
L k+l ij is defined on a finite time-horizon either by a constant function (equal to the thermal limit on line ij, minus the value of the margin) or a stairway profile as in Fig. 2, depending on the type of situation.

If a congestion on a line cannot be eliminated in the allotted time, the line is automatically disconnected. This can result in a cascading lines opening, which is one of the main danger in power system operation. Note however, that this should not be considered as an instability from the dynamical point of view but rather as a drastic loss of performances.

The system (2) is subject to power flow limits described in (3). The shape of power flows limits (constant or stairway profile) depends on the network state. It is fixed before the resolution of the current optimal control problem and can only change between two resolutions of the optimal control problem. System constraints also contain bounds on batteries capacities (E min , E max and P batt,min , P batt,max ) and bounds on generation curtailment (P curt,max ). The state and input constraints can be written in the following form:

H x x k + H C u u k curt + H B u u k batt ≤ H k 0 with H x =         1 n L ×n C 0 0 0 0 -1 n B ×n B 0 0 0 1 n B ×n B 0 0 0 0 1 n C ×n C 0 0 0 0 -1 n B ×n B 0 0 0 1 n B ×n B         , H C u =         0 n L ×n C 0 n B ×n C 0 n B ×n C 1 n C ×n C 0 n B ×n C 0 n B ×n C         , H B u =         0 n L ×n B ∆t * 1 n B ×n B ∆t * 1 n B ×n B 0 n C ×n B -1 n B ×n B 1 n B ×n B         , H k 0 =         (L k ij ) ij∈Z Lines (E min ) n∈Z Batt (E max ) n∈Z Batt (P curt,max n ) n∈Z Curt (P batt,min n ) n∈Z Batt (P batt,max n ) n∈Z Batt        
The index k in the matrix H k 0 refers to the limits on the lines that can vary with time (constant function or stairway profile).

E. Control strategy

The system is able to receive orders, such as a desired charge level of batteries (if a battery charges to address the congestion problem, it will have to discharge at some point to be able to charge again when a new congestion problem appears). Orders can also be given regarding the generation curtailment. However, repetitive curtailment requests should be penalized. We define two objectives for the controller:

• a stage cost: J 1 (x) = N t=1 ||x k+t -x k+t ref || 2 Q1
. The stage cost represents the desired battery charge and the desired curtailment level.

• a control cost:

J 2 (u) = N -1 t=0 ||u k+t -u k+t ref || 2 Q2
representing the cost of each control. The choice of weightings allows penalizing curtailment more than battery usage.

||x|| 2 Q1 := x T Q 1 x, with Q 1 0.

III. MODEL PREDICTIVE CONTROL FOR CONGESTION MANAGEMENT

A. MPC for time-delay systems

The foregoing model offers the key elements for a prediction-based control strategy allowing the evaluation of the impact of the decisions beyond the dead-time. By considering a finite receding-horizon optimal control problem, the following formulation can be obtained for the decision making at time step k:

min x,u J 1 (x) + J 2 (u) s.t. x k+t+1 = Ax k+t + B curt • u k+t-d curt curt + B batt • u k+t-d batt batt + B w • w k+t , t ∈ {0, N -1}, H x x k+t + H u u k+t ≤ H k+t 0 , t ∈ {0, N }, (4)
Within the predictive control formulation, the length of the prediction window represents the main tuning parameter from both feasibility/stability and performance point of view [START_REF] Lombardi | A predictive control scheme for systems with variable timedelay[END_REF], [START_REF] Laraba | Linear Model Predictive Control and Time-delay Implications[END_REF]. In order to enhance the prediction and ensure its capability to cope with the time-delay, the length of the horizon must be greater than the maximal time-delay (in this case τ curt = 45s corresponding to d curt = 22):

N ≥ max(d curt , d batt ).
The state estimation problem for x k is avoided as long as this information is available via measurements. However, the uncertainty has to be considered with respect to the power flow along the prediction horizon.

The matrix H k+t 0 contains the time-dependant constraint on the overloaded lines flow (3). This constraint also depends on the initial flow on lines. The change in constraints from one time step to another can be handle with a reformulation of the problem as a multiparametric program. This reformulation will also deal with the problem of orders previously sent. These orders do not appear in the state x k and have been considered as parameters for the optimization problem. This choice is mainly related to the length of the delay and the impact on the structure of the constraints in the finitetime optimal control problem (4).

B. MPC as a parameterized optimization problem

The previous problem is reformulated as a parameterized optimization problem [START_REF] Bemporad | The explicit linear quadratic regulator for constrained systems[END_REF], [START_REF] Grancharova | Explicit nonlinear model predictive control: Theory and applications[END_REF]. The parameters are including the past control inputs, the current state and the measured disturbance. The constraints taken into account are time varying but their structure remains linear along one prediction window. Thus, the finite-dimensional optimization can be written as:

min U batt ,Ucurt J(x k , w k , U P batt , U P curt , U batt , U curt ) s.t. g(x k , w k , U P batt , U P curt , U batt , U curt ) ≤ 0 (5)
with a quadratic cost J(.), a linear set of constraints g(.) and U P batt , U P curt the vectors collecting the orders sent previously to the input of the system.

U P batt = [u k-d batt batt , u k-d batt +1 batt , ..., u k-1 batt ], U P curt = [u k-dcurt curt , u k-dcurt+1 curt , ..., u k-1 curt ], U batt = [u k batt , u k+1 batt , ..., u k+N -1 batt ], U curt = [u k curt , u k+1 curt , ..., u k+N -1 curt ]
The optimal solution U * batt (x k , w k , U P batt , U P curt ) and U * curt (x k , w k , U P batt , U P curt ) can be computed online efficiently based on Quadratic Programming (QP) solvers as the optimization problem is convex. For the simulations presented in section IV. the solver Fico Xpress [START_REF]FICO Xpress. Optimization commercial solver[END_REF] was used .

C. Feasibility

The recursive feasibility of the optimization problem cannot be guaranteed using the classical arguments [START_REF] David Q Mayne | Constrained model predictive control: Stability and optimality[END_REF] which employ the tail of the optimal sequence at the previous time instant. Indeed, the structure of the constraints in ( 3) is time-varying and the switch in the structure is activated by the exogenous signal w k and thus a priori unknown in the prediction scheme. For instance, gaps between power flows and lines capabilities can be too important to be addressed, or sudden increases in power flow cannot be reduced immediately because of input delays. The feasibility can be studied with two methods: the elimination of time-dependence or the introduction of slack variables. The elimination of time-dependence in the formulation ( 5) is computationally prohibitive and over-conservative from the performance viewpoint as it relies on the enumeration of all the possible structural constraints and is therefore not employed here. The second method is to introduce slack variables ∈ Z Lines on the constraint (3):

|F k+t ij | ≤ L k+t ij + k+t ij , t ∈ {1..N } k+l ij
≥ 0 and is included in the cost function by adding the penalizing term:

J s = N t=1 ij∈Z Lines ( k+t ij ) 2
The problem is then feasible for each time t at the price of overloads whenever > 0. It is obvious to see that it exists ≥ 0 to render U batt = 0 and U curt = 0 as an admissible solution.

IV. SIMULATIONS

The behaviour of the MPC scheme has been simulated on a zone around Savignac in the Auvergne region (center of France), see the map of the zone in Fig. 3. The dimensions of the problem (4) are

n N = 21, n B = 1, n C = 11, n L = 22. It follows that dim(x k ) = 35, dim(u k curt ) = 22 and dim(u k batt ) = 1.
A major growth in renewable generation is expected in this area and congestions are anticipated. The introduction of a battery is currently studied. For our simulations, we situate the battery in Massiac and consider a capacity of 30M W -30M W h. The section shows the behaviour of the MPC controller facing three cases:

• Constant loads and generation with one overloaded line • Constant loads and generation with two overloaded lines • Volatile injections In the three cases, overloads appear due to incidents on the network. This means as described in II-D that flows can cross thermal limits, but should stay below the stairway profile describing permitted overloads. We show that in the three cases, flows respect the permitted overloads, thanks to the MPC controller action. Data used has been extracted from RTE network analysis tool Convergence1 . Limitations and injections have been modified in the data, so that congestion can be observed. The modifications are representative of the increase in power flow due to the growth of renewable energy. Data for the first two cases has been simplified to better illustrates the behaviour of the controller. Generation and loads are kept constant once the incident has occurred, meaning that flows without any action of the controller are constant. A drop in a flow on a line is thus the result of the controller action only and not just the result of a variation in generation or loads.

Constant loads and generation with one overloaded line

Fig. 4 and Fig. 5 illustrate the behaviour of the controller when one line is congested: the line between Massiac and Brioude. Fig. 4 shows the flow on the congested line with and without the controller action, as well as the actions taken. Fig. 5 illustrates the control: when the actions are taken and when they are carried out.

An incident occurred at time 0, meaning that the flow should stay under the stairway profile describing permitting overloads. The flow increases progressively until t = 24s and then is stabilizing around 88 MW. The reference flow (without any action of the controller) is settled at 88 MW after 24s. This flow is violating capacity constraints. The graph shows the difference between the reference flow and the flow on Massiac-Brioude when the controller is acting and when it is not. The controlled flow respects these constraints: the battery charges at its maximal power (30 MW) and generation is curtailed to bring the flow down.

The controller can curtail generation in 11 places: it chose Massiac because of the values of the PTDF (see TABLE I). The biggest PTDF is in Massiac ; for the same amount of curtailment, the decrease in Massiac-Brioude flow will be more important if the curtailment is in Massiac in comparison to other places. The battery, located in Massiac, is used at its maximum power as it is cheaper than curtailment. The curtailment order in Massiac is sent at t = 27s, 46s before the order realization at t = 72s : the optimization problem shows that the battery action is not sufficient for guaranteeing the feasibiblity of the congestion problem and a complementary lever is used. The other lines are considered to be far from their limit and are not represented in the graph for readability.

The strategy of the controller here is simple to analyze: the battery is used in priority as the cheapest lever and generation with the largest impact (PTDF) is then curtailed. Optimal curtailment comes as an automatic decision with the resolution of the optimization problem. Constant loads and generation with two overloaded lines Fig. 6 and Fig. 7 show a situation where several overloads appear at the same time. Massiac-Peyrusse line is now congested, in addition to Massiac-Brioude. As before, we see on the graph that the controller acts to reduce the flows on the overloaded lines in order to respect the capacity The strategy of the controller is more complex to analyze than in the previous case. The controller arbitrates between the two levers to find the optimal solution. The arbitration between the different levers depends on several factors: the PTDF values, the initial flows values, the activated capacity constraints and the levers costs in the objective function. The notion of delays has not been mentioned here because of the constant loads and generation but is presented in the next paragraph.

Volatile injections

Overloads in Fig. 8 and Fig. 9 case appear on the same lines: Massiac-Brioude and Massiac-Peyrusse. The other lines, far from their limits, are not represented. The two graphs illustrate the behaviour of the system with volatile injections. Fig. 8 shows that flows on the two overloaded lines respect their capacity constraints as a result of the controller action. Levers used are the same as in Fig. 6: curtailment in Allan and battery charge, the constraints being the same. The delays influence can be noted here. The system can not foresee variations in flows due to variations in load and generation. Its prediction horizon is constant and the assumption on the power injections (w k+t = w k ) does not hold. As curtailment is decided 45 seconds before its real impact on the system, the amount of generation curtailed is not always optimal because of the variations between the time of the decision making and order realization. The battery is used to compensate the errors in curtailment as its action is not delayed. The controller begins to send curtailment orders at t = 26s. The first order is effective at t = 72s. We can note that no generation is curtailed between t = 96s and t = 106s. It results from the decrease in the reference flows between t = 50s and t = 60s which are below limitations. The battery charges between t = 78s and t = 84s to compensate the insufficient curtailment (sent between t = 32s and t = 38s).

This section illustrates the behaviour of the MPC controller and shows that levers used depend strongly on the situation of overloaded lines and on the overload on each line. On the positive side, the use of levers is accurate within considered scenario. On the negative side, the performance is strongly related to the assumptions made regarding power injections. Two options being available to mitigate this problem : either increase the prediction capability on disturbances or accept a decrease in performance by considering several scenarios and optimizing the worst case.

V. FUTURE WORK

A. Uncertainties

Several uncertainties are present in the system and were not taking into account. It is essential to

B. Network reconfiguration

Network reconfiguration is another possible lever. Network reconfiguration for congestion management has been studied. [START_REF] Granelli | Optimal network reconfiguration for congestion management by deterministic and genetic algorithms[END_REF] presents a methodology to find the optimal topological configuration of a power transmission system using genetic algorithms. [START_REF] Ld Arya | Line switching for alleviating overloads under line outage condition taking bus voltage limits into account[END_REF] presents an interactive line switching algorithm for overload alleviation. Discrete variables are introduced for topological changes. Adding network reconfiguration as one of the possible level in the MPC controller will lead to an hybrid formulation. This formulation will necessitate the resolution of a Mixt Integer Programming problem every two seconds. Moreover, PTDF used in the formulation depend on the topology. Modification of the topology will lead to PTDF variations. The model will have to deal with this problem.

C. Discrete generation curtailment

As of now, the curtailment of a renewable farm is all or nothing. It is impossible to curtail only a part of the generation and the technical interface with Distribution System Operators is difficult to change. It could be necessary to introduce discrete generation curtailment in the model. Wind farms will be curtailed taking into account not only their position but also their size.

VI. CONCLUSION

We have presented a MPC controller for congestion management in electrical transmission network using high power batteries along with renewable generation curtailment. The MPC strategy proved to be well suited for this problem as it takes into account the permitted overloads and their different duration, as well as the delays and orders on the reference charge batteries. The MPC scheme allows us to exploit the batteries speed of action and to combine them with the slower acting lever: generation curtailment. Simulation results show the behaviour of the controller in representative scenarios.

  is the set of lines in the zone considered, n L its cardinal. • F ij refers to the power flow on line ij • P curt n is the amount of curtailment at node n ∈ Z Curt • P batt k is the battery power injection at node k ∈ Z Batt • E batt k refers to the battery energy at node k ∈ Z Batt II. MODELING

Fig. 2 .

 2 Fig. 2. Example of overload capabilities

Fig. 3 .

 3 Fig. 3. Map of Savignac zone

Fig. 4 .Fig. 5 .

 45 Fig. 4. Power flows on Massiac-Brioude with constant generation and load, one overload

Fig. 6 .Fig. 7 .

 67 Fig. 6. Power flows on Massiac-Brioude with constant generation and load, two overloads

Fig. 8 .Fig. 9 .

 89 Fig. 8. Power flows on Massiac-Brioude with volatile generation and load

  consider a system robust to these uncertainties. If a flow exceeds the capacity line, it result in an activation of the line protection : the line is opened automatically. It can disturb the electrical network operation in a dramatic way. The uncertainties are due to: • The absence of load and generation forecast. The controller prediction horizon is constant. It is relatively short and it is not possible in practice to have precise forecasts on a short notice. For the controller, flows can vary only with control (curtailment and batteries) over the horizon, which means flows variations due to other factors (demand, wind, sun...) are not considered for the predicted trajectory. • The approximation of the DC modelization. It results in prediction errors. • Unknown topology outside the observed zone. PTDF depend on the network topology. The topology can be changed upon network operation. If PTDF are not updated, it will introduce an error in the controller flows representation. • Imperfect measures. Additive disturbances in the prediction model.

TABLE I PTDF

 I FOR MASSIAC AND ALLAN ON THE OVERLOADED LINES

See[START_REF] Josz | AC power flow data in MATPOWER and QCQP format: iTesla, RTE snapshots, and PEGASE[END_REF] for Convergence software short description

*This work has been supported by the RTE-CentraleSupélec Chair "The Digital Transformations of Electrical Networks"(https://rtechair.fr/)


K Kumar

Bandi Siva

U M Sarma

Satish Mohabe

Madhusudana Reddy

Joël Boustie

Ashok K Tiwari

Rama Rao

Suresh Babu

# V U M Sarma

A Madhusudana Reddy

Joel Boustie

N Rama Rao

K Suresh
email: suresh@iict.res.in

UPLC-MS/MS quantitative analysis and structural fragmentation study of five Parmotrema lichens from the Eastern Ghats

Keywords: Parmotrema tinctorum, Parmotrema andinum, Parmotrema praesorediosum, Parmotrema grayanum, Parmotrema austrosinense, Parmeliaceae, Matrix solid-phase dispersion, UPLC-ToF-MS/MS, Metabolite profiling, Fragmentation studies

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Lichens are nutritionally specialized fungi living in symbiotic association between fungi and algae/cyanobacteria. Several lichen species have been used in traditional medicine for centuries and are gaining considerable interest as an alternative medicine for the treatment of various ailments in different parts of the world. Symbiosis in lichens leads to production of typical secondary metabolites that includes depsides, depsidones, dibenzofurans, anthraquinones, xanthones, pulvinic acid derivatives and napthoquinones [START_REF] Huneck | Identification of Lichen substances[END_REF][START_REF] Elix | A Catalogue of Standardized Chromatographic Data and Biosynthetic Relationships for Lichen Substances[END_REF]. These lichen substances are responsible bio-markers for a wide range of biological activities and ecological roles [START_REF] Molnára | Current Results on Biological Activities of Lichen Secondary Metabolites: a Review[END_REF][START_REF] Vasudeo | Biopharmaceutical potential of lichens[END_REF].

In India, most of lichenological investigations are restricted either to Himalayan or the Western Ghats region. Nevertheless, recent studies indicate that the Deccan Plateau (DP) and the Eastern Ghats (EG) in southern part of India also present rich diversity of lichens. Around 180 lichen species are identified from this region of the country that has gained biological and economical importance [START_REF] Reddy | New distributional records and checklist of lichens for Andhra Pradesh, India[END_REF][START_REF] Nayaka | Eastern Ghats, biodiversity reserves with unexplored lichen wealth[END_REF]. Several Parmotrema species are available in the EG region and most of them became part of folklore medicine in the tribal areas of Andhra Pradesh (AP), India [START_REF] Anjali | Antimicrobial activities of 2-Propanol crude extract from lichen Parmotrema tinctorum (Despr.ex. Nyl.) Hale, collected from Eastern Ghats, India[END_REF]. Although the species are medicinally important, very few species have been verified scientifically with respect to their chemical constituents [START_REF] Ganesan | Antioxidant and antibacterial activity of parmeliod lichens from Shevoroy hills of Eastern Ghats, India[END_REF]. Right identification of lichen species

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is also a challenge and out of bar-coding studies, classifications of lichens are usually carried out by morphology, anatomy along with chemical data based on color reactions obtained on thallus and medulla and metabolite characterization based on thin layer chromatography (TLC) methods. However, most of these tests have some limits to distinguish minute differences between species [START_REF] Honda | A Química Dos Liquens[END_REF]. Alternatively, study of lichen compounds by usual LC-MS techniques [START_REF] Shukla | Ecological implication of variation in the secondary metabolites in Parmelioid lichens with respect to altitude[END_REF] or direct spectroscopic analysis [START_REF] Alcantara | Chemometric analysis applied in 1 H HR-MAS NMR and FT-IR data for chemotaxonomic distinction of intact lichen samples[END_REF][START_REF] Oettl | Dereplication of depsides from the lichen Pseudevernia furfuracea by centrifugal partition chromatography combined to 13 C nuclear magnetic resonance pattern recognition[END_REF][START_REF] Le Corvec | Chemotaxonomic discrimination of lichen species using an infrared chalcogenide fibre optic sensor: a useful tool for on-field biosourcing[END_REF][START_REF] Le Pogam | Matrix-Free UV-Laser Desorption Ionization Mass Spectrometry as a Versatile Approach for Accelerating Dereplication Studies on Lichens[END_REF][START_REF] Mittermeier | Metabolic Profiling of Alpine and Ecuadorian Lichens[END_REF][START_REF] Le Pogam | In situ DART-MS as a Versatile and Rapid Dereplication Tool in Lichenology: Chemical Fingerprinting of Ophioparma ventosa[END_REF][START_REF] Kai | Establishment of a Direct-Injection Electron Ionization-Mass Spectrometry Metabolomics Method and Its Application to Lichen Profiling[END_REF] offers a helpful tool for chemotaxonomic determination of compounds and dereplication strategies [START_REF] Hiserodt | Identification of atranorin and related potential allergens in oak moss absolute by high-performance liquid chromatographytandem mass spectrometry using negative ion atmospheric pressure chemical ionization[END_REF][START_REF] Parrot | Comparative metabolite profiling and chemical study of Ramalina siliquosa complex using LC-ESI-MS/MS approach[END_REF]. Accurate techniques as UPLC-HRMS are now available to identify a number of compounds [START_REF] Salgado | Secondary Metabolite Profiling of Species of the Genus Usnea by UHPLC-ESI-OT-MS-MS[END_REF][START_REF] Torres-Benitez | Metabolomic Analysis of Two Parmotrema Lichens[END_REF][START_REF] Musharraf | Sensitive analysis of bioactive secondary metabolites in lichen species using liquid chromatography-mass spectrometry[END_REF][START_REF] Thadhani | Antioxidant activity of some lichen metabolites[END_REF] but protocols are not still standardized.

Although the number of compounds identified in such analysis is impressive, discrepancies between described compounds and expected compounds are in some cases disturbing. For instance, in the recent description of 37 metabolites found in a Colombian sample identified as Parmotrema robustum [START_REF] Torres-Benitez | Metabolomic Analysis of Two Parmotrema Lichens[END_REF], it is questionable why protocetratic acid is not found while this depsidone and the depside atranorin are considered to be the major markers of this species [START_REF] Smith | The Lichens of Great Britain and Ireland, British Lichen Society[END_REF].

Parmotrema species are also widely distributed in India and this genus comprises about 350 species from the Parmeliaceae family which is considered to be the largest family with 2,765 species all over the world [START_REF] Blanco | Molecular phylogeny of parmotremoid lichens (Ascomycota, Parmeliaceae)[END_REF][START_REF] Crespo | Phylogenetic generic classification of parmelioid lichens (Parmeliaceae, Ascomycota) based on molecular, morphological and chemical evidence[END_REF][START_REF] Gomez -Serranillos | Parmeliaceae family: phytochemistry, pharmacological potential and phylogenetic features[END_REF][START_REF] Lücking | The 2016 classification of lichenized fungi in the Ascomycota and Basidiomycota -Approaching one thousand genera[END_REF]. Although P. robustum could not be found, five Parmotrema species where collected in a same location of the Eastern Ghats to be compared for their metabolite content. As part of our continuous studies on the exploration of natural flora for isolation of bioactive secondary metabolites [START_REF] Le Pogam | Minor Pyranonaphthoquinones from the Apothecia of the Lichen Ophioparma ventosa[END_REF][START_REF] Bandi | New seco-limonoids from Cipadessa baccifera: Isolation, structure determination, synthesis and their antiproliferative activities[END_REF], we conducted a phytochemical study on P. tinctorum (Delise ex Nyl. Hale) which is abundant in the EG region of AP. Five compounds were isolated and fully characterized from its acetone extract and used as standards in subsequent profiling survey. Indeed, a liquid chromatography tandem mass spectrometry (UPLC-MS/MS) method was developed using two complementary UPLC-MS systems for identification,

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characterization and comparative metabolite profiling of Parmotrema species. The first system consisted of a high resolution UPLC-PDA-QToF-MS/MS spectrometer from which metabolites are identified through their MS fragmentation pattern and second system consisted of a UPLC-MS/MS in Multiple Reaction Monitoring (MRM) mode for quantitative analysis of major constituents in the five Parmotrema species. Three extractive techniques were compared to optimize the lichen extract to be analyzed along with various mass spectrometric conditions. This study resulted in the characterization of about fifty compounds (47 secondary metabolites identified) along with ten unknown compounds (Fig. 1). All the metabolites were systematically identified through exact molecular masses from their MS/MS spectra, literature data and comparison of retention times with those of standard compounds, giving additional data to be valued in chemotaxonomy or natural compound discovery. Herein, we report quantitative and qualitative analysis along with a structural fragmentation study of metabolites of Parmotrema species along with free radical scavenging and advanced glycation end-products (AGEs) inhibitory capacities of extracts from five Parmotrema species.

Materials and Methods

Lichen Samples

Samples of Parmeliaceae family Parmotrema tinctorum, P. andinum, P. praesorediosum, P. grayanum and P. austrosinense species were collected from Horsely Hills of Eastern Ghats, Chittor district, Andhra Pradesh, India in the month of February 2015 with a referenced voucher specimen kept in the Yogi Vemana University Herbarium (SI, Table 1). Geographical location of horsely hills where lichens were collected at an altitude of 930-1150 m, 13°39.123´ N and 78° 34.117´ E, India. The morphological features of lichen thallus and ascomata were observed under magnüs MS 24/13, and spot test for color reaction were carried out standardized reagents given in (SI, Table1). For anatomical investigation of fruiting bodies light microscope of ZEISS

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Axiostar was used. The lichen substances were identified with thin layer chromatography in solvent system 'A' following White and James [START_REF] Orange | Microchemical methods for the identification of lichens[END_REF][START_REF] White | A new guide to microchemical techniques for the identification of lichen substances[END_REF][START_REF] Mohabe | An appraisal of lichen biota in Chittoor district of Andhra Pradesh, India[END_REF]. The standard literatures [START_REF] Awasthi | A Compendium of the Macrolichens from India, Nepal and Sri Lanka[END_REF][START_REF] Divakar | Parmelioid Lichens in India (A Revisionary Study)[END_REF][START_REF] Jayalal | The Lichen Genus Parmotrema in South Korea[END_REF] were referred for identification of lichen samples.

Chemicals and Reagents

HPLC-grade acetonitrile was obtained from Biosolve Chimie SARL (Dieuze, France), formic acid (Optima LC/MS grade) from Fisher Scientific (Geel, Belgium,) and methanol (LiChrosolv) was purchased from Merck (Darmstadt, Germany). Ultra-pure water was used throughout study which was produced by Milli-Q water purification system (Millipore, Milford, MA, USA). Isolated pure compounds were used as standards for quantification.

Experimental procedure for Isolation of major constituents from P. tinctorum

Finely ground dry thalli of P. tinctorum (50g) were extracted with acetone (2x1L) at room temperature for 48h.

Extraction procedures for preparation of lichen extracts for analysis

In order to obtain the best extraction yields and the wider variety of lichen compounds from lichen thalli, we investigated various extraction procedures/conditions on P. tinctorum The butanol, ethanol, methanol and Milli Q water with 5 mg/mL], the extraction temperature (both hot and ambient conditions) and ultra-sonication (Fig. 2A). Each extraction condition was performed in triplicate and amount of extracted material was determined. Overall, it turned out that acetonitrile was a better extraction solvent than the other solvents. Based on this optimized solvent parameter, we moved to matrix solid phase dispersion (MSPD) extraction method for all lichens using acetonitrile as solvent (see supporting information for detailed extraction procedures).

The type of dispersant is a critical factor due to significant differences in adsorption capacity and selectivity of various dispersants [START_REF] Capriotti | Recent developments in matrix solid-phase dispersion extraction[END_REF]. In the present work, three types of dispersants (SiO2, Al2O3, and RP C18) were investigated. As shown in Fig. 2C, 1:2 ratio of sample to C18 dispersant is the most favorable proportion to extract lichen compounds with acetonitrile whatever the Parmotrema lichen thallus studied.

Instrumental conditions 2.5.1.Chromatographic conditions

Chromatographic separations were performed using a reverse phase hypersil gold column (150 X 2.1mm, 1.9µm) (USA) with the maintenance of ambient temperature (25 0 C) throughout the experiment. Mobile phase was a mixture of millipore water (A), acetonitrile (B) and methanol (C) with 0.1% formic acid in all the solvents used as mobile phase at a flow rate of 0.

2.5.2.Mass spectrometric conditions

The chromatographic analysis was performed on a shimadzu nexera X2 UPLC system (Shimadzu Corporation, Nakagyo, Kyoto, Japan) equipped with a quaternary pump, an online degasser (DGU-20A 5R), a thermo stated auto sampler (SIL-30AC), a thermostatically controlled column compartment (CTO-20AC), and a diode array detector (PDA) (SPD-M20A), which were communicated through bus module (CBM-20A). High-resolution masses of metabolites were measured after UPLC separation.

Chromatographic separation was performed on acquity H Class UPLC system (Waters, Milford, MA, USA) with a conditioned auto sampler, using an Acquity BEH C18 column (100 mm X scavenging activity was performed as reported [START_REF] Priyanka | Presence of postprandial antidysmetabolic and antioxidative stress properties in aqueous methanol extract of seeds and tuber of aquatic food plant Nymphaea nouchali (Burm.f.)[END_REF]. Decolorization of ABTS

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were prepared and studied to find radical scavenging 50% concentrations. Trolox was taken as standard reference compound.

2.6.2.Advanced glycation end products (AGEs) inhibitory assay

Glycation of bovine serum albumin protein was induced in hyperglycemic environment seven days [START_REF] Poornima | Advanced glycation end-products inhibitors isolated from Schisandra grandiflora[END_REF]. Aminoguanidine was choice of reference AGEs inhibitor. The vesperlysine-like (ʎexc 370 nm; ʎem 440 nm) and pentosidine-like (ʎexc 335 nm; ʎem 385 nm) AGEs inhibitory capacity of lichen extracts were analyzed [START_REF] Séro | Tuning a 96well microtiter plate fluorescence -based assay to identify AGE inhibitors in crude plant extracts[END_REF].

Results and Discussion

Collection and identification of samples

In the present study, five species of Parmotrema having a closely shaped grey thallus [P.

tinctorum (Delise ex Nyl.) Hale (PT), P. andinum (Mull. Arg.) Hale (PA), P. praesorediosum (Nyl.) Hale (PP), P. grayanum (Hue) Hale (PG), P. austrosinense (Zahlbr.) Hale (PS)] were collected on rocks from Horsely Hills of Eastern Ghats at ca. 1000m altitude (SI, collection site and Table 1S). As usual, they were identified by morphological characters and thallus reactions which clearly distinguished PG and PP (negative reaction of the medulla to calcium hypochlorite solution (C-)) from the three other species (PA, PS and PT with a C+ red medulla) (Table 1S).

However, thallus reactions can be variable and give poor indications for the identification of secondary metabolites of the studied Parmotrema lichens. HPTLC (Fig. 1S) and UPLC-PDA profiles (Fig. 2S) were more informative for chemical constituents as atranorin [START_REF] Anjali | Antimicrobial activities of 2-Propanol crude extract from lichen Parmotrema tinctorum (Despr.ex. Nyl.) Hale, collected from Eastern Ghats, India[END_REF] and chloratranorin [START_REF] Ganesan | Antioxidant and antibacterial activity of parmeliod lichens from Shevoroy hills of Eastern Ghats, India[END_REF] were visualized in all the species while abundant yields of lecanoric acid [START_REF] Musharraf | Sensitive analysis of bioactive secondary metabolites in lichen species using liquid chromatography-mass spectrometry[END_REF] and orsellinic acid [START_REF] Smith | The Lichens of Great Britain and Ireland, British Lichen Society[END_REF] appear to be present in PT, PS and PA only, confirming the two subgroups. Lens-magnified and microscope observed anatomical characters were considered to discriminate the five species (Fig. 2S) but a more accurate information was expected from a

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qualitative and quantitative mass analysis for secondary metabolites analysis from optimized lichen extracts.

Isolation of compounds from P. tinctorum (Despr.ex Nyl) Hale

Parmotrema tinctorum was abundantly available from seashore rocks or bark trees in EG, we first carried a phytochemical study on this lichen which also appears to be a good source for standards. 50g of P. tinctorum were extracted in acetone and further subjected to repeated column chromatography and preparative TLC to result in the isolation of five known compounds (2, 7, 19, 24, 26). Structures of these compounds were identified as monoaromatic phenols orsellinic acid [START_REF] Smith | The Lichens of Great Britain and Ireland, British Lichen Society[END_REF] and methyl β-orsellinate [START_REF] Crespo | Phylogenetic generic classification of parmelioid lichens (Parmeliaceae, Ascomycota) based on molecular, morphological and chemical evidence[END_REF], depsides lecanoric acid (2) and atranorin [START_REF] Anjali | Antimicrobial activities of 2-Propanol crude extract from lichen Parmotrema tinctorum (Despr.ex. Nyl.) Hale, collected from Eastern Ghats, India[END_REF], and the depsidone norlobaridone [START_REF] Parrot | Comparative metabolite profiling and chemical study of Ramalina siliquosa complex using LC-ESI-MS/MS approach[END_REF] from the analysis of their spectroscopic data (Figure 8S-12S) and comparison with literature data [START_REF] Huneck | Identification of Lichen substances[END_REF]. Presence of a particular type of metabolite has been proposed based on the occurrence of characteristic molecular ion peak and further analysis of its fragmentation ions implied the structure of metabolite [START_REF] Le Pogam | Matrix-Free UV-Laser Desorption Ionization Mass Spectrometry as a Versatile Approach for Accelerating Dereplication Studies on Lichens[END_REF][START_REF] Musharraf | Rapid identification of lichen compounds based on the structure-fragmentation relationship using ESI-MS/MS analysis[END_REF]. In the present study a total of 47 compounds were clearly characterized from the five lichen species by molecular formula generated by ToF-MS/MS and Relative Double Bond Equivalence (RDBE) including their biogenetic pathway as reported in the literature [START_REF] Calcott | Secondary metabolism in the lichen symbiosis[END_REF][START_REF] Duong | New meta-depsidones and diphenyl ethers from the lichen Parmotrema tsavoense (Krong & Swinscow) Krong & Swinscow, Parmeliaceae[END_REF]. Among them, 47 secondary metabolites were tentatively identified and characterized by their diagnostic fragment ion peaks in the MS/MS spectrum in Table 1.

Identification and comparative analysis of secondary metabolites from

The representative LC-MS base-peak chromatograms of Parmotrema species are presented (Fig. 3). As shown, five compounds (orsellinic acid [START_REF] Smith | The Lichens of Great Britain and Ireland, British Lichen Society[END_REF], lecanoric acid (2), methyl β-orsellinate [START_REF] Crespo | Phylogenetic generic classification of parmelioid lichens (Parmeliaceae, Ascomycota) based on molecular, morphological and chemical evidence[END_REF], norlobaridone [START_REF] Parrot | Comparative metabolite profiling and chemical study of Ramalina siliquosa complex using LC-ESI-MS/MS approach[END_REF], and atranorin (7)) were found at 4.34 min, 7.71 min, 7.87 min, 10.62 min, and 11.94 min in LC-PDA chromatograms (Fig. 3S) at 254nm for P. tinctorum and these compounds were confirmed with the comparison of pure authentic compounds. By taking these compounds as representative standards, we further also compared and analyzed the distribution of these major metabolites among the remaining four species. LC-QToF-MS/MS analysis (TIC) of the optimized lichen extracts confirmed the presence of the main common compounds already described in these Parmotrema species but also a series of 10 additional lichen metabolites not previously described in any of the studied species. Structures are tentatively assigned to lichen secondary metabolites from which some remain to be specified as ambiguous isomers (e.g. dihydrolichesterinic acid which can corresponds to roccellaric acid or nephromopsic acid), non described compounds (e.g. orsellinylgyrophorate, dehydronephrosterinic acid,

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norprotopraesorediosic acid) and ten unknown compounds. We generated a venn diagram (Fig.

7S) which clearly shows distribution and classification of known compounds in the five

Parmotrema species. While atranorin [START_REF] Anjali | Antimicrobial activities of 2-Propanol crude extract from lichen Parmotrema tinctorum (Despr.ex. Nyl.) Hale, collected from Eastern Ghats, India[END_REF] and chloratranorin [START_REF] Ganesan | Antioxidant and antibacterial activity of parmeliod lichens from Shevoroy hills of Eastern Ghats, India[END_REF] are produced by all these species, some compounds are only found in a given species (e. g. papulosic derivatives in P.

andinum). A real chemotaxonomic value cannot be ascertained without a statistical analysis of multiple specimens but the Venn diagram (Fig. 7S) suggests a clear distinction between P.

praesorediosum which produces a variety of paraconic acids and P. tinctorum containing depsides and depsidones predominantly. The chemical profile of these species is more complete and in accordance with the presence of the major compounds described by lichenologists [START_REF] Smith | The Lichens of Great Britain and Ireland, British Lichen Society[END_REF][START_REF] Castro | Metabolomic Analysis of the Lichen Everniopsis trulla using Ultra High Performance Liquid Chromatography-Quadrupole-Orbitrap Mass Spectrometry (UHPLC-Q-OT-MS)[END_REF]. Additional compounds have been isolated or characterized in recent studies for P.

praesorediosum [START_REF] Jayalal | The Lichen Genus Parmotrema in South Korea[END_REF][START_REF] Huynh | New Phenolic compounds from the lichen Parmotrema praesorediosum (Nyl.) Hale (Parmeliaceae)[END_REF][START_REF] Huynh | New γ-Lactone Carboxylic acids from the Lichen Parmotrema praesorediosum (Nyl.) Hale, Parmeliaceae[END_REF], P. grayanum [START_REF] Thadhani | Antioxidant activity of some lichen metabolites[END_REF][START_REF] Musharraf | Rapid identification of lichen compounds based on the structure-fragmentation relationship using ESI-MS/MS analysis[END_REF], and P. andinum [START_REF] Torres-Benitez | Metabolomic Analysis of Two Parmotrema Lichens[END_REF]. In addition to compounds found in such analysis, diphenylethers and phtalides have been isolated and identified from P. praesorediosum by a Vietnamese team from large quantities of a lichen sample collected in Thailand [START_REF] Jayalal | The Lichen Genus Parmotrema in South Korea[END_REF]. A mixture of collected species cannot be excluded as the unexpected usnic acid and isousnic acids are described. Moreover, extensive use of MeOH in the process could have generated artefacts [START_REF] Huneck | tert-Butanolysis of lichen depsides[END_REF] as methyldivaricatic acid but these differences also suggest the analytical techniques cannot be considered as fully exhaustive, whatever accurate and informative they are. Considering P. grayanum from which compounds have been isolated

and identified from samples collected in Sri Lanka, it is highly questionable to find lecanoric acid and usnic acid mentioned in a first publication [START_REF] Thadhani | Antioxidant activity of some lichen metabolites[END_REF]. Usnic acid is not described again in recent LC MS/MS QTOF analysis of this species collected in Sri-Lanka [START_REF] Musharraf | Sensitive analysis of bioactive secondary metabolites in lichen species using liquid chromatography-mass spectrometry[END_REF][START_REF] Musharraf | Rapid identification of lichen compounds based on the structure-fragmentation relationship using ESI-MS/MS analysis[END_REF]. Additionally, the chemical profile with the depsides lecanoric acid, divaricatic acid sekikaic acid and absence of paraconic acids is not fitting the described P. grayanum typus profile [START_REF] Smith | The Lichens of Great Britain and Ireland, British Lichen Society[END_REF][START_REF] Elix | Parmotrema[END_REF]. This suggests a

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misidentification of the collected samples to be checked again from the deposited voucher samples. One of the studied species, P. andinum was also analysed by UPLC HR-ESI MS/MS collected from northern Peru [START_REF] Torres-Benitez | Metabolomic Analysis of Two Parmotrema Lichens[END_REF] reporting the presence of 30 metabolites versus 18 in our analysis. However only five compounds were found as the same in the two experiments including the two depsides lecanoric acid and atranorin recognized as markers of this species [START_REF] Winnem | Parmelia subgenus Amphigymnia in Ethiopia[END_REF] . Differences in protocols used to prepare the extracts to be analysed can explain part of these discrepancies. Parallel analysis of a variety of specimens in a standardized protocol and a barcoding analysis of the studied samples would be the best approach to be conclusive. Facing this situation, we consider a sharp chemotaxonomic discussion is beyond the frame of this study, most of all carried out to investigate the contribution of hyphenated accurate mass spectrometry techniques to lichen chemical profiling.

3.3.2.Mass fragmentation study

In the present work, identification of minor compounds in each species was analyzed by UPLC-QToF-MS/MS in the ESI negative mode using a high-resolution detection. Accordingly, each species was subjected to UPLC-QTOF-MS/MS in ESI mode (negative) in order to determine molecular formula of detected depsides, depsidones, paraconic acids and monophenolic compounds. Consideration of their UV absorption in PDA, triple quadruple mass and high resolution masses allowed dereplication of the known compounds as well as preliminary characterization of new metabolites in all the species. Results are shown in Table 1.

All the metabolites were classified based on their common fragmentation ion in MS/MS spectra.

Depside class of compounds possesses common fragmentation through the breakage of ester bond between two phenolic rings as shown [START_REF] Musharraf | Rapid identification of lichen compounds based on the structure-fragmentation relationship using ESI-MS/MS analysis[END_REF][START_REF] Holzmann | Applications of negative fast atom bombardment and MS/MS to screening of lichen compounds[END_REF][START_REF] Otter | Metabolic diversity of lichen forming ascomycetous fungi: culturing, polyketide and shikimate metabolite production, and PKS genes[END_REF] (Fig. 4). Similarly, in depsidones fragmentation ions appear through the simple loss of CO2, H2O, CH2O, followed by cyclization,

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while loss of CO2 and alkane chain breakage were seen in paraconic acids. Initially, known compounds atranorin [START_REF] Anjali | Antimicrobial activities of 2-Propanol crude extract from lichen Parmotrema tinctorum (Despr.ex. Nyl.) Hale, collected from Eastern Ghats, India[END_REF], orsellinic acid [START_REF] Smith | The Lichens of Great Britain and Ireland, British Lichen Society[END_REF], norlobaridone [START_REF] Parrot | Comparative metabolite profiling and chemical study of Ramalina siliquosa complex using LC-ESI-MS/MS approach[END_REF] and salazinic acid ( 14) were taken as representative compounds for each group and their ToF-MS/MS spectra were analyzed (Fig. 4S). Then efforts were made to analyze secondary metabolites of each class through their fragmentation patterns.

Structural analysis and fragmentation pattern of Depsides (1-11)

Compounds

Structural analysis and fragmentation pattern of Depsidones (12-22)

The [M-H] -ions for compounds 12-22 were detected in negative ion mode and the fragmentation profiles are similar to the standard depsidone type of compound, salazinic acid ( 14) indicating similar skeletons with substitutions. Salazinic acid ( 14) is used as a representative compound for the following discussion and structure analysis. A high abundance product ion at m/z 343.0455 was formed from the precursor [M-H] -ions by sequential loss of CO2 in MS/MS spectrum, as seen from fragmentation patterns for the depsidones [START_REF] Parrot | Comparative metabolite profiling and chemical study of Ramalina siliquosa complex using LC-ESI-MS/MS approach[END_REF]. Further, fragmentation afforded product ions at m/z 313.0346 by loss of CH2O, at m/z 269.0451by loss of CO2. The molecular weight of 12 differs from salazinic acid ( 14) with 2Da and fragmentation pattern of 12 was indicating the product ions at m/z 371.0401, 345.0607, 327.0505, 309.0401, 297.0401by sequential loss of CO2, H2O and CH2O etc. Furthermore, lack of one DBE in 12 when compared to salazinic acid, was indicating the presence of -CH2OH group in 12 instead of -CHO as in salazinic acid. Thus, structure of compound 12 was assigned as a consalazinic acid. Based on above strategy and fragmentation pathways (Fig. 5), structures of remaining depsidones were assigned and detailed fragmentation studies are shown in supporting information.

3.3.5.Structural analysis and fragmentation pattern of mono-phenolic compounds (23-29)

It is well known fact that biosynthetically lichen substances were formed from simple phenolic compounds [START_REF] Le Pogam | Matrix-Free UV-Laser Desorption Ionization Mass Spectrometry as a Versatile Approach for Accelerating Dereplication Studies on Lichens[END_REF][START_REF] Otter | Metabolic diversity of lichen forming ascomycetous fungi: culturing, polyketide and shikimate metabolite production, and PKS genes[END_REF]. The orsellinic acid [START_REF] Smith | The Lichens of Great Britain and Ireland, British Lichen Society[END_REF] was taken as a standard for structural analysis of mono-phenolic compounds [START_REF] Thadhani | Antioxidant activity of some lichen metabolites[END_REF][START_REF] Smith | The Lichens of Great Britain and Ireland, British Lichen Society[END_REF][START_REF] Blanco | Molecular phylogeny of parmotremoid lichens (Ascomycota, Parmeliaceae)[END_REF][START_REF] Crespo | Phylogenetic generic classification of parmelioid lichens (Parmeliaceae, Ascomycota) based on molecular, morphological and chemical evidence[END_REF][START_REF] Gomez -Serranillos | Parmeliaceae family: phytochemistry, pharmacological potential and phylogenetic features[END_REF][START_REF] Lücking | The 2016 classification of lichenized fungi in the Ascomycota and Basidiomycota -Approaching one thousand genera[END_REF][START_REF] Le Pogam | Minor Pyranonaphthoquinones from the Apothecia of the Lichen Ophioparma ventosa[END_REF]. Analysis of MS data obtained for 26 and 27 indicated similarities with orsellinic acid [START_REF] Smith | The Lichens of Great Britain and Ireland, British Lichen Society[END_REF] and its fragmentation ions. From MS data, it is also observed that molecular weight of 26 was more than orsellinic acid (24) by 14Da with an

A C C E P T E D M A N U S C R I P T
additional DBE. Further analysis of its product ion at m/z123.0446 [M-H] -indicated the sequential loss of CO2, CO which provided information about presence of aldehyde group instead of methyl group. Similarly, presence of the product ion at m/z 79.0556 in MS/MS spectrum of 27 indicated the presence of -CH2OH group instead of methyl group as in orsellinic acid [START_REF] Smith | The Lichens of Great Britain and Ireland, British Lichen Society[END_REF]. Based on these fragmentation pathway parameters (Fig. 6), the structures of remaining mono-phenolic compounds were analyzed and compounds [START_REF] Gomez -Serranillos | Parmeliaceae family: phytochemistry, pharmacological potential and phylogenetic features[END_REF][START_REF] Lücking | The 2016 classification of lichenized fungi in the Ascomycota and Basidiomycota -Approaching one thousand genera[END_REF] were found to be tentatively new compounds for which the fragmentations were proposed for the first time.

3.3.6.Structural analysis and fragmentation pattern of paraconic acids (30-47)

As analyzed, compounds 30-47 belong to the class of paraconic acid/aliphatic acid-type compounds. The fragmentation pathways and profiles of product ions for 30-47 were same in each case. To determine their structures, we compared the fragmentation pathways and profile of product ions with reference, DBE and UV absorbance. It was found that the fragmentation pathways of major product ions are very similar but crossing data was informative. As for compounds 30, 31 and 34 compounds with same molecular formula had proposed structures based on fragment ions, Rf values and literature. Protolichesterinic acid (36) taken as an example [START_REF] Horhand | Separation of a mixture of paraconic acids from Cetraria islandica (L.) Ach. employing a fluorous tag-catch and release strategy[END_REF], ToF-MS/MS spectrum indicated the product ions at m/z 279.2325, 235.2428 formed from the molecular ions by sequential CO2 losses and aliphatic chain breakage. Losses of acetyl group and side chains in some of the compounds are also observed. Based on this fragmentation pathway (Fig. 7), molecular formula and HR-MS/MS fragments (Table 1), structures of 39-40 and 42-47 were proposed in Fig. 1. Fragmentation patterns for these compounds were shown in supporting information.

3.3.7.Structural analysis of other compounds 48 to 57

A C C E P T E D M A N U S C R I P T
From these four Parmotrema species, ten additional compounds were characterized from elemental constituents and fragmentation pathways, including an additional chlorinated compound in PP (Table 1). Skeleton could not be identified because of a lack of reference compounds but the potential for discovering new chemical entities in lichens is once again illustrated

Quantitative analysis of six major compounds in Parmotrema species

Quantitative analysis of five compounds (orsellinic acid, lecanoric acid, methyl βorsellinate, norlobaridone and atranorin) (Fig. 1) were performed using UPLC-APCI-MS/MS in multi reaction monitoring (MRM) mode of detection (Fig. 5S). The derived calibration curves of five compounds were characterized by adequate linearity (R 2 ≥ 0.998) and LODs were defined in the range 0.05-0.005μg/mL, while LOQs ranged from 0.20 to 0.02 μg/ mL as given in Table 2S.

Method was also precise, even for trace analysis of compounds. The relative standard deviation (% RSD) value of retention times (Rt) for the precision (intra-day and inter-day variability) were less than 5 % in Table 1S while % RSD (n = 3) of peak areas ranged from 0.952 to 4.338 in Table 1S. The mean recovery of each compound revealed desirable figures between 96.09±1.14% to 103.69±1.15% in Table 2S. The results of the quantitative analysis were shown in Table 2, which clearly indicated that atranorin [START_REF] Anjali | Antimicrobial activities of 2-Propanol crude extract from lichen Parmotrema tinctorum (Despr.ex. Nyl.) Hale, collected from Eastern Ghats, India[END_REF] and methyl β-orsellinate [START_REF] Crespo | Phylogenetic generic classification of parmelioid lichens (Parmeliaceae, Ascomycota) based on molecular, morphological and chemical evidence[END_REF] were present in all Parmotrema species while orsellinic acid [START_REF] Smith | The Lichens of Great Britain and Ireland, British Lichen Society[END_REF] is found in two species (PT and PA) and norlobaridone [START_REF] Parrot | Comparative metabolite profiling and chemical study of Ramalina siliquosa complex using LC-ESI-MS/MS approach[END_REF] in PT only. Lecanoric acid (2) is found as the major compound in three species of Parmotrema (PT, PA, PS), among them PT contains high quantity (# 0.71 mol/mg).

Although yields can be significantly modified in a given species by environmental factors [START_REF] Asplund | Stimulated global warming increases usnic acid but perlatolic acid in the mat-forming terricolous lichen Cladonia stellaris[END_REF] the contrasted ratio between common compounds could be considered as a chemotaxonomic marker. PS and PT being collected in a close location and at the same period, atranorin [START_REF] Anjali | Antimicrobial activities of 2-Propanol crude extract from lichen Parmotrema tinctorum (Despr.ex. Nyl.) Hale, collected from Eastern Ghats, India[END_REF] and

Biological activity

Lichens are a rich resource of novel bioactive compounds and their antioxidant potential is well documented [START_REF] Marijana | Antioxidant properties of some lichen species[END_REF]. Their antidiabetic potential has received considerable attention in the recent past. The Parmotrema species, including P. tinctorum [START_REF] Salin Raj | Parmotrema tinctorum exhibits antioxidant, antiglycation and inhibitory activities against aldose reductase and carbohydrate digestive enzymes: as in vitro study[END_REF] has shown promising potential in both antidiabetic and antioxidant [START_REF] Vinitha | Potential of Lichen Compounds as Antidiabetic Agents with Antioxidative Properties: A Review[END_REF]. Therefore, investigation of lichens as an alternative antidiabetic food source presents an exciting opportunity.

3.5.1.Free radical scavenging antioxidant activity

All the crude acetonitrile extracts of Parmotrema species were evaluated for their ABTS •+ radical scavenging antioxidant activity. Results are presented in Table 3. Decolorization assay of ABTS •+ is most popular and simple assay applicable for evaluating antioxidant activity of natural food materials [START_REF] Re | Antioxidant activity applying an improved ABTS radical cation decolorization assay[END_REF]. Among five lichen extracts, PP extract followed by that of PT happened to be the most potent extracts bearing antioxidant activity. These activities might be arising due the presence of huge number of polyphenolic and acid compounds in these lichens [START_REF] Lopes | Radical-scavenging activity of orsellinates[END_REF]. In PS extract however, we could not detect ABTS •+ scavenging activity.

3.5.2.Advance glycation end products (AGEs) inhibition

Oxidative stress in hyperglycemic individuals is identified as crucial step in initiating development of diabetic complication [START_REF] Giacco | Oxidative stress and diabetic complications[END_REF]. Formation of increased AGEs in hyperglycemic condition promotes development of oxidative stress [START_REF] Sottero | Postprandial dysmetabolism and oxidative stress in type 2 diabetes: Pathogenetic mechanisms and therapeutic strategies[END_REF]. Therefore, inhibition of AGEs formation is an important step in controlling development of diabetic complications [START_REF] Priyanka | Presence of postprandial antidysmetabolic and antioxidative stress properties in aqueous methanol extract of seeds and tuber of aquatic food plant Nymphaea nouchali (Burm.f.)[END_REF]. However, only PT and PS extracts could inhibit vesperlysine-like AGEs (Table 3). The pentosidine-like AGEs are identified in plasma, erythrocytes [START_REF] Grillo | Advanced glycation end products (AGEs): Involvement in aging and in neurodegenerative diseases[END_REF] and in bone of diabetic people [START_REF] Vashishth | Advanced Glycation End-products and Bone Fractures[END_REF] whereas vesperlysine-like AGEs are recorded in lens of diabetic individuals [START_REF] Grillo | Advanced glycation end products (AGEs): Involvement in aging and in neurodegenerative diseases[END_REF]. The P.

austrosinense extract has a good activity on these too targets with no antioxidant activity in the ABTS assay, which is suggesting a possible specific mechanism of action. So this lichen species will be investigated in order to better assess its potential against development of diabetic complications.

Conclusions

Overall, the comparative metabolite profiling of five lichen species of Parmotrema were performed using two complementary UPLC-MS systems. After optimization of parameters, the UPLC-QToF-MS/MS method led to identify a total number of about 47 compounds including nine new compounds. Further, minor compounds were identified through their exact molecular masses from their MS/MS spectra, the comparison of literature data and fragmentation pathways were proposed for each compound. On the other hand, we also developed UPLC-APCI-MS/MS in MRM for the quantification of five common lichen substances (orsellinic acid, lecanoric acid, methyl β-orsellinate, norlobaridone, and atranorin) in five lichen species. Both UPLC-PDA-QToF-MS/MS and UPLC-APCI-MRM methods helped in identification of several compounds in all species including standards, which were useful for the dereplication to decrease the tedious process of isolation. As suitable for minute amount of raw material and more informative than the thallus reactions and TLC profiles usually performed in lichen identification, these methods are of great interest for lichen analysis. However as illustrated by major discrepancies in metabolite profiles according to authors, a reliable bank data has to be built using a standardized

  considered parameters included the different (non-polar and polar) solvents for extraction [i.e. nhexane, diethyl ether, dichloromethane, tetrahydrofuran, ethyl acetate, acetone, acetonitrile, n-

For

  LC-APCI-MS experiments, shimadzu triple quadruple mass spectrometer (LCMS 8040) (Shimadzu Corporation, Kyoto, Japan) equipped with an atmospheric chemical ionization (APCI) source was connected to UPLC instrument. The APCI source parameters were set as follows: ion spray voltage, 4.5 KV; Desolvation line temperature, 250°C; APCI source temp at 350 °C, Heat Block Temperature, 250 °C; Nebulizing (N2) and Dry gas (N2) flow rates, 3.0 and 5.0 L/min, respectively. Argon gas was used as CID gas for MRM experiments. The mass analyzer was operated in positive and negative ion mode for MRM experiments with polarity switching at 15 msec, with a mass range of 50 to 500 m/z. Accurate masses were calibrated according to the manufacturer's guidelines using TQ Standard Sample (PEG, PPG and Raffinose) (Shimadzu corporation, Kyoto, Japan). Data were recorded and processed using the LCMS Lab Solutions 5.60 SP2 software (Shimadzu Corporation, Kyoto, Japan).

2 .

 2 1mm i.d., 1.7 μm particle size) (Waters, Milford, MA, USA). The column temperature was maintained at 25 °C. The mobile phase consisting of water with 0.1% formic acid in water (solvent A) and acetonitrile (solvent B) was pumped at a flow rate of 0.4mL/min. The gradient elution program was as follows: 0 min, 5%B; 3.00 min, 20% B; 5.00min, 35%B; 7.50min, 50%B; 10.00min, 70% B; 11.50 min , 85% B; 12.50 min 95% B; 17.00 min 95% B; 18.00 min 5% B. Equilibration time was 5 min and the injection volume was 1 μL. LC-MS e mode was applied to analyze the samples in both TIC as well as MS/MS mode where collision energy was ramped at 5 eV -40 eV. Eluted compounds were detected from m/z 50 to m/z 1200 using Xevo G2-XS QTOF mass spectrometer (Waters, Manchester, UK), which was connected to Electrospray ionization (ESI) interface with negative ion mode using the following instrument settings, capillary voltage, 2.0KV; sample cone, 30V; source temperature, 120 °C; desolvation temperature 350 °C; cone gas flow rate 50 L/Hr; desolvation gas (N2) flow rate 1000 L/Hr, Argon as CID gas for MS/MS experiments. All analyses were performed using the lock spray, which ensured accuracy and reproducibility. Leucine -Enkephalin (5ng/mL) was used as lock mass generating a reference ion in negative mode at m/z 554.2615 and introduced by a lock spray at 10 μL/min for accurate mass acquisition. Data acquisition was achieved using MassLynx v 4.1. Acquiring data in this manner provided the collection of information of intact precursor ions as well as fragment ions.2.6. Biological Activity2.6.1.ABTS •+ free-radical scavenging assay [2, 2'-azinobis-(3-ethylbenzothiazolin-6-sulphonic acid] radical cation (ABTS •+ )

  Parmotrema species3.3.1.UPLC-ToF-MS/MS analysisUPLC-MS is a powerful tool for the qualitative and quantitative analysis of secondary metabolites from lichens[START_REF] Musharraf | Rapid identification of lichen compounds based on the structure-fragmentation relationship using ESI-MS/MS analysis[END_REF]. Recently Carlos Areche' team described lists of compounds in two Parmotrema and four Usnea species from South-America[START_REF] Musharraf | Sensitive analysis of bioactive secondary metabolites in lichen species using liquid chromatography-mass spectrometry[END_REF][START_REF] Calcott | Secondary metabolism in the lichen symbiosis[END_REF]. Lichen secondary metabolite structures frequently have carboxyl or phenyl groups and thus could be readily ionized via electrospray ionization (ESI) source. Initially, chemical constituents of P. tinctorum were analyzed by reversed-phase UPLC-MS eluted with gradient mobile phase consisting of acetonitrile and water containing 0.1% formic acid. This allowed elution of all analytes within 18 minutes. Based on these optimized conditions, acquired UPLC-PDA and MS total ion chromatograms (TIC) of five Parmotrema species were analyzed in ESI negative ionization mode and these results are presented (Fig.3). To confirm results and structures of metabolites, ToF-MS/MS analysis was performed. The peak results were identified based on their MS spectral data (accurate mass and fragmentation pattern), retention times, comparison to the standard compounds, and searching in public online-databases (DNP, Reaxys, SciFinder).

1 - 10

 110 belong to depside class of metabolites and [M-H] -ions for these were detected in ESI-QToF-MS (negative mode) scan. The CID-MS profiles were almost similar to those of standard depsides as shown (Fig.5S&4), which clearly indicate similar skeletons including position of substituted groups of these compounds (2, 7 and 1-8). Compound 1 is used as a representative compound for the following discussion and structure analysis of depsides.The molecular formula of 1 was confirmed as C16H13O8 [M-H] -from the accurate mass, relative isotopic abundance (RIA) measurements and the MS/MS spectrum. The high abundance product ion at m/z 183.0297, 167.0342 were formed from pseudo-molecular ion [M-H] -at m/z 333.0611 by cleavage of ester bond (Fig.4). Further fragmentation of these ions afforded product ions due to sequential losses of CO2 and H2O, respectively. Similarly, ESI-MS/MS spectrum showed [M-H] -ions of more substituted phenols such as compound 10 which showed molecular formula C16H11O9 [M-H] -, indicating 14 Da more than papulosic acid (1) in

  concluded the structures of remaining depsides (1-9) and detailed fragmentation patterns are shown in supporting information.

  lecanoric acid (2) are the two major depsides for PT while only lecanoric acid should be considered for PS. It is also worth mentioning that norlobaridone (19) is only found in PT (# 0.02 mol/mg) in trace amount and can therefore explain the absence of description in PT from usual TLC used.

  and PS were equipotent in inhibiting pentosidine-like AGEs as aminoguanidine.

Fig. 1 :Fig. 2 :Fig. 3 :Fig. 5 :Fig. 6 :Fig. 7 :

 123567 Figure Legend:

Fig. 3 A

 3 Fig. 3

Table 1

 1

	and an

identified as a new compound (Table

1

). By following similar fragmentation pathways, we

Table 2

 2 Comparative yields of the five metabolites isolated from P. tinctorum from LC-QQQ-MS analysis of the crude acetone extracts of the studied Parmotrema species (mol/mg dry weight ±

	SD)

Table 3

 3 ABTS % scavenging and formation of AGEs inhibition by lichen extracts.

				U S C R I P T
				N
			A
		Lichen extracts	ABTS % scavenging at 50 µg/mL M	*AGEs % Inhibition at 20 µg/mL
	concentration (SC50 µg/mL) 99.3 (2.64) 99.5 (4.74) 94.41 (1.35) 98.01 (7.42) NA 99.6 (0.96) C C E P T E D PT PA PP PG PS Trolox	V type 56.3±1.7 NA 8.0±1.3 NA 68.2±4.2	P type 47.6 ±1.3 88.6±2.9 75.7±0.6 42.3±1.0 85.3±5.5
	A	Amino guanidine		97.2±0.3	83.3±0.4
			*Values represent mean±SD, n=4

Acknowledgements

Didier Masson is highly acknowledged for his insightful comments and expertise on Parmeliaceae lichens. This research was performed as a part of the Indo-French LIA 'Natural Products and Synthesis for Affordable Health' and acknowledgments are due to CSIR (India) and CNRS (France). Authors thank to Director, IICT for his constant encouragement and support. BS thanks to CSIR for fellowship program and financial support.