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MAN AND ENERGY A case for Sustainable Living through Renewable and Green Energy Ali Keyhani Professor of Electrical and Computer Engineering The Ohio State University Columbus, OH-43210 [email protected] 4/30/2017 [email protected] 1 In part I, the use of energy by man, environment and sustainable living were presented. Then the use energy in present time was discussed. Based on British Petroleum (www. Bp.com), there is only ten more years of petroleum reserve remain in US , if the current rate of utilization continues. British Petroleum data shows that the Middle East oil would last only another one hundred years at the current worldwide rate of consumption. British Petroleum data shows that the world can continue to use petroleum at current rate for only another forty years. Challenge of future is to replace petroleum with renewable energy sources. 4/30/2017 [email protected] 2 Distributed Generation System Technologies 4/30/2017 [email protected] 3 Fuel Cell Technology Fuel Cells : Features and Types Electrochemical energy conversion device. Clean energy source with low emissions. Characterized by the type of electrolyte used by them. Fuel Cells : History First demonstration – (in 1839 ) by Sir William Grove (English physicist) Produced DC electric power by performing electrolysis experiment. Demonstration of the first fully operational fuel cell – (in 1959), by Francis Thomas Bacon, (British Engineer) In 1960, General Electric (GE) developed PEM fuel cells for NASA which were used on NASA’s first manned space vehicle . 4/30/2017 [email protected] 4 Important Fuel Cell Candidates for DG applications Important Fuel Cell Candidates for DG applications Fuel Cell Types Phosphoric Acid Fuel Cells (PAFC) Solid Oxide Fuel Cells (SOFC) 1 kW- 10 MW Molten Carbonate Fuel Cells (MCFC) 0.25 – 10 MW Proton Exchange Membrane Fuel Cells (PEMFC) 0.5-250 kW Size 100-200 kW Operating Temperature 180 – 2000C 800 – 10000C 600 – 7000C 35 – 1000C Installation Cost (/kW) Peak Power Density (mW/cm3) $2000-3500 $1200-4000 $800-3000 $1000-3000 ~200 ~200-500 ~160 ~700 Efficiency (Electrical) 36 - 42 % 45 - 60 % 45 - 55 % 30 – 45 % Efficiency (with Co-generation) Up to 80 – 85 % Up to 80 – 85 % Up to 80 – 85 % Up to 80 – 85 % Start-up Time 1-4 hrs 2-8 hrs 2-5 hrs 20 sec – 6 mins Current Manufacturers UTC Fuel Cells, Fuji Electric Company Ltd, Mitsubishi Electric Corp. Siemens Westinghouse Power Corp, Global Thermoelectric, ZTEK Corp. Fuel Cell Energy, Hitachi Ltd. Ballard Power Systems, Avista Labs, UTC Fuel Cells, Nuvera Fuel Cells, Plug Power, H power, Ida Tech 4/30/2017 [email protected] 5 PROBLEM FORMULATION Schematic Diagram of PEM Fuel Cell based Stand-alone DG System Analyze the performance and the operating characteristics of stand-alone PEM fuel cell based (5 kW) DG system feeding to the residential loads. Develop dynamic models for PEM fuel cell and for its power conditioning unit (dc/dc boost converter, three-phase dc/ac inverter with L-C filter and transformer ). Develop control techniques to achieve desired performance of the system. Determine energy capacity of the storage device needs to be connected at DC bus 4/30/2017 [email protected] 6 PROBLEM FORMULATION-FUEL CELLS What are the desired performance characteristics of stand-alone PEM fuel cell based DG system ? Provide output voltage to residential loads at magnitude 208 V(L-L)/120 V (L-N) and at 60 Hz frequency up to its rated value (5kW). Provide power during peak load demand and during load transients. Output voltage of the system must have low load regulation (< 5 %) - system must be able to maintain steady-state output voltage independent of load conditions up to its rated value. Provide output voltages with low total harmonic distortion (THD) – (Reduction in 5th and 7th harmonic) Protect itself from overload conditions such as short circuit faults. 4/30/2017 [email protected] 7 PROBLEM FORMULATION 1) Operation of Power Conditioning Unit (dc/dc boost converter, three-phase dc/ac inverter with L-C filter with transformer ) under Dynamic DC Bus Voltage For 500-W PEM fuel cell (rated current 25 A) – output voltage varies between 40 V (noload) to 23 volts (full load). Output voltage of PEM fuel cell is not constant. As more power is drawn from PEM fuel cell, output voltage of 500- W PEM fuel cell decreases from 40 volts (no-load voltage) to 23 volts (full-load voltage at rated current 25 A). Control techniques are needed - To control the output voltage of PEM fuel cell To control the operation of PEM fuel cell - model is required. 4/30/2017 [email protected] 8 PROBLEM FORMULATION-FUEL CELLS 2) Determination of Energy Capacity of Storage device to be connected at DC bus PEM fuel cell cannot quickly respond to fast load changes during peak load demand and during load transients. Storage device is required to be connected at the dc bus Energy capacity of the storage device must be determined based on peak load demand and requirement of transient current during load switching. 3) Control of DC/DC Boost Converter Typical output voltage of 500-W PEM fuel cell is 48-60 V. PEM is rated for up to $250Kw. It can be connected in series or parallel to obtain the desired rating. DC/DC converter boost converter is to boost the output voltage of PEM fuel cell to desired dc bus voltage level (480V – 540 V, rated 10 kW). Control technique should be designed - To control the output voltage of the boost converter such that the dc bus voltage is regulated within 5% of its desired value. 4/30/2017 [email protected] 9 PROBLEM FORMULATION-FUEL CELLS 4) Control of Three-phase (VSI) DC/AC Inverter The control technique should be designed for inverter [480 V dc/ 208 V ac (L-L), rated 10 kW] to satisfy following performance characteristics: 1. Low Load Regulation (less than 5%) The ac output voltage of the DG system should be maintained at 208 V (L-L)/120 V (L-N) independent of load conditions. 2. Minimum THD DG system when feeding to the nonlinear loads, such as rectifiers, switch mode power supplies (SMPS), must generate minimum harmonics currents. 3. Fast Transient Response System must be able to produce output ac voltage with minimum overshoot or undershoot. 4. Short Circuit Protection System must be able to provide protection from excessive overload conditions 4/30/2017 [email protected] 10 EXPERIMENTAL AND SIMULATION TESTBED 1) Dynamic Modeling Develop dynamic model of PEM fuel cell , rated 500-W, rated current 25 A, 40V (no-load voltage)-23 V(full-load voltage at rated current 25 A) Validate 500- W PEM fuel cell model with published results of SR-12 PEM fuel cell manufactured by Avista Labs. Scale the model to 5 kW PEM fuel cell, rated current 100 A, 48 V (no-load voltage) - 24 V (V(full-load voltage at rated current 100 A) Simulate PEM fuel cell model to study its dynamic response - Transient response and Steady-state response Develop dynamic model for dc/dc boost converter, (48 V – 480 V, rated 10 kW). Develop dynamic model for three-phase dc/ac inverter (VSI), [480 V dc/ 208 V ac (L-L), rated 10 kW]. 4/30/2017 [email protected] 11 DISTRIBUTED GENERATION STAND-ALONE 2) Determination of Energy Capacity of storage device Perform Load following analysis of stand-alone DG system 4/30/2017 [email protected] 12 SINGLE FAMILY DG SYSTEM Following load profile of a typical residential home ( 3000-ft2 house occupied by 2adults and 4-children) will be used. Average Power Demand (base load) - Less than 5kW - satisfied by PV array unit (rated 5 kW). Peak Load demand = Up to 8 kW Period of peak load demand = 100 seconds (from 10.30 a.m. to 12.10 p.m.) 4/30/2017 [email protected] 13 STORAGE DEVICE Response Time of PEM fuel cell = 20 sec – 6 minutes. Storage device should be designed to satisfy peak load demand for 100 seconds. Energy capacity of the storage device is given by: Estorage 1 C Vi 2 V f2 2 Vi = initial voltage of the storage device V f = final voltage of the storage device C = capacitance of the storage device Energy to be stored can be given as: Energy to be stored kW .h 4/30/2017 Total Peak Load demand (kW ) x Period of peak load demand ( s) 3600 [email protected] 14 STORAGE DEVICE SELECTION To perform simulation – Model of storage will be developed. The storage device will be selected based on computed energy capacity. It will be shown that during 100 seconds period of peak load demand: 1) The discharge current of storage device is high. 2) There exists a voltage drop across the storage device. 3) The state-of-charge (SOC) of the storage device varies. 4/30/2017 [email protected] 15 CONTROL PROBLEM 3) Development of Control Techniques Control of DC/DC Boost Converter Objective of control : Regulate dc bus voltage within 5% from its desired value (480 V). 4/30/2017 [email protected] 16 DC/DC CONVETER Model of the Boost Converter is needed. (48 V – 480 V, rated 10 kW). Lbc 1.8 mH Cbc 55 F DC/DC boost converter can be modeled by state space averaging technique proposed by Middlebrook and Cuk . Inductor current Input and capacitor voltage V 48 V 24 V fc are selected as state variables. Vdc (desired ) 480 V is the output of PEM fuel cell. iL ,bc vc ,bc ubc V fc 4/30/2017 [email protected] 17 DC/DC CONVERTER MODELING State space model of DC/DC Boost Converter : x1bc iL ,bc 0 Abc 1 D Cbc x2bc vc ,bc 1 D Lbc 1 Rbc .Cbc 1 Bbc Lbc 0 ubc V fc Main reasons to use sliding mode control approach: a) Sliding mode control has low sensitivity to system parameter variations and uncertainties (load current) in the system. b) Sliding mode control is based on switching control action. All dc/dc converters use switching devices. 4/30/2017 [email protected] 18 CONTROL PROBLEM In boost converter - rate of change of current is much faster than rate of change of output voltage . According to theory of singular perturbations, control problem can be solved by using cascaded control structure with two control loops – inner current control loop and outer voltage control loop. Inner sliding mode current controller provides fast response with minimum overshoots or undershoots and linear control techniques can be used to design voltage controller. 4/30/2017 [email protected] 19 CONTROL PROBLEM Control of PEM Fuel Cell Output Voltage Objective of control: Regulate the output voltage of PEM fuel cell Output voltage of PEM fuel cell can be changed by varying partial pressure of hydrogen PH or partial pressure of oxygen PO . 2 2 VO , FC nS .E0 Cell 0.5 nS RT PH 2 .( PO2 ) ln 2F P H 2O V fc VO, FC n S .(Vloss 4/30/2017 Act Vloss Vloss O Conc ) [email protected] 20 FUEL CELL CONTROL Control of PEM Fuel Cell Output Voltage 4/30/2017 [email protected] 21 FUEL CELL DYNAMIC MODEL As partial pressure of hydrogen at the anode of PEM fuel cell increases, it increases output of PEM fuel cell. Dynamic equations of partial pressure of hydrogen in PEM fuel cell can be given as: dpH 2 dt dpH 2 dt RT mH 2 ,net mH 2 ,cons Va RT mH 2 ,in mH 2 ,out mH 2 ,cons Va (mH 2 ) net (mH 2 ) in (mH 2 ) out Amount of hydrogen consumed in the reaction is directly related to the output current of PEM fuel cell. Flow rate of hydrogen consumed in the electrochemical reaction is given by mH 2 ,cons 4/30/2017 nS . I fc 2F [email protected] 22 FUEL CELL DYNAMIC MODEL Hydrogen utilization factor is defined as: UH mH 2 ,cons mH 2 ,in High utilization factors (65-85 %) are desired in PEM fuel cell operation as it minimizes the required hydrogen flow. The reference value of hydrogen flow rate can be computed as : mH 2 ,ref nS . I fc,ref 2 FU H Difference between the required flow rate of hydrogen and flow rate of hydrogen consumed in the electrochemical reaction is fed to the fuel flow controller. Hydrogen flow controller controls the valve on hydrogen line to the PEM fuel cell. 4/30/2017 [email protected] 23 DC/AC INVERTER Control of Three-phase Inverter Inverter model is needed Inverter output line-to-line voltage can be represented by the vector – Three-phase inverter output current scan be represented by - , , Vi ViAB iiA 4/30/2017 [email protected] iiB ViBC ViCA T iiC 24 INVERTER MODELING Inverter Line current vector can be defined as - = I i iiAB iiBC Transformer primary side - Delta - connected Primary side line-to-line voltage vector – iiCA T iiA iiB iiB iiC iiC iiA T Primary side line current vector - Transformer secondary side – Wye - connected Secondary side phase voltage vector – V p VpAB VpBC VpCA I p I pA Secondary side phase current vector – I pB I pC T T Load voltage vector - Load current vector - Vs Vsa Vsb Vsc T I s I sa I sb I sc T VL VLa VLb VLc T I L I La 4/30/2017 I Lb I Lc T [email protected] 25 INVERTER MODELING Primary side voltage V p , inverter current I i , load voltageVL , and secondary side current are selected as the state variables of the model. Is Model of three-phase dc/ac inverter (VSI) with L-C Filter and delta-wye transformer: xi Ai xi Bi ui Ei di V pqd I iqd xi VLqd I sqd V ui iq , Vid 4/30/2017 02 x 2 1 I L f 2x2 Ai 02 x 2 1 Tvqd LT i di iq , iid 1 I 2x2 3C f 02 x 2 02 x 2 02 x 2 02 x 2 02 x 2 02 x 2 1 I 2x2 LT 1 Tiqd 3C f 02 x 2 1 I2x2 CL RT I2x2 LT 8 x8 Tvqd Tvqd 0 [email protected] row1, 2 02 x 2 1 I 2x2 Bi L f 02 x 2 02 x 2 8 x 2 1 Ns 1 2 Np 3 3 1 26 VOLTAGE AND CURRENT CONTROL Voltage control technique for single inverter system based on perfect control of robust servomechanism problem (RSP) See References. Voltage control technique is combined with a fast current controller using discrete time sliding mode controller for limiting the inverter currents under overload conditions. RSP Voltage controller is used in outer loop and is cascaded with current controller in the inner loop. • M.N. Marwali and A. Keyhani, “Control of distributed generation systems, part I: voltages and currents control,” IEEE Transactions on Power Electronics, Vol. 19, No.6, pp 1541-50, Nov. 2004. M.N. Marwali, J.W. Jung, and A. Keyhani, “Control of distributed generation systems, Part II: Load Sharing Control,” IEEE Transactions on Power Electronics, Vol. 19, No.6, pp. 1551-61, Nov. 2004. • 4/30/2017 [email protected] 27 CONTROL OF DC/AC INVERTERS The control techniques needs to achieve: 1. 2. 3. 4. Low Load Regulation Minimum THD Fast Transient Response Short Circuit Protection 4/30/2017 [email protected] 28 PEM FUEL DYNAMIC PERFORMANCE Dynamic Model of PEM Fuel Cell The model of 500-W PEM fuel cell , rated 500-W, rated current 25 A, 40V (no-load voltage)-23 V(full-load voltage at rated current 25 A) is developed. Two approaches are used to develop the model. A) State Space Modeling of PEM Fuel Cell i) Open-circuit Output Voltage ii) Irreversible Voltage Losses iii) Humidification iv) Mass Balance v) Thermodynamic Energy Balance vi) Formation of charge Double Layer 4/30/2017 [email protected] 29 PEM FUEL DYNAMIC PERFORMANCE The model is trained and used to obtain: i) V-I characteristics. ii) Polarization curves for different values of input iii) Transient response over short-time period (2-5 seconds) and long-time period (5-6 minutes). iv) Robustness of against the measurement noise is investigated . 4/30/2017 [email protected] 30 WORKING OF PEM FUEL CELL Oxidation reaction at Anode 2 H 2 4 H 4e Reduction reaction at Cathode O2 4e 4 H 2 H 2 O - 4/30/2017 [email protected] 31 STATE SPACE MODELING OF PEM FUEL CELL Open-Circuit Output Voltage of PEM Fuel Cell The reversible electric potential of one cell: E Cell G 2F F The change in Gibb’s free energy: PH .( PO2 ) G G 0 RT ln 2 PH 2O 0.5 PH 2 : Partial pressure of hydrogen E 4/30/2017 E0 Cell : Partial pressure of water PH 2O 0.5 RT PH 2 .( PO2 ) ln 2 F PH 2O : Stack temperature : Universal gas const R Open-circuit output voltage of one cell: Cell : Partial pressure of oxygen PO2 T : Faraday’s const. where, [email protected] E0 G 0 2F Cell 32 STATE SPACE MODELING OF PEM FUEL CELL Open-circuit output voltage of PEM fuel cell: VO, FC nS .E Cell VO , FC n S .E 0 Cell 0.5 n S RT PH 2 .( PO2 ) ln 2F P H 2O E Cell : Reversible cell potential E0 4/30/2017 Cell n S : Number of PEM fuel cell stacks : Standard reference potential at standard operating conditions [email protected] 33 STATE SPACE MODELING OF PEM FUEL CELL Irreversible Voltage Losses in PEM Fuel Cell Output voltage of PEM fuel cell at normal operating conditions is determined by voltage losses in PEM fuel cell. Three types of voltage losses exist: a) Activation losses b) Ohmic losses and c) Concentration losses. A) Activation Losses Governance of sluggish electrode kinetics by the rate of electrochemical reaction at an electrode surface gives rise to activation losses Dominant at low current density (i.e. at the beginning of V-I characteristic curve). The activation losses for a single cell stack can be modeled by Tafel equation: Vloss 4/30/2017 Act RT I ln T .[a b ln( I )] 2F I d [email protected] 34 STATE SPACE MODELING OF PEM FUEL CELL B) Ohmic losses Ohmic resistance of PEM fuel cell that includes the resistance of anode and cathode due to imperfections in electrode manufacturing and the resistance of polymer electrolyte membrane to movement of ions. Ohmic voltage loss for a single PEM fuel cell stack can be given as: Vloss I .R O VA VC VM O O O O C) Concentration losses Formation of concentration gradients of reactants at the surface of the electrodes give rise to concentration losses The concentration losses for a single cell stack can be given as: Vloss Conc RT I ln 1 eF I L Significant at higher currents ( at the end of V-I characteristics of the PEM fuel cell). 4/30/2017 [email protected] 35 STATE SPACE MODELING OF PEM FUEL CELL Hence, actual output voltage of PEM fuel cell at normal operating conditions : V fc VO, FC n S .(Vloss 4/30/2017 Act Vloss Vloss [email protected] O Conc ) 36 STATE SPACE MODELING OF PEM FUEL CELL Humidification in PEM Fuel Cell In PEM fuel cell, conduction of hydrogen ions through the polymer membrane depends on the membrane humidity. The ohmic resistance of the membrane increases as membrane dries out. Hence, it is essential that membrane remains humidified for efficient operation of PEM fuel cell. Therefore, hydrogen gas and air are passed through the humidifier before reaching the electrodes. The total vapor transfer through the polymer membrane can be given as : The relative humidity at anode and at cathode can be given as: a n I a (mv ) M M v . AS .nS d d c tm F a 4/30/2017 PH 2O PH 2O Sat c PH 2O PH 2O c Sat [email protected] 37 STATE SPACE MODELING OF PEM FUEL CELL Mass Balance in PEM Fuel Cell Material conservation of oxygen at cathode can be given as: mO2 (mO2 ) in (mO2 ) out (mO2 ) cons Net mole flow rate of oxygen at cathode is: (mO2 ) net (mO2 ) in (mO2 ) out Rate at which oxygen is consumed at cathode in the reaction can be given as: m O2 cons mO2 (mO2 ) net (mO2 ) cons nS .I 4F Net mole flow rate of oxygen at cathode can be given as: M O2 , net I (mO2 ) net C 4F 4/30/2017 [email protected] 38 STATE SPACE MODELING OF PEM FUEL CELL Mass Balance in PEM Fuel Cell Material conservation of hydrogen at anode can be given as: mH 2 (mH 2 )in (mH 2 ) out (mH 2 ) cons Net mole flow rate of hydrogen at anode is: (mH 2 ) net (mH 2 ) in (mH 2 ) out Rate at which hydrogen is consumed at anode in the reaction can be given as: m H 2 cons mH 2 (mH 2 ) net (mH 2 ) cons nS .I 2F Net mole flow rate of hydrogen at anode can be given as: M H 2 , net I (m H 2 ) net A 2F 4/30/2017 [email protected] 39 STATE SPACE MODELING OF PEM FUEL CELL Mass Balance in PEM Fuel Cell x1 M O2 , x 2 M O2 , net x3 M H 2 , x 4 M H 2 , net 1 n x1 0 C x1 1 4 F S 4 F I x 1 x 1 2 2 0 C 4F 1 n x 3 0 A x3 1 2 F S 2 F I x 1 x 1 0 4 A 4 2F Material conservation of water can be given by subtracting rate of flow water going outside the cell from rate of generation of water in the cell: x 5 M H 2O 4/30/2017 x5 nS .I 2F [email protected] 40 STATE SPACE MODELING OF PEM FUEL CELL PEM Fuel Cell Stack Temperature Temperature of PEM fuel cell assembly increases as electrochemical reaction proceeds in PEM fuel cell The net increase in temperature of PEM fuel cell assembly can be given by as: dT 1 dQC dQE dQL dt M fcC fc dt dt dt Let x6 T , x10 QC , x11 QE , x12 QL x 6 4/30/2017 1 x10 x11 x12 M fc C fc [email protected] 41 STATE SPACE MODELING OF PEM FUEL CELL Dynamic equations of partial pressures of hydrogen can be given as: m m R.T . mH 2 dt V a dPH 2 Let H 2 out in H 2 cons x7 PH 2 R.T M H 2 ,net R.T . .I x 7 V 2 . V F A a a 1 x 7 .u PA 1 ( x6 ).I A where, 4/30/2017 R.x 6 2.Va F 1 ( x6 ) [email protected] 42 STATE SPACE MODELING OF PEM FUEL CELL Dynamic equations of partial pressures of oxygen can be given as: x8 PO2 , x9 PH 2O 1 x8 .u PC 2 ( x6 ).I c Let R.x 6 4.Vc F 2 ( x6 ) where, Dynamic equations of partial pressures of water can be given as: x9 3 ( x5 ).x6 4 ( x6 ).I where, 4/30/2017 R.x 6 2.Va F 1 ( x6 ) [email protected] 43 STATE SPACE MODELING OF PEM FUEL CELL Thermodynamic Energy Balance in PEM Fuel Cell Heat generation during electrochemical reaction QC : Function of change in Gibbs’s free energy and rate of consumption of molar mass of hydrogen during the reaction nI x10 G. S 2F x10 5 ( x6 , x7 , x8 , x9 ).I where, 4/30/2017 n S G 0 n S R.x 6 x 7 .x8 0.5 5 ( x 6 , x 7 , x8 , x 9 ) ln x 2 F 2 F 9 [email protected] 44 STATE SPACE MODELING OF PEM FUEL CELL Thermodynamic Energy Balance in PEM Fuel Cell Heat generation due to electrical output power : depends on the open-circuit voltage and the stack current of PEM fuel cell x11 [VO , FC ].I x11 6 ( x6 , x7 , x8 , x9 ).I where, 4/30/2017 0.5 n S R.x 6 x 7 .x 8 Cell 6 ( x 6 , x 7 , x 8 , x 9 ) n S E 0 ln x 2F 9 [email protected] 45 STATE SPACE MODELING OF PEM FUEL CELL Thermodynamic Energy Balance in PEM Fuel Cell Heat loss due to air convection dQL (T uTR ).h S .nS . AS dt x12 [hS n S AS ].x6 [hS n S AS ].uTR The net increase in temperature of PEM fuel cell assembly can be given by: x 6 1 x10 x11 x12 M fc C fc h n A x 6 S S S M fc C fc where, 4/30/2017 hS n S AS x ( x , x , x , x ). I 6 7 6 7 8 9 M fc C fc u TR Cell x 7 .x8 0.5 nS E0 n S R.x 6 7 ( x 6 , x 7 , x8 , x 9 ) ln M fc C fc FM fc C fc x 9 [email protected] 46 STATE SPACE MODELING OF PEM FUEL CELL Formation of Charge Double Layer in PEM Fuel Cell In PEM fuel cell, electrons from anode flow towards cathode via external circuit and positive hydrogen ions reach cathode through the polymer membrane. Two charged layers of opposite polarities are formed at cathode. Charge double layer can store electrical charge and behaves like a capacitor. 4/30/2017 [email protected] 47 STATE SPACE MODELING OF PEM FUEL CELL FORMATION OF CHARGE DOUBLE LAYER IN PEM FUEL CELL The electric charge formed at the cathode can be modeled by capacitor as The voltage across the capacitor is given as dV VC I C C R Act R Conc dt The value of the capacitance is given as : C e AS dl 4/30/2017 [email protected] 48 STATE SPACE MODELING OF PEM FUEL CELL OVERALL STATE SPACE MODEL OF PEM FUEL CELL x (t ) A( ).x(t ) B( ).u (t ) G ( ).w(t ) y (t ) C ( ).x(t ) v(t ) x(t ) = system states y (t ) = system output u (t ) = control input w(t ) = disturbance v (t ) = measurement noise = state-dependent parameter vector 4/30/2017 [email protected] 49 STATE SPACE MODELING OF PEM FUEL CELL 0 0 0 0 A 0 0 0 2 x1 0 0 2 x1 0 0 1 C 0 0 0 0 01x 6 C 0 0 0 0 01x 6 0 0 A 0 0 01x 6 1 1 1 0 0 A 0 0 01x 6 0 0 0 0 0 0 0 0 0 2 x1 0 0 2 x1 0 0 0 2 x1 0 0 2 x1 0 0 0 2 x1 0 0 2 x1 0 0 0 2 x1 0 0 2 x1 0 0 0 A6 x 6 0 2 x1 3 x5 0 2 x1 hS .nS . AS 0 01x 6 01x 6 02 x6 01x 6 02 x6 01x 6 01x 6 h .n . A A6 x 6 S S S M fc .C fc 0 5 x1 0 1 B A 0 0 3 x1 0 0 0 5 x1 0 0 1 C 0 3 x1 0 0 0 0 0 3 x1 hS .nS . AS 0 0 5 x1 hS .n S . AS M .C fc fc 1 , A13x13 Act Conc C R R C 01x5 8 ( x7 , x8 , x9 ) 01x 6 4/30/2017 0 0 0 0 0 0 0 2 x1 0 0 2 x1 0 A13x13 nS 8 ( x7 , x8 , x9 ) [email protected] nS R x7 .x80.5 ln 2 F x9 50 STATE SPACE MODELING OF PEM FUEL CELL x [M O2 M O2 ,net M H2 u u PA u PC M H 2 ,net uTR M H 2O T PH 2 PO2 PH 2O QC QE QL VC T T 1 ( x6 ) 2 ( x6 ) 3 ( x5 ) 4 ( x6 ) 5 ( x6 , x7 , x8 , x9 ) 6 ( x6 , x7 , x8 , x9 ) 7 ( x6 , x7 , x8 , x9 )8 ( x7 , x8 , x9 )T 1 n 1 G S 4 F 4 F 4 F 4 ( x6 ) 1 nS 7 ( x6 , x7 , x8 , x9 ) 2F 2F 5 ( x6 , x7 , x8 , x9 ) 6 ( x6 , x7 , x8 , x9 ) w I 4/30/2017 n 1 S 2F 2F v nS .RO 0 1 C 1 ( x6 ) 2 ( x6 ) T [email protected] 51 STATE SPACE MODELING OF PEM FUEL CELL Parameters of 500-W PEM Fuel Cell (Avista Labs SR- 12 PEM Fuel Cell) 4/30/2017 [email protected] 52 IMPLEMENTATION OF MODEL IN MATLAB/SIMULINK 4/30/2017 [email protected] 53 SIMULATION RESULTS V-I Characteristics of PEM Fuel Cell Model - Model is simulated for 2720 seconds with of input variables: u P = 2 pa, u P = 1 pa, uT = 308 K A C R Validation of PEM Fuel Cell Model -Simulation results are validated with published results of Avista Labs SR-12 PEM Fuel Cell by Caisheng Wang, Nehrir, M.H., Shaw S.R** - The current is varied from 1 A to 25 A over a period of 2720 seconds in steps of 0.4A ** - Caisheng Wang, Nehrir, M.H., Shaw S.R., “Dynamic Models and Model Validation for PEM Fuel Cells Using Electrical Circuits”, IEEE Transactions on Energy Conversion, Vol. 20, Issue 2, pp. 442-451, June 2005. 4/30/2017 [email protected] 54 SIMULATION RESULTS Temperature Response of PEM Fuel Cell Model Stack temperature of PEM fuel cell increases to 316 K from 308 K as electrochemical reaction proceeds in PEM fuel cell u P A = 2 pa, 4/30/2017 u P= C 1 pa, uT = R 308 K [email protected] 55 SIMULATION RESULTS Power vs. Current characteristics of PEM Fuel Cell Model Maximum output power is obtained close to the fuel cell rated current (25A) but not exactly at the rated current. PEM fuel cell goes in the concentration region near rated current (25 A) Output power decreases with increasing load current due to decrease in PEM fuel cell’s output voltage 4/30/2017 [email protected] 56 SIMULATION RESULTS Polarization Curves of PEM Fuel Cell Model for Different values of Input Variables V-I Characteristics of PEM Fuel Cell V-I Characteristics of PEM Fuel Cell Model for increasing values of Model for increasing values of uPA u PC = 2 pa, 10 pa, 30 pa, 50 pa uPA = 1 pa , u PC 4/30/2017 = 1 pa, 10 pa, 30 pa, 50 pa u PC = 308 K = 2 pa, uT R uPA [email protected] = 308 K uT R 57 SIMULATION RESULTS Transient Response of PEM Fuel Cell Model Transient Response of PEM Fuel Cell Model over Short-Time Period Transient Response of PEM Fuel Cell Model over Long-Time Period u P A = 5 pa, u PC = 5 pa, 4/30/2017 [email protected] uT R = 308 K 58 SIMULATION RESULTS Behavior of PEM Fuel Cell Model under Resistive (R) Load uPA = 5 pa, = 5 pa, u PC = 308 K uT R - Response at : No load, 1/4th (quarter) resistive load, 1/2 (half) resistive load, 3/4th resistive load and full resistive load - As the load is increased from no-load to fullload condition, output voltage is reduced - Stack temperature of PEM Fuel Cell with corresponding increase in resistive load 4/30/2017 [email protected] ncreases 59 SIMULATION RESULTS Transient Response of PEM Fuel Cell Model Transient Response of PEM Fuel Cell Model over Short-Time Period u P A= 2.5 pa , 4/30/2017 Transient Response of PEM Fuel Cell Model over Long-Time Period u PC= 1 pa, uT R= 308 K [email protected] 60 Distributed Generation Systems 4/30/2017 [email protected] 61 • • • • • • Distributed Energy Sources: Photo voltaic Energy Wind Energy Fuel Cells Micro Turbines Storage Devices 4/30/2017 [email protected] 62 contains a 100W solar panel, a 12V battery and a charge controller, and a 12VDC/220VAC power inverter. 100 W Solar Photo Voltaic Energy Source 12VDC/220VAC Power Inverter 12V/100W Solar Panel Charge Controller 4/30/2017 12V Battery [email protected] 63 APET018 - 2MVA UPS Loss budget Large UPS NXL750kVA – Raptor (With Transformer) Q3 Main & Bypass Input – 12P Raptor 750kVA LNA 12P Loss budget Static Switch & Output Bypass Input 380V/400V/415V/50Hz, 3ph/4w Q2 SCR 7-9 V_Byp_A V_Byp_B 1.60% V_Byp_C V_Byp_N V_PE SCR 1-3 3 Tin Input Transformer DCFA LR0 DCFB DCCT DCFC Tout Output Transformer & Inductor SCR 10-12 F1-3 CT 7-9 F 16-18 1.40% LR0 DCCC DCCB DCCA Bypass & Main input connect as default configuration 1.20% CT 3-4 HPA-C Q4 Lin Q1 IGBT 1-4 IGBT 5-8 1.00% IGBT 9-12 V_Inp_A SCR 4-6 V_Inp_B Inverter CT 1-2 F4-6 LR0 V_Inp_C Main Input 380V/400V/415V/50Hz, 3ph/3w 0.80% C 13-15 CT 5-6 Battery Cabinet M1 BCB CT10 2 HP1 Batt_POS Battery Output Transformer & Filter 0.60% Batt_NEG LTx Rectifier – 12P 1 C 10-12 Internal Optional passive filter Input Filter and REC Front End – 12P 0.40% M1 is an option for Internal optional passive filter 2 Tin is WYE/Delta connection for Raptor B 3 The position of LR0 may change to downstream of F1 to F3 0.20% 0.00% Lin AC tot Ca p • Total losses – 44.8kW Re DC ctifi e T Ca r S in p CR & Bl s ee d T o IN V ut IG BT Ou L t A ou C t C S n ap ub be Fu r se s Fa A B u ux ns s S PS tru U ct ur e 1 In p ut • Efficiency – 93.8% • Switching frequency – 2.5kHz • Low frequency 12 pulse isolated input and PWM inverter isolated output 4/30/2017 Transformer and IGBT switches are the most significant, … followed by the fans. [email protected] 64 APET018 - 2MVA UPS Loss Budget Medium UPS NXA200kVA (Without transformer) NX 200kVA ENPC PWM Loss Budget 1.60% 1.40% 1.20% 1.00% 0.80% 0.60% 0.40% 0.20% • Efficiency – 92.8% • Switching frequency – 5kHz 0.00% In Lin pu t A (L3 C ) L1 Cap RE ( Re C c) IG D C BT Ba Cap lI IN GB V T IG B Ou L1 T t A ou ou C C t tp ut ap SC Fu R se s Fa A n B u ux s P sS S tru U cu re • Total losses - 12.4kW • PWM rectifier and inverter • Input and output not isolated Inductors and IGBT switches are the most significant 4/30/2017 [email protected] 65 1400A/1200V IGBT Infineon APET018 - 2MVA UPS • Cooligy cold plate with Infineon Liquid cooling of semiconductors modules for UPS Refrigerant R134a • Wind power project ENPC Water cooling Semikron Skiip copper base plate less 1800A/1200V Semikron Skiip module - Water cooled 4/30/2017 [email protected] 66 APET018 - 2MVA UPS Liquid cooling of semiconductors (Liebert XD - extreme density) Pre-piping assembly Retrofit Any floor Any space Any time Refrigerant pipes directly connected to the cold plate under the semiconductors 4/30/2017 [email protected] 67 APET018 - 2MVA UPS Example of size difference PFC power components Option 12 PFC cabinet Option 8 PFC cabinet Topology affects directly size and performance for same switching frequency 4/30/2017 [email protected] 68 • Distributed Generation – Distributed sources close to end users – Island mode • Standby backup power – Grid-connected mode • Grid support – peak shaving – Solid-state power conversion in DG • Technical Areas – – – – 4/30/2017 Power electronics Controls DSP and embedded systems Electromechanical systems [email protected] 69 Three-Phase Four-Wire Inverter Control 4/30/2017 [email protected] 70 Three-Phase Four-Wire Inverter Control (1) • The 3-ph 3-wire topology, for comparison 4/30/2017 [email protected] 71 Three-Phase Four-Wire Inverter Control (2) • The 3-ph 4-wire transformerless split dc bus topology 4/30/2017 [email protected] 72 Three-Phase Four-Wire Inverter Control (3) • Specifications – Input: 3-ph utility 240 V line-to-line, 60 Hz – Dc link: ± 270 V – Output: 3-ph 120 V line-to-neutral, 60 Hz 4/30/2017 [email protected] 73 Three-Phase Four-Wire Inverter Control (4) • About the topologies: 4-wire vs. 3-wire – Without output isolation transformer • Less weight, volume, and cost • Lower order in the model • Both the rectifier and the inverter requires 3 dimensional control – the 0 sequence • More challenge for THD control – the triplets – Center grounded dc link • Lower dc voltage utilization in PWM 4/30/2017 [email protected] 74 Three-Phase Four-Wire Inverter Control (5) • Control goals – voltage control – – – – Low steady state error Low THD Robust to load disturbances Fast transient response • Challenges – – – – 4/30/2017 Nonlinear load Unbalanced load Transient load disturbances Model uncertainties [email protected] 75 Three-Phase Four-Wire Inverter Control (6) • Output L-C filter design – differential filtering – Cut-off frequency 1 fC 2 L f C f – Limit Lf and Cf values to lower weight, volume, and cost – Small enough C to limit fundamental filter current – Choose Lf = 10.2 mH and Lf = 55 μF. • Therefore, fC=212 Hz • Common mode choke issue for the 0-axis component 4/30/2017 [email protected] 76 Three-Phase Four-Wire Inverter Control (7) • The control strategy – Discrete-time sliding mode controller (DSMC) • Used for current control • Fast response without overshoot – Robust servomechanism controller (RSC) • • • • 4/30/2017 Used for voltage control and THD elimination Zero tracking error Elimination of harmonics of specified frequencies Overall stability and robustness [email protected] 77 Three-Phase Four-Wire Inverter Control (8) • Control system structure: –The inner loop: current control –The outer loop: voltage control –Current limiter: limit the inductor current Vref, 0 + ev,0 - VL, 0 4/30/2017 RSC Icmd, 0* Current Limiter IL Vi,cmd,0 Icmd, 0 ei,0 + DSMC SVPWM Vi Plant X - Ii, 0 [email protected] X 78 Three-Phase Four-Wire Inverter Control • Inner loop design (4-wire): DSMC – The plant AX Bu Ed X y1 C1X VL 0 X I i 0 033 A 1 I L f 33 Vi u Vi Vi 0 iL d iL iL 0 4/30/2017 1 I 33 Cf 033 033 B 1 I 33 L f C1 033 [email protected] 1 I 3 3 E Cf 033 63 I3 79 Three-Phase Four-Wire Inverter Control • Reference frame transformation – αβ0 vs. abc β b α a 1 f 2 f 0 3 f 0 1 2 1 2 3 2 1 2 1 2 f a 3 fb 2 1 f c 2 c 4/30/2017 [email protected] 80 Three-Phase Four-Wire Inverter Control • Convert into per-unit values – Per-unit equivalent circuit 1 Sb S rated 3 Ib 2 R C Vb 2Vrated Sb Vrated Rf Zb Zb L 1 L f Zb Vb Ib 1 1 Lf Zb 1 1 C f Zb 1 1 1C f Zb 4/30/2017 [email protected] 81 Three-Phase Four-Wire Inverter Control –Plant model in discrete time X(k 1) A* X(k ) B*u(k ) E*d (k ) y1 (k ) C1X(k ) A e * ATs Ts B e * 0 A (Ts ) Bd Ts E e A (Ts ) Ed * 0 –Discrete-time sliding mode control: • For an arbitrary finite-dimensional discrete-time system, a continuous equivalent control law yields system modes on manifold s=0 within one sampling period. If control force is bounded, sliding mode s=0 can take place in finite number of steps. 4/30/2017 [email protected] 82 Three-Phase Four-Wire Inverter Control –The equivalent control ueq (k ) C1B* I 1 cmd , 0 (k ) C1A* X(k ) C1E*d(k ) –The final control, u0 is determined by SVPWM inverter u eq (k ) for u eq (k ) u 0 u( k ) u 0 u (k ) for u eq (k ) u 0 u (k ) eq eq 4/30/2017 [email protected] 83 Three-Phase Four-Wire Inverter Control (14) • RSC –Internal model principle • Asymptotic tracking of controlled variables toward the corresponding references in the presence of disturbances (zero steady state tracking error) can be achieved if the modes that generate these references and disturbances are included in the stable closed loop systems. –Optimal control • Overall stability guaranteed • Arbitrary good transient response 4/30/2017 [email protected] 84 Three-Phase Four-Wire Inverter Control (15) –The original discrete-time model X(k 1) A * X(k ) B*u(k ) E*d(k ) –Include the dynamics of the DSMC X(k 1) A d X(k ) B d u1 (k ) E*d(k ) y (k ) C d X(k ) where A d A* B* C1B* B d B* C1B* 1 C1A* 1 Cd 1 0 u1 (k ) I cmd , 0 (k ) 4/30/2017 [email protected] 85 Three-Phase Four-Wire Inverter Control (16) –Design of the servocompensator • Specifying the tracking/disturbance poles: – j1, j3, j5, and j7, • The servocompensator 0 2 1 Ac 1 0 0 1 32 0 • In discrete time 4/30/2017 0 1 52 0 0 72 1 0 η A c η B cev 0 0 1 0 1 Bc 0 1 0 1 η(k 1) A*c η(k ) B*cev 0 (k ) [email protected] 86 Three-Phase Four-Wire Inverter Control – Design of the servocompensator 4/30/2017 [email protected] 87 Three-Phase Four-Wire Inverter Control –Design of the control gain K • The augmented system: ˆX ˆ (k 1) A ˆ (k ) B ˆ u (k ) E ˆ d(k ) E ˆ y (k ) X 1 1 2 ref ˆ ( k ) X( k ) X η(k ) ˆ Ad A B * C c d u1 (k ) I cmd , 0 (k ) 0 ˆ B d B A *c 0 d(k ) I L 0 (k ) * E ˆ E 1 0 ˆE 0 2 B * c y ref (k ) Vref , 0 (k ) • Linear quadratic performance index ˆ T (k )QX ˆ (k ) u T (k )u(k ) J X k 0 4/30/2017 [email protected] 88 Three-Phase Four-Wire Inverter Control • The Algebraic Riccati Equation • The control gain ˆ T P PA ˆ Q 1 PBˆ Bˆ T P 0 A 1 ˆT K B P ˆ (k ) u1 (k ) I cmd , 0 (k ) KX • The control 4/30/2017 [email protected] K 0 X( k ) K1 K 0 X(k ) K1η(k ) η(k ) [email protected] 89