《电池与能量存储》课程教学课件（PPT讲稿）Battery Parameter Estimation

Battery ParameterEstimation

Battery Parameter Estimation

ImportanceofBatteryparameterEstimationThe model parameters changes with operatingconditions and battery aging. If they are notupdated, the model is no longer accurate. ThenSoc estimation will lose accuracy.The capacity Q reduces due to battery agingEstimation of Q is the main task for SOHestimationThe parameters reflect battery conditions andare critical indicators for battery diagnosis

Importance of Battery parameter Estimation • The model parameters changes with operating conditions and battery aging. If they are not updated, the model is no longer accurate. Then SOC estimation will lose accuracy. • The capacity Q reduces due to battery aging. Estimation of Q is the main task for SOH estimation. • The parameters reflect battery conditions and are critical indicators for battery diagnosis

Parameter Estimation of RC-BranchBatteryModelsRpOCIState equation is linearROutput equation is nonlinearv(t) = vocv + Ri(t)+v,(t) = f(s(t)+v,(t)+ Ri(t)Theparametersto beestimated:Q,R, Rp,Cp,VocvThe nonlinearfunction f(s)

State equation is linear 1 1 Q  s(t) = 1 i(t)   vp (t) =− v p (t) + i(t)  RpCp Cp Rp R v i vocv vp + - + - Cp v(t) = vocv + Ri(t) + vp (t) = f (s(t)) + vp (t) + Ri(t) Output equation is nonlinear The parameters to be estimated: Q, R, Rp, Cp, Vocv The nonlinear function f(s) Parameter Estimation of RC-Branch Battery Models

APractical Method forObtaining R,Vp,Rp,VocvinRC-BranchModels byOff-line Experimental MethodRVocv

Rp R v i vocv vp + - + - Cp A Practical Method for Obtaining R, Vp, Rp, Vocv in RC-Branch Models by Off-line Experimental Method

Switchoffatt=oBatteryDigital storageoscilloscopeMeasureboththeterminal voltage(V)andcurrent (l)atatime ofdischarge

Battery Measure both the terminal voltage (V) and current (I) at a time of discharge Switch off at t = 0

ObservetheTerminalVoltage(Data Collection)VoltageUsethis curvetoidentifyRpand CpSlowfinal riseV2toOcV,Immediaterise involtage,V,VoUsethisjumptoidentifyRTimeTimeofcurrentinterruptVocychangesslowlyandisassumedtobeaconstant.The RC branch is at the steady state, so that V,is a constant before switching

Observe the Terminal Voltage (Data Collection) Use this curve to identify Rp andCp Use this jump to identifyR V1 V2 V0 • Vocv changes slowly and is assumed to be a constant. • The RC branch is at the steady state, so that Vp is a constant before switching

CalculationofParameters(1) Voc,= Vo +Vi + V2VR:(2) V。 +Vi = Vocv - I(0-)R=)I(0-)V2R=(3) V2 = V,(O) = R,I(0-) =)I(0-)(4) V =V,(0), V,(t) = V,(0)e R.c, Use any data point on the curve to calculate C

Calculation of Parameters t RpCp V1 − (1) Vocv = V0 +V1+V2 (2) V0 +V1 =Vocv − I(0−)R  R = I(0−) V2 (3) V2 = Vp (0) = Rp I(0−)  R = I(0−) (4) V2 =Vp (0), Vp (t) =Vp (0)e  Use any data point on the curve to calculate Cp

ToEstimate Q,we dolocal linearization of f(s) firstAt an SOC point So, the vocy equation can be linearized locallyvo = f(so),af(s)~ +SSy.+c0oCoCVoCVasLinearizedFunctionIs=Soneartheoperatingpoints=(s -so)v= v(t) -vo=cs+v (t) +Ri(t)1oCVp30[ci,1]+ Ri(t)= Cx + Ri(t)2VocvVp.na5uedoC =[ci,1],x =Vs1Supposethatis C,known.010.200.3oTsState ofCharge (SOC)0andRhavealreadybeencalculated.SoVocv

To Estimate Q, we do local linearization of f(s) first 0 1 ocv ocv ocv At an SOC point s0 , the vocv equation can be linearized locally v 0 s=s0 = f (s ), v  v 0 + f (s) (s − s ) = v 0 0 ocv + c s, s s = (s − s0 ) v = v(t) − v 0 = c s + v (t) +Ri(t) ocv 1 p  s  = [c1 ,1]  + Ri(t) = Cx + Ri(t)  vp   s  C = [c1 ,1], x =  v   p  s0 0 V ocv Linearized Function near the operatingpoint • Suppose that is C1 known. • 0 V ocv and R have already been calculated

Estimation of OSupposethat C,isknown.0andRhavealreadybeencalculatedVocvaFrom the operating SOC point s and vodefine0OCVs(t) = s(t)-s, v(t) = v(t)-vo=cs+v (t)+Ri(t)1OCVps(t) = li(t)QLet a= I that is to be estimated.9(tRLet the sampling interval be t.Define the sampledvaluesSk= s(kt),Vp,k=V,(kt),i =i(kt),Vh=v(kt)Sk+I=S,+atik'p.k+I=Vpp.kRNote: yp, can be calculated from yp.o step by step (iteratively) since all parameters are known

Estimation of Q From the operating SOC point s and v 0 , define 0 ocv s(t) = s(t) − s , v(t) = v(t)−v 0 = c s + v (t) +Ri(t) 0 ocv 1 p • Suppose that C1 is known. • 0 V ocv and R have already been calculated. 1 i(t) 1 RpCp 1 Cp Let = that is to be estimated. Q p,k +1  s(t) = 1 i(t)  Q  vp (t) =− vp (t) +  Let the sampling interval be  . Define the sampled values sk = s(k ),vp,k = vp (k ),ik = i(k ),vk = v(k ) sk +1 = sk + ik p,k p,k R p C p C p Note: vp,k can be calculated from vp,0 step by step (iteratively) since all parameters are known. v = v +  − 1 v + 1 i   k   

Vk+1=C,Sk+I+Vp.k+I+Rik+1+dk =CiS++Ac,Tik +Vp,k+I+Rik+1+dkd, is the measurement noise or error.Vk+1-Vp.k+1-Rik+= CSt +Ac,Ti+dk=CiSk-I +Ac,Tik-I +Ac,Tit+dk...= c,So+ a(c,tik-1 +Ctio+Cti)+dDefine yk = Vk+I-Vp,k+1-Ri+1, u = CTik-I +CTio +CTikk=1,2....,Nyh=Aus+dk,Now, we can use the least-squares estimation method[d uyi..Yn = ::D.IdI[u ]LyNYN=UNa+DNN =(UTUN)"UTYN

dk is the measurement noise or error. Define yk vk +1 = c1 sk +1 + vp,k +1 + Rik +1 + dk = c1 sk+ c1ik +vp,k +1 + Rik +1 + dk vk +1 − vp,k +1 − Rik +1 = c1 sk + c1ik + dk = c1 sk −1 + c1ik −1 + c1ik + dk = = c1 s0 + (c1ik −1 + c1i0 + c1ik ) + dk YN N N N N N N N ˆ ) −1UT Y = vk +1 − vp,k +1 −Rik +1 , uk = c1ik −1 + c1i0 + c1ik yk = uk + dk , k = 1,2, ,N Now, we can use the least-squares estimation method:  y1   u1   d1   , U  = , D  =  =          yN  uN  dN  YN = UN  + DN = (U TU