SYSTEM AND METHOD FOR STOCHASTIC IMBALANCE OPTIMIZER

BY STORAGE SCHEDULING

TECHNICAL FIELD

[0001]

The present invention is in the general field of imbalance energy and cost reduction using demand side energy storage system. More specifically, the present invention is in the technical field of imbalance reduction by effective charge/discharge scheduling for spatially distributed energy storage system that is robust against uncertainty imposed by energy demand and contracted supply.

BACKGROUND ART

[0002]

The design of a demand side based energy service requires execution of some levels of operation that mostly controlled by the Power Producer and Supplier (PPS). In an online energy management operation in demand side, it is necessary for the PPS to keep the supply and demand matched for a particular granularity of time. However, due to the uncertainty in online energy consumption (compared with day-ahead demand prediction), the gap between supply and demand is highly likely to occur for a particular time grain (e.g. 30 minutes duration). The current practice is to buy (in case of demand is higher than the supply) or to sell (in case of supply is higher than the demand) energy from/to Energy Imbalance Market (EIM). EIM mitigates such mismatch between online supply and demand by transacting necessary energy with the PPS. The involvement of EIM goes higher with the increasing gap between the supply and the demand. The price setting of EIM, on the other hand, is very high compared with conventional energy tariff. Therefore, the reduction of imbalance cost can be treated as one of the important problems to tackle for demand side based energy service. The reduction of the imbalance cost can be realized by the effective on-line charge/discharge (CD) scheduling of batteries (with associated energy dispatch) in order to mitigate the on-line demand gap.

[Documents of the prior art]

[0003]

[Patent Literature]

[Patent Literature 1]

United States Patent Application Publication No. US 2015/0127179 Al

[Patent Literature 2]

United States Patent Application Publication No. US 2014/0350743 A 1

[Patent Literature 3]

United States Patent Application Publication No. US 2011/0208365 Al

[Patent Literature 4]

United States Patent Application Publication No. US 2013/0119939 Al

DISCLOSURE OF INVENTION

[0004]

The most effective on-line strategy to reduce the imbalance energy and cost requires predicting the future demand (for a short-term), then utilizing the short-term demand prediction to solve an optimization problem that minimizes the imbalance energy and cost while deciding the CD scheduling of the battery. As an on-line signal, only the 1st CD scheduling is applied to the battery management system. This strategy follows the inherent architecture of Model Predictive Control (MPC). However, demand prediction is uncertain, since demand prediction at particular period depends when the prediction is performed. Such prediction is subjected to change each time the prediction is performed while accumulating the real-time measurement. Moreover, contracted supply may also vary due to the environmental factor and/or inclusion of renewable energy sources. In this invention, a method of optimal charging/discharging schedule of battery is proposed, which is robust against uncertainty imposed by demand prediction and variance in contracted supply.

BRIEF DESCRIPTION OF THE DRAWINGS

[0005]

Fig. 1 is a block diagram schematically illustrating an outline of the stochastic imbalance optimizer with basic input and output blocks;

Fig. 2 is a block diagram of the internal architecture of scenario generator module;

Fig. 3 is a flow chart illustrating procedure for optimizing imbalance energy and cost by stochastic scheduling of battery;

Fig. 4 is a diagram that illustrates an exemplary box plot showing the standard deviation of demand prediction error for each lag of the window;

Fig. 5 is an exemplary demand prediction error (DPE) statistics vector where each element represents normal distribution information (mean and standard deviation);

Fig. 6 is an exemplary scenario generation process for demand utilizing demand prediction error (DPE) statistics as shown in Fig. 5; Fig. 7 is an exemplary imbalance pricing scheme that contains both cost and revenue segments depending on the deviation and a threshold;

Fig. 8 is a diagram that shows the effectiveness of the disclosed stochastic imbalance optimizer over a deterministic (non-stochastic) optimizer in terms of imbalance cost reduction;

Fig. 9 is a diagram that illustrates the effect of battery size with imbalance cost reduction and compares the outcome with the deterministic optimizer;

EMBODIMENTS FOR CARRYING OUT THE INVENTION

[0006]

Exemplary embodiments of the present invention will be described below with reference to the drawings. In the drawings, the same elements are denoted by the same reference numerals, and thus a repeated description is omitted as needed.

[0007]

Following embodiments are described to enable any person skilled in the art to make and use the disclosure, and are provided with the context of a particular application and its requirements. Embodiment of a system, a method and a computer program product (e.g. software) for demand based energy balancing group formation is described. This operation may be performed by PPS. In particular, the PPS utilizes the disclosed imbalance optimizer with energy storage system (e.g. battery) that will provide stochastic online CD scheduling of the battery.

[0008]

The present invention identifies two influential statistical measures and designs a criterion combining these criteria for the demand aggregation. The present invention designs a demand aggregation strategy using the criterion that creates multiple energy balancing groups.

First Embodiment

[0009]

A stochastic imbalance optimizer to a first embodiment will be described. Fig.

1 is a block diagram schematically illustrating an outline of the stochastic imbalance optimization 110 method according to the first embodiment. In the stochastic

imbalance optimization method according to the first embodiment, historical demand profiles of the customers 101 up to the current time t (i.e. demand up to t— 1), actual supply at time t— 1 102, contracted supply information for the next several periods (e.g. w periods) 103, imbalance pricing scheme (from EIM) 104, and state of charge (SOC) of battery at time t— 1 104 are utilized as input data. The required CD scheduling with energy dispatch for period t 122 and resultant imbalance energy at t 121 are generated as the output of the stochastic imbalance optimizer.

[0010]

The stochastic imbalance optimizer contains three functional modules; the short-term demand predictor 111, the scenario generator 112, and the core optimization module 113. The short term demand predictor 111 utilizes the historical demand information to predict demand for next w periods. The scenario generator 112 generates deviation (difference between supply and demand) scenarios. The statistical scenarios for predicted demand and contracted supply are determined by utilizing demand prediction error (DPE) statistics and supply estimation error (SEE) statistics, respectively. Finally, the core optimization module 113 ^" performs a mathematical optimization that minimizes imbalance energy and cost and produces battery CD schedule to the battery controller (to be operated in current period t) and resultant required imbalance energy to EIM (at period t).

[0011]

The scenario generator 112 is an important part of the invention. Fig. 2 is the functional breakdown of scenario generator. The scenario generator 112 maintains a DPE statistics calculator 201 and SEE statistics calculator 203. The DPE statistics calculator takes the predicted demand signals from short-term demand predictor and calculates the accumulated error statistics appeared in each lag of the prediction window, w. The SEE statistic calculator takes the contracted supply for next w periods and the actual supply at t— 1 and calculates the potential error in the supply contract. The demand scenario generator 202 generates demand scenarios by utilizing the predicted demand signals and the error statistics from 201. Similarly, the supply scenario generator 204 generates supply scenarios utilizing the supply contract and the error statistics from 203. Finally, the deviation scenario generator 205 creates deviation scenarios by taking a Cartesian product of demand and supply scenario sets.

[0012]

The detailed flow of the method is shown in Fig. 3. The input blocks are dotted and output blocks are grayed. The rest are the functional blocks.

Step SI

[0013]

The stochastic imbalance optimizer collects recent historical demand from the demand database (from t— N to t— 1). Here, N is the number of past periods (e.g. for history of 30 days, containing 30-minutes granular data, N is 30 x 48 = 1440).

The demand at period i is represented as Dm;.

Step S2

[0014] The short-term demand predictor 111 predicts demand for next periods utilizing the historical demand. A support vector machine (SVM) based time series prediction methodology is applied in order to predict the demand. The demand signal is a time series, which follows a certain trend line (regulated by e.g. periods, weekdays, holidays, etc.). The SVM finds optimal regression (Support Vector Regression, SVR) models while minimizing the training error and model complexity. The developed SVR based demand prediction engine models the (recent) past demand patterns to predict demand for a short window (for a window size of w, typically for next 4-hours). At a certain period t, the predictor produces the estimated demand D _mt to D _{mt χ} .. This expression can be written as D _mt+i | _{t l} , i = 0, . . . , w— 1. The predictor creates separate models for each of the lagged periods. For example, while predicting demand D _7nt | _t _ ₁ , the SVR engine creates and trains the model (of lag 1) by fitting a particular demand m; with a non-linear mapping of its previous demands, starting from demand at t— 1 down to demand at a particular training horizon. Note that, the training data set only considers the recent demand set (instead of the whole data set) to avoid over-training the model by seasonally differed demand data. So, the SVR tries to generate the non-linear model as the following function ^ _0£iei for lag I (I =

0, . . . , w - l),

[0015]

fmociei - Drrii.^, Dmi-i-2 , ·■■ , Dm^p^, F _t ] ·→ Dm<

[0016]

where i = t— TH— 1, . . . , t— 1, TH is the training horizon, NP is the number of past periods, _j is additional feature vector containing temporal information such as, holiday/weekend indicator, time of the day, and day of the week (that influence the demand). The radial basis function is used as the SVM kernel that transforms the data into a higher dimensional space while performing the regression.

Step S3

[0017]

The predicted demand is transferred to 201 for calculating the DPE statistics.

The demand prediction error trivially follows a normal distribution with mean error closer to 0 and a particular standard deviation. Fig. 4 is an exemplary standard deviation of demand prediction error performed for each lag. DPE Statistics calculator keeps track of the previous error statistics and updates the error statistics accumulating the new demand prediction signal. The demand prediction error for each lag, I (where, I = 0, .. . , w— 1) at a particular prediction period, i (where i = t— N, ... , t— 1) is calculated as

[0018]

de^ . = Dm _i+l - D^ _i+l

[0019]

The lag- wise prediction error is modelled into a Normal Distribution according to the following equation (where μ _∑ and σ _ι are the mean and standard deviation)

[0020]

Step S4

[0021]

The normally distributed prediction error statistics (determined according to the previous equations) is utilized to generate the Demand Prediction Scenarios. The vector of demand prediction error statistics is shown in Fig. 5. Considering ST> is the demand scenario set, the demand for scenario s _d 6 ST) and for lag I generated at period i

[0022]

Dmi+i,s _d = Drrii+i + Ν(βι, σΰ

[0023]

An exemplary generated demand scenario is shown in Fig. 6.

Step S5

[0024]

The contracted supply information for next w period is collected at this step. The contracted supply is denoted as Sc _i+i (where I = 0, . .. , w— 1)

Step S6

[0025]

The actual supply information for the period t— 1 is collected at this step.

Step S7

[0026]

The SEE is calculated at this step. The supply estimation error (sej), at a particular period, i is calculated by taking the difference between the actual supply (5 _έ ) and contracted supply (Sc), using the following equation (where i = t— N, ... , t— 1) [0027]

sei = Sai— SCi

[0028]

The supply error is modelled into a Normal Distribution according to the following

Step S8

[0029] The normally distributed SEE statistics (determined according to the previous equations) is utilized to generate the Supply Scenarios. Considering SS is the supply scenario set, the supply for scenario s _s £ SS at period i is determined by

[0030]

SCi+i,s _s = Sc _i+l + J\f ( , σ)

Step S9

[0031]

The deviation scenario is generated at this step. The deviation scenario generator 205 utilizes the error statistics from 202 and 204 and produces a number of deviation scenarios. The following equation is utilized for generating deviation scenario, Dv _i+liS ,Vs E S nd \S\ = \SS\ x |<£D|

[0032]

Dv _i+liS = Sp _i+liSs - Dm _i+ i _,Sd

[0033]

Therefore, the deviation scenario is taken as the Cartesian product of the two sets by taking the differences between ordered pair of supply (Sp _{i Ss} ) and demand (Dm _{i Sd} ). Step SlO

[0034]

The imbalance pricing information is collected. The pricing information contains a threshold value beyond which a certain rate is applied. Fig. 7 is an example of imbalance pricing scheme where the threshold value is 50k Wh. The pricing scheme follows nonlinear curve where a higher penalty has to be paid by PPS if the imbalance energy goes beyond the threshold i.e. 50k Wh), in case of buying from EIM. On the other hand, PPS will receive no additional revenue if the energy to be sold is higher than the threshold (-50kWh).

Step Sll

[0035]

Collect the current (at period t— 1) SOC of the battery (or aggregated batteries). Step S12

[0036]

In this step, the optimization is performed in the optimization module 113. The stochastic optimization problem formulation with associated constraints is described. The objective function is a scalarization of multiple objectives. The 1 ^st objective is to reduce the imbalance energy and the 2 ^nd objective is to reduce the imbalance cost.

[0037]

0038]

Where,

S is the scenario set,

Pr(s) is the probability of scenario s E S

Sc is the contracted supply at period i [t, t + w

Dm _{i s} is the predicted demand at period i for scenario s

B is the set of batteries

E _{i b} is the energy output from battery b £ B at period i

X _{i b} is the charge/discharge status of battery b at period i

/C(/m _{i s} ) is the imbalance cost at period i for scenario s

The imbalance energy amount for scenario [0039]

Im _iiS = Dv _s - ^ E _{i b}

b≡B

[0040]

E _{i b} and X _{i b} are the decision variables of the above objective function. The probability distribution of scenarios is crucial while performing optimization. The probability distribution essentially measures the likelihood (in a form of a weighted function) scenarios towards contributing to the overall optimization. The probability assigned to each scenario s is determined by the distance of a scenario from zero (since deviation zero yields no imbalance). The following equation is utilized to determine the probability of a scenario, Pr(s G S), s.t. \§\ > 1. The probability of assigned to scenario is determined as

[0041]

Pras e s) - 7(|S| - 1)

[0042]

Where, e is a very small number close to 0 to avoid extreme values of 0 for a certain Pr(s E S). The constraints that are required to be satisfied are provided below.

Battery SOC (Xi _b ) dynamics and related constraints

[0043]

Xb.min≤ ^x At≤ X _bi max

[0044]

Where, charge and discharge efficiency are μ _Γ and μ _ά , respectively. The battery power output is P _{i b} (+ve for charging and -ve for discharging). The SOC is limited within [X _b ,min _> Xb,max - The auxiliary constraint Ax _{i b} is utilized to integrate charging/discharging conditional statement and can be represented by

[0045]

A ^X ifi ⁼ Si,b ^x Pi,b

[0046]

The energy output of the battery E _{i b} is the power integration over the time. In case of Δί = 1, E _iib = P _iib .

The non-linearities in the above equations are effectively transformed to establish the optimization problem as a Mixed-Integer Linear Problem (MILP). The non-linear and convex cost function also needs to be linearized to be fitted into the MILP formulation. The transformation is conducted by introducing additional mixed-integer variables. For the sake of simplicity, the scenario s notation of original equations is avoided. The exemplary imbalance cost (according Fig. 6) is equivalently transformed into a segmented combination of sub-costs (for a particular period i, as shown in below)

[0047] lC{lm = ) PS _k x Z _iik

[0048]

Where, PS _k is the k-t imbalance unit price. The imbalance energy is constrained to be the sum of segmented energies, i.e.

[0049] [0050]

The activation of Z _{i k} is activated by a set of binary variables. The absolute value of imbalance energy minimization is also required to be transformed into an equivalent function by introducing the lower- and upper-bound variable, since absolute value cannot be readily solvable in MILP.

Step S13

[0051]

One of the outputs of the stochastic imbalance optimizer is the optimized imbalance energy that is required to be transacted with EIM at a particular period t. Step S14

[0052]

Another output of the stochastic imbalance optimizer is the battery CD schedule with energy dispatch for a particular period t. Result of stochastic imbalance optimizer

[0053]

Fig.8 shows dominance of the stochastic scheduling (output of the stochastic imbalance optimizer) over an equivalent deterministic scheduling (considering battery storage capacity of 320 kWh, applied over aggregated demand of an apartment building). The imbalance cost is reduced significantly. As seen from the figure, initially both of these algorithms attain approximately similar imbalance cost reduction. However, from the periods 1500 and onwards, a significant jump in cumulative imbalance cost is experienced by the deterministic scheduling algorithm, where the jump in corresponding robust (stochastic) scheduling algorithm is relatively lower. Such improvement is attained by better planning and scheduling of battery storage so that in the critical moments (around period 1500) the battery storage is able to deliver appropriate energy that avoids costly imbalance market interactions. In other words, robust scheduler was prepared for the sudden large change in the predicted demand (w.r.t. actual realized demand) and thus handles the uncertainty smoothly. The cost reduction depends on the size of battery storage. Fig.9 is presented to show the effect of storage capacity with imbalance cost reduction (as a percentile of basic imbalance cost incurred without any battery). A target line (of 20% of basic imbalance cost) is drawn to notice the required battery capacity to reach the line. The equivalent curve generated by the deterministic scheduler is plotted to compare with the stochastic imbalance optimizer. It is notable that the stochastic imbalance optimizer requires 20% less battery capacity to achieve the similar imbalance cost reduction than that of the deterministic scheduler. Depending on the target line settings, the performance of the stochastic imbalance optimizer varies. For example, it takes 14% less battery (compared to the deterministic scheduler) when the target line is set as 30% of the basic imbalance cost.

Other embodiment

[0054]

Note that the present invention is not limited to the above exemplary

embodiments and can be modified as appropriate without departing from the scope of the invention.

[0055]

In the above exemplary embodiments, the present invention is described as a method configuration, but the present invention is not limited to this. According to the present invention, any processing can be implemented by causing a CPU (Central Processing Unit) to execute a computer program. The program can be stored and provided to a computer using any type of non-transitory computer readable media.

Non-transitory computer readable media include any type of tangible storage media. Examples of non-transitory computer readable media include magnetic storage media (such as floppy disks, magnetic tapes, hard disk drives, etc.), optical magnetic storage media (e.g. magneto-optical disks), CD-ROM (Read Only Memory), CD-R, CD-R/W, and semiconductor memories (such as mask ROM, PROM (Programmable ROM), EPROM (Erasable PROM), flash ROM, RAM (Random Access Memory), etc.). The program may be provided to a computer using any type of transitory computer readable media. Examples of transitory computer readable media include electric signals, optical signals, and electromagnetic waves. Transitory computer readable media can provide the program to a computer via a wired communication line, such as electric wires and optical fibers, or a wireless communication line.

[0056]

While the present invention has been described above with reference to exemplary embodiments, the present invention is not limited to the above exemplary embodiments. The configuration and details of the present invention can be modified in various ways which can be understood by those skilled in the art within the scope of the invention.

[Reference Signs List]

[0057]

101 Demand Database

102 Actual Supply

103 Supply (Contract) Database

104 Imbalance Pricing [EIM] 105 SOC From Battery Controller

110 Stochastic Imbalance Optimizer

111 Short-Term Demand Predictor

112 Scenario Generator

113 Optimization Module

121 Imbalance Energy [EIM]

201 DPE Statistics Calculator

202 Demand Scenario Generator

203 SEE Statistics Calculator

204 Supply Scenario Generator

205 Deviation Scenario Generator