A multi-stage hybrid artificial intelligence based optimal solution for energy storage integrated mixed generation unit commitment problem

Abstract

Inclusion of renewable energy resources with existing conventional generation resources summons revisit to optimization methods used in the field of generation scheduling. The Unit Commitment problem in itself is a highly convoluted problem governed by complex time varying constraints. It gets even more complicated when additional constraints are added due to inclusion of renewable generation backed up by battery storage system. An effort has been made in this paper to improve the model for solving the Unit Commitment problem of conventional thermal generation in conjunction with renewable energy based generation system with storage. A hybrid artificial intelligence based multiple stage solution methodology is envisaged to provide a techno-economical optimal solution to the problem. The proposed methodology provides economically better solution to the Unit Commitment problem of ten thermal generators when integrated with battery supported wind and solar generation. The overall operational cost gets reduced due to integration of renewable resources which gets further reduced by incorporating battery with a novel optimized charge/discharge scheduling technique.

Keywords

Unit commitment problem (UCP)priority list method (PLM)particle swarm optimization technique with time varying acceleration coefficients (PS0_TVAC)renewable energy resources (RERs)battery energy storage (BES)

1 Introduction

The advancements in green energy technology have taken hikes during last three decades, even though the increasing energy demand across the world can’t be met alone by renewables in coming future [1]. This critical aspect warrants an optimal generation scheduling scheme, where conventional thermal generation works in conjunction with renewable energy resources (RERs) in order to satisfy prevailing demand.

The Wind Energy Resource (WER) and Solar Energy Resource (SER) are preferred over other RERs as they are more sustainable, cleaner and cheaper [2 –5]. The wind speed and solar radiation alter significantly over 24 hours leading to intermittency in output power of RERs. This intermittent nature brings in load dispatch problems in the Grid. This problem can be circumvented up to an extent by implementing Battery Energy Storage (BES) in conjunction with RERs [6]. The battery storage is preferred over other storage systems as it has demonstrated its dominance due to techno-economic benefits involved in high storage applications[7 –13].

The Unit Commitment Problem (UCP) is a highly intricate non-linear optimization problem steered by multiple constraints. Combinations of the variety of available generation resources need to be designated optimally in order to achieve the overall optimized cost of generation while meeting the prevailing demand. The problem becomes more complex when RERs with BES are imbibed in UCP model [14, 15].

In order to solve the complex UCP, three cases have been conceived in this paper. In Case One, the prevalent demand gets satisfied by only thermal generation. In Case Two, the demand gets satisfied by thermal generation in conjunction with RERs (without battery). In Case Three, the demand gets satisfied by thermal generation in conjunction with BES integrated RERs. In the third case, the BES integrated RERs generation scheduling is interwoven asa co-optimization problem.

2 Problem formulation

The objective of the study is to obtain most economical operating schedule of thermal generation for all the three cases narrated above. The operating costs of RERs and BES are neglected. Thus the objective function of the problem is to minimize the overall operating cost of thermal generation for 24 hours in this new environment [14, 15].

$Cos t_{NH} = \sum_{h = 1}^{H} \sum_{i = 1}^{N} [{FC}_{i} (P_{ih}) + {SC}_{i} (1 - U_{i (h - 1)})] U_{ih}$ (1)

Where,

U_ih is the ON/OFF status of the i^th unit at h^th hour.FC_i(P_ih) is the fuel cost of i^th unit with power output (P_ih) at the h^th hour and SC_i is the start-up cost of i^th unit.

FC_i is a quadratic polynomial with coefficients a_i, b_i and c_i. It is represented by Equation (2). ${FC}_{i} (P_{ih}) = a_{i} + b_{i} P_{ih} + c_{i} P_{ih}^{2}$ (2)

SC_i is given by Equation (3). ${SC}_{i} = {\begin{matrix} {HSc}_{i} : & X_{i}^{off} \leq ({MD}_{i} + {Cs}_{i}) hrs \\ {CSc}_{i} : & X_{i}^{off} > ({MD}_{i} + {Cs}_{i}) hrs \end{matrix}$ (3)

Where,

H_sc is the hot start-up cost, C_sc is cold start-up cost. Cs_i is cold start-up hours, $X_{i}^{off}$ is the duration in which i^th unit is continuously OFF.

The particulars of thermal generators and day ahead load profile is given in Appendix 1 and Appendix 2 respectively.

The constraints of UCP considered here are as follows.

2.1 Thermal generation constraints

(i) Power Balance Constraint

The power balance constraints for Case One, Case Two and Case Three are given as Equations (4a), 4(b) and 4(c) respectively. $\sum_{h = 1}^{H} [\sum_{i = 1}^{N} P_{ih} U_{ih}] = {LD}_{h}$ (4a) $\sum_{h = 1}^{H} [\sum_{i = 1}^{N} P_{ih} U_{ih} + P {rer}_{h}] = {LD}_{h}$ (4b) $\sum_{h = 1}^{H} [\sum_{i = 1}^{N} P_{ih} U_{ih} + P {rer}_{h}^{D} + P_{h}^{BD}] = {LD}_{h}$ (4c)

Where,

P_ih is the thermal generation (MW) of i^th unit at h^th hour, Prer_h is the hourly generation from RERs (MW), $P {rer}_{h}^{D}$ is the hourly renewable power direct dispatched (MW) to grid, $P_{h}^{BD}$ is the hourly power dispatched (MW) to grid by battery. LD_h is the load demand (MW) at h^th hour.

(ii) Spinning Reserve Constraint $\sum_{i = 1}^{N} P_{i}^{max} U_{ih} \geq {LD}_{h} + {SR}_{h}$ (5)

$P_{i}^{max}$ is the maximum generation in MW of i^th unit and SR_h is the spinning reserve at h^th hour. The spinning reserve is taken as 5% of total load.

(iii) Generation Limit Constraint $P_{i}^{min} \leq P_{ih} \leq P_{i}^{max}$ (6)

$P_{i}^{min}$ is the maximum generation in MW.

(iv) Minimum up time Constraint $X_{i}^{on} (t) \geq {MU}_{i}$ (7)

$X_{i}^{on}$ is the duration in which i^th unit is continuously ON.

(v) Minimum down time Constraint $X_{i}^{off} (t) \geq {MD}_{i}$ (8)

$X_{i}^{off}$ is the duration in which i^th unit is continuously OFF.

(vi) Initial Status

It is the initial down time status that is required to be considered in the first hour of scheduling. The data regarding thermal generating units and load profile is taken from [14, 15].

2.2 RERs generation model

In RERs model the hourly wind power generation can be calculated from Equation (9) [14, 15]. ${Pw}_{h} = {\begin{matrix} 0 : & {Vw}_{h} < V_{1}; {Vw}_{h} > V_{3} \\ ξ ({Vw}_{h}) & V_{1} \leq {Vw}_{h} \leq V_{2} \\ {Pw}_{n} & V_{2} \leq {Vw}_{h} \leq V_{3} \end{matrix}$ (9)

Where,

V₃, V₂ and V₁ are the Cut out, rated and Cut in speeds respectively, for the wind turbine [17]. Vw_h is wind speed in Hovsore (Denmark), the turbine height is taken as 80 meters [16]. The function ξ (v_{w
_h}) determines wind to energy conversion. Pw_n is the rated power of wind generation plant taken as 500 MW. ξ (v_{w
_h}) can be expressed by Equations (10–12) [14, 15]. $ξ (v_{w_{h}}) = k_{o} + k_{1} v_{w_{h}}^{2}$ (10)

Where,

k_o and k₁ are constants given as Equations (10–11). $k_{o} = \frac{P_{wn} * v_{1}^{2}}{v_{1}^{2} - v_{2}^{2}}$ (11) $k_{1} = \frac{P_{wn}}{v_{2}^{2} - v_{1}^{2}}$ (12)

The hourly solar power output can be calculated by Equations (13–14) [14, 15]. ${Ps}_{h} = P_{sn} \frac{s_{h}}{s_{std .} * R_{s}}; 0 \leq s_{h} \leq R_{s}$ (13) ${Ps}_{h} = P_{sn} \frac{s_{h}^{2}}{s_{std .}}; s_{h} > R_{s}$ (14)

Where,

s_h is the hourly forecasted solar radiation, s_std. is solar radiation in standard environment taken as 1000 W/m² and R_s is the cut-in radiation point set as 150 W/m² [14, 15]. P_sn is maximum generation capability of solar system taken as 500 MW. The data regarding radiation is provided in Appendix 3. The total available hourly RERs power output can be represented as Equation (15). $P {rer}_{h} = {Pw}_{h} + {Ps}_{h}$ (15)

2.3 BES integrated RERs model

Prer_h is optimally utilized for Case Three as Equation (16). $P {rer}_{h} = P {rer}_{h}^{D} + P {rer}_{h}^{BC}$ (16)

Where,

$P {rer}_{h}^{D}$ is renewable power output (MW) direct dispatch to grid and $P {rer}_{h}^{BC}$ is renewable power output utilized in charging of battery. To avoid additional computational burden the efficiency of converters for ac/dc conversions are taken as 100% [17].

The Lead-acid battery model has been considered whose charging and discharging are explained with the help Equations (17–24) [18, 19].

The State of Charge (SOC) of battery during charging process is given as Equation (17). $S O C_{h + 1} = S O C_{h} * [1 - σ_{h}] + \frac{I_{h}^{b} * Δ h * η_{h}}{C_{b}}$ (17)

Where,

is the hourly self-discharge rate taken as 0.02%. C_b is battery capacity taken as 200 MWh. Δh is taken as 1.η_h is charge efficiency factor given as Equation (18). $η_{h} = 1 - exp [\frac{y * {SOC}_{h} - 1}{(\frac{I_{h}^{b}}{I_{0}} + z)}]$ (18)

Where,

y, z and I₀ are the parameters depending upon working conditions of battery. The battery charging current $I_{h}^{b}$ , is given as Equation (19).

$I_{h}^{b} = \frac{P {rer}_{h}^{BC}}{V_{h}^{b}} * η_{h}^{conv}$ (19)

$η_{h}^{conv}$ is converter efficiency.

The battery discharge process is computed as expressed in Equations (20–21). ${SOC}_{h + 1} = {SOC}_{h} * [1 - σ_{h}] - (\frac{I_{h}^{b} * Δ h}{C_{b}})$ (20) $I_{h}^{b} = - [\frac{P_{h}^{BD}}{V} * η_{h}^{conv}]$ (21)

Where,

P_h^BD is battery power discharged to the Grid.

Meanwhile, the charged quantity of the battery is subjected to following constraints [18, 19]. ${SOC}_{min} \leq {SOC}_{h} \leq {SOC}_{max}$ (22)

and, $I_{h}^{b \max} = \max {0, \min [I^{\max}, C_{b} * k ((A^{'}) + (B^{'}) * (1 - k)) / Δ h]}$ (23)

Where, $\begin{matrix} A^{'} = S O C_{\max} - S O C_{h}; & B^{'} = S O C_{h} - S O C_{\min} \end{matrix}$

k = 1 for charging and k = 0 for discharging.

Where, ${SOC}_{max} = 1; {SOC}_{min} = DOD$

DOD is Depth of Discharge, taken as 30% [18, 19].

The battery terminal voltage $(V_{h}^{b})$ is given as Equation (24) [18, 19]. $V_{h}^{b} = V_{h}^{oc . b} + I_{h}^{b} * R_{h}^{b}$ (24)

Where,

$V_{h}^{oc . b}$ is open circuit voltage of battery and $R_{h}^{b}$ is battery internal resistance.

3 Solution methodology

A four stage solution methodology is formulated for solution of UCP. In First stage, the ON/OFF schedule of thermal generators is obtained by Priority List Method (PLM). In second stage, the Economic allocation of load among thermal generators is done by Particle Swarm Optimization Technique with Time Varying Acceleration Coefficients (PSO_TVAC). The combination of PLM with PSO gives better results as against the other techniques used in solving thermal UCP [20]. In Case Three, the hourly generation from RERs is calculated and load demand is updated by subtracting hourly RERs generation from day-ahead load profile, which again gets satisfied by stage one and stage two processes. In fourth stage, BES integrated RERs generation scheduling involving charge/discharge of battery is solved as a co-optimization problem.

An incremental cost based novel analytical method is devised to solve this co-optimization problem. The BES integrated RERs hourly generation schedule is subtracted from the day-ahead load profile to obtain updated load profile. It can be explained from the below Fig. 1.

Fig.1

Schematic representation of solution methodology.

3.1 Stage one (PLM)

The initial priority vector is obtained as Equation (25) [21].

$priorityvector = \frac{P_{(max), vec}}{max . [P_{(max), vec}]} + \frac{{MD}_{vec}}{max . [{MD}_{vec}]}$ (25)

This initial priority vector is updated with the help of the pseudo code as Fig. 2 [21].

Fig.2

Pseudo Code.

3.2 Stage two (PSO_TVAC)

The PSO_TVAC can be expressed as Equations (26–30) [22]. The velocity and position updates of particle are given as Equations (26–27). The linearly varying ω and acceleration coefficients c _ 1 and c _ 2 are given as Equations (29–30).

$v_i d^{(k + 1)} = [w * v_{i d}^{k} + c_1 * R a n d_1 () * (A^{″}) + c_2 * R a n d_2 () * (B^{″})]$ (26)

Where, $\begin{matrix} A^{'} = P_{b e s t i d} - - x_{i d}^{k}; & B^{″} = G_{b e s t g d} - - x_{i d}^{k} \end{matrix}$ $c_{1} = (c_{1 f} - c_{1 i}) * \frac{iter}{{iter}_{max}} * c_{1 i}$ (27) $w = w_{max} - (\frac{w_{max} - w_{min}}{{iter}_{max}}) * iter$ (28) $c_{1} = (c_{1 f} - c_{1 i}) * \frac{iter .}{{iter}_{max}} * c_{1 i}$ (29) $c_{2} = (c_{2 f} - c_{2 i}) * \frac{iter .}{{iter}_{max}} * c_{2 i}$ (30)

The velocity limits and PSO_TVAC parameters are taken as [22].

3.3 Stage three

Hourly RERs generation is calculated as discussed in section 2. The updated hourly demand () gets updated as Equation (31).

$L D_{h}^{'} = L D_{h} - Pr e r_{h}$ (31)

3.4 Stage four

The stage four optimization process is explained with the help of Fig. 3 and Equation (32). From the Fig. 3 the information about renewable power direct dispatch to grid ( $P {rer}_{h}^{D}$ ) is obtained from Pren_allocate array and information about hourly battery power output ( $P_{h}^{BD}$ ) is obtained from Battery_Schedule. The day ahead load demand profile is further updated as Equation (32).

Fig.3

Optimization of BES Integrated RERs Generation Scheduling.

$L D_{h}^{''} = L D_{h} - (P re r_{h}^{D} + P_{h}^{B D})$ (32)

The is satisfied by stage one and stage two processes to obtain final dispatch schedule for Case- Three.

4 Simulation and results

The ON/OFF and dispatch schedules obtained from stage one and stage two for all the three cases are shown in Fig. 4. The ON thermal generators are indicated as symbol “G” and corresponding MWs generation is given adjacent to it.

Fig.4

ON/OFF and Dispatch status of Thermal generators.

There are three rows associated with every hour, the first row indicates the prevalent demand satisfied by only thermal generation. The second row indicates the prevalent demand getting satisfied by thermal generation along with RERs. The third row indicates the demand getting satisfied by thermal generation in conjunction with BES integrated RERs.

The comparison of generation costs for all the three cases and the result obtained from co-optimization process are given in Tables 1 and 2 respectively.

Table 1

Comparison of Generation Costs for all the three cases

Generation Costs ($)
Thermal Generators	Case One			Case Two			Case Three
	Fuel Cost	Start-up Cost	Total Cost	Fuel Cost	Start-up Cost	Total Cost	Fuel Cost	Start-up Cost	Total Cost
G1	203180	0	203180	198063	0	198063	203180	0	203180
G2	194581	0	194581	152458	0	152458	154514	0	154514
G3	37593	1650	39243	0	0	0	0	0	0
G4	51492	560	52052	0	0	0	0	0	0
G5	42658	900	43558	21990	1800	23790	16852	1800	18652
G6	12619	510	13129	4001	340	4341	0	0	0
G7	4696	520	5216	0	0	0	0	0	0
G8	3963	120	4083	920	60	980	0	0	0
G9	1876	120	1996	0	0	0	0	0	0
G10	0	0	0	0	0	0	0	0	0
Total	552658	4380	557038	377432	2200	379632	374546	1800	376346

Table 2

RERs direct dispatch and battery charging/discharging schedules

Power (MWs)
Hours	Prer_h	$P {rer}_{h}^{D}$	$P {rer}_{h}^{BC}$	$P_{h}^{BD}$	Hours	Prer_h	$P {rer}_{h}^{D}$	$P {rer}_{h}^{BC}$	$P_{h}^{BD}$
Hr1	266	95	171	0	Hr13	499	499	0	0
Hr2	266	145	121	0	Hr14	543	468	75	0
Hr3	203	203	0	42	Hr15	468	450	18	0
Hr4	148	148	0	172	Hr16	446	321	125	0
Hr5	148	148	0	77	Hr17	411	269	142	0
Hr6	148	148	0	0	Hr18	324	324	0	47
Hr7	189	189	0	0	Hr19	337	337	0	114
Hr8	330	330	0	0	Hr20	266	266	0	199
Hr9	390	390	0	0	Hr21	337	337	0	0
Hr10	426	426	0	0	Hr22	300	300	0	0
H 11	483	483	0	0	Hr23	266	266	0	0
Hr12	546	546	0	0	Hr24	300	300	0	0

The hourly available RERs generation is shown in Fig. 5.

Fig.5

Hourly Generations from RERs (Case Two).

The optimized generation scheduling of RERs is shown in Fig. 6.

Fig.6

Hourly Generation from BES integrated RERs (Case Three).

The hourly updated SOC of battery is shown in Fig. 7.

Fig.7

Hourly SOC level of Battery.

The thermal generation schedules obtained from stage two for all the three cases satisfying the corresponding load demands are shown in Fig. 8.

Fig.8

Thermal Generation for all the three cases.

The convergence of the proposed method for all the three cases is shown in Fig. 9.

It is evident from Fig. 4 that out of ten available thermal generators nine contributed to cater the prevalent demand for Case One, five thermal generators are sufficient to cater the demand for Case Two and only three thermal generators are required to cater the demand for Case Three.

Fig.9

Convergence for all the three cases.

It is culminated in Table 1 that the overall operational cost of thermal generation is minimum for Case Three. The peak load shavings achieved from Case Two and Case Three are shown in Fig. 8. The proper scheduling of battery with RERs for Case Three has provided the lowest operational cost for thermal generation as the expensive thermal generation is relieved by battery power during peakload hours.

The entire study has been carried out in MATLAB environment with system specifications as 4 GB RAM, Intel core processor. The execution time of the program is 45 seconds.

5 Conclusion

A widely accepted PSO technique with time varying acceleration coefficients, hybridized with classical Priority List Method and analytical method based on incremental cost of thermal generators has been considered in this paper for obtaining optimal solution for thermal generation Unit Commitment Problem in mixed generation environment. The study has been carried out for ten thermal generating units with inclusion of nearly 30% renewable generation with battery storage. The inclusion of RERs resulted in saving of $177406 per day and after optimizing the BES integrated RERs generation scheduling the savings are further optimized by $3286 per day. Thus, optimization of generation scheduling of RERs with battery storage provided optimal techno-economic solution to the UCP. The proposed method is found to be reliable and robust based on running the simulations several times.

Footnotes

Appendices

Acknowledgments

The authors would like to acknowledge Technical Education Quality Improvement Program (TEQIP), IET, Lucknow, APJAKTU, for funding this research.

References

James

, The biggest Clean Energy Advances in 2016, Sustainable Energy, MIT Technology Review, 2016. https://www.technologyreview.com/s/603275/the-biggest-clean-energy-advances-in-2016/

Vine

, Breaking down the silos: The integration of energy efficiency, renewable energy, demand response and climate changes, Energy Efficiency1(1) (2008), 49–63.

Evans

, Strezov

and Evans

T.J.

, Assessment of sustainability indicators for renewable energy technologies, Renewable and Sustainable Energy Reviews, Elsevier13(5) (2009), 1082–1088.

Islam

, Mekhilef

and Saidur

, Progress and recent trends in wind energy technology, Renewable and Sustainable Energy Reviews, Elsevier21 (2013), 456–468.

Pandey

A.K.

, Tyagi

V.V.

, Jeyraj

, Selvaraj

, Rahim

N.A.

and Tyagi

S.K.

, Recent advances in solar photovoltaic systems for emerging trends and advanced applications, Renewable and Sustainable Energy Reviews, Elsevier53 (2016), 859–884.

Suberu

M.Y.

, Mustafa

M.W.

and Bashir

, Energy Storage Systems for renewable energy power integration and mitigation of intermittency, Renewable and Sustainable Energy Reviews, Elsevier35 (2014), 499–514.

Diouf

and Pode

, Potential of lithium ion batteries in renewable energy, Renewable Energy76 (2015), 375–380.

Castillo

and Gayme

D.F.

, Grid Scale energy storage applications in renewable energy integration: A Survey, Energy Conversion and Management, Elsevier87 (2014), 885–894.

Hadjipaschalis

, Poullikkas

and Efthimiou

, Overview of current and future energy storage technologies for electric power applications, Renewable and Sustainable Energy Reviews, Elsevier13 (2009), 1513–1522.

10.

Zhao

, Wu

, Hu

, Xu

and Rasmussen

C.N.

, Review of energy storage system for wind power integration support, Applied Energy137 (2015), 545–553.

11.

Reihani

, Sepasi

, Roose

L.R.

and Matsuura

, Energy Management at the distribution grid using a Battery Energy Storage System (BESS), International Journal of Electric Power and Energy Systems, Elsevier77 (2016), 337–344.

12.

Chatzivasileiadi

, Ampatzi

and Knight

, Characteristics of electrical energy storage technologies and their applications in buildings, Renewable and Sustainable Energy Reviews, Elsevier25 (2013), 814–830.

13.

Wade

N.S.

, Taylor

P.C.

, Lang

P.D.

and Jones

P.R.

, Evaluating the benefits of an electrical storage system in a future smart grid, Energy Policy, Elsevier38(11) (2010), 7180–7188.

14.

Shukla

and Singh

S.N.

, Advanced three stage pseudo inspired weight improved crazy particle swarm optimization for Unit Commitment Problem,y 96, Elseveir Energ96 (2016), 23–36.

15.

Shantanu

, Senjyu

, Saber

A.Y.

, Yona

and Funabashi

, Optimal thermal unit commitment integrated with renewable energy sources using advanced particle swarm optimization, IEEJ4 (2009), 609–617.

16.

Wagner

, Antoniou

, Pederson

S.M.

, Courtney

M.S.

and Jorgensen

H.E.

, The influence of the wind speed profile on wind turbine performance measurements, Interscience Wind Energy12 (2009), 348–362.

17.

Powell

, Power system load flow analysis, Mc Graw. Hill Professional Series, 2004.

18.

Yang

, Lu

and Zhou

, A novel optimization sizing model for hybrid solar-wind power generation system, Solar Energy, Elsevier81 (2007), 76–84.

19.

Bhandari

, Poudel

S.R.

, Lee

K.T.

and Ahn

, Mathematical modelling of hybrid renewable energy system: A review on small Hydro-solar-wind power generation, International Journal of Precision Engineering and Manufacturing-Green Technology, Springer1(2) (2014), 157–151.

20.

Tiwari

, Dwivedi

and Dave

M.P.

, A Two stage solution methodology for Deterministic Unit Commitment problem, In: Proceedings of 3rd IEEE International Conference on Electrical, Computer and Electronics(UPCON-2016), 09-11 Dec., 2016, pp. 317–322.

21.

Khanmohammadi

, Amiri

and Tarafdar

, Haque, A new three stage method for solving unit commitment method, Elsevier Energy35 (2010), 3072–3080.

22.

Chaturvedi

K.T.

and Pandit

, Srivastava laxmi,self-organizing hierarchical particle swarm optimization for non-convex economic dispatch, IEEE Transactions on Power Systems23 (2008), 1079–1087.