Transmission Expansion Planning Considering Wholesale Electricity Market and Integration of Renewable Generation Artjoms Obushevs
Irina Oleinikova
Riga Technical University Riga, Latvia Email:
[email protected]
Institute of Physical Energetics Riga, Latvia Email:
[email protected]
Abstract—A new network operation conditions creates new requirements for transmission planning which include electricity market figures and considerable integration of renewable generation. This paper focuses on transmission expansion planning techniques in a perfect competitive electricity market based on optimal power flows calculations with development planning and sustainability concept. For the proposed concept validation the Garvers’s 6-bus test system was used. The simulation and validation results show the possibility of the ACOPF/DCOPF models implementation to transmission planning tasks solution. Keywords—electricity market, optimal power flow, power system development, renewable generation
I. INTRODUCTION Liberalised electricity market effects the power system development. It is determined by the condition that electricity generators are independent from transmission and distribution operators and their interests differ. In this connection in development tasks necessary to consider price formation mechanisms, for a more detailed definition of benefits and costs with the introduction of new or liquidation of old power system elements. To foster climate targets and estimate the technical and economic impact of renewable energy sources accommodation to transmission networks, several theories based on the social impact of the investments in competitive markets and marginal pricing are created by different authors [1-3]. Electricity market and Smart Grid Technology’s integration in energy sector brings completely new problem setup in many countries and many recent studies are addressing this problem from different perspectives: System operation and reliability issues; Network planning including future uncertainties; RES integration in different voltage levels; Completion of the Internal Energy Market in EU; Implementation of novel SGT and ICT solutions. The great majorities of studies describe only one-time static problems investment models and do not consider additional This work has been supported by the European Social Fund within the project «Support for the implementation of doctoral studies at Riga Technical University», Nr. 2009/0144/1DP/1.1.2.1.2/09/IPIA/VIAA/005.
factors that can affect the network expansion in future years. A new network operation conditions creates new requirements for transmission planning, which include electricity market figures and considerable integration of renewable generation. The main point of this paper is to demonstrate the new deterministic concept for transmission planning based on technical and market – economic regulation principals. Traditional approach is taken as starting point, where expansion/development plan is checked for operational constraints. For this purpose AC or DC models can be implemented, both of them have pros and cons regarding load flows power losses and stability analysis etc. However, power system operation in market condition introduce new terms such as: capacity allocation and congestion management, which will significantly affect previous modeling techniques. A coordinated approach for capacity calculation including optimal power flow implementation will show the best use of the electricity transmission lines and open additional opportunities for planning with social welfare estimation. This paper provides the base for the transmission planning methodology according to the needs for new methods and tools for the future power system with considerable integration of renewable generation. In order to achieve these targets sustainable development planning concept with OPF techniques was proposed and AC/DC OPF algorithms with planning approach was created. Determination of optimal expansion planning strategy will ensure adequacy of the grid, generation and demand in the future. II. DEVELOPMENT PLANNING & SUSTAINABLE DEVELOPMENT CONCEPT
Development planning is a process to determine an optimal strategy to expand the existing power system transmission network to meet the demand of the possible load growth and the proposed generators, while maintaining reliability and security performance of the power system. The general objective of the power system transmission network development planning task is to determine ‘where’, ‘how many’ and ‘when’ new element must be added to a network in order to make its operation viable for a pre-defined horizon, with a costs minimization and social welfare maximization for optimal expansion/development plan determination.
978-1-4799-6095-8/14/$31.00 ©2014 IEEE
Main concepts of development planning based on: Development Action (D-action); Development Step (D-step); Development Plan (D-plan) explained in reference [4]: D action ( s )
Realized
e t 1 ... ... ...
Existing state
New state
P e t
(1)
Development plan formation is complicated process that requires extensive studies to determine many new network elements. Creation of the optimal development plan will ensure adequacy of the grid, generation and demand in the future. Electricity market effects not only power system operation as whole, but also its development practices. It is determined by default that electricity generators are independent from transmission and distribution operators and their interests differ. This fact creates higher uncertainty conditions and time resolutions accuracy for the perspective forecasts than before, therefore power system development planning and optimization is hampered. For sustainable development solutions of the network, estimation period must be assumed longer than economic life cycle period – advisable up to 30 years. The selection of optimal development plans under uncertainty require: information package set, representing information credibility range – prognosis, credibility estimation criteria and comparable development plans. If the compromise between network estimation problems and development aggregated results has not been reached, the quality of the planning results will be impaired. The solution to compile AC and DC models (see Fig. 1): x
x
For short-term analysis, to include intermitted generation and market conditions, of several years and subject to initial information availability can be used the full ACOPF model; Considering the complexity and dimension of development and optimization tasks, as well as information uncertainty conditions, appropriate method for the long-term analysis and estimation of criteria is simplified DCOPF method.
max F (T , g )
max g ^ G
T
¦ (SW (t , e (t )) IC (t , e (t ))
`t 1
(2)
where: t – development step serial number;
T – number of development steps in estimation period; SW (t , e (t )) – social welfare criterion in development step t and development state e t ;
IC (t , e (t )) – investment costs in development step t and development state e t ;
g – development process e 1 , e 2 ,! , e t ,! , e T ;
^G`
– set of all possible development plans. III. DEVELOPMENT MODEL
Development modeling should include network dynamic behaviors and represent the network real processes as much as possible. Based on main functioning factors proposed in chapter II the following development model was created (see Fig. 2). t=1
Development process
Network scheme and parameters formation re = 1
Development step model
Formation of load and generation bids, RES production Solve simplified unit commitment considering alternating/direct current security-constrained optimal power flow in operational state re Social Welfare, nodal/zonal prices, define congestions, solution is feasible/unfeasible in operational state re re = re + 1
Yes
UH 8760 No
Objective function calculation by t steps
t=t+1
Yes
W T No
Fig. 2. Development process Fig. 1. Example of models combination for time frames
In real tasks the number of comparable development plans attains astronomic quantity, therefore it is required to apply specialized dynamic optimization methods. Overall multiobjective function for network development plan displays and integrates technical, economic, power supply reliability, ecological, electricity market etc. parameters. The objective function in (2) represents the social welfare, where the welfare is expressed as aggregated demand utility bid function minus generator offer function, minus investment cost in new lines. Objective function is a network development plan g quality criterion, denoted as F T , g is calculated by a formula:
This process allows hourly consideration of renewable generation impacts to a power system and market formation. In order to evaluate the effect of the renewable generation integration to the price formation as well as level of system penetration, methodology was proposed in references [5, 6]. IV. THE AC/DC SCOPF FORMULATIONS The optimal power flow is a very large and difficult mathematical programming problem. The main aim of the OPF is to determine the optimal steady-state operation of a power system, which simultaneously minimizes or maximize the value of a chosen objective function and satisfies certain physical and operating constraints. To provide complex solutions for the network operation problem analysis and its
consideration in development the following mathematical formulations can be implemented. A.
Formulation of OPF
OPF is a technique that has been used in the electricity industry for several decades. The objective function of an OPF problem may take many different forms according to the different applications. The general objective in OPF is to maximize social welfare which comprises producers’ and consumers’ surpluses or minimize costs of production. The costs and benefits may be defined as polynomials or as piecewise-linear functions [7]. B.
Alternating Current and Direct current OPF
The AC version of the standard OPF problem is a general non-linear constrained optimization problem, with both nonlinear costs and constraints. In a system with nb buses, ng generators, nl branches and nc consumers, the optimization variable x is defined as follows:
x [4;V ; PG ; QG ; PL ; QL ]
(3)
The objective function is a consumers’ utility minus producers’ cost (represented by function BLi ( PLi ) and CGj ( PGj ) , respectively) shall be maximised subject to equality and inequality constraints:
SW ( PG , PL )
ng ° nc i i ½ j j ° (4) B ( P ) ®¦ p L ¦ CG ( PG ) ¾ o 4 ,V , Pmax G , QG , PL , QL j 1 ¯° i 1 ¿°
The equality constraints consist of two sets of nb nonlinear nodal power balance equations, one for real power and one for reactive power.
g P (4, V , PG , QG , PL , QL )
0
(5)
gQ (4, V , PG , QG , PL , QL )
0
(6)
The inequality constraints consist of two sets of nl branch flow limits as non-linear functions of the bus voltage angles and magnitudes, one for the from end and one for the to end of each branch.
h f (4, V , PG , QG , PL , QL ) d 0
(7)
ht (4, V , PG , QG , PL , QL ) d 0
(8)
The variable limits include an equality limited reference bus angle and upper and lower limits on all bus voltage magnitudes, real and reactive generator and consumption injections.
T ref d Tl d T ref ,
l
lref
(9)
vlmin d vl d vlmax ,
l 1...nb
(10)
PGj,min d PGj d PGj,max ,
j 1...ng
(11)
j 1...ng
(12)
j G ,min
Q
dQ dQ j G
j G ,max
0dP dP i L
i L ,max
,
,
i 1...nc
(13)
0 d QLi d QLi ,max ,
i 1...nc
(14)
Here lref denotes the index of the slack bus. When using DC network modelling assumptions, the standard OPF problem above simplified to a quadratic program, with linear constraints. In this case the DC power flow greatly simplifies the power flow by making a number of approximations [8]. The optimization variable is:
x [4; PG ; PL ]
(15)
and the overall problem reduces to the form, subject to (4) – (14) without V , QG , QL variables. OPF development has been carried out following the progress in numerical optimization techniques and computer technology. Many different approaches have been proposed to solve the OPF problem: nonlinear programming, quadratic programming, linear programming, mixed programming, as well as interior point and artificial intelligence algorithms. The most successful interior point methods are based on using a primal–dual formulation and applying Newton’s method to the system of equations arising from the barrier method. This method has been widely used in power system optimization problems because of its favorable convergence, robustness, and insensitivity to infeasible starting points. The primal-dual interior point method (PDIPM) has become the algorithms of choice for long-term development planning strategies [9,10]. C.
Security-Constrained OPF
SCOPF problem is an extension of the OPF problem and contains important features of reliability in the optimization model. It guarantees stable work of the whole power system, without changing active power generation, when some predetermined contingencies occur (such as outages of transmission line). Fig. 3 provides the flowchart of the iterative SCOPF algorithm, which starts by solving an OPF with (N-0) constraints. When it has solved the contingency analysis starts to identify the critical group of lines and selected according to these criteria:
K L* , re where
L
F L PsL , re ,
transmission line ordinal number;
(16)
PsL , re
transmission line flow in operational state; F L interruption probability of transmission line L; In development planning tasks for optimal steady-state operation determination only 10% of electric transmission lines should be taken into consideration in which transmission line flow, transmission line interruption probability and therefore criteria K* are the highest values. This criterion is necessary in order to select critical group of lines and thus reducing size of optimization problem and calculation time. The UC problem in traditional form involves determining the start-up and shut down schedules of thermal units to be used to meet forecasted demand over a future short term period [11]. UC problem is a complex mathematical optimization problem and significantly increases development planning tasks complexity. In this regard some assumptions were made
to simplify problem: not assume start-up and shut-down cost, reserve requirements, ramp rates (each hourly base steady-state operation is independent from other hours).
TABLE I.
Solve base AC/DC optimal power flow with all (N-0) limits Assessment of transmission lines and compilation of critical lines group
i = i +1
Solve AC/DC power flow disconnecting 1st critical line
Solve AC/DC power flow disconnecting 2nd critical line
Solve AC/DC power flow disconnecting last critical line
save contingency constraints
save contingency constraints
save contingency constraints
No Set of Yes Optimum power constraints? system operating state
i>3
Yes
Solution not feasible
No Solve AC/DC optimal power flow with contingency constraints
Fig. 3. Security-constrained OPF
D.
Simplified Unit commitment
Fig. 4 provides the flowchart of the iterative simplified UCSCOPF algorithm, which starts by solving an SCOPF without units’ low MW limits. When it has solved, compilation of power plants group VWDUWV ZLWK JHQHUDWLRQ OHVV WKDQ İ LQ FDOFXODWLRQ İ DVVXPHG WR LGHQWLI\ WKH JURXS RI SRZHU plants which should be switched off. Obtained steady-state operation, social welfare and nodal prices reflects simplified power system dynamic processes and taken for development modeling. V. CASE STUDIES In this section, modified Garver’s 6-bus system is studied and the simulation results are demonstrated. A.
Load parameters
Bus No.
i=1
Modified Garver’s 6-Bus System
Basis for calculations of the modified scheme is taken from sources [12, 13]. Modified Garver’s 6-bus system has 14 existing lines, 5 loads and 4 generators. The system parameters are listed in Tables I, II and III. For the present structure of the network are considered following four case strategies of development: x
Without wind PP and investments;
x
Without wind PP and with investments for new line 15;
x
With wind PP and investments;
x
With wind PP and investments for new line 1-5.
1 2 3 4 5 6
GENERATOR AND LOAD DATA
3ș PQ PV PQ PQ PV
PD MW
QD MVAr
80 240 40 160 240 -
16 48 8 32 48 TABLE II.
Generator parameters PGMAX
PGMIN
QGMAX
QGMIN
MW 160 100 370 610
MW 0 0 0 0
MVAr 65 0 150 200
MVAr -10 0 -10 -10
LINE DATA
Branch
rij, p.u
xij, p.u
bij, p.u
1–2 1–4 1–5 2–3x2 2–4 2–6x2 3–5x3 4–6x3
0.04 0.06 0.02 0.02 0.04 0.03 0.02 0.03
0.4 0.6 0.2 0.2 0.4 0.3 0.2 0.3
0.04 0.06 0.02 0.02 0.04 0.03 0.02 0.03
TABLE III.
Capacity MW
MVA
100 80 100 100 100 100 100 100
120 100 120 120 120 120 120 120
GENERATOR COSTS AND DEMAND BENEFITS Generators
Node
Fuel source
1 2 3 4 5 6
Gas Wind Coal Coal
Demands
bj aj ci (EUR/MW2h) (EUR/MWh) (EUR/MW2h)
0.0298 0 0.0081 0.0035
83.9 0 58 69.71
0 0 0 0 0 -
di (EUR/MWh)
200 200 200 200 200 -
Solve security constrained optimal power flow without PGmin level Compilation of power plants group with generation PG < PGminÂİ Group of No Solve SCOPF with PGmin level and disconnected power power plants plants?
Yes Disconnect power plants with generation PG < PGminÂİ Solve SCOPF flow without PGmin level and disconnected power plants
Fig. 4. Simplified Unit Commitment
For development modeling calculation were made the following assumptions: 1. We consider a time horizon of ten years. For this time scale we estimate the demand, the generation offers and the demand bids. Therefore, our model represents a “Dynamic Transmission Expansion Planning” problem, for which the net social welfare is maximized.
2. Each development step is calculated in accordance with the present algorithm in fig. 2 (AC and DC models of the network are used). 3. Generator costs changed for all the periods of study, such that gas price grow each year by 1% and coal price by 2%. We considering perfect competition strategy, generators offer at their marginal costs.
The presented results clearly show the behavior and changes in the power system which subsequently must be considered with decision making theory for the future sustainable development of transmission networks.
4. Each load defined by individual demand pattern and grow up each year by 0,5% (see Fig. 5) 5. Fig. 6 represent annual wind production curve for 100MW power plant obtained from wind production curve simulation algorithm provided in [5,6]. Production curve is fixed for each development step and not participate in automatic generation control.
Fig. 7. First and last development step SW patterns
TABLE IV.
Fig. 5. Demand pattert for first development step
SW VALUES FOR THE CASE STUDY WITHOUT WIND PP Without investment
SW OPF, MEUR
SW SCOPF, MEUR
SW OPF, MEUR
SW SCOPF, MEUR
1 2 3 4 5 6 7 8 9 10 Total
578.664 576.030 573.241 570.292 567.180 563.899 560.445 556.812 552.996 548.992 5648.551
574.939 572.247 569.405 566.408 563.252 559.932 556.444 552.782 548.943 544.922 5609.274
578.664 576.030 573.241 570.293 567.180 563.899 560.445 556.812 552.996 548.992 5648.553
575.525 572.847 570.021 567.042 563.905 560.605 557.137 553.496 549.678 545.678 5615.934
TABLE V.
Fig. 6. Annual wind production curve for 100MW power plant
B.
Analysis of results
Fig. 7 provides one year results of social welfare for first and last development steps without investing. Table IV and V represent changes of annual SW values of OPF and SCOPF problems for different development strategies. Integration of wind production significantly increase annual SW values and reduce need of most expensive conventional plants which can lead to lower average prices for electricity, however expansion of power production capacities with low marginal costs of production have negative impact to the conventional generators, mostly reducing ability sufficiently cover total production costs. Effects of renewable generation integration into generating portfolio could be evaluated as positive, regarding to improved generation and transmission adequacy as well as system reliability.
With investment
Step
SW VALUES FOR THE CASE STUDY WITH WIND PP
Without investment
With investment
Step
SW OPF, MEUR
SW SCOPF, MEUR
SW OPF, MEUR
SW SCOPF, MEUR
1 2 3 4 5 6 7 8 9 10 Total
649.103 646.845 644.440 641.884 639.171 636.299 633.261 630.054 626.672 623.110 6370.839
644.525 642.193 639.715 637.087 634.303 631.360 628.252 624.977 621.528 617.902 6321.842
649.175 646.919 644.514 641.958 639.247 636.375 633.338 630.131 626.750 623.189 6371.596
645.317 643.000 640.538 637.927 635.162 632.238 629.151 625.896 622.469 618.865 6330.563
VI. CONCLUSIONS This paper provides the base for the transmission planning methodology according to the needs for new methods and tools for planning of the future power system with considerable integration of renewable generation. The main attention is focused on existing method of long-term development planning analysis and criterion calculations in development tasks with
special attention to market conditions and integration of renewable generation. Methods for solving SCOPF problem and assumptions in development tasks are provided. Considering the complexity and dimension of development tasks, as well as information uncertainty conditions, appropriate method for the steepest calculating of OPF to define criteria is simplified DC method with polynomials or piecewise costs functions. For short-term analysis of several years and subject to initial information availability can be used the full AC model. REFERENCES [1]
[2]
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[4]
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