for Smart Power and Energy Systems 20.Nov.2019 Yi Wang, - PowerPoint PPT Presentation

31 Combining Density Forecasts The applications of the CRPS have been hampered by a lack of readily computable solutions to the integral:           2   CRPS , = 1 F y F z z y dz t t t t  This drawback is overcome by [1]: 1   Y     CRPS , = F y E Y y E Y t t 2 Let’s consider a simple case: Gaussian Mixture Distribution [1] L. Baringhaus and C. Franz, “On a new multivariate two - sample test,” Journal of Multivariate | 31 Analysis, vol. 88, no. 1, pp. 190 – 206, 2004.

32 Combining Density Forecasts 1   Y     Two lemmas for Gaussian model: CRPS , = F y E Y y E Y t t 2 Lemma 1 : The expectation of an absolute value of a finite mixture distribution is the weighted sum of the corresponding expectations of absolute values of the components of the finite mixture distribution. If are the N components of the finite mixture distribution X with , , X X X 1 2 N      N  , , weights , then E X E X 1 2 N  n n 1 n Lemma 2 : If X and Y are independent random variables that are finite mixtures of normal distributions, then their sum is also a finite mixture of normal distributions . i.e., if L M             ( ) ( | , ), ( ) ( | , ) f x x f y y X l l l Y m m m   1 1 l m L M           0, 0, 1, 1 l m l m   1 1 l m     N   ( | , ) where is the PDF of normal distribution , then the PDF of Z=X+Y is: ( , ) L M            2 2 ( ) ( | , ) f z x Z l m l m l m   1 1 l m | 32

33 Combining Density Forecasts ( ) f x If individual density forecasts are Gaussian distributed , the combined n forecast follows Gaussian mixture distribution:   N  ( ) ( ) f x f x X n n  1 n Then, the CRPS can be calculated as: N N N 1           CRPS( , ) F y E Y y E Y Y n n i j i j 2    1 1 1 n i j N   The expectation of the absolute value of a normal distribution can be ( , ) calculated as follows:   0        ( ) ( ) ( ) E X x f x dx xf x dx x f x dx   0  2   2        2 2 [2 ( ) 1] e   | 33

34 Combining Density Forecasts Thus, we have: N N N          CRPS( , ) F y , i j i j n n    1 1 1 i j n where          2 ( ) ( ) 1          2 2 i j i j i j exp( ) [2 ( ) 1]    i j ,  i j 2 2    2( ) 2 2 2 2 i j i j     2 2 ( ) ( ) y y          n n exp( ) ( )[2 ( ) 1] y    n n 2 n 2 n n Finally, we have:     QP problem! T T min Q c  Is this convex?     1 T s.t. 1 0 | 34

35 Combining Density Forecasts PDFs of predictions of four typical days given by the base models and their combination Performances of combined models CRPS of the best individual model and combined models | 35

36 Combining Density Forecasts Relative MAPE improvements of Relative CRPS improvements of the three combination methods the three combination methods | 36

37 Combining Density Forecasts Weights of the base models in the CRPS-guided model Weights of the base models in the MAPE-guided model | 37

Outline  Introduction to Power and Energy Systems  Probabilistic Load Forecasting  Electricity Consumer Behavior Modeling  Multi-Energy Systems Integration  Research Plan | 38

Backgrounds System/ No. Data Source Data Type Frequency Data Structure Data GDP 、 CPI 、 PMI （ Purchasing Economic Managers Index ）、 Sales Value 、 1 Statistic Bureau Per Month Non structural Information Prosperity Index Energy Energy Electrical Load 、 Output 、 Power Non structural 2 Consumption Efficiency 15Min Quality 、 Temperature /Structural Data Platform Temperature 、 Humidity 、 Meteorological Meteorological 3 Per Day Structural Data Bureau Rainfall Current 、 Voltage 、 Charging EV Charging Charging-Pile 4 15Min Structural Rate 、 State of Charge Data RTU Customer Customer 5 Service Voice Customer Voice Data Real Time Non structural Service System Data Variety Velocity Value??? 10 million Smart Meters, 15min 60GB per day, 21TB per year. Volume | 39

Backgrounds Participators and their businesses on the demand side | 40

Backgrounds Data Analytics is commonly dissected into three stages: descriptive analytics (what do the data look like), predictive analytics (what is going to happen with the data), and prescriptive analytics (what decisions can be made from the data). | 41

Electricity Consumer Behavior Modeling  Customer behavior refers to the electricity consumption activities and related attitudes of customers under a certain environment to maximize the overall utility. Spatial Environment Utility Extension Aggregation Forecasting Temporal Subject Results Means Extension  It has five basic parts: behavior subject, behavior environment, behavior means, behavior utility, behavior results.  We can also have two extensions from spatial and temporal perspectives. | 42

Research Summary | 43

Socio-demographic Information Identification Retailers attempt to analyze customers’ electricity consumption behaviors, so that they can provide diversified and personalized services. Can we identify the social-demographic information of the consumers? Challenges: 1)Problem formulation; 2)High-dimensional load data; 3)High time-shift invariance; | 44

Socio-demographic Information Identification | 45

Socio-demographic Information Identification | 46

Socio-demographic Information Identification  Among these ten questions, the accuracies of #2 ( chief income earner has retired or not ), #4 ( have children or not ), and #8 ( cooking facility type ) are higher than 75%;  The accuracies of #7 (number of bedrooms) and #9 (energy-efficient light bulb proportion) are lower than 60%;  The accuracies of the remaining questions are between 60% and 75%. | 47

Electricity Consumption Patterns Extraction Characteristics of Individual Smart Meter Data Sparsity : only a small fraction of the time has higher electricity consumption while the rest approximates to zero. Diversity : load profiles are various with different customers and in different days, but it can be decomposed into different parts. | 48

Electricity Consumption Patterns Extraction Partial Usage Pattern (PUP) Idea of Sparse Coding K   x a d i ik k  | 49 1 k

Electricity Consumption Patterns Extraction Non-Negative Sparse Coding  2 min X DA Minimize the recovery error F    . . , 1 Sparsity Constrains s t a s i M 0 i 0      0, 1 ,1 a i M k K , i k Non-Negative Constrains      0, 1 ,1 d k K n N , k n 1) Search a redundant dictionary D that captures the features or PUPs of load profiles as well as possible 2) Optimize the coefficient vector A of each load profile to guarantee its sparsity and an acceptable reconstruction error. | 50

Electricity Consumption Patterns Extraction | 51

Electricity Consumption Patterns Extraction Dictionary Learning Load Profiles Performance Method Classification Evaluation Validation Sparse Coding Linear SVM | 52

Electricity Consumption Patterns Extraction  Ten most relevant PUPs for SMEs and residential customers Shape Duration Peak times SME Vaulted Long Dawn, working hours Resident Sharp peak Short Morning, night | 53

Electricity Consumption Patterns Extraction  TP TN  1 K M   Accuracy   2 ( ) RMSE x a d    TP TN FP FN i i i K   1 1 i i   2 precision recall  K M 1   1 F   MAE x a d  i i i precision recall K   1 1 i i Data Compression-Based Classification-Based  Comparison with Different Techniques Parameter RMSE MAE Accuracy F1 5, 80 0.099 0.060 0.874 0.793 K-SVD k-means 80 0.120 0.180 0.786 0.752 5 0.111 0.167 0.771 0.764 PCA 5 0.141 0.327 0.667 0.688 DWT PAA 6 0.112 0.181 0.706 0.725 48 / / 0.735 0.724 Original | 54

55 Personalized Retail Price Design  The opening of electricity retailing market  The need for diversified service  Consumers choose freely in market How to provide diversified services for different consumers to enhance the competitiveness of the retailers? | 55

56 Personalized Retail Price Design Main Idea  Data-driven price design. Smart meter data contains great value which may help retailing price design.  Respect self-selection. Consumers’ willingness and rights to choose must be respected. Challenges  Diversified service Data-driven price design  Mine consumers’ inner need  Satisfying consumers Compatible incentive design  Self-selection in a real market  Proper incentive | 56

57 Personalized Retail Price Design Problem formulation Leader —— Retailer  Design pricing scheme  Predict consumer behaviors A Stackelberg game Follower —— Consumers  Choose pricing scheme  Adapt electricity consumption | 57

58 Personalized Retail Price Design Problem formulation - consumer Consumer Utility Consumer Strategy  Measure satisfaction  Strategic and rational consumers:  Comparison between different plans Utility Maximization  Diminishing marginal utility How can smart meter data be useful? Original electricity consumption is the realization of Utility Maximization! | 58

59 Personalized Retail Price Design Problem formulation - incentive Compatible incentive Individual rationality If the retailer wants consumer k to If the retailer wants consumer k to choose new pricing scheme r , the choose pricing scheme r , the retailer must guarantee retailer must guarantee choosing r is consumer k ’s choosing r is at least as good as previous situation dominant strategy | 59

60 Personalized Retail Price Design Problem formulation - retailer Where the retailer purchases electricity Day-ahead market Real-time market Forward contracts Balance unpredictable load Balance predictable load Price uncertainty Which is considered more important? Price and load uncertainty Risk Weighting factor Purchasing strategy Risk loss measure —— CVaR | 60

61 Personalized Retail Price Design Problem formulation - clustering Clustering evaluation Different Clustering Methods Why clustering? • Hierarchical Clustering Davies Bouldin Index One method may • K- means With-cluster compactness not fit all data sets Between-cluster seperation • Fuzzy C-means • Gaussian mixture Centroid as representative | 61

62 Personalized Retail Price Design Problem formulation – optimization framework Optimization framework – an MINLP model  Objective ： Retailing profit maximization  Constraints ： • Load balance • Consumer reaction • Compatible incentive • Risk measure CVaR • Price structure: Various choices Lower Risk  Price category ： CPP RTP ToU Less changes | 62

63 Personalized Retail Price Design Problem formulation – optimization framework Optimization framework – an MINLP model  Objective ： Retailing profit maximization Consumer payment Forward contracts DA Risk Loss in DA & RT  Constraints ： Predictable load balance  Constraints ： Compatible incentive DA=Day-ahead market RT= Real-time market Consumer load Forward contracts DA Choosing p r is consumer k ’s dominant strategy, k likes p r than any other pricing schemes Choosing p r is consumer k ’s rational choice, k likes p r than the old pricing schemes * nonlinear terms are marked in red | 63

64 Personalized Retail Price Design Problem formulation – optimization framework Optimization framework – an MINLP model  Constraints ： Utility and response Reactions Utility  Constraints ： Risk measure CVaR Loss in DA Loss in RT  Constraints ： Price structure Price category ： CPP RTP ToU Lower Risk Less changes m block ToU * nonlinear terms are marked in red | 64

Personalized Retail Price Design Solution method Nonlinear model  Power exponent  Two variables’ product Linear model  Linear segment approximation Take as a whole | 65

Personalized Retail Price Design Solution method Nonlinear model  Binary variables times continuous variables  Absolute value  CVaR Linear model  Add auxiliary variables Conversed to linear equations * new variables are marked in blue | 66

Personalized Retail Price Design Case Study  6435 consumers in Ireland.  Data collected every 30 minutes. Linear segment approximation(12 segments) | 67

Personalized Retail Price Design Case Study - clustering Clustering result DB index result | 68

Personalized Retail Price Design Case Study – prices and responses Consumer response Personalized price | 69

Personalized Retail Price Design Case Study – sensitivity analysis on elasticity Total load under different elasticity Retailing profit under different elasticity Elasticity Original -0.2 -0.3 -0.4 -0.5 Retailing 752 833 977 1186 1385 Profit($) ToU under different elasticity Elasticity Willingness to change | 70

Personalized Retail Price Design Case Study – sensitivity analysis on risk weighting factor How CVaR, the quantity of power bought from day-ahead market and through forward contracts changes with the change of risk weighting factor? risk weighting factor rises attach more importance to risk minimize CVaR buy less from day-ahead market buy more through forward contracts | 71

Personalized Retail Price Design Case Study - sensitivity analysis on clustering methods RP SW AP F/SC How much profit does the retailer get? Original 752.03 0 0.2 -/-  RP=Retaling Profit($) HIA-COMP 1186.01 339.72 0.1947 65%/89% How much welfare do the consumers get?  SW=Social Welfare HIA-WARD 1188.70 10.01 0.1971 33%/59%  AP=Average Price($/kWh) KM-PLUS 1145.68 7.01 0.1973 9%/20% How well does clustering perform?  F/SC=First/Second Choice KM-SAMPLE 1137.61 4.50 0.1975 22%/48% KM-UNIFORM 1142.61 15.76 0.1973 11%/31% FCM(m=1.1) 1150.43 9.43 0.1970 30%/47%  The most accurate prediction FCM(m=1.2) 1176.08 18.64 0.1968 19%/35%  The most profitable FCM(m=1.3) 1208.06 0.64 0.1970 8%/20% for consumers GMEM-PLUS 1145.82 36.01 0.1965 13%/28% GMEM-RAND 1144.85 46.60 0.1967 10%/24% | 72

Outline  Introduction to Power and Energy Systems  Probabilistic Load Forecasting  Electricity Consumer Behavior Modeling  Multi-Energy Systems Integration  Research Plan | 73

Backgrounds  Switzerland ETH 2003 Vision of Future Energy Networks v v ,1 out ,1 in Gas Heat Energy v v ,2 in ,2 out Cooling Electricity Hub … … v v , out n , in m Heat Electricity Focus more on energy conversion Focus more on energy delivery | 74

Backgrounds Transmission Consumption Generation • No delay, less loss • Clean consumption, • Centralized primarily • Real time balance, Electricity intelligence uneconomical storage • Renewable energy integration • Can be transformed into other • Long distance transmission energy • Have delay ， more loss • Distributed ： Low efficiency • Heating and industrial use • Centered ： Coupling of Heat • Easy to stored • Less intelligence electricity and heat • Local balance • Used for power generation • Central development • Have delay ， more loss Gas • Low efficiency • Easy to stored depending on the distribution of • Pollution • Long distance transmission sources. Energy • Interconnection ： Generation-Transmission-Distribution-Consumption in both power and information. • Interaction ： Source-Network-Load, Multi-energy Supplement Internet • Virtual ： From real energy system to virtual information system Large potential in supplementary for renewable energy accommodation Power system is the core of the multiple energy systems | 75

Backgro Ba grounds nds  Why is the electric-heat coordination important?  Large-sized Combined Heat and Power (CHP) units have been installed  The output power of CHP is determined by heat demand, which makes the CHP units less flexible  This leads to huge wind power curtailment | 76

Ba Backgro grounds nds | 77

Research Summary D Key Simulation Platform A Modelling technique of MES problem 1 Unit/system modelling Key B Planning theory of MES problem 2 Coupling C Operation theory of MES theory | 78

Standa St dardiz rdized ed Matrix rix Modelin ling g of EH EH  EH tries to model the energy conversion as port based unit with multiple inputs and multiple outputs. v v out ,1 in ,1 Gas Heat  V CV Energy v v ,2 ,2 out out in in Cooling Electricity Hub … … v v , out n , in m Heat Electricity   V = v   ,F in in v WARG v RWARG QWARG T v   CHP out ,R v  v V = v v v   in FCHP R v ,R ,Q ,W out out out out   QCHP v ,Q out Q W T v         v WCHP C = out ,W   Q R R Q Q W | 79

St Standa dardiz rdized ed Matrix rix Modelin ling g of EH EH | 80

St Standa dardiz rdized ed Matrix rix Modelin ling g of EH EH  A MES consists of two basic elements: energy conversion devices and their connection relationship. Node v 1 #2 #2 v , in e v 4 v v l , out c #1 #1 2 8 Port v Branch Output v Input 6 , in g v 5 v v v out q , 3 7 #3 #3 Branch , describes the energy flow. Node , is the abstract of the energy converter, but also the abstraction of branch endpoints. Port , is defined as the interface of a node that exchange energy with others. | 81

Ba Basic c Model  Port-Branch Incidence Vectors and Matrices v WARG v RWARG QWARG v CHP ,R  out v v in FCHP R v   QCHP v out ,Q Q W v v WCHP ,W out The port-branch incidence matrix is defined to describe the connection relation between the ports of a node and the branches.  1 branch is connected to input port of node b k g  T       , ,..., A M M M   1 branch is connected to output port of node m b k g ,1 ,2 , g g g g k b   0 branch is not connected to any port of node b g   1 0 0 0 0   T       V v v v v v  = 0 1 1 0 0 A   FCHP QWARG QCHP WCHP RWARG 1    0 0 0 1 0   | 82

Ba Basic c Model  Converter Characteristic Matrices v WARG v RWARG QWARG v CHP out ,R v  v in FCHP R v   QCHP v ,Q out Q W v v WCHP out ,W The nodal converter characteristic matrix H g of node g defines the energy conversion characteristics of the node.     1 H Type 1: single input port and single output port 2 R Type 2: single input port and multiple output ports   i f is the number of the input port k  1 if is the number of input port k i    h   1 i f is the number of the output port h k i  1, k 1 if is the number of output port  k i , i k  i 0 otherw ise         1 0 = 1 1 1 H   Q H =   1 Q W  1  0 1  W | 83

Ba Basic c Model  Energy Conversion Matrices Given the port-branch incidence matrix and the converter characteristic matrix, we can calculate the branch energy conversion matrix for node g :  Z H A g g g The system energy conversion matrix Z is the combination of the nodal energy conversion matrix of all nodes in EH: T     T T T , ,..., Z Z Z Z  1 2 N      1 1 0 0 Q =   Z   1  0 0 1 0  v WARG v RWARG QWARG W v CHP ,R  out v v in FCHP R v   QCHP v   out ,Q Q W  = 0 0 0 1 Z v v 2 R WCHP out ,W | 84

St Standa dard rd Modeling ing of Multipl iple e En Energy y Sy System em The system energy conversion matrix Z is the combination of the nodal energy conversion matrix of all nodes in EH: T     T T T , ,..., Z Z Z Z  1 2 N For the MES, the system energy conversion matrix Z is:    -1 -1 0 0 Q v WARG   v RWARG QWARG  v CHP = 0 0 -1 0 ,R Z v  out v   in FCHP W R v   QCHP v    ,Q out Q W  0 0 0 -1  v R v WCHP ,W out Then, we can obtain the energy conversion equation of the EH: ZV  0 | 85

Extended Analysis  Case Studies v v v out ,W1 in ,W1 1 v v 2 CERG in ,W2 v v v out ,R1 11 5  v C 6 CHP v v v v ,F1 W out ,W2 in 3 v 7 v v WQ   ,Q3 v Q out C Q W  WQ v out ,Q1 TS v D 1   v v TC out ,Q4 TD D 2 v 8 v WARG v v 12 v 4 ,F2 in AB v out ,R2 9   R AB v 10 v out ,Q2 | 87

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Planning: Starting from Scratch  Problem Statement | 89

Planning: Starting from Scratch  Input and Output Ports Incidence Matrix 1 ① 1 ② 2 ③ 2 3 ④ 3 ⑤ 4 … Output port Input port Branch #1 #2 #3 #N Output EH input   EH output x x x x x x x   1,1 1,2 1,3 1,4 1, n 2 1, n 1 1, n   Input x x x x x x x     2,1 2,2 2,3 2,4 2, n 2 2, n 1 2, n   x x x x x x x #1   3,1 3,2 3,3 3,4 3, 2 3, 1 3,  n n n   x x x x x x x  #2   4,1 4,2 4,3 4,4 4, 2 4, 1 3, n n n   …     x x x x x x x          m 2,1 m 2,2 m 2,3 m 2,4 m 2, n 2 m 2, n 1 m 2, n   #N-1 x x x x x x x            1,1 1,2 1,3 1,4 1, 2 1, 1 1, m m m m m n m n m n   x x x x x x x #N     ,1 ,2 ,3 ,4 , 2 , 1 , m m m m m n m n m n | 90

Planning: Starting from Scratch  K G (1 )     r r S T M min  TC C C  in = C C I C f V I O , , , , I g g O s m t s m t s   K (1 ) 1 r     1 1 1 s t m g 1       x  s.t. 0 , 0,1 x I M l g 2 ij l g  l g    0 , , V x M l t s , , 1 l t s l     X V in      Y V V     out         Z 0 | 91

Planning: Starting from Scratch Investment Connection Operation Operation Operation …… Decisions Relationship Scenario 1 Scenario 2 Scenario S Investment Constraints Connection Relationship Constraints Operation Constraints | 92

Planning: Starting from Scratch The Beijing government is planning to build a subsidiary administrative center in the undeveloped district of Tongzhou in the southeast of Beijing, containing Beijing municipal government and consist of offices, commercial buildings and residential buildings.  Total area: – 155 square kilometers  Core district area: – 6 square kilometers  Planned building area – 3.8 million square meters. | 93

Planning: Starting from Scratch 80 70 60 50 Load/MW 40 30 20 10 0 1 192 383 574 765 956 1147 1338 1529 1720 1911 2102 2293 2484 2675 2866 3057 3248 3439 3630 3821 4012 4203 4394 4585 4776 4967 5158 5349 5540 5731 5922 6113 6304 6495 6686 6877 7068 7259 7450 7641 7832 8023 8214 8405 8596 Time/Hour Heating Load Cooling Load Electricity Load | 94

Planning: Starting from Scratch 200 1600 180 1400 160 1200 140 Price/RMB/MWh 1000 Demand/MW 120 100 800 80 600 60 400 40 200 20 0 0 Scenario #5 Scenario #1 Scenario #2 Scenario #3 Scenario #4 Electricity Cooling Heat Electricity Price | 95

Planning: Starting from Scratch | 96

Planning: Starting from Scratch EHP : electric heat pump CERG : compression electric refrigerator group HS : heat storage WARG : water absorption refrigerator group | 97 CS : cooling storage

Planning: Starting from Scratch  Potential planning for Tongzhou Case 1: Case 2: Planning results from the model Wind power heating case Case 3 Case 4 Case 5 Import city heat Combine cooling and Gas boiler plan network plan heating plan | 98

Planning: Starting from Scratch Comparison of the costs and emissions Plan 1 2 3 4 5 Total operation cost (10 4 ￥ ) 85049 88673 88622 87677 126582 Total emission (10 4 kg CO2) 220.97 238.92 241.82 231.22 241.27 | 99

Outline  Introduction to Power and Energy Systems  Electricity Consumer Behavior Modeling  Probabilistic Load Forecasting  Multi-Energy Systems Integration  Research Plan | 100

Work Packages Analytics and Optimization of Local Power and Energy Systems | 101