Cooperative & Distributed Control of High-Density PVs in Power Grid
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1 Cooperative & Distributed Control of High-Density PVs in Power Grid Huanhai Xin Associate Professor College of Electrical Engineering Zhejiang University
2 Biography Dr. Huanhai Xin was born in Jiangxi, China in He has been with the faculty, currently an associate professor in the department of Electrical Engineering, Zhejiang University, China, after he obtained the Ph.D. degree from the same department in June He was a post-doctor in the EECS department of the University of Central Florida from June 2009 to July His research interests include power system stability analysis, and renewable energy. 1
3 Presentation Outline 1. Research Background 2. NQI based PV Power Control Method 3. Distributed Control Mode & Graph Theory 4. Self-Organizing Power Flow Control Stratergy 5. DCAGE Method for PVs Cooperative Strategy 6. Conclusions 2
4 The Current Status of PV in China China climbed to third place in terms of total installed capacity in 2012, ahead of the USA and Japan; In 2012, Germany was the world s top PV market, (7.6 GW newly connected systems), followed by China (5 GW); Newly installed capacity doubled every year since Global PV cumulative installed capacity share in
5 Incentives to the Development of PV Environmental Pressure; Price is lower Policy Incentive from the Government. 4
6 Negative Impacts of High PV Penetration PVs operate in the maximum power point tracking (MPPT) mode; As PV penetration is high, - Frequency regulation capability decreases in power systems; - System inertia (mainly provided by synchronous generators) decreases; - Power congestion problem; - The imbalance between power supply and demand increases. Variation of PV power (MPPT) Variation of Load Demand 5
7 Possible Solutions Energy Storage Systems Power Curtailment Dump Load High cost for the ESS and its maintenance. PVs operate in the MPPT mode No extra equipment required. PVs operate below the maximal available power The cost is relatively cheap PVs operate in the MPPT mode Power curtailment and dump load method are more economically efficient than ESS in certain occasions! W. Omran, M. Kazerani and M. Salama, IEEE Trans. Energy Convers.,
8 NQI based PV Power Control Method 7
9 Problem Formulation The relation between the power output and terminal voltage is P U I PV U, PV PV PV PV Objective: flexibly adjust the PV power according to Pref. A PV system should be able to operate in MPPT mode: P converges to P if P > P Power dispatch mode: P converges to P if P P Y. Liu, H. Xin, Z. Wang, T. C. Yang, "A Novel Power Control Strategy for PV System Based on the Newton Quadra tic Interpolation," IET Renewable Power Generation,
10 Control Design (1) Basic idea: obtain the exact voltage by approximating the P-V characteristic curve with a quadratic curve. In the kth iteration step, assume 3 points on the PV curves are known: U, P, U, P and U, P, whereu U U k k k k k k k k k Quadratic Interpolation out 2 P U au bu c Quadratic Equation 2 ref au bu c P PV 0 Discriminant 2 ref b 4a c P PV 9
11 Control Design (2) Extreme Point Left Root Right Root Iterations Iteration Rule: Remove U, P and U, P in turn. Convergence Criterion: k k max P P i1, 2,3 i PVref 10
12 Simulation Result PV Power Output tracks its reference 900 Irradiance (W/m 2 ) Time (Second) Power (MW) Voltage (kv) Time (Second) Time (Second) 11
13 Distributed Control Mode & Graph Theory 12
14 Control Mode Comparison Centralized control mode : control strategy is explicit and easy. : 1) Require global and synchronous information; 2) Not plug-and-play, not scalable;; 3) High performance processor. Decentralized control mode : only use local information : difficult for the coordination. Centralized Control Decentralized Control 13
15 Control Mode Comparison Distributed control mode : : 1) Distributed communication, Distributed calculation; 2) Plug-and-Play, scalable;; 3) Robust to communication interruption; Cooperation among DGs 14
16 Graph Theory Graph G = V, E V: set of vertices in the network E V V: set of edges in the network. i, j E if i j Undirected or directed? Connected or strongly connected? Neighborhood set: N ={k V (k,i) E} Adjacency matrix A 0 nonnegative Eigenvalue λ = 1 aik 0 if k, i E and k i N AG 1 aij if ki ik j1 0 Otherwise Right eigenvector Aν = ν: ν= 1,, 1 Row-stochastic Left eigenvector A γ = γ: γ= γ,, γ 15
17 Consensus & Distributed Algorithm If the graph is strongly connected (sufficient condition), Continuous case:, 0 0 xt A I xt x x x (t) a ( x x ) i ij j i jn i Discrete case: Consensus value: 1, 0 0 xk Axk x x x * T x 0 16
18 Self-Organizing Power Flow Control Stratergy 17
19 Problem Formulation To design a control such that, for PVs: P tran c () P V () V ref ref PV 16 Extern grid P P tran ref c ref ( ) the active power over the chosen transmission line given reference values V ( ) the voltage of the selected bus V given reference values Gas turbine generator PV 13 PV 9 PV 14 PV 15 PV 8 PV 2 (b) (a) PV 6 Pref Line 1 PV 5 PV 7 (c) PV 1 Huanhai Xin, Zhihua Qu, John Seuss, and Ali Maknouninejad, A Self-Organizing Strategy for Power Flow Control of Photovoltaic Generators in a Distribution PV 12 PV 3 Network, IEEE Transactions on Power Systems, vol. 26, no. 3, 2011 PV 11 PV PV 4
20 Control Design Same output ratio for all PVs P1 P2 Pn 0... P P1max P2max Pn max Q1 Q2 Qn... Q1max Q2max Qn max Utilization Control law 0 Q Three phase PV convert er model: ref Idi u1 i ref Iqi u2i P U I, Q U I i i di i i qi n KdiP i max 0 P DP i ij j u1 i Di0 P U i Pimax j 1 P jmax n KqiQ imax D 0 Q i ijq j u2i D i0 Q U i Qimax j1 Q jmax 19
21 Control Design Control determining the desired ratio of P z 0 KP( Pref Ptran) 0 P z0 Control for determining the desired ratio of Q z 0 Kv( Vref Vc ) 0 z Q 0 Conclusion: the closed-loop system is asymptotically stable, even the communication network is not ideal. 20
22 Simulation Results Chang in the loads and intermittent communication 21
23 DCAGE Method for PVs Cooperative Strategy 22
24 Problem Formulation Assumption 1: DG refers to the combination of a PV (or another type of distributed energy resource) and a controllable load. Assumption 2: The communication network is directed and strongly connected. Definitions Leader set L: DGs that can directly receive P ; Power output of the ith DG: P = P P ; Utilization ratio of the ith DG: α P. Objective 1: aggregated power Objective 2: common utilization ratio N i i1 P i DG P P D *, i 1,, N Easy, if undire cted commu. Huanhai Xin, Yun Liu, Zhihua Qu, and Deqiang Gan, Distributed Control and Generation Estimation Method for Integrating High-Density Photovoltaic Systems, IEEE Transactions on Energy Conversion,
25 Comparison of the two methods Self-Organizing Power Flow Control Strategy The total power can be measured directly from a bus bar. Method is good for some special power networks such as a radial network, otherwise the output of each DG must be measured directly and it needs a center collecting global information. DCAGE Method for PVs Cooperative Control Strategy Provided the corresponding adjacency matrix is doubly stochastic, the total aggregated power output can be distributively estimated regardless of the topology of the power network., 0 0 xt A I xt x x x * T x 0 24
26 Control Strategy(Outline) Distributed Control and Generation Estimation (DCAGE) Method (1) Distributed Algorithm of Making Adjacency Matrix doubly stochastic. Property: ν = γ = 1,, 1 (2) Distributed Estimate of Aggregated Power Generation Capacity of the DGs. P total i1 (3) Distributed Control for Consensus of Utilization Ratios. * PD P N P total i MPP 25
27 Distributed Algorithm of Making Adjacency Matrix doubly stochastic Basic idea: Distributively and adaptively adjust γ to an all-one vector. (1) Distributed estimation of the first left eigenvector Define the observer states at the ith DG as θ = θ,, θ evolves as N i j i sint if k i k a ij k k j1 sin t if k i where µμ and ω are sufficiently large. The ith entry of γ can be calculated by ˆ lim where Δ = 2κπ ω. i t t t i cos cos i d t cos cosd t 2, and θ 26
28 Distributed Algorithm of Making Adjacency Matrix doubly stochastic (2) Evolvement of the adjacency matrix Suppose γ = max γ,, γ, γ = min γ,, γ S = argmax γ,, γ, S = argmin γ,, γ Diagonal entry a Non-diagonal entries a, j N i i 1 sign if and aii min max i Smax aii amin i i aii 1aii sign max min if ismin and aii amin 0 if is S or a a i i sign if and max min ii min aij min max i Smax aii amin i i aij aijsign max min if ismin and aii amin 0 if is S or a a max min ii min 27
29 Distributed Algorithm of Making Adjacency Matrix doubly stochastic Theorem 1: Suppose that matrix A is initialized to be row-stochastic. Then, under the control laws, A has the properties: (i) It remains to be non-negative and row-stochastic, (ii) it converges to a column stochastic matrix. Directed 28
30 Distributed Control for Consensus of Utilization Ratios The power output of the ith DG is i i i P P DG MPP P_total is P P * N total average Utilization ratio evolves as i PD * il Ptotal N i j i aij t if j1 xt () ( I Axt ) () d T T xi (t) 1 x( t) 1 ( I A) x( t) 0 dt i1,... N 1 1 xt ( ) xi(t) xi(0) N i1,... N N i1,... N Average Value! Conclusion: Under the above control, the utilization ratios of all the DGs converge uniformly and asymptotically to the consensus value of α. 29
31 Simulation Results DG No Inactive 30
32 Conclusions The NQI based Power Control Method makes the PV s power output follow the given command, or automatically switch to the MPPT mode if the command is higher than the maximum available power. The self-organizing strategy for power flow control guarantees that the distribution network can adjust itself to a feasible operating point and that all the PVs converge to a prescribed utilization profile. The distributed algorithm of making adjacency matrix doubly stochastic solves an open problem in cooperative control theory. With the algorithm, many existing methods can be generalized from undirected to directed graph. The DCAGE method can be applied to a variety of DGs. Also, it can be used to solve the economic dispatch problem in a distributed way, etc.. 31
33 References [1] H. Xin, Y. Liu, Z. Qu, "Distributed Control and Generation Estimation Method for Inte grating High-Density Photovoltaic," IEEE Trans. on Energy Conversion, [2] Y. Liu, H. Xin, Z. Wang, T. Yang, "A Novel Power Control Strategy for PV System Bas ed on the Newton Quadratic Interpolation," IET Renewable Power Generation, [3] H. Xin, M. Zhang, J. Seuss, Z. Wang, D. Gan, "A Real-Time Power Allocation Algorith m and its Communication Optimization for Geographically Dispersed Energy Storage Syst ems," IEEE Trans. on Power System, [4] H. Xin, Y. Liu, Z. Wang, D. Gan, T. Yang, "A New Frequency Regulation Strategy for P hotovoltaic Systems without Energy Storage," IEEE Trans. on Sustainable Energy, [5] Xin H, Lu Z, Qu Z, Gan D, Qi D. Cooperative Control Strategy for Multiple Photovolta ic Generators in Distribution Networks. IET Control Theory & Applications, 2011, 5(14): [6] H. Xin, Z. Qu, J. Seuss, A. Maknouninejad, "A Self Organizing Strategy for Power Flo w Control of Photovoltaic Generators in a Distribution Network," IEEE Trans. on Power sy stems, [7] H. Xin, Z. Lu, Z. Qu, D. Gan, D. Qi, "Cooperative Control Strategy for Multiple Photo voltaic Generators in Distribution Networks," IET Control Theory & Applications, 2011.
988 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 29, NO. 4, DECEMBER 2014
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