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Stochastic Multi-objective Short-term Hydro-thermal Self-scheduling in Joint Energy and Reserve Markets Considering Wind-Photovoltaic Uncertainty and Small Hydro Units

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Abstract

In this paper, a stochastic multi-objective structure is introduced in joint energy and reserve market to allow energy generation companies (GENCOs) participating in the short-term hydro-thermal self-scheduling with wind, photovoltaic uncertainty and small-hydro units. In addition, uncertainties including energy price, spinning and non-spinning reserve prices as well as the uncertainty of renewable energy resources such as output power of the wind, PV and small-hydro power plants are mentioned. One pivotal feature of this study is that two methods are used to generate stochastic multi-objective scenarios, namely lattice monte carlo simulation and roulette wheel mechanism. After that, the main purpose of the study is described, i.e., making GENCOs able to achieve the maximum profit and the minimum emission by using a multi-objective function considering a stochastic process. To reach this aim, the mixed integer programming which includes a set of multi stage deterministic scenarios is employed. However, some special cases should be introduced in the formulation structure of the presented scheduling regarding hydro-thermal units to make the SMO-HTSS problem with wind, PV and SH units alike real time modeling. Since optimal Pareto solutions are produced in this method, one can allude to the application of the ε-constraint method. Nevertheless, in order to select one of the most appropriate solutions among Pareto solutions obtained, the utilization of fuzzy method has been presented. In the end, some tests are carried out on an IEEE 118-bus test system to verify the accuracy and validity of the proposed method.

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Abbreviations

i :

Thermal unit index

h :

Hydro unit index

w :

Wind unit index

ν:

Photovoltaic unit index

q :

Small-hydro unit index

t :

Time interval (hour) index

s :

Scenario index

\(\pi_{t}^{b}\) :

Bilateral contract price ($/MWh)

\(\Theta\) :

Number of periods of the planning horizon

SDC i :

Shut-down cost of unit i ($)

SUC h :

Start-up cost of unit h ($)

SUC q :

Start-up cost of unit q ($)

\(b_{i}^{n}\) :

Slope of block n of fuel cost curve of unit i ($/ MWh)

\(b_{h}^{n}\) :

Slope of the volume block n of the reservoir associated with unit h (m3/s/Hm3)

\(b_{h\,k}^{n}\) :

Slope of the block n of the performance curve k of uni t h (MW/m3/s)

\(be_{i}^{n}\) :

Slope of segment n in the emission curve of unit i ( lbs /MWh)

\(e_{{^{i} }} ,\,\;f_{{^{i} }}\) :

Valve loading cost coefficients

V :

Wind speed (m/s)

p r :

Rated output power (KW)

\(Eg_{{i{\kern 1pt} ns}}^{off}\) :

Emission produced by the off unit when providing non-spinning (lbs)

\(E(p_{n - 1\,i}^{u} )\) :

Emission of the n-1th upper limit in emission curve of unit i (lbs)

EGC :

Emission group consisting of SO2 and NOx

\(F(p_{n - 1\,i}^{u} )\) :

Generation cost of the n-1th upper limit in the fuel cost curve of unit i ($/h)

\(Ra{\kern 1pt} in_{{h{\kern 1pt} t{\kern 1pt} s}} \,\) :

Forecasted natural water inflow of the reservoir associated with unit h (Hm3/h)

L :

Number of performance curves

M :

Number of prohibited operating zones

\(N_{l}^{bp}\) :

Number of blocks in the piecewise linearization of start-up fuel function

NP :

Number of price levels

Ns :

Number of scenarios after scenario reduction

\(p_{t}^{b}\) :

Power capacity of bilateral contract (MW)

\(p_{s}^{{}}\) :

Probability of scenario s

\(p_{s}^{nr}\) :

Normalized probability of scenario s

\(pout_{i}^{\min }\) \(pout_{i}^{\max }\) :

Minimum and maximum output power of unit i (MW)

\(pout_{h\,n}^{\min }\) :

Minimum output power of unit h for performance curve n (MW)

\(p_{\,h}^{\,c}\) :

Capacity of unit h (MW)

\(p_{{n{\kern 1pt} i}}^{d}\) :

Lower limit of the nth prohibited operating zone of unit i (MW)

\(p_{{n - 1{\kern 1pt} \,i}}^{u}\) :

Upper limit of the n-1th prohibited operating zone of unit i (MW)

\(Qout_{h\,}^{\min }\), \(Qout_{h\,}^{\max }\) :

Minimum and maximum water discharge of unit h (m3/s)

\(RDL_{i\,}^{n}\), \(RUL_{i\,}^{n}\) :

Ramp -down and ramp-up limits for block n (MW)

\(SUE_{i\,}^{{}}\), \(SDE_{i\,}^{{}}\) :

Start-up and shut-down emission generated by unit i (lbs)

\(SUR_{i} (i_{i} )\), \(SDR_{i} (i_{i} )\) :

Start-up and shut-down ramp rate limits of unit i (MW/h)

\(RDL(P_{i\,t\,s} \,)\), \(RUL(P_{i\,t\,s} \,)\) :

Ramping-down and ramping -up limits of unit i (MW)

\(vol_{h\,}^{\min }\) :

Minimum content of the reservoir associated with unit h (Hm3)

\(vol_{h\,n}^{\max }\) :

Maximum content of the reservoir h associated with the nth performance curve (L) (Hm3)

\(N_{WG}\) :

The number of wind turbine generators

\(A_{W}\) :

Total swept area

\(\eta\) :

Efficiency of wind turbine generator

\(p_{t}^{WG}\) :

Actual power available from the wind farm

\(\beta \,_{rs\,}^{s}\) :

Solar irradiance in standard environment (1000 W/m2)

\(R\,_{r\,}^{c}\) :

Certain irradiance point (150 W/m2)

\(P\,_{rpo\,}^{e}\) :

Rated output power of the solar PV unit

\(\beta_{t}\) :

Solar irradiation forecast in W/m2

\(\eta_{SH}\) :

Efficiency of turbine generator (0.85)

\(\rho_{SH}\) :

Water density (1000 kg/m3)

\(g_{SH}\) :

Acceleration due to gravity (9.81 m/s2)

\(H_{SHW}\) :

Effective pressure head (25 m)

\(Q_{SHW}\) :

Water flow rate

\(G\,_{i\,t\,s}^{n}\) \(,\) :

n of fuel cost curve of unit i (MW)

\(\psi \,_{i\,t\,s}^{n}\) \(,\) :

Generation of block n of unit i of valve loading effects curve (MW)

\(\pi \,_{{t{\kern 1pt} s}}^{sp}\) \(,\) \(\pi \,_{{t{\kern 1pt} s}}^{sr}\) \(,\) \(\pi \,_{{t{\kern 1pt} s}}^{ns}\) :

Market prices for energy, spinning, non-spinning reserves ($/MWh)

\(SUC_{i\,t\,s}\) \(,\) :

Start-up cost of unit i ($)

\(VLC_{i\,t\,s}\) \(,\) :

Cost of valve loading effects of unit i ($)

\(E_{ob\,f}^{main}\) \(,\) :

Main objective function (expected profit of GENCOs)

\(F_{i\,t\,s}\) \(,\) :

Fuel cost of unit i ($)

\(E\,_{ob\,f}^{s}\) \(,\) :

Second objective function (expected emission generated in each Pareto optimal solution) (lbs)

\(N_{i\,t\,s}^{d}\) \(,\) \(N_{i\,t\,s}^{u}\) :

Non-spinning reserves of unit i in the spot market when the unit is off and on, respectively (MW)

\(N_{h\,t\,s}^{d}\) \(,\) \(N_{h\,t\,s}^{u}\) :

Non-spinning reserves of unit h in the spot market when the unit is off and on, respectively (MW)

\(N_{q\,t\,s}^{d}\) \(,\) \(N_{q\,t\,s}^{u}\) :

Non-spinning reserves of unit q in the spot market when the unit is off and on, respectively (MW)

\(pout_{i\,t\,s}\) \(,\) :

Power output of unit i (MW)

\(pout\,_{i\,t\,s}^{\max }\) \(,\) :

Maximum power output of unit i (MW)

\(pout_{h\,t\,s}\) \(,\) :

Power output of unit h (MW)

\(pout_{w\,t\,s}\) \(,\) :

Power output of wind unit w (MW)

\(p_{\,t\,s}^{\,sp}\) \(,\) :

Power for bidding on the spot market (MW)

\(profit_{\,s}\) \(,\) :

Profit of scenario s

\(Qout_{h\,t\,s\,}^{n}\) \(,\) :

Water discharge of unit h and block n (m3/s)

\(SR_{i\,t\,s}\) \(SR_{h\,t\,s}\), \(SR_{q\,t\,s}\) :

Spinning reserve of a thermal unit i, hydro unit h and small-hydro unit q in the spot market(MW)

\(vol_{h\,t\,s}\) \(,\) :

Water content of the reservoir associated with unit h (Hm3)

\(\overline{x}_{v}\) :

Vector of decision variables

\(p_{n}\) :

Number of competing objective functions of the MMP problem

\(f^{U}\) :

Utopia point

\(f^{N}\) :

Nadir point

\(f^{SN}\) :

Pseudo nadir point

Φ :

Payoff table

\(q^{p}\) :

Number of intervals

\(\mu_{ps}^{k}\) :

Most preferred solution known as the Pareto solution

\(I_{i\,t\,s}\) \(,\) :

1 if Unit i is online

\(I_{h\,t\,s}\) \(,\) :

1 if Unit h is online

\(I\,_{i\,t\,s}^{d}\) \(,\) :

1 if Unit i provides non-spinning reserve when the unit is off

\(\delta \,_{i\,t\,s}^{n}\) \(,\) :

1 if Block n from fuel cost curve of unit i is selected

\(\delta \,_{h\,t\,s}^{n}\) \(,\) :

1 if The volume of reservoir water is greater than vn (h)

\(\chi \,_{i\,t\,s}^{n}\) \(,\) :

1 if The power output of unit i has exceeded block n of valve loading cost effects curve

\(Z_{i\,t\,s}\) \(,\) :

1 if Thermal unit i has started-up

\(I_{h\,t\,s}\) \(,\) :

1 if Hydro unit h has started-up

\(Y_{i\,t\,s}\) \(,\) :

1 if Unit i is shut-down

SMO-HTSS:

Stochastic multi-objective hydro-thermal self-scheduling

ST-HTS:

Short-term hydro-thermal scheduling

LMCS:

Lattice monte carlo simulation

RWM:

Roulette wheel mechanism

MIP:

Mixed integer programming

MMP:

Multi-objective mathematical programming

PDF:

Probability distribution function

SHPPs:

Small-hydro power plants

RERs:

Renewable energy resources

PV:

Photovoltaic

SH:

Small hydro

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Authors and Affiliations

  1. Department of Electrical Engineering, Dezful Branch, Islamic Azad University, Dezful, Iran

    Mohammad Reza Behnamfar & Hassan Barati

  2. Department of Electrical Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

    Mahdi Karami

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  1. Mohammad Reza Behnamfar
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Behnamfar, M.R., Barati, H. & Karami, M. Stochastic Multi-objective Short-term Hydro-thermal Self-scheduling in Joint Energy and Reserve Markets Considering Wind-Photovoltaic Uncertainty and Small Hydro Units. J. Electr. Eng. Technol. 16, 1327–1347 (2021). https://doi.org/10.1007/s42835-021-00688-7

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