Effects of Various Uncertainty Sources on Automatic Generation Control Systems D. Apostolopoulou, Y. C. Chen, J. Zhang, A. D. Domínguez-García, and P. W. Sauer University of Illinois at Urbana-Champaign May 3, 2013 (UIUC) May 3, 2013 1 / 28
Outline 1 Introduction 2 Power System and AGC Models 3 Numerical Results 4 Concluding Remarks (UIUC) May 3, 2013 2 / 28
Outline 1 Introduction 2 Power System and AGC Models 3 Numerical Results 4 Concluding Remarks (UIUC) May 3, 2013 3 / 28
Demand and Generation Balance 32 30 Available Resources Forecast (GW) 28 26 24 22 20 Day Ahead Demand Forecast Actual Demand (GW) 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Hour Source: www.caiso.com (UIUC) May 3, 2013 4 / 28
Who is in charge? The Balancing Authority (BA) is the responsible entity that integrates resource plans ahead of time, maintains load-interchange-generation balance within a BA Area, and supports interconnection frequency in real time Source: www.nerc.com (UIUC) May 3, 2013 5 / 28
Frequency deviation from nominal value Load Losses Power Generated DEMAND Decrease Frequency Increase 60 - + SUPPLY Source: www.nerc.com (UIUC) May 3, 2013 6 / 28
Control Processes Load Frequency Control { primary control secondary control tertiary control optimal power flow unit commitment 1 10 10 2 10 3 10 4 10 5 time(s) 1 sec 1 min 1 hour 1 day (UIUC) May 3, 2013 7 / 28
Load Frequency Control Source: http://www.e-control.at/en/businesses/electricity/electricity-market/balancing-energy (UIUC) May 3, 2013 8 / 28
Automatic Generation Control (AGC) Role of AGC in power systems To hold system frequency at or very close to a specified nominal value. To maintain the correct value of interchange power between control areas. AGC implementation The AGC accepts measurements of the real power interchange between areas, the area s frequency and the generator s output as input signals from field devices. The output control signals represent the shift in the area s generation required to restore frequency and net interchange to the desired values. (UIUC) May 3, 2013 9 / 28
Challenges in AGC Deepening penetration of renewable resources, which are highly variable and intermittent. Renewable Portfolio Standards www.dsireusa.org / February 2010 VT: (1) RE meets any increase WA: 15% x 2020* MN: 25% x 2025 in retail sales x 2012; MT: 15% x 2015 (Xcel: 30% x 2020) (2) 20% RE & CHP x 2017 OR: 25% x 2025 (large utilities)* ND: 10% x 2015 MI: 10% + 1,100 MW 5% - 10% x 2025 (smaller utilities) x 2015* SD: 10% x 2015 WI: Varies by utility; NY: 29% x 2015 10%x2015goal NV: 25% x 2025* IA: 105 MW OH: O 25% x 2025 CO: 20% by 2020 (IOUs) 10% by 2020 (co-ops& large munis)* IL: 25% x 2025 WV: 25% x 2025* CA: 33% x 2020 UT: 20% by 2025* KS: 20% x 2020 VA: 15% x 2025* MO: 15% x 2021 AZ: 15% x 2025 DC NC: 12.5% x 2021 (IOUs) 10% x 2018 (co-ops& munis) NM: 20% x 2020 (IOUs) 10% x 2020 (co-ops) ME: 30% x 2000 New RE: 10% x 2017 NH: 23.8% x 2025 MA: 15% x 2020 + 1% annual increase (Class I RE) RI: 16% x 2020 CT: 23% x 2020 PA: 18% x 2020 NJ: 22.5% x 2021 MD: 20% x 2022 DE: 20% x 2019* DC: 20% x 20200 TX: 5,880 MW x 2015 HI: 40% x 2030 6 State renewable portfolio standard Minimum solar or customer-sited requirement State renewable portfolio goal Extra credit for solar or customer-sited renewables Solar water heating eligible * Includes non-renewable alternative resources 29 states + DC have an RPS (6 states have goals) Source: www.dsireusa.org April 2013 (UIUC) May 3, 2013 10 / 28
Challenges in AGC Highly automated system, which lead to increase noised signals that are measured and transmitted to the AGC. Source: http://www.electronicproducts.com (UIUC) May 3, 2013 11 / 28
Proposed Framework We propose a framework to evaluate the effects of uncertainty in AGC by explicitly representing the system dynamics network effects uncertainty sources We approximate the probability distribution function of system characteristics to investigate if the AGC mechanism is functional (UIUC) May 3, 2013 12 / 28
Outline 1 Introduction 2 Power System and AGC Models 3 Numerical Results 4 Concluding Remarks (UIUC) May 3, 2013 13 / 28
Synchronous Generating Units For the timescales of interest we chose a 4-state model for the synchronous generators that includes the mechanical equations and the governor dynamics T do i de q i dt dδ i dt 2H i dω i ω s dt T SVi dp SVi dt = X d i X d i E q i X d i X d i X d i cos(δ i θ i )+E fd0i (1) = ω i ω s (2) = P SVi E q i X d i V i cos(δ i θ i ) (3) + X q i X d i 2X d i X qi V 2 i sin(2(δ i θ i )) D i (ω i ω s ) = P SVi +P Ci 1 R Di ( ωi ω s 1 ) (4) We denote x = [E q 1,δ 1,ω 1,P SV1,...,E q I,δ I,ω I,P SVI ] T (UIUC) May 3, 2013 14 / 28
Network Power flow equations P s i +P w i P d i = n ( V i V k Gik cos(θ i θ k )+B ik sin(θ i θ k ) ) (5) k=1 n Q s i Qd i = ( V i V k Gik sin(θ i θ k ) B ik cos(θ i θ k ) ) (6) k=1 where P s i = E q i X d i V i cos(δ i θ i ) Xq i X d i 2X d i X qi V 2 i sin(2(δ i θ i )) and Q s i = E q i X d i V i cos(δ i θ i ) 1 X d i V 2 i cos2 (δ i θ i ) 1 X qi V 2 i sin2 (δ i θ i ) We denote y = [θ 1,V 1,...,θ n,v n ] T, P d = [P d 1,...,Pd n ]T and Q d = [Q d 1,...,Qd n ]T (UIUC) May 3, 2013 15 / 28
AGC Model Area control error Frequency f = ACE = b(f f nom ) (7) n i=1 γ i ( f nom + 1 2π dθ ) i dt where γ i some weighting factors with n i=1 γ i = 1 AGC control dz dt We denote u = [P C1,...,P CI ] T = z 1 η 2 ACE + I i=1 (8) P s i (9) P Ci = κ i z (10) (UIUC) May 3, 2013 16 / 28
Wind generation and communication noise The wind generation model at node i P Wi = γ 1i P Wi +γ 2i v i +γ 3i (11) dv i = a i v i dt+b i dw t (12) Uncertainty in the measurements Γ of the vector Γ, containing the frequency and the generators output, is modeled as Gaussian white noise η Γ Γ = Γ +ηγ (13) The area control error as well as the AGC mechanism is affected by η Γ as may be seen in (10) We denote P W = [P W1,...,P Wn ] T and v = [v 1,...,v n ] T (UIUC) May 3, 2013 17 / 28
System Model The system dynamic behavior is described by a set of differential algebraic equations ẋ = f(x,y,u) (14) ż = h(x,y,ẏ,z) (15) u = k(z) (16) 0 = g(x,y,p L,P W ) (17) We linearize the system along a nominal trajectory and obtain where X = [ x, z, P W, v] T dx t = AX t dt+bdw t (18) (UIUC) May 3, 2013 18 / 28
Calculation of desired moments Generator of the stochastic process X (Lψ)(X) := ψ(x) X AX + 1 ( ) 2 Tr B 2 ψ(x) X 2 B T (19) The evolution of the expected value of ψ(x) is governed by Dynkin s formula de[ψ(x t )] = E[(Lψ)(X t )] (20) dt Cross-moments evolution dσ(t) = AΣ(t)+Σ(t)A T +BB T dt (21) E[X t Xt T ] = Σ(t)+E[X t]e[x t ] T (22) (UIUC) May 3, 2013 19 / 28
Outline 1 Introduction 2 Power System and AGC Models 3 Numerical Results 4 Concluding Remarks (UIUC) May 3, 2013 20 / 28
4-bus system V 1 θ 1 1 4 V 4 θ 4 V 2 θ 2 2 3 V 3 θ 3 P w P 3 +jq 3 (UIUC) May 3, 2013 21 / 28
Deterministic case: Wind change by 0.1pu 1 ω 1 0.5 ω 4 rad/s 0 0.5 0 200 400 600 800 1000 time (s) 0 0.05 pu 0.1 P SV1 0.15 P SV4 0.2 0 200 400 600 800 1000 time (s) (UIUC) May 3, 2013 22 / 28
Incorporating uncertainty Variation of wind generation 0.02 0.01 pu 0 0.01 0.02 0 10 20 30 40 50 60 70 80 time (s) The variation in system s frequency may be expressed as a linear combination of the system states The mean value and second moment of f are f = CX t (23) E[ f] = CE[X t ] (24) E[ f 2 ] = CE[X t X T t ]C T (25) (UIUC) May 3, 2013 23 / 28
Mean and Second moment of f 0.05 0 Dynkin s formula Monte Carlo Hz 0.05 0.1 0.15 0.2 0 20 40 60 80 100 120 time (s) Hz 2!'!(!'!"!'!& )! &!! &&! &"! # " *+&!!$!,-./0.12+3456789 :4.;<+=9584!! "! #! $! %! &!! &"! time (s) (UIUC) May 3, 2013 24 / 28
Increasing the wind penetration 6 x 10 6 P W0 2P W0 4 Hz 2 2 0 0 20 40 60 80 100 120 time (s) (UIUC) May 3, 2013 25 / 28
Outline 1 Introduction 2 Power System and AGC Models 3 Numerical Results 4 Concluding Remarks (UIUC) May 3, 2013 26 / 28
Concluding Remarks and Applications We proposed a methodology of propagating any uncertainty in either P W or noise in the communication channels η Γ and study their effect on the AGC signals u and eventually on the system performance We may use this framework to to detect, in a timely manner, the existence of a cyber attack, by computing the system frequency statistics determine which buses are more critical if noise is inserted in the measurements obtain upper bounds for the frequency variation, by using Chebyshev s inequality, and investigate if they meet the frequency regulation criteria (UIUC) May 3, 2013 27 / 28
Thank you! (UIUC) May 3, 2013 28 / 28