Overview of Energy Systems 8 PDF

Password: esys2024 1 Yasumasa FUJII, Ryoichi KOMIYAMA Department of Nuclear Engineering and Management The University of Tokyo  Password: esys2024...

Password: esys2024 1 Yasumasa FUJII, Ryoichi KOMIYAMA Department of Nuclear Engineering and Management The University of Tokyo  Password: esys2024 2 5. Power Systems 5.1 Introduction (1) Typical Form of a Power System Elements of the power system ▫ Power Plants ▫ Transmission and Distribution Lines ▫ Substations  Switching equipment (Distribution line selections)  Protection and control equipment (Circuit breakers, Static VAR compensators …)  Transformers (Voltage step-up and step-down) Hydro Power Plants Large Large Industries Industries Distribution Poles Service Lines Small Industries Distribution lines Distribution Distribution Nuclear Power Plants Lines Substation Distribution Transmission Transformers Lines Intermediate Transmission Substation Distribution Lines Lines Service Lines High Voltage Transmission Substation Substation Transmission& Commercial Underground Distribution Lines Underground Distribution Sector Distribution Lines Lines Service Lines Residential Buildings & Sector Large Buildings Middle Industries Thermal Power Plants Railway Substation 電力設備の概要(東京電力の例) （引用：「電気事業連合会 INFOBASE 2016 電力設備」）  Password: esys2024 3 5.1 Introduction (1) Typical Form of a Power System Shape of Transmission Networks ▫ Open-ring shape network for large cities such as Tokyo, Osaka and Nagoya  Under ground cables are used to connect the ring and the center of cities  Maximum transmission distance of cable is around 30 km. A,B: Thermal Power Plants, C: Nuclear Power Plants, D: Hydro Power Plants, E:Puming-up storage bay y  Password: esys2024 4 5.1 Introduction (2) National Power Systems of Japan Power Companies and Trunk line Connections (As of March 31, 2009) System peak load : 178,995MW Electricity sales: 888,935GWh 7GW 600MW Total: 200GW 300 MW 17GW 8GW 64GW 33GW 300MW 12GW 34GW 7GW 20GW 2GW 1400MW 1130MW FCF: Frequency Converter Facilities Total cap. 2,100 MW From Web site of the Federation of Electric Power Companies of Japan  Password: esys2024 5 5.1 Introduction (2) National Power Systems of Japan Hourly Power Usage on Peak Power Days Source :Graphical Flip-chart of Nuclear & Energy Related Topics https://www.ene100.jp/map_title_en  Password: esys2024 6 5.1 Introduction (2) National Power Systems of Japan Power Generation Costs http://www.npu.go.jp/policy/policy09/archive02_hokoku.html [Yen/kWh] Risk Policy Social Cost Fuel O&M Cost of Electricity Generation Capital Value of heat Nuclear Coal Fired LNG Fired Wind Wind Geothermal Small Hydro Biomass Oil Fired PV Gas C0-gene (Onshore) (Offshore) (Wood) (Rooftop) in 2030 【Capacity Factor(%)/Life Time(year)】(Discount Rate 3%) (Lower end (left) and Higher end(right) for renewables, 50% (left) and 10% (right) of capacity factors for oil fired)  Password: esys2024 7 5.1 Introduction (2) National Power Systems of Japan Business categories and structure From Web site of the Federation of Electric Power Companies of Japan  Password: esys2024 8 5.2 Power and Frequency Control (1) Frequency of a power system The nominal frequency of commercial power systems is 50Hz or 60Hz. ▫ 60 Hz  North America, Western Japan, South Korea, Chinese Taiwan, Philippine etc ▫ 50 Hz  Eurasia, Africa, Oceania, Eastern Japan etc The frequency of the systems in Japan is controlled to be equal to the respective nominal value with the error range of 0.1~0.2Hz. ▫ The quality of electricity service  The frequency may have the direct influence on the rotational speed of AC motors. ▫ The avoidance of mechanical resonance of turbines and generators  Password: esys2024 9 5.2 Power and Frequency Control (2) Generator Rotational Speed Rotational Speed and Dynamic Equation ▫ Rotational speed ω is proportional to frequency f ω = 2πf ▫ Basic Equation d∆f x = g + 2π ⋅ m f = f n + ∆f dt x : mechanical input, g : electrical output, m : moment of inertia of a turbine and a generator, f : rotational speed in frequency, fn : nominal frequency (50Hz or 60Hz), Δf : frequency deviation  If x is larger (smaller) than g, then the rotational speed of rotor is increased (decreased). Control Valve Boiler x→ g→ Turbine Generator  Password: esys2024 10 5.2 Power and Frequency Control (3) Control of a Power Plant 3 Types of Plant Control Modes ▫ Governor Free Operation (GF)  Local control of plant to respond quickly to frequency deviation  Control of valves by a turbine governor ▫ Load Frequency Control (LFC)  Governor settings adjustment by the control center of a power system ▫ Economic Dispatching Control (EDC)  Control according to the prepared daily dispatching plan to minimize fuel costs  Control of governor settings and daily start and stop from the control center of a power system Control Turbine Valve Boiler GF Generator Governor ∆f Control Center Controller LFC/EDC  11 Password: esys2024 5.2 Power and Frequency Control (3) Control of a Power Plant A=B+C+D A:Total demand curve EDC Electric Demand B: Long cycle component EDC C: Short cycle component LFC Amplitude of Fluctuation D: Very short cycle component GF Self Regulation Time of Load EDC LFC http://www.meti.go.jp/committee/materials2/downloadfiles/g90126a12j.pdf GF 0 0.5 1 20 60 Cycle (minute)  Password: esys2024 12 5.2 Power and Frequency Control (4) Governor-Free Control f fc Droop characteristics of GF −r fn ▫ If the speed is too fast, mechanical input is to be reduced. ▫ If the speed is too slow, mechanical input is to be enhanced. x 1 x0 ∆x = − ∆f r Droop curve of governor Δx : changed mechanical input by a governor, r : speed regulation rate. Response to the change in electrical output ▫ The required electrical output of a certain plant should be changed according to the changes in electric demand as well as system disturbances such as accidents. 1 d∆f fn (∆x + x0 ) = (∆G + g 0 ) + 2π ⋅ m d∆f f − ∆f = ∆G + 2π ⋅ m rΔG dt r dt g ΔG : change in electrical output x0, g0 ΔG x  We can assume x0=g0 as initial condition. 2πmr t1 t  Password: esys2024 13 5.2 Power and Frequency Control (4) Governor-Free Control GF of N Plants ▫ Response of N plants to the change in required electrical output of the system d∆f N N 1 d∆f 1 2π dt ∑ mi + ∆f ∑ i =1 i =1 ri = −∆G 2πM dt + ∆f = −∆G R mi : rotor moment of inertia of i-th plant, ri : speed regulation rate of i-th plant N 1 N M = ∑ mi R= G0 = ∑ g 0i N 1 fn f i =1 ∑ i =1 ri i =1 RΔG G ∆f R ⋅ ∆G G0 ΔG ∆xi = − = ri ri 2πMR t1 t Δxi : mechanical input change of i-th plant, ▫ Frequency deviation Δf cannot be suppressed completely.  The stationary off-set of the frequency deviation is RΔG. ∆f = − R ⋅ ∆G  Password: esys2024 14 5.2 Power and Frequency Control (5) Power-Frequency Coefficient Power-Frequency Coefficient of Generator KG ∆G 1 1 100 KG =− = [MW/Hz] = [MW/0.1Hz] %KG = K G [%MW/0.1Hz] ∆f R 10 R G0 ▫ Empirical value of %KG in Japan % K G = 0.7 ~ 1.4[%MW / 0.1Hz] Power-Frequency Coefficient of Electric Load KL ▫ If the frequency of a power system drops, the electric load level of the system should drop as well. This is because the electric load of AC motors is a function of the frequency. ▫ Self regulation characteristics of load ∆L[MW] ∆L[%MW] 100 KL = %K L = = KL ∆f [0.1Hz] ∆f [0.1Hz] L0 L0 : reference electric load, ΔL : resultant load level change due to frequency deviation ▫ Empirical value of %KL in Japan % K L = 0.2 ~ 0.6[%MW / 0.1Hz]  Password: esys2024 15 5.2 Power and Frequency Control (5) Power-Frequency Coefficient Supply and Demand Balance of the power system G0 + ∆PG − K G ⋅ ∆f = L0 + ∆PL + K L ⋅ ∆f ΔPG : change in electrical output due to facility incidents, ΔPL : change in electrical load due to the changes in social and weather condition ∆P(= ∆PG − ∆PL ) = ( K G + K L )∆f = K ⋅ ∆f ∆P = K ⋅ ∆f ΔP : imbalanced power, K : power system constant (power-frequency coefficient) ▫ Empirical value of %K in Japan % K = % K L + % K G = 1 ~ 2[%MW / 0.1Hz] Frequency Supply Demand (Generation) (Consumption) http://www.enecho.meti.go.jp/denkihp/bunkakai/5th/5thshiryou5.pdf  Password: esys2024 16 5.2 Power and Frequency Control (6) Load Frequency Control (LFC) Governor-Free and Load Frequency Control ▫ Relation between imbalanced power and frequency deviation ∆P = K ⋅ ∆f ▫ The frequency deviation Δf cannot be suppressed completely by GF and self regulation of load. ▫ The droop curves of respective plants must be shifted so as to eliminate the frequency deviation. N N ∆P + ∑ ∆ci = K ⋅ ∆f ∑ ∆c i =1 i = ∆C = −∆P f i =1 Δci : mechanical input change of i-th plant at nominal frequency ΔC : LFC command to change the total mechanical input of the fc' fc power system ▫ Δci can be obtained with the integral control. fn N lim ∑ ∆ci (t ) = −∆P t ∆ci (t ) = −ki ∫ ∆fdt t →∞ ∆ci t0 i =1 gi  ki : integral gain of i-th plant control gi0 gi0+Δci  The response time of LFC is slower than that of GF.  Password: esys2024 17 5.2 Power and Frequency Control (6) Load Frequency Control (LFC) LFC of inter-connected power systems ▫ (1) Independent power system A ∆PA + ∆C A = K A ⋅ ∆f ΔPA : power imbalance of system A, ΔCA : LFC command of system A, KA : power-frequency coefficient of system A  There are 2 variables of ΔCA and Δf in one equation. A B  If we assume that Δf is 0 (FFC), then ΔCA can be obtained as follows. ΔPT ∆C A = −∆PA ∆PA, KA ∆PB, KB ▫ (2) Interconnected power systems A and B ∆PA + ∆C A − ∆PT = K A ⋅ ∆f ∆CA ∆CB ∆PB + ∆C B + ∆PT = K B ⋅ ∆f ΔPB : power imbalance of system B, ΔCB : LFC command of system B, KB : power-frequency coefficient of system B, ΔPT : power flow change of tie line from A to B  There are 4 variables of ΔCA, ΔCB, ΔPT and Δf in 2 equations. (2 degrees of freedom)  In order to determine the variables, we need to fix two of the four variables, to add two equations, or to fix one variable and to add one equation.  Password: esys2024 18 5.2 Power and Frequency Control (6) Load Frequency Control (LFC) Types of LFC and their mathematical representations ▫ Flat Frequency Control (FFC)  ΔC is determined so that Δf=0. TBC ▫ Flat Tieline Control (FTC) FTC  ΔC is determined so that ΔPT=0. − K′ PT ▫ Tieline Bias Control (TBC)  ΔCA and ΔCB are determined so that ARA=0 and ARB=0. 0 ARA = K ′A ⋅ ∆f + ∆PT for system A f FFC ARB = K B′ ⋅ ∆f − ∆PT for system B ARi : area requirement for system i K’i : estimated power-frequency coefficient of system i ▫ No LFC  ΔC = 0  Password: esys2024 19 5.2 Power and Frequency Control (6) Load Frequency Control (LFC) Behaviors of the inter-connected power systems ▫ (I) No LFC for both A and B (only GF and self regulation of load) ∆C A = 0 ∆PA + 0 − ∆PT = K A ⋅ ∆f ∆P + ∆PB K B ∆PA − K A ∆PB ∆f = A ∆PT = ∆C B = 0 ∆PB + 0 + ∆PT = K B ⋅ ∆f K A + KB K A + KB ▫ (II) FFC for A and no LFC for B (including case of very slow LFC for B) ∆f = 0 ∆PA + ∆C A − ∆PT = K A ⋅ 0 ∆PT = −∆PB ∆C A = −(∆PA + ∆PB ) ∆C B = 0 ∆PB + 0 + ∆PT = K B ⋅ 0 All the imbalanced power is compensated by system A. ▫ (III) FTC for A and no LFC for B (including case of very slow LFC for B) ∆PT = 0 ∆PA + ∆C A − 0 = K A ⋅ ∆f ∆P KA ∆f = B ∆C A = ∆PB − ∆PA ∆C B = 0 ∆PB + 0 + 0 = K B ⋅ ∆f KB KB In this case, ΔPB may cause a lager frequency deviation than case (I).  Password: esys2024 20 5.2 Power and Frequency Control (6) Load Frequency Control (LFC) Behaviors of the inter-connected power systems ▫ (IV) TBC for A and no LFC for B (including very slow LFC for B) ∆PB ∆PB ∆f = ≈ ∆PA + ∆C A − ∆PT = K A ⋅ ∆f K ′A + K B K A + K B ARA = 0 ∆PB + 0 + ∆PT = K B ⋅ ∆f ∆C A = −∆PA + (K A − K ′A ) ⋅ ∆f ≈ −∆PA ∆C B = 0 K ′A ⋅ ∆f + ∆PT = 0 K ′A KA ∆PT = − ∆PB ≈ − ∆PB ′ K A + KB K A + KB ΔCA is approximately determined so as to compensate only ΔPA. K'＝0 K'＝K K'＝∞ FTC TBC FFC ← Insufficient control → ← Excessive control →  Password: esys2024 21 5.2 Power and Frequency Control (6) Load Frequency Control (LFC) Behaviors of the inter-connected power systems ▫ (V) TBC for A and FFC for B ∆PA + ∆C A − ∆PT = K A ⋅ 0 ∆C A = −∆PA ARA = 0 ∆PB + ∆C B + ∆PT = K B ⋅ 0 ∆PT = 0 ∆f = 0 ∆C B = −∆PB K ′A ⋅ 0 + ∆PT = 0 ΔCA and ΔCB are determined so as to compensate ΔPA and ΔPB, respectively. The control speed of TBC should be faster than that of FFC to avoid excessive control. ▫ (VI) TBC for both A and B ∆PA + ∆C A − ∆PT = K A ⋅ ∆f ARA = 0 ∆C A = −∆PA ∆f = 0 ∆PB + ∆C B + ∆PT = K B ⋅ ∆f ARB = 0 ∆C B = −∆PB ∆PT = 0 K ′A ⋅ ∆f + ∆PT = 0 if K ′A = K A and K B′ = K B K B′ ⋅ ∆f − ∆PT = 0 ΔCA and ΔCB are approximately determined so as to compensate ΔPA and ΔPB, respectively.  Password: esys2024 22 5.2 Power and Frequency Control ∆CA ∆CB A B (6) Load Frequency Control (LFC) PAB ∆PA, KA ∆PB, KB Interconnected power systems A, B and C PCA C PBC ∆PA + ∆C A + ∆PCA − ∆PAB = K A ⋅ ∆f ∆PB + ∆C B + ∆PAB − ∆PBC = K B ⋅ ∆f ∆P C , K C ∆PC + ∆CC + ∆PBC − ∆PCA = K C ⋅ ∆f ∆CC ΔPC : power imbalance of system C, ΔCC : LFC command of system C, KC : power-frequency coefficient of system C, ΔPAB : power flow change of tie line from A to B, ΔPBC : power flow change of tie line from B to C, ΔPCA : power flow change of tie line from C to A  There are 7 variables in 3 equations. (4 degrees of freedom)  By considering LFC representations of 3 systems, we can reduce the degrees of freedom by 3. However, we still have 1 degree of freedom in the total system.  In order to determine all the variables, we need to fix the power flow of one of the three tielines at specific value in addition to LFCs of the 3 systems.  In real systems in Japan, DC connection is employed to fix the power flow. (Kansai-Shikoku and Chubu-Hokuriku).  23 Password: esys2024 5.2 Power and Frequency Control (6) Load Frequency Control (LFC) The necessary capacity for LFC is around 5% of the total system capacity. ▫ Thermal power plants and large hydro power plants are generally used as frequency control facilities due to their high manoeuvring capability. Load Hokkaido FFC AC connection DC connection Tohoku Load TBC Transmission Hokuriku TBC & Distribution Self Regulating Chugoku Network Characteristics TBC 50Hz Load Kyusyu 60Hz TBC Tokyo Control Kansai Chubu Valve Tie Line FFC Turbine Shikoku TBC TBC Boiler TBC ∆f 1 − ∆f Generator Okinawa ri FFC Governor ∆f Control Center ∆PT LFC/EDC Controller t ∆ci (t ) = −ki ∫ (K ′ ⋅ ∆f + ∆PT )dt + EDCi t0  Password: esys2024 24 5.2 Power and Frequency Control (7) Economic Dispatching Control (EDC) What is EDC? ▫ EDC is defined as the process of allocating generation output levels to the generating units in the power system, so that the system load can be supplied most economically. Mathematical Formulation ▫ Objective function  Total operation cost of the system over the time horizon  Fuel costs of thermal and nuclear power plants including costs for start-ups and shut-downs ▫ Constraints  Electricity demand and supply balances  Transmission line capacities  Electricity storage capacities of pumping-up hydro power stations  Load following capabilities  Minimum and maximum output levels of the plants   Password: esys2024 25 5.2 Power and Frequency Control (8) Comments on Nuclear Power Plants Nuclear power plants (NPPs) have the capability of load following and frequency control. ▫ For example, according to the current version of the European Utilities Requirements, NPPs must at least be capable of daily load cycling operation between 50% to 100% of its rated power with a change speed of 3-5% of the rated power per minute.  PWR: Control rod and Boric acid（ホウ酸）  BWR: Coolant flow rate and/or Control rod ▫ There is some influence of variable output operation of NPPs on the ageing of some operational components such as valves, and thus a slight increase of the maintenance costs are expected. Some NPPS in Europe operate in the load-following mode with large daily power variations of about 50% of rated power, and some of NPPs also participate in the frequency control of the total power system. ▫ France: High share of NPP (about 75%) ▫ Germany (in the past): Extensive deployment of intermittent renewable power generation such as wind turbines and solar cells ▫ In Japan, the NPPs are operated in the constant output mode.