Optimal Provision of Concurrent Primary Frequency and Local Voltage Control from a BESS Considering Variable Capability Curves: Modelling and Experimental Assessment

Optimal Pro vision of Concurrent Primary Frequenc y and Local V oltage Control from a BESS Considering V ariable Capability Curv es: Modelling and Experimental Assessment Antonio Zecchino, Zhao Y uan, Rachid Cherkaoui, Mario Paolone Distributed Electrical Systems Laboratory EPFL - Lausanne, Switzerland { antonio.zecchino, zhao.yuan } @epfl.ch Fabrizio Sossan Centre for processes, renew able energies and energy systems MINES ParisT ech - Nice, France Abstract —This paper proposes a control method for battery energy storage systems (BESSs) to provide concurrent primary frequency and local voltage regulation services. The actual variable active and reacti ve power capability of the con verter , along with the state-of-charge of the BESS, are jointly considered by the optimal operating point calculation process within the real-time operation. The controller optimizes the pro vision of grid services, considering the measured grid and battery statuses and predicting the battery DC voltage as a function of the current trajectory using a three-time-constant model (TTC). A computationally-efficient algorithm is proposed to solve the formulated optimal contr ol problem. Experimental tests validate the proposed concepts and show the effectiveness of the employed control framework on a commercial utility-scale 720 kV A/560 kWh BESS. Index T erms —Battery Energy Storage System, Primary Fre- quency Control, V oltage Regulation. I . I N T R O D U C TI O N Battery energy storage systems (BESSs) are broadly rec- ognized as essential assets for the operation of modern power systems thanks to their wide controllability and po wer ramping rate that can be exploited for grid balancing regulation pur- poses [1]. As extensiv ely demonstrated in the literature, one of the most popular power system services achieved by BESS is primary frequency control (PFC), which is increasingly needed from transmission system operators (TSOs) giv en the progres- siv e displacement of con ventional generation plants in fav or of stochastic renew able-based generation units [2]–[6]. PFC is typically performed by a frequency droop controller that determines the variation of the activ e power (∆ P ) exchanged with the A C grid for a giv en frequency deviation from a reference value. Since power con verters are normally able to operate on the 4 quadrants of their PQ capability curve, they are also capable of exchanging reacti ve power concurrently This work was supported by the European Union’ s Horizon 2020 research and innovation program under agreement no. 773406. with the acti ve po wer . W ithin this context, the proposed control approach considers the additional simultaneous exchange of reactiv e po wer , which is seen as a viable mean for local voltage regulation at distribution grid level [7]–[11]. Similarly to the case of PFC, local voltage deviations from the nominal value can be used as input for determining the necessary variation on reacti ve power (∆ Q ) . Although a dedicated market framework is not existing at distribution grid lev el, distribution system operators (DSOs) are yet keen to have the possibility of acquiring voltage regulation services via reactiv e power support coming from distributed energy resources, e.g., by imposing relev ant requirements to photov oltaics plants [12], [13]. The proposed joint PFC-v oltage control actions are achiev ed within the real physical constraint of having a non-unique PQ region of feasibility of the BESS power conv erter: this region is in fact a function of the battery DC-link and AC grid statuses. This aspect goes beyond the typical assumptions present in the existing scientific literature where it is assumed that the PQ capability curve of the BESS con verter is static and does not depend on battery state-of-charge (SOC) and A C grid voltage conditions. In fact, to the best of the Authors’ knowledge, neither the studies that consider only acti ve power control (e.g., [2]–[6]) nor those including concurrent reactiv e power control (e.g., [7], [8]) do take into account limitations giv en by the v ariability of the BESS con verter capability curve. Another contribution proposed in this work is the design of a real-time control algorithm with a time execution ≤ 1 s , capable of computing the maximum grid support from the BESS as function of the battery and A C grid conditions. This is done by solving, in real time, an optimization problem that includes constraints based on battery status predictions, giv en by a three-time-constant (TTC) equiv alent model, whose parameters hav e been experimentally estimated via a series of model identification tests [14], [15]. In this approach, the noncon vex constraints are relaxed and con ve xified to make them easier to be solved. Similar approaches have been also 21st Power Systems Computation Conference PSCC 2020 Porto, Portugal — June 29 – July 3, 2020 used and validated to solve power system operation problems in [16], [17]. Ultimately , the paper reports an experimental v al- idation of the proposed control approach. Finally , the real-time optimal controller is implemented and tested on the utility- scale 720 kV A/560 kWh BESS installed at EPFL campus in Lausanne, Switzerland. In sum, the main research contributions of this paper are three-fold: i) propose a method that accounts for the variability of the feasibility PQ region of the BESS power conv erter as function of both the AC grid and internal BESS conditions; ii) dev elop a control framew ork for concurrent provision of power system frequency and local voltage control based on the real-time solution of an optimization problem to maximize the contribution to grid support that the BESS can provide for giv en actual and predicted operating conditions; iii) provide the experimental validation of the proposed method in a real grid. The paper is structured as follows: Section II outlines the proposed methodology . In Section III, the utility-scale BESS deployed for the v alidation experimental activities is described, including the estimations of the identified parameters of the equiv alent battery model. Section IV reports the results of rel- ev ant experimental test study cases. Conclusions and possible future works are included in Section VI. I I . P R O P O S E D M E T H O D O L O G Y The BESS con verter is controlled to provide primary fre- quency and local voltage regulation adjusting the activ e and reactiv e power set-points, respectively . The initial power set- points are achiev ed via droop logics: P AC 0 ,t = α 0 ∆ f t ; Q AC 0 ,t = β 0 ∆ v AC t , (1) where t ∈ T is the discrete index of time, P AC 0 ,t , Q AC 0 ,t are the initial activ e and reactive power set-points that the BESS will set for giv en grid frequency and A C voltage magnitude deviations from their nominal values (∆ f t , ∆ v AC t ) , according to the initial droop coefficients α 0 , β 0 . These active and reactiv e power set-points will be adjusted when considering the conv erter capability curves, as described later in the paper . T o maximize the frequency and voltage regulation perfor- mance, the initial droop coefficients α 0 , β 0 can be set as: α 0 = P max ∆ max f t ; β 0 = Q max ∆ max v AC t , (2) where P max and Q max are the maximum active and reactiv e power that the BESS can exchange, as specified by the BESS technical specifications. Historical measurements can be used to determine the maximum frequency and voltage de viation ∆ max f t , ∆ max v AC t , as shown in Section III. During real-time operations, the employed α t , β t are adjusted by relying on BESS status (av ailable storage capacity and SOC) and solving an optimal power set-points calculation problem (14). Commonly , in the current literature the con verter capabil- ity is considered to be constantly expressed as ( P AC t ) 2 + ( Q AC t ) 2 ≤ ( S AC ) 2 , where P AC t , Q AC t , and S AC are the con verter output active, reacti ve and maximum apparent power of the grid con verter , respectiv ely . This assumption, howe ver , does not hold in practice. In this work, the realistic feasible operation re gion identified by the PQ con verter capability curves h in Fig. 1, are considered as: h ( P AC t , Q AC t , v DC t , v AC t , S O C t ) ≤ 0 (3) being v DC t the voltage of the BESS DC bus and v AC t the module of the direct sequence component of the phase-to- phase voltages at the AC side. Notably , the capability curves h are specific for the employed hardware, but similar dependen- cies are expected in all kinds of utility-scale BESS con verters. More detailed information about the PQ curves considered in this study are included in Section III. -800 -600 -400 -200 0 200 400 600 800 P [kW] -800 -600 -400 -200 0 200 400 600 800 Q [kvar] Vac = 300 V, Vdc = 500 V Vac = 300 V, Vdc = 550 V Vac = 300 V, Vdc = 600 V Vac = 330 V, Vdc = 500 V Vac = 270 V, Vdc = 500 V Fig. 1. BESS conv erter PQ capability curves as function of v AC t and v DC t . The v DC t voltage needed for the selection of the capability curve is estimated via the TTC model shown in Fig. 2, whose parameters are deriv ed by dedicated model identification tests. Since the BESS has to be controlled in a very small time resolution ( ≤ 1 s ), we estimate the battery status based on the TTC model state equations: C 1 d v C 1 d t + v C 1 R 1 = v s R s (4) C 2 d v C 2 d t + v C 2 R 2 = v s R s (5) C 3 d v C 3 d t + v C 3 R 3 = v s R s (6) v s + v C 1 + v C 2 + v C 3 = E − v DC t , (7) where v c = [ v C 1 ; v C 2 ; v C 3 ] are the TTC state voltage vari- ables that are updated by solving (4)-(7) in each control loop. At each time step, the initial value of the state variables can be estimated via the use of dedicated state observers as proposed in [2]. The model (4)-(7) is discretized at a 1s resolution in this paper . The TTC model capacitance parameters C 1 , C 2 , C 3 and resistance parameters R s , R 1 , R 2 , R 3 are identified by generating activ e power pseudo random binary signals (PRBS) and then by measuring the corresponding current dynamics. This process is explained in Section III. The voltage source E is the open circuit voltage of the battery , which depends on the SOC as shown in (8). E is modelled as a linear function of the battery SOC, where the parameters a and b are identified within the TTC model identification process. E ( S O C t ) = a + b · S O C t (8) 21st Power Systems Computation Conference PSCC 2020 Porto, Portugal — June 29 – July 3, 2020 𝑣 𝑠 𝑣 𝐶1 𝐶 1 𝐶 2 𝐶 3 𝑣 ' () 𝑖 ' () 𝑣 𝐶2 𝑣 𝐶3 𝑅 1 𝑅 2 𝑅 3 𝑅 𝑠 𝐸 Fig. 2. Three time constant TTC model. After updating v c = [ v C 1 ; v C 2 ; v C 3 ] , considering v s = P DC t v DC t R s , equation (7) is equiv alent to: ( v DC t ) 2 + ( 1 T v c − E ) v DC t + P DC t R s = 0 , (9) where 1 T = [1 , 1 , 1] . Solving constraint (3) jointly with (9) gives feasible power set-points P AC t , Q AC t satisfying the ev olving capability curves during the control loop. Giv en the initial state-of-charge S O C 0 , its value at each discrete time control iteration, S O C t , can be expressed as: S O C t = S O C t − 1 + R t t − 1 i DC t dt C max ≈ S O C t − 1 + P DC t v DC t C max ∆ t, (10) where C max is the maximum storage capacity of the battery in Ampere-per -hour and i DC ≈ P DC t v DC t is the charging or discharging DC current. The active power at the DC bus P DC t is related the activ e power at the A C side of the conv erter as: P DC t = ( η P AC t , ∀ P AC t < 0 P AC t η , ∀ P AC t ≥ 0 , (11) where η = 97% is the efficienc y of conv erter . P AC t < 0 means charging of the BESS and P AC t ≥ 0 means discharging. The state-of-charge S O C t should be always kept in the secure limits during all the operational periods t ∈ T : S O C min ≤ S O C t ≤ S O C max (12) The magnitude of the direct sequence component v AC t of the phase-to-phase voltages needed for the selection of the con verter capability curve is estimated via the Th ´ evenin equi v- alent circuit of the A C grid. As shown by Equation (13), the estimation considers the direct sequence component v AC,m t of the measured phase-to-phase v oltages and the e xpected v oltage drop due to the three-phase complex power S AC 0 ,t exchanged by the BESS ov er the grid equiv alent impedance Z eq . Z eq can be approximated as the BESS step-up transformer reactance j X T . Since, as shown in Fig. 3, measurements are acquired at the primary side of the BESS step-up transformer whereas the estimation is done for the voltage at the secondary side, the voltage v AC,m t in (13) is referred to the secondary side as v AC,m t = v AC,m M V ,t 1 n , being n the transformer ratio. 𝒗 ! "# 𝒁 !" ≈ 𝑗𝑋 # 𝒗 $% ,! "# ,' Fig. 3. Reference BESS scheme for the AC voltage prediction. v AC t = v AC,m t + Z eq conj ( S AC 0 ,t √ 3 v AC,m t ) v AC t ≈ s ( v AC,m t ) 2 + X 2 T ( P AC 0 ,t ) 2 + ( Q AC 0 ,t ) 2 3( v AC,m t ) 2 (13) The optimal active and reactive power set-points are giv en by solving the following optimization problem: Minimize λ P ( P AC t − P AC 0 ,t ) 2 + λ Q ( Q AC t − Q AC 0 ,t ) 2 (14) subject to (1) − (3) , (9) − (13) Where λ P and λ Q are weight coef ficients used by the modeler to prioritize the provision of active or reactiv e power , i.e., to prioritize one grid service over the other . In the case of equal priority for frequency and voltage control, the weight of 1 is assigned to both coefficients, meaning that the optimal power set-points P AC t , Q AC t are the closest to the initial po wer set- points P AC 0 ,t , Q AC 0 ,t inside the feasible operational region of the BESS defined by (1)-(3) and (9)-(12). After finding the optimal power set-points P ∗ AC t , Q ∗ AC t , the optimal droop parameters α ∗ t , β ∗ t are defined as: α ∗ t = P ∗ AC ∆ f t ; β ∗ t = Q ∗ AC ∆ v AC t (15) This optimization problem is noncon ve x due to the noncon- ve x constraints (9), (10) and (11). T o efficiently find a local optimal solution, constraint (9) is firstly conv exified to: ( v DC t ) 2 + ( 1 T v c − E ) v DC t + P DC t R s ≤ 0 (16) This relaxation sho ws better computational efficienc y in real-time control experiments. Then, to find the optimal power set-points, we propose the computationally-efficient solution algorithm sho wn in Algorithm 1, where V DC i ∈ { (500 , 550] , (550 , 600] , (600 , 800] } is i -th set of the DC volt- age range and where V AC j ∈ { (270 , 330] , (330 , + I nf ) } is j -th set of the A C voltage range. Algorithm 1 works by firstly assuming the ranges that could include the DC voltage v DC t and the A C voltage v AC t solutions. Then, one capability curve is selected based on the assumed DC voltage and the predicted A C voltage. If the calculated v DC t and v AC t are consistent with the initial assumed DC and A C voltage ranges V DC i and V AC j , the algorithm con ver ges. Otherwise, the assumption of the DC and A C voltage ranges is changed and another capability curve is selected until a consistent solution is found. The block diagram of the proposed controller during one time step is illustrated in Fig. 4. 21st Power Systems Computation Conference PSCC 2020 Porto, Portugal — June 29 – July 3, 2020 Algorithm 1: Optimization Solution Algorithm Result: Optimal Power Set-Points P AC t , Q AC t Initialization P AC 0 , Q AC 0 , i = 1 , j = 1 ; while v DC t / ∈ V DC i and i < i max do Assume v DC t ∈ V DC i ; while v AC t / ∈ V AC j and j < j max do Assume v AC t ∈ V AC j ; Select one capability curve: h ( P AC t , Q AC t , v DC t , v AC t , S O C t ) ; if P AC 0 < 0 then P DC t = η P AC t ; else P DC t = P AC t η ; end Solve the Optimization Problem; j = j + 1 ; end i = i + 1 ; end Re a l - t i m e gr i d m e a s ur e m e nt s I ni t i a l P - Q set - poi nt s c a l c ul a t i on us i ng ⍺ 0 , β 0 ( 1) O pt i m i z a t i on pr obl e m ( 14) BESS 𝑓 ! , 𝑣 "# , ! %& , ' 𝑃 ( , ! %& , 𝑄 ( , ! %& 𝑃 ! ∗ %& , 𝑄 ! ∗ %& Re a l - time B E S S s t a t us 𝑣 ! *& , 𝑆𝑂 𝐶 ! 𝑣 "# ,! %& , ' Lege nd 𝑓 ! : fr e quency meas ured at time ste p t 𝑣 "# , ! %& ,' : direct s equence component of the AC voltage meas ured at time ste p t 𝑣 ! (& : DC voltage measured at time st ep t 𝑆𝑂 𝐶 ! & : sta te of charge meas ured at time st ep t 𝑃 ) ,! %& , 𝑄 ),! %& : init ia l active and r e active power values 𝑃 ! ∗ %& , 𝑄 ! ∗ %& : actual active and reactive power values set to the converter at time st ep t Fig. 4. Block diagram of the proposed real-time controller . I I I . U T I L I T Y - S C A L E B E S S C A P A B I L I T Y C U RV E S A N D A S S E S S M E N T O F I T S E Q U I V A L E N T C I R C U I T M O D E L The testbed of the proposed validation study consists in an utility-scale BESS installed at the EPFL campus in Lausanne, Switzerland. The system is based on a 720 kV A/560 kWh Lithium-T itanate-Oxide (L TO) battery , utilized for a number of po wer grid support experimental activities [18]. The BESS is equipped with a 720 kV A 4-quadrant conv erter , which can be controlled via Modbus TCP with a refresh rate up to 50 ms. The BESS is connected to one of the feeders of the EPFL campus medium voltage (MV) grid via a 630 kV A 3-phase 0.3/21 kV step-up transformer . The paramenters of the main components of the employed BESS are reported in T able I. The selected MV feeder presents all the peculiarities of modern activ e distribution grids: the lines are relativ ely short, the load demand is largely variable during the day (office buildings with 300 kWp), and a substantial amount of rooftop PV units is connected (for a total of 95 kWp). Such characteristics make the testbed suitable for in vestigations not only on system frequency regulation, but also on local voltage control solutions such as the one proposed in this work. T ABLE I S P EC I FI C A T I O NS O F T H E E M PL OY E D U T I LI T Y - S CA L E B E S S Parameter V alue Energy Capacity 560 kWh Maximum Power 720 kV A Nominal Active Power 640 kW Rated AC grid voltage 0.3 kV , three-phase Maximum AC current 1385 A A C current distortion (THD) 3 % Nominal DC voltage 750 V DC voltage range 500-890 V In verter efficienc y ≥ 97 % T ransformer rated power 630 kV A T ransformer high voltage 3 x 21 kV T ransformer low voltage 3 x 0.3 kV T ransformer short-circuit voltage 6.28 % T ransformer group Dd0 As commonly known, a peculiarity of BESS installations is the modular structure. For the specific commercial MW - class BESS under analysis, 3 series of 20 cell elements are connected in parallel to compose the battery module, 15 modules in series compose one string, and finally 9 strings connected in parallel guarantee the desired BESS energy storage and po wer capacity . The main advantage of such modular structure is the absence of the limiting single point of failure typical of conv entional power grid service providers. In fact, the system can be operated even if one element is not correctly in operation. W ithin this context, in the analysis proposed in this work a configuration with reduced number of strings is considered. Specifically , 7 strings out of 9 are utilized, meaning that the a vailable storage capacity is 7/9 of the total value, i.e., 435 kWh. One has to note that the reduced number of usable strings should be considered also in the setting of the maximum power exchange capability , being the strings connected in parallel. This is done to prev ent string ov er-currents and over -temperatures, without jeopardizing the cycle aging process of the cells. In this respect, at the imple- mentation stage of the controller , the constraints of the po wer con verter PQ capability curves presented in Fig. 1 have been shrank by the factor C shrink , which in this case is 7/9. As shown in Fig. 1, the region of feasible operating points of the power con verter depends on the grid AC voltage and on the DC battery voltage in a non-linear way . In fact, for increasing battery DC voltages only the maximum positive Q value is increasing. The curve is shifted down vertically for A C voltages higher than the nominal value, meaning that both the maximum positi ve Q is decreased, whereas the maximum negati ve Q is increased. A different pattern is present for A C voltages lo wer than the nominal value: the limit values are shrank both for the active and the reactiv e part of the apparent power set-point in both negativ e and positiv e signs. At the implementation stage of the proposed 21st Power Systems Computation Conference PSCC 2020 Porto, Portugal — June 29 – July 3, 2020 controller , the dependency of the feasibility region on the grid and battery statuses is considered in a discretized way , by selecting two of the five PQ curves and by considering the ov erlapping area between them. As mentioned, this is done in accordance with the respective factor C shrink . The capability curves of the employed power con verter are fitted using datasheet information from the manufacturer and, then, scaled proportionally to the a vailable BESS capacity . The fitted capability curves consist of a series of linear and quadratic functions, which are reported in T able II. T ABLE II F I TT E D F U N C TI O N S O F T H E C O N V ERT E R P Q C A PA BI L I T Y C U R V E S v DC v AC Functions 600 V 300 V P ≥ − 681 . 89 P ≤ 678 . 71 P 2 + Q 2 ≤ 723 . 03 2 , ∀ Q ≥ 0 P 2 + Q 2 ≤ 719 . 19 2 , ∀ Q < 0 Q ≤ 659 . 67 − 8 . 29 − 18 P − 2 . 16 − 4 P 2 Q ≤ 657 . 1 550 V 300 V P ≥ − 681 . 89 P ≤ 678 . 71 P 2 + Q 2 ≤ 723 . 03 2 , ∀ Q ≥ 0 P 2 + Q 2 ≤ 717 . 93 2 , ∀ Q < 0 Q ≤ 459 . 43 − 1 . 5 − 3 P − 2 . 12 − 4 P 2 Q ≤ 439 . 98 500 V 300 V P ≥ − 680 . 62 P ≤ 682 . 45 P 2 + Q 2 ≤ 721 . 4 2 Q ≤ 286 . 64 + 1 . 4 − 3 P + − 2 . 33 − 4 P 2 Q ≤ 225 . 22 500 V 330 V P ≥ − 679 . 21 P ≤ 681 . 06 P 2 + Q 2 ≤ 794 . 34 2 Q ≤ 38 . 47 500 V 270 V P 2 + Q 2 ≤ 649 . 5 2 Q ≤ 382 . 95 + 1 . 6 − 3 P − 2 . 21 − 4 P 2 A dedicated experimental in vestigation allowed the estima- tion of the equiv alent TTC circuit parameters via a grey-box modeling-based approach, in line with the analogue estimation activity proposed in [15] for the same BESS in case of full av ailable storage capacity (9 strings). The model identification tests are based on pseudo-random binary sequence (PRBS), i.e., a two levels square wave with on-off periods of normally distributed random durations, capable of exciting a wide range of system dynamics. Fig. 5 shows the binary power set-points, the SOC, v dc and i dc . Since the TTC model parameters depend on the BESS SOC, the test has been repeated for different SOC ranges. The obtained TTC model parameters are in T able III. W ith reference to (2), in order to properly set the initial values of the droop constants α 0 and β 0 , the maximum deliv erable acti ve and reactive powers P max and Q max hav e been used along with the calculated maximum deviation of the input variables of the controller , i.e., ∆ max f and ∆ max v AC . SOC = 34-66% 14:00 14:15 14:30 14:45 15:00 15:15 15:30 15:45 Sep 12, 2019 -200 0 200 Active Power [kW] 40 45 50 55 60 SOC [%] 14:00 14:15 14:30 14:45 15:00 15:15 15:30 15:45 Sep 12, 2019 620 640 660 680 Voltage [V] -500 0 500 Current [A] Fig. 5. PRBS activ e po wer reference and measured SOC, v DC and i DC for the SOC range of 34-66% in case of 7 strings in operation. T ABLE III E S TI M E T ED B ES S P A R A M ET E R S F O R 7 ST R I N GS F OR D IFF E R EN T SO C R A NG E S SOC=0-33% SOC=34-66% SOC=67-100% a 607.2 607.1 590.0 b 190.8 113.9 188.9 R s [ Ω ] 0.0221 0.0165 0.0155 R 1 [ Ω ] 0.0131 0.0120 0.0109 C 1 [ F ] 1511 1844 1917 R 2 [ Ω ] 5.26E-05 2.24E-05 2.55E-04 C 2 [ F ] 1.00E+06 1.00E+06 1.00E+06 R 3 [ Ω ] 5.10E-06 6.50E-07 1.55E-05 C 3 [ F ] 1.00E+07 1.00E+07 1.00E+07 Historical measurements acquired by the synchrophasor network on the EPFL MV network are used for this purpose, whose P-class phasor measurement units (PMUs) allowed the acquisition of data with a timestamp of 20 ms [19]. The values of ∆ max f and ∆ max v AC hav e been obtained by approximating their distribution with normal distribution functions and by considering a relev ant multiplication factor for the standard deviations σ . On the one hand, the maximum deviations of ± 3.3 σ f was considered for the system frequency measurements, meaning that the thresholds µ f ± 3.3 σ f are statistically exceeded only 0.1 % of the times, being µ f the av erage value of the frequency dataset, equal to 50.000 Hz. This rather strict assumption is motiv ated by the requirement from the Swiss TSO grid code on the quality of the supply of primary frequency control power , which sets a maximum tolerable time of 0.1 % of the tender period for which the regulating power cannot be delivered without running into penalties [20]. On the other hand, since less strict requirements regulate the quality of the supply of local voltage control, smaller maximum deviations can be considered: the calculated thresholds for the activ ation of the maximum reactiv e power capacity are µ V ± 1 σ V , where µ V is the average value of the A C phase-to-phase voltage dataset, equal to 21.192 kV . Since the obtained µ V differs from the nominal value of 21 kV , it was decided to consider µ V as reference for the calculation 21st Power Systems Computation Conference PSCC 2020 Porto, Portugal — June 29 – July 3, 2020 of ∆ max v AC in (1). Giv en the considered historical dataset, ∆ max f = ± 3.3 σ f = ± 58.8 mHz and ∆ max v AC = ± 1 σ V = ± 0.0672 kV . The calculated ∆ max f and ∆ max v AC enable the computation of the initial droops α 0 and β 0 for different BESS configurations considering the number of av ailable strings, i.e., the shrink factors C shrink , as shown in T able IV. T ABLE IV C A LC U L A T E D α 0 A N D β 0 F O R D I FFE R E N T S H RI N K FAC T O RS C shrink C shrink α 0 [ k W/H z ] β 0 [ k var /V ] 1 11575 10.78 8 / 9 10289 9.58 7/9 9003 8.39 6 / 9 7717 7.19 5 / 9 6430 5.99 4 / 9 5144 4.79 3 / 9 3858 3.59 2 / 9 2572 2.40 1 / 9 1286 1.20 49.9 49.95 50 50.05 50.1 Frequency [Hz] 0 0.05 0.1 0.15 0.2 Density (PDF) Probability density function for 1 month frequency measurement 20.8 20.9 21 21.1 21.2 21.3 21.4 21.5 AC Voltage [kV] 0 0.02 0.04 0.06 Density (PDF) Probability density function for 1 month AC voltage measurement Fig. 6. 1 month historical data of frequency and phase-to-phase voltage at the BESS PCC at 21 kV , acquired via PMUs installed at the EPFL MV network. The dashed lines represent the limits of µ f ± 3.3 σ f and µ V ± 1 σ V for frequency and voltage measurements, respectiv ely . I V . E X P E R I M E N TA L I N V E S T I G AT I O N A number of scenarios hav e been inv estigated considering different combinations of initial droops α 0 and β 0 . T able V reports the overvie w of the analysed cases. Each test has been carried out for a 5-minute time window , and the real- time BESS battery and A C grid statuses have been monitored and processed in order to compute the optimal P and Q set- points as described in Section II. The same priority has been giv en to the provision of P and Q by setting λ P = λ Q =1 in the implementation of (14). A time granularity of 1 second has been used for data acquisition and optimal set-point computation, meaning that at each second a new operating point within the corresponding feasible PQ region is sent to the BESS con verter controller . The choice of 1-second response is considered as a realistic assumption in BESS applications as indicated, for instance, by the newly-released grid code by the Danish TSO Energinet.dk [21]. Howe ver , the Authors are aware that in lo w-inertia po wer systems rapid (i.e., sub-second) frequency variations are more likely to be experienced [22], meaning that ev en faster response from control providers may be needed. T ABLE V C A LC U L A T E D α 0 A N D β 0 F O R D I FFE R E N T S H RI N K FAC T O RS C shrink S cenar io α 0 β 0 #1 9003 [kW/Hz] 8.39 [kvar/V] #2 9905 [kW/Hz] 8.39 [kvar/V] #3 19810 [kW/Hz] 8.39 [kvar/V] #4 29715 [kW/Hz] 12.57 [kvar/V] Fig. 7 shows results for S cenar io #1 , for which α 0 and β 0 are calculated as in Section III. The top subplots of (a) and (b) report the measured A C grid frequency and the mean value of the three phase-to-phase voltages at the MV connection point, with the respective reference values used for the calculation of ∆ f t and ∆ v AC t as in (1). The computed P-Q set-point calculated implementing the standard droop control equation in (1) are reported in red in the bottom subplots. Additionally , the actual set-points computed as result of the optimization problem are shown with the blue lines. Note that, as already stated in Section II, for the selection of the appropriate con verter PQ capability curve at each time-step, the A C voltage measured at the 21 kV busbar is scaled down to the L V side voltage lev el of the BESS step-up transformer using the associated transformation ratio. Firstly , it can be seen that for frequency measurements larger than 50 Hz, the BESS behav es as a load: the sign of the exchanged activ e power is negati ve, meaning that the BESS is charging. Symmetrically , when the frequency is below the 50 Hz, the BESS discharges by injecting activ e power with positi ve sign into the grid. Similar considerations are valid for the local voltage control. In general, for ∆ v AC > 0 , i.e., in case of over -voltages, negati ve reactiv e power is provided by the BESS, meaning that the BESS behav es as an inductor . On the contrary , for ∆ v AC < 0 , i.e., in case of under-voltages, capacitive reactive power is provided, as in the case of the whole time-window for the test of S cenar io #1 . Secondly , it can be noticed that the desired primary frequency support is fully achiev ed since the expected activ e power is provided at any moment of the considered time window . By contrast, the relatively lar ge value of the initial droop β 0 and the measured deviations of the AC voltage from the reference v alue, caused a mismatch between the expected and the pro vided voltage control service for more than half of the time of the test. In fact, in these cases the desired Q set-point would hav e been out of the feasible region of the employed hardware, hence the proposed optimal control approach moved it to the edge of the corresponding PQ capability curve. The test for S cenar io #2 presented in Fig. 8 shows a case when the local voltage control via reactive po wer is achiev ed 21st Power Systems Computation Conference PSCC 2020 Porto, Portugal — June 29 – July 3, 2020 (a) (b ) 49.95 50 50.05 f [Hz] PFC 17:38 17:39 17:40 17:41 17:42 17:43 Sep 24, 2019 -100 0 100 200 P [kW] P * AC P AC 0 21.15 21.2 v AC [kV] Local voltage control 17:38 17:39 17:40 17:41 17:42 17:43 Sep 24, 2019 200 300 400 Q [kvar] Q * AC Q AC 0 Fig. 7. S cenario #1 Results. (a): PFC; (b): local voltage control. continuously , although the implemented initial droop β 0 is the same as in S cenar io #1 . Also the primary frequency control action is performed continuously , responding as desired to the measured frequenc y signal for the whole duration of the test. In this case a larger initial droop α 0 was implemented, namely a value calculated considering ± 3 σ f as the maximum frequency deviation, i.e., with a confidence interval of 99.7 % . (a) (b ) 49.95 50 50.05 f [Hz] PFC 17:59 18:00 18:01 18:02 18:03 18:04 Sep 24, 2019 -200 -100 0 100 P [kW] P * AC P AC 0 21.15 21.2 v AC [kV] Local voltage control 17:59 18:00 18:01 18:02 18:03 18:04 Sep 24, 2019 -200 -100 0 Q [kvar] Q * AC Q AC 0 Fig. 8. S cenario #2 Results. (a): PFC; (b): local voltage control. In S cenar io #3 an ev en larger value of α 0 was used, cor- responding to ± 1.5 σ f as the maximum frequency deviation, i.e., with a confidence interval of 86.6 % . In this test case, the solution of the optimization problem enabled the BESS to operate also when the calculated P set-points falls outside the feasible region of the considered PQ capability curve. In fact, the values at the edge of the feasible region were set, meaning that the frequenc y service was not performing as desired, although the maximum po wer was still provided to partially support the grid. From Fig. 9, it can be seen that this happens in the first 38 seconds of the test and for a shorter period of time also around the mid point. Fig. 9- (c) maps the operating points before and after the implementation of the proposed optimal set-point calculation. It can be noticed that, thanks to the proposed method, the points falling outside the feasible region have been retriev ed to the edge of the light blue con verter feasible region, thus assuring the continuity of the deli very of the two grid services. Furthermore, it is of paramount importance to note that without the proposed optimal controller the too high value of the computed P set- point would have made the BESS con verter either trip or go to 0 kW for safety reasons. Under these circumstances, the expected service would hav e been fully undeliv ered, enhancing the probability of reaching the 0.1 % threshold imposed by the Swiss TSO for undeliv ered regulating power when providing primary frequency control. It is in fact rele vant to quantify the amount of regulating energy actually deliv ered during the regulation session and to compare it with the energy that w ould hav e been deliv ered without optimization and in the ideal case of un-constrained BESS po wer con verter . So, the quantification - as for PFC provision - of the concrete effects of the proposed controller with control time granularity ∆ t during a control session of duration T ∆ t is done as described in equations (17)-(19). They define the expected energy E exp , the actual deliv ered energy with the optimal control E ∗ , and the energy that would hav e been deliv ered without the proposed optimal approach E 0 , respectiv ely . Such quantification is included in T able VI. E exp = T X i =1 ∆ t | α 0 ∆ f i | (17) E ∗ = T X i =1 ∆ t   P ∗ AC i   (18) E 0 = T X i =1 ∆ t   P AC 0 ,i   (19) Finally , S cenar io #4 is analysed to assess the situation in case of a very large initial droops α 0 and β 0 , corresponding to maximum de viations of ± 1.5 σ f and ± 0.75 σ V . Although the very lo w measured voltage de viations made the computed Q set-point be inside the feasible PQ region all the time, the same is not valid for P . In fact, Fig. 10 shows that for almost the whole duration of the test, the P set on the con verter is at the edge of the selected feasibility curve, meaning that the primary frequency grid service is not fully delivered. The mapping of the PQ set-points before and after the solution of the proposed optimization problem is shown in Fig. 10- (c) . As for S cenar io #3 , the continuity of the delivery of the two grid services is possible thanks to the projection of the initially- calculated set-points to the edge of the light blue conv erter feasible region. The quantification of the effecti veness of 21st Power Systems Computation Conference PSCC 2020 Porto, Portugal — June 29 – July 3, 2020 (a) (b ) -800 -600 -400 -200 0 200 400 600 800 P [kW] -500 0 500 Q [kvar] Vac = 300 V, Vdc = 600 V Vac = 270 V, Vdc = 500 V PQ working point before OPT PQ working point (c) 21.16 21.18 21.2 21.22 [kV] 18:08 18:09 18:10 18:11 18:12 18:13 Sep 24, 2019 -200 -100 0 [kvar] Q * AC Q AC 0 49.95 50 50.05 [Hz] 18:08 18:09 18:10 18:11 18:12 18:13 Sep 24, 2019 -1000 -500 0 [kW] P * AC P AC 0 Fig. 9. S cenar io #3 Results. (a): PFC; (b): local voltage control; (c): PQ set-points before and after the proposed optimization algorithm. the optimal controller in terms of expected and deli vered regulating energy is reported in T able VI. T ABLE VI E X PE C T E D A N D D E LI V E RE D EN E R G Y F O R P F C W I T H A N D W I T HO U T T H E P RO P OS E D O P T I MI Z A T I ON A LG O R I TH M S cenar io E exp E ∗ E 0 #1 8.3 [kWh] 8.3 [kWh] 8.3 [kWh] #2 10.5 [kWh] 10.5 [kWh] 10.5 [kWh] #3 20.0 [kWh] 18.4 [kWh] (91.90 % ) 13.7 [kWh] (68.47 % ) #4 45.7 [kWh] 35.0 [kWh] (76.49 % ) 9.1 [kWh] (19.91 % ) V . C O N C L U S I O N S The work presented a BESS control framew ork for optimal provision of concurrent power system services. In particular , primary frequency and local voltage control are achieved via the modulation of acti ve and reactive power set-points, respectiv ely , exploiting the flexibility given by the 4 quadrant power con verter . The proposed algorithm considers the work- ing conditions of the A C utility grid as well as the battery DC voltage as a function of the current trajectory using the battery TTC model, in order to select the suitable con verter capability curve, which is not unique for all the possible (a) (b ) 21.15 21.2 v AC [kV] Local voltage control 18:19 18:20 18:21 18:22 18:23 18:24 Sep 24, 2019 -100 0 100 200 Q [kvar] Q * AC Q AC 0 -800 -600 -400 -200 0 200 400 600 800 P [kW] -500 0 500 Q [kvar] Vac = 300 V, Vdc = 600 V Vac = 270 V, Vdc = 500 V PQ working point before OPT PQ working point (c) 49.95 50 50.05 [Hz] 18:19 18:20 18:21 18:22 18:23 18:24 Sep 24, 2019 0 500 1000 [kW] P * AC P AC 0 Fig. 10. S cenario #4 Results. (a): PFC; (b): local voltage control; (c): PQ set-points before and after the proposed optimization algorithm. operating conditions, hence optimizing the provision of grid services. A computationally-efficient algorithm was proposed to solve the formulated optimal power set-points calculation problem. A set of experimental tests on a commercial utility-scale 720 kV A/560 kWh BESS showed the capability of the controller to enable PFC and local voltage control not only by charging or discharging the battery , but also by means of reactiv e power exchange, namely behaving as inductor or capacitor in case of ov er- or under-voltages, respectively . When in case of large initial droop constants or large frequency/voltage deviations the PQ feasible region is passed, the proposed controller enabled the operation at the edge of the selected PQ capability curve, dramatically reducing the amount of accumulated non- deliv ered regulating power during the control session. Hence, the paper highlighted the importance of accurately modelling the employed hardware in order to enable an optimal grid service provision even under non-nominal BESS conditions (e.g., reduced av ailable number of strings) as well as under commercial hardware embedded technical limitations (e.g., variable capability curves of the power con verter). Future works include the extension of the complexity of the model by considering the power con version efficienc y as a function of the exchanged A C activ e power , and a series of experimental tests to map more systematically all the possible capability curves for a wider range of combinations of battery 21st Power Systems Computation Conference PSCC 2020 Porto, Portugal — June 29 – July 3, 2020 DC voltage and grid voltage conditions. Further, in vestigations on BESS control logics as voltage source in combination with the provision of ancillary services are of interest. 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