Optimal Reactive Supervision of Grid Connected PV

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Optimal Reactive Supervision of Grid Connected PV Systems with Batteries in Real Conditions Y. Riffonneau, S. Bacha, F. Barruel, Y. Baghzouz, E. Zamaï

Abstract – This study deals with reactive and optimal supervision of power flow in a grid connected PV system with batteries in real conditions. Four different reactive supervisions, derived from the predictive power flow from the forecasts, are presented. . An innovative method is proposed to perform optimal adjustment of the predictive strategy according to real conditions while avoiding high computation demand from a new calculation of the global optimal solution. Results from simulations in a restrictive case show that the proposed closed loop supervisions can save up to 40% of the operation cost when compared to the open loop supervision. Keywords: Photovoltaic power systems, Energy management, Optimization, Dynamic Programming, Battery Energy Storage, Supervision Paper submitted to IREE , January 2007 Praise Worthy Prize- Preprint version

I. Nomenclature PV : Photovoltaic MILP : Mixed Integer Linear Programming SOC : State of Charge of the battery SOH : State of Health of the battery DP : Dynamic Programming CF : Cash Flow EgP : Electricity grid Price HEV : hybrid electric vehicles FiT : Feed In Tarif PBAT : Batteries Power PGRID : Grid Power PbOL : PBAT in open loop PgOL : PGRID in open loop PgCL : PGRID in closed loop PbCL : PBAT in closed loop BiC : Battery investment Cost FiT : Feed in Tariff GpF : Grid penalty Factor II. Introduction With the launch of this second decade of the 21th century, renewable energy development is poised to make a significant dent as a substitute for fossil fuel sources. In this context, important works are carried out on the integration of renewable energy resources into the electric grid. In particular, solar energy appears most promising for small distributed electricity production in the residential and commercial sectors. However the intermittent and irregular nature of power production by photovoltaic (PV) systems is considered one of the main barriers for further proliferation

[1] [2] [3]. An interesting and promising solution would be self consumption of the local solar electricity, as achieved in Germany [4]. To perform it an alternative method is the application of a local storage system to shift the local production with the local consumption [5]. However, as introduced in [6], integration of distributed storage into the grid is limited by two constraints, namely, regulation and grid management. With energy storage, the owner of the system can control its charge and discharge, and become, in this way, an active participant on the distribution grid [7]. Consequently, specific agreements, laws, restrictions and constraints have to be developed and dealt with the grid operator. Moreover, agreements with the grid operator would take into account the power balance and grid management. The owner of the energy storage system is primarily interested in the optimal strategy that will achieve the lowest cost. With this objective in mind, previous works have carried out optimal power flow scheduling for gridconnected PV systems with energy storage [6] [7] [7]. These studies, however, focused only on the predictive optimization stage, where dynamic programming was used to determine the optimal power management from the forecasts data. These studies concluded that in the case of errors in the forecast (perturbations), predictive strategies often do not meet the constraints imposed. Hence, according to the agreements with the grid operator, such situations are not allowed to occur [8]. In this context, this paper deals with the reactive supervision of power flow in the grid-connected PV system with energy storage. In [9] supervision in real condition is approach but not in optimal consideration. In the present work, the idea is basically to determine the optimal power scheduling in real time

according to real conditions. Reference [10] presented a similar approach but it used a Mixed Integer Linear Programming (MILP) solver at each adjustment, which requires significant computation time. In this paper, two open loop supervision strategies are presented as a base, and compared with two proposed closed loop supervision strategies with some adjustment. The content of this paper is arranged as followed: Section II briefly reviews the previous work conducted by the authors in [6] in order for the reader to easily understand the rest of the paper. Section III studies the different supervision strategies including the proposed supervision. Section IV compares the performance of these strategies through computer simulations. Finally, Section V draws a conclusion of the study, and points out to future work. III. Description of System Under Study Fig. 1 presents the system studied in this paper and in the previous work conducted by the authors [6][20]. The sign convention of the power flows shown in the figure is used as a reference throughout the paper. As can be seen, the main components of this hybrid system are the PV array, the battery energy storage, the user loads, the distribution grid and the electronics power converters. The parameters « SOC » and « SOH » correspond to the State of Charge and State of Health of the battery. Modeling of the elements of the system and calculations of “SOC” and “SOH” are presented in [6], [11] and [12]. PV converter

=

Bidirectional inverter

PPV (t) < 0

PGRID (t) < 0

=

=

PGRID (t) > 0

Grid

PBAT (t) > 0

PBAT (t) < 0

PLOADS (t) > 0

PV generator Batteries converter

=

=

User Loads Batteries SOC(t), SOH(t)

Fig. 1: Power direction and sign convention in the system studied

According to the sign convention, the laws of physics require the power balance in the system described by : =

+

+

(1)

The physical constraints described by (2) to (4) below are imposed to limit the battery degradation and ageing. These constraints are considered to be “strict”, i.e., they have to be guaranteed, and no violation is allowed at all time. Energy management is performed day to day such as an important constraint is imposed on the SOC of the batteries at the end of the day. This has to be equal to the value of SOC at the beginning of the day as indicated by (5). ≤



(2)



≤ ≥ =

(3) (4) (5)

To assist with the electric grid operation, the system should perform peak shaving such that the power exchange with the grid is limited to a maximum threshold value as formulated by (6) below. This constraint is “flexible” as it is allowed to be violated, but at the expense of a penalty cost. This situation should exist only when the system physical constraints are reached. ≤

(6)

In the previous work [6], Dynamic Programming (DP) was used to determine the power scheduling that minimizes the cost (cash flow CF) over one day, while verifying constraints (2) to (6) according to the following forecasts : solar irradiance (GT [W/m²]), ambient temperature (Tamb[°C]), user load consumption profile (PLOADS[W]), and Electricity grid Price (EgP) [€/kWh]). Dynamic programming has already been used for the same kind of optimization problem when applied to hybrid electric vehicles (HEV) [7], [13]. In this paper, it is assumed that the owner of the system has to guarantee a profile of power exchange with the grid during the day, by using the results of the predictive optimization performed at the end of the previous day. A small flexibility around the guaranteed power exchange is allowed, after which a penalty cost will be applied. The predictive strategy guarantees an optimal power schedule according to forecasts that are never perfect. Consequently, without a reactive supervision system, the profile of power exchanged with the grid is not guaranteed in real conditions. In this situation, a supervision that adjusts the predictive strategy according to actual conditions is essential. The best supervision should manage the power flow such that the final cost is minimized. This problem of real time global optimization is similar to the HEV applications reported in [11] and [14]. In the following subsection, different supervisions are compared and a method for an “optimal supervision” is proposed. IV. Supervisions in real conditions In this paper, only the PV power production and load consumption profile are assumed to be subject to perturbations. The economical parameters (Feed In Tarif (FiT), Electricity Grid Prices (EgP)) are considered to be constant. III.1 Supervision to guarantee physical constraints The first and indispensable supervision to develop is a “security” algorithm to guarantee verification of the physical constraints in (2) to (4) under any circumstance. This is a simple rule-based algorithm that verifies the physical constraints and limits the batteries power PBAT to

3 the threshold values. In this case, the new value of grid power PGRID is calculated according to the power balance (1). III.2 Supervision of “PBAT” in open loop (PbOL): A block diagram of this supervision is presented in Fig. 2 below. In here, the battery power calculated in the predictive optimization stage is imposed on the system. The resulting power to be exchanged with the grid is the result of the power balance (1) according to real conditions. With this supervision, the physical constraints are always verified as they have been taken into account in the calculation of the predictive battery power that is imposed. However, the power exchanged with the grid depends on the real conditions since there is no supervision of this variable. In case of an agreement with the grid operator and as a participant on the grid, this supervision is considered not appropriate in helping the development of gridconnected PV systems. Real conditions PPV (t)

+

PLOAD (t)

+

Forecasts PPV * (T) PLOAD * (T)

Min [Σ CF (T)]

PBAT * (t)

PGRID (t) PGRID real to guarantee the control on PBAT in real conditions

+

Tariffs * (T) Predicitve optimization + Memorization of the PBAT profile Performed the day before for the entire period “T”

Batteries

SOC SOH

Real system

Fig. 2: Supervision of battery power in open loop (PbOL)

III.3 Supervision of “PGRID” in open loop (PgOL) From the optimal predictive strategy of “PBAT”, the optimal power schedule of “PGRID” is obtained from (1) according to the forecasts and is imposed on the system. The battery power is calculated according to real conditions. A block diagram of this supervision is presented in Fig. 3. This supervision guarantees the power exchanged with the grid in real conditions, while battery bank is used as a “buffer” energy tank according to real conditions. However, the battery power is not supervised and is different from the one calculated from the forecasts. The first limitation of this supervision that it is not possible to guarantee the final battery State of Charge (SOC). Since this is a constraint of the optimization problem, it makes the supervision in the days that follow less efficient. The second limitation is that in open loop, calculations of the setting of the grid power do not take into account the variations of the SOC of the batteries. The result is that the strategy applied is optimal according to the forecasts and not to real conditions. This can achieve unsatisfactory results with respect to a real optimal strategy if the perturbations are sufficiently large. The following closed loop supervisions can eliminate or minimize these limitations. III.4 Discrete adjustment of PGRID in closed loop (PgCL) In here, a closed loop of the grid power is inserted in the

supervision diagram of Fig. 3, as shown in Fig. 4. The setting of the grid power is adjusted according to the real state of the batteries (SOC and SOH) after the perturbations. This adjustment is performed such that the constraint on the final state of the batteries is guaranteed with the lowest cost according to the context (forecasts, prices, agreement…). Moreover, it is possible to update the short-term forecasts (from on time step to the next one) for the calculations of the new setting. At the first approach, this supervision appears very laborious as all the optimization has to be performed at each adjustment. What follows is a proposed method that is designed to avoid this high computation demand. This method needs the use of DP ([15] and [16]), which is an optimization technique oftene used in power systems as in. [17] and [18]. III.5 Adjustment process The adjustment calculations are based on the results of the predictive optimization stage which provides the optimal trajectory through a graph of the state of the system. If the search for the best trajectory is performed in the opposite direction (i.e from the final state at the final time step to the initial state), the results (the trajectory and its corresponding cost) are the same. According to the dynamic programming process for finding the best trajectory, calculations of all the possible sub-optimal trajectories are computed [6], [15].[16] Fig. 5 illustrates an example with all the sub-optimal trajectories, their corresponding cost, and where the calculation is performed (from the final state to the initial one). The optimal trajectory is shown in solid line and the sub-optimal trajectories are shown in dashed lines. Note that suboptimal trajectories do not all reach the initial state. According to the DP algorithm and the direction of calculations, the cost “Cii” attached to each state is the cost of the best trajectory to reach the considered state from the final state. If the graph is read from left to right, these values are the minimum costs to reach the final state from the considered state, according to the forecasts. Memorization of the sub-optimal costs enables the knowledge of all the sub-optimal optimal trajectories to reach the final state from all the states of the graph. By this, one can find the optimal trajectory according to the state of the batteries without computing again global optimization at each time step. In summary, the predictive optimization stage is performed backward (from the final state to the initial one) and the cost at each state of the graph is memorized. This method needs more memory, but avoids over computation demand for iterative global optimization.

Real conditions PPV (t)

-

PLOAD (t)

-

Forecasts PPV * (T) PLOAD * (T)

Min [Σ CF (T)]

PGRID * (t)

PBAT (t) Command on PBAT to guarantee control on PGRID in real conditions

Safety algorithm

PBAT (t)*

Batteries

SOC, SOH

Real system

+

Tariffs * (T) Predicitve optimization + Memorization of the PRES profile Performed the day before for the entire period “T”

Fig. 3: Supervision of PGRID in open loop (PgOL) PPV (t)

-

PLOAD (t)

-

PGRID * (∆t)

Security algorithm

SOC (t) SOH (t) PBAT (t)

Batteries Forecasts

Real system

+

Cost of sub-optimal strategies PGRID * (∆t)

Adjustment

Memory block

Performed every ∆t

PPV * (T) CF * (T)

Min [Σ CF (T)]

PGRID * (∆t0)

PLOAD * (T) Tariffs * (T)

Predictive optimization + Memorization of the first PGRID(∆t)

Tariffs * (∆t) PPV * (∆t) PLOAD * (∆t)

Performed the day before for the entire period “T”

Possible upload of forecasts

Fig. 4: Block diagram of the discrete adjustment of PGRID in closed loop (PgCL)

t

0

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2.∆t

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0 SOCend

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C23 SOC2(2.∆ ∆t)

C33

Final SOC

SOC2(3.∆ ∆t)

C14

C24

C34

SOCmax

SOCmax

SOCmax

Fig. 5: Optimal and sub-optimal trajectories and corresponding costs in reverse optimization in the graph of SOC of batteries

Two ways are possible to take into account the real SOC of batteries for adjustment: - The simplest one is to consider the closest discretized

-

value from the measured one. In this case, no calculations are necessary as the best trajectories from all the states of the graph are memorized. The second choice is to consider the exact measured value. In this case, calculations of the costs of the transitions from the real SOC value to the discretized values at the next time step are necessary (weight of the arcs in the next time step). The best trajectory is the one of which the sum of the weights of the arcs and the cost of the sub-optimal trajectory from the next time step is minimal. This computation is also required if the forecasts over the next time step are updated. As in the predictive optimization stage, evolution of the SOC of the batteries is discretized in time the adjustment is discrete and performed at each time step. All these calculations are very simple and need low computation demand.

III.6 Continuous adjustment on PBAT in closed loop (PbCL) The continuous adjustment in closed loop is based on the same method as the discrete one. However, the setting is the

5 battery power instead of the power exchanged with the grid. During the optimization stage, the calculations of the variation of the optimal and sub-optimal trajectories during each time step are also performed in reverse. These variations are computed according to the forecasts subjected to perturbations in PV power production and load power consumption as expressed by (7). In order to minimize the computation demand, the variation of battery power is considered linear with respect to the perturbations, i.e.,

dPBAT =

∂PBAT ∂P × dPPV + BAT × dPLOAD ∂PPV ∂PLOAD

According to the DP algorithms, the best strategies during each time step are calculated from the forecasts. The linear variation of theses strategies are determined by performing the calculations again with different values of PV power production and the load consumption. These second calculations are performed with values of PV production and load consumption that are different from the forecasts during the time step considered. As such data is difficult to predict, an error of up to 30 % is considered as a representative perturbation. As linear variations, the two results (from the forecasts and 30 % up) enable to determine the slope coefficients “a” and “b”. It is found that the extra computation demand from the supplementary calculations increases the computation time of the predictive optimization stage by a factor of around 0.5. However, this extra time is acceptable as the duration of calculations is around one minute, and is performed the day before. The main limitation could be the need for extra memory which depends of the consideration of the real SOC of batteries during the adjustment process.

(7)

The linear factors of variation “a” and “b”, respectively according to the PV power and the load profile, are constant over one time step, but are different at each step, as expressed by (8) below:

dPBAT = a (∆t ) × dPPV + b(∆t ) × dPLOAD

(8)

As for the discrete adjustment two solutions are possible: - If the SOC is considered as the closest discretized value from the measures, then no calculations are necessary. The best trajectory and its variation coefficients are directly known as computed and memorized during the predictive optimization stage. This solution does not reduce the computation demand for the predictive optimization and requires high memory.

Hence, the new setting is expressed by : PBAT ( t ) = (a( ∆t ) × dPPV + b( ∆t ) × dPLOAD ) + PBAT ( ∆t ) *

(9)

where PBAT* is the optimal setting and PBAT ( ∆t ) is the predictive setting during the time step. Fig. 6 represents the block diagram of the supervision according to this expression. The coefficients of variations “a” and “b” are computed during the predictive optimization calculations.

+ PPV (t)

a.dPPV

-

+

PPV * (∆t) PLOAD (t)

Real conditions

-

+

PLOAD * (∆t)

Real conditions

+

PPV (t)

a (∆t) b.dPLOAD

Security algorithm

+

SOC (t) SOH (t) PBAT (t)

b (∆t)

Batteries

PLOAD (t)

Real system

+

+ Forecasts

+

Cost of sub-optimal strategies + grad (PBAT)

PBAT * (∆t) b (∆t)

Adjustment

Performed every ∆t

a (∆t)

Memory block

Tarifs * (∆t) PPV * (∆t) PLOAD * (∆t) PLOAD * (∆t)

.

PRES (t)

PPV * (T)

CF * (T)

Min [Σ CF (T)]

PBAT * (∆t0)

PLOAD * (T) Tarifs * (T)

Predictive optimization + Memorization of the first PGRID(∆t) Performed the day before for the entire period “T”

PPV * (∆t)

Fig. 6: Continuous adjustment on PBAT in closed loop

-

If one considers the real value of the SOC, the main limitation of the continuous adjustment will be avoided. In this case, only memorization of the costs of the suboptimal trajectories is necessary. Trajectories are not memorized as it is re-calculated at each time step. As for the discrete adjustment, costs of the transitions

from the real SOC values to the discretized values at the next time step are computed “online” at each time step. Calculation of coefficients “a” and “b” is performed only on the best trajectory over the time step. In this way, computation demand and memorization in the predictive optimization stage are reduced. Calculations “online” are necessary but are low computation demand as performed

for only one time step. Similar to the discrete adjustment, this solution is applied in the case of updating the forecasts. The next subsection presents and analyses the results of the simulation carried out on Matlab/Simulink of the four supervision strategies presented above. V. Simulation and results IV.1 Simulated conditions and parameter values The four supervision strategies, PbOL, PgOL, PgCL and PbCL respectively have been modeled using Matlab/Simulink software to evaluate their performance. The predictive optimization stage is computed from a Matlab program using the parameter values listed in Table I. Herein, the symbol “T” represents the time period studied, “∆t” the time step of the optimization stage, “δSOC” the step of discretization of the SOC for the application of the DP algorithm, “∆SOCmin ” and “∆SOCmax ” the minimum and maximum variation of SOC that are allowed during one hour of discharge and charge, and “SOC(t0)” the initial battery SOC. This initial value is imposed on each day to perform day-to-day management. The maximum power to extract from the grid is “PGRIDmax” and the economic parameters “BiC”, “EgP”, “FiT”, “GpF” are the Battery investment Cost, the Electricity grid Price, the PV Feed in Tariff, and the Grid penalty Factor, respectively. As described in [6], a penalty factor is applied to the power extracted from the grid when the constraint (6) is violated. The simulations have been performed for one week from the 1st to the 7th of April 2009, but for a better visibility, the graphs that follow are zoomed on the 5th and 6th day (i.e., 96h-144h) of the week as the best exemplary days. The input data include the meteorological forecasts of solar flux and ambient temperature (‘GT’ & ‘Tamb’), forecasts on the load consumption profile (‘PLOADS’), and the electricity prices (‘EgP’ & ‘FiT’). The meteorological and load forecasts are actual measurements taken at the INES Institute and at a residence in Chambéry (France) with an on peak/off peak electricity agreement. As the load profile is already optimized according to the on peak/off peak electricity prices, the simulation and optimization presented below have been performed in a context of a single fixed electricity price. The sizes of the battery, PV array, and local load in the system under study are listed in Table II below. These sizes were determined using the sizing method proposed in Ref. [19].

Table I: Values of parameters for predictive optimization 24*7 (h) 1 week T 10 (min) ∆t 0.01 δSOC 0.2 / 0.9 SOCmin / SOCmax 0.6 SOC(t0) -0.7 / 0.7 (during 1h) ∆SOCmin / ∆SOCmax 3 (kW) PGRIDmax 150 (€/kWh) Pb BiC 0.11 (€/kWh) EgP 0.11 (€/kWh) FiT 10 GpF Table II: Size of the elements of the system studied 5.5 (kW), peak load demand PLOADSmax 3 (kW), PV peak power PPVp 5 Number of PV modules in series NPV_S 2 Number of PV modules in parallel NPV_P 100 (Ah) Capacity of the total storage Cref,nom 12 (V) Voltage of 1 battery Vbat,nom 10 Number of batteries in series Ns 1 Number of batteries in parallel Np

Simulations are performed on the four reactive supervisions presented by adding “artificial” perturbations on the PV power (perturbations on the load power consumption will be added in future studies). In addition, adjustment of the schedule associated with the battery SOC in the two closed loop supervisions is performed with a time step of 10 minutes. The “artificial” perturbations on PV are considered of two types: - Global error on the daily power production according to the forecasts. This error is due to imperfect and approximate forecasts of the meteorological data used to predict the PV power generation over one day. This is considered a “low frequency” perturbation. Generally, the error in the daily PV production is low (20%-30%). This perturbation is created by multiplying the predictive PV production by a factor that varies between 0.6 and 1.4 as a sinusoidal function during the daily PV production period. In this way, the pattern of the PV power production profile is modified but the error of the daily production is in the range of the perturbation considered. - Local error of the power production with rapid variations. This perturbation is due to fast moving clouds and is considered a “high frequency” perturbation. This error is created by multiplying the predictive PV power by a random factor that varies as a Gaussian distribution around 1 with a variance of 0.01. The sample time for this perturbation is 10 seconds. The forecasted and the real PV power for the 5th and 6th of the simulated week are plotted in Fig. 7. The load consumption profile and the power exchanged with the grid from the predictive optimization are shown in Fig. 8. Note that the peak load consumption occurs at the beginning of the 6th day (from 122h to 126h) and it exceeds the maximum value of the power allowed from the grid (3kW) by a significant amount. Because of this important peak power, even the strategy obtained with the predictive

7 optimization is not able to limit the power extracted from the grid to the maximum value imposed. The maximum overflow is about 3.25kW during 10 minutes at hour 124.

supervisions are presented in terms of the SOC and SOH evolutions of the battery in Fig. 9 and 10, respectively. The figures also include an “ideal” strategy corresponding to the case of perfect forecasts (i.e., equal to the real values).

IV.2 Results and analyses The simulation results of each of the 4 reactive

6

5 PV-prev. PV-real

5

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PV-prev Loads Grid-prev

Power (kW)

Power (kW)

4 3

2

PGRIDmax

3 2 1

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Fig. 7: Predicted and real PV power (5th and 6th of April 2009)

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Fig. 8: Loads profile and power exchanged with the grid from predictive optimization (5th and 6th of April 2009) 0.999

0.9 0.8

PbOL PgOL PgCL PbCL Ideal

0.9985

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SOH

SOC

0.998 0.6 0.5

0.997

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PbOL PgOL PgCL PbCL Ideal

0.3 0.2 96

0.9975

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120 Time (h)

0.9965

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Fig. 9: Comparison of the battery SOC evolution of the 4 supervisions

The first remark is that the battery SOC of the “PgOL” supervision does not verify the constraint on the SOC at the beginning of each day. This is due to the fact that there is no supervision on the power of the batteries with the “PgOL” strategy. The batteries are used as an energy “buffer” for the perturbations. The result is an accelerated ageing of the battery as observed on Fig. 10. The second remark is that the two closed loop supervisions (“PgCL” and “PbCL”) guarantee the constraint imposed on the SOC value at the beginning of each day. These two supervisions have very similar SOC strategies, but the “PgCL” results in smaller variations. According to the battery SOH at the end of the 6th day (Fig. 10), the best supervision is the “PbCL”, followed by the “PgCL”, the “PbOL” and the “PgOL”. This order is the

0.996 96

108

120 Time (h)

132

144

Fig. 10 : Comparison of the battery SOH evolution of the 4 supervisions

same at the end of the week. The main remark is that the final value of SOH of the “PbCL” strategy is higher than the one of the ideal strategy. As it is not possible to be better than the ideal strategy, this shows that the final SOH cannot be used as a reference to evaluate the performances of supervision. The differences in SOH are very low and generate a small over cost according to the final value of the cash flow (CF). Moreover, an over cost from ageing can be balanced with a higher gain or a lower consumption at another time. The only representative parameter for evaluation is the objective function which is, in our case, the final value of the cash flow. The evolution of the cash flow for each of the 4 supervisions throughout the entire simulated week is shown in Fig. 11, along with the final value of each cost.

As expected, the ideal strategy gives the lowest cost, and the best of the 4 supervisions is “PbCL”, followed by “PgCL”, “PbOL”, and “PgOL”. Note that a significant change in the cost is observed at the beginning of the 6th day (122h). This time corresponds to the peak power consumption that largely exceeds the maximum value of power allowed from the grid, as pointed out earlier. In here, the battery is deeply discharged to limit the power extracted from the grid, thus resulting in an important ageing cost. Moreover and as expected, no strategy, even the predictive one, can guarantee the limited value of the power extracted from the grid. In this case, the penalty cost is applied, and when added to the ageing cost, it generates a steep variation in the cash flow. 70 60 50 Cash flow (€)

66

PbOL PgOL PgCL PbCL Ideal

64

strategy does not lead to the predicted battery SOC profile. According to the “PgOL” SOC profile in Fig. 9, the battery is not fully discharged at 126h hence it has the ability to limit the power exchanged with the grid. However, as open loop supervision applies only the predictive strategy (i.e., without reactivity), it generates avoidable over cost as expected. As a final remark, it is clear that the two closed loop supervisions give better results. Note that the reactivity of the closed loop limited the amount of cost increase at 122h by a significant amount relative to the open loop strategies, but such a jump cannot be completely eliminated even in the ideal case. The “PgCL” strategy is more expensive as the batteries are used in here as a buffer to face to the perturbations during each time step of reactivity (10 minutes). On the other hand, the “PbCL” is the cheapest supervision, given its reactivity in real time. According to the final cash flow value after one week, the cost associated with the “PbCL” supervision is 40% less than the open loop case and only 18% more than the ideal case.

43

VI. Conclusion and future work

38 32

This paper studied the reactive supervision of grid connected PV systems with battery energy storage in a context of a liberalized electricity market with an agreement between the owner of the system and the grid operator. To improve the performance of open loop strategies, two closed loop strategies have been investigated. A method is proposed to optimize the predictive strategy when using real conditions, while avoiding the high computation demand from a new resolution of the global optimization problem. Perturbations in PV power production have been simulated for a one week period (using actual weather and load data) on the four reactive supervisions, and the results have been compared with an “ideal” solution. The simulated results clearly show that the open loops supervisions do not guarantee constraints satisfactions. These strategies do not favor the integration of PV systems into the power grid as they violate the agreement with the grid operator and generate over-costs to the system owner. Better results are obtained with the closed loop supervisions, particularly with the continuous optimal adjustment. This latter supervision “PbCL” leads to a cost that is nearly 18% higher than in the ideal case, but over 40% lower than with the opened loops supervisions. This gain is obtained from an optimal management of the battery SOH and avoidance of constraint violation. More favorable results are expected when taking perturbations in load consumption profile into account. Future work includes further simulations which take into account errors in the forecasted load demand and electricity prices. The impact of different agreements with the grid operator will also be investigated. The ultimate goal is to implement the proposed closed loop supervision in an industrial energy management system, test the hardware,

40 30 20 10 0

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72 96 Time (h)

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Fig. 11: Comparisons of the evolution of the objective functions

The steep increase in cost of the “PbOL” strategy around 108h in Fig. 11 is another result of the weakness of open loops strategies. According to the predictive SOC profile, (same as the “PbOL” strategy in Fig. 9) the predictive strategy is to charge the battery when the PV production is suitable for this. As shown in Fig. 7, the real PV power production is lower than predicted value. Hence, the predictive SOC strategy in open loop (with the lack of PV production) leads to excessive power extracted from the grid, and to an over cost which can be avoided when using a closed loop supervision. The steepest increase in cost occurs at 120h for the strategy “PgOL” strategy, and this is due to the fact that the power extracted from the grid at this time exceeds the imposed limit by the largest amount relative to other strategies. According to the predictive battery SOC profile (refer to “PbOL” curve in Fig. 9), the battery went onto full discharge mode from 122h to 126h in order to limit the power extracted from the grid. After 126h, the battery is at its minimum SOC, thus the overflow from the grid cannot be balanced and this resulted is an excess of power extracted from the grid. In real conditions, applying the predictive grid power

9 and conduct field tests. References [1]

[2]

[3]

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Acknowledgements This work was supported in part by the ADEME (Agency of Environement & Energie management, France)

Authors’ information Yann Riffonneau was born in Tours, France, in 1983. He received his Master degree in renewable energy in 2006 from Savoie University and a PhD degree in electrical engineering at Joseph Fourier University, Grenoble, France, in 2009. His is currently doing a post doc in energy management of multiple power sources at G2Elab. His fields of interest include energy management, optimization, quality of power and renewable energy. Seddik Bacha received his Engineer and Master from National Polytechnic Institute of Algiers respectively in 1982 and 1990. He joined the Laboratory of Electrical Engineering of Grenoble (G2Elab) and received his PhD and HDR respectively in 1993 and 1998. He was manager of Power System Group of G2Elab (2001/2012) and Professor at the University Joseph Fourier of Grenoble. His main fields of interest are Renewable integration and power quality. Franck Barruel received the Engineer and Masterr degrees from Ecole Nationale Supérieure d'Ingéieurs Ilectriciens de Grenoble-France, in 2002, and the Ph.D. degree from Joseph Fourier University - Laboratoire d'Electrotechnique de Grenoble (LEG) in 2005. He joined the Commissariat à l'Energie Atomique et aux Energies Alternatives (CEA) in the French National Solar Institut (INES) in 2006. He specializes in solar system modeling, mobil solar systems, and energy flow management. Yahia Baghzouz received B.S., M.S. and Ph.D. degrees in electrical engineering from Louisiana State University, Baton Rouge, LA, in 1981, 1982 and 1986, respectively. He is currently professor of Electrical Engineering, and Associate Director of the Center for Energy Research at the University of Nevada, Las Vegas. His interests are in power quality, power conversion and renewable energy. He is a senior Member of IEEE and a registered Professional Engineer in the State of Nevada. Eric Zamaï Eric Zamaï was born in France in 1971. He received a Ph.D in electrical engineering from the University of Toulouse, France, in 1997. He is currently an associated professor at the Grenoble Institut of Technology (Grenoble INP) and does his research at the Laboratory of Grenoble for Sciences of Conception, Optimisation and Production (G-SCOP). His research interests include supervision, monitoring, and control of discrete events systems.