energies Article
On Variable Reverse Power Flow-Part II: An Electricity Market Model Considering Wind Station Size and Location Aouss Gabash * and Pu Li Department of Simulation and Optimal Processes, Institute of Automation and Systems Engineering, Ilmenau University of Technology, Ilmenau 98693, Germany;
[email protected] * Correspondence:
[email protected]; Tel.: +49-3677-69-2813; Fax: +49-3677-69-1434 Academic Editor: Rodolfo Araneo Received: 23 November 2015; Accepted: 18 March 2016; Published: 25 March 2016
Abstract: This is the second part of a companion paper on variable reverse power flow (VRPF) in active distribution networks (ADNs) with wind stations (WSs). Here, we propose an electricity market model considering agreements between the operator of a medium-voltage active distribution network (MV-ADN) and the operator of a high-voltage transmission network (HV-TN) under different scenarios. The proposed model takes, simultaneously, active and reactive energy prices into consideration. The results from applying this model on a real MV-ADN reveal many interesting facts. For instance, we demonstrate that the reactive power capability of WSs will be never utilized during days with zero wind power and varying limits on power factors (PFs). In contrast, more than 10% of the costs of active energy losses, 15% of the costs of reactive energy losses, and 100% of the costs of reactive energy imported from the HV-TN, respectively, can be reduced if WSs are operated as capacitor banks with no limits on PFs. It is also found that allocating WSs near possible exporting points at the HV-TN can significantly reduce wind power curtailments if the operator of the HV-TN accepts unlimited amount of reverse energy from the MV-ADN. Furthermore, the relationships between the size of WSs, VRPF and demand level are also uncovered based on active-reactive optimal power flow (A-R-OPF). Keywords: active-reactive energy losses; variable reverse power flow (VRPF); varying power factors (PFs); wind station size-location
1. Introduction The extended active-reactive optimal power flow (A-R-OPF) with reactive power of wind stations (WSs) in [1,2] is utilized in this paper to analyze an electricity market model using a real medium-voltage active distribution network (MV-ADN) connected to a high-voltage transmission network (HV-TN), as shown in Figure 1. Our particular focus will be on the impact of charging (paying) schemes for reactive energy which are applied, typically, by transmission system operators for users connected to a HV-TN in Europe [3]. The power flow direction of the forward/reverse active PS1 and reactive QS1 power at a slack bus S1 is shown in Figure 1. In general, an operating point represents the measured apparent power, e.g., at the secondary side of a transformer (TR). It is to note that an operating point can be in one of the four quadrants shown in Figure 1, but without violating the maximum TR capability [4–7].
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Figure 1. The medium‐voltage active distribution network (MV‐ADN) case study with active‐reactive Figure 1. The medium-voltage active distribution network (MV-ADN) case study with active-reactive power flow direction definitions and capability diagram of a transformer (TR) at slack bus S1 [5]. power flow direction definitions and capability diagram of a transformer (TR) at slack bus S1 [5]. Here, Here, different locations and sizes of a wind station (WS) are depicted to show the effect of variable different locations and sizes of a wind station (WS) are depicted to show the effect of variable reverse reverse power flow (VRPF).
power flow (VRPF).
Recent studies [8–18] on reactive power planning and management, active power scheduling
Recent studies [8–18] on reactive power planning and management, active power scheduling and losses, active distribution network (ADN) management, and sizing as well as siting distributed and losses, active distribution network (ADN) management, and sizing as well as siting distributed generation (DG) (e.g., WSs) show clearly the importance of variable reverse power flow (VRPF) in generation (e.g.,it WSs) show clearly of variable reverse power flow ADNs. (DG) However, is also shown, e.g., the in importance [12], that there are yet no definite answers on (VRPF) how in exporting power to the upstream network or VRPF [1] can be accomplished. Therefore, the aim of ADNs. However, it is also shown, e.g., in [12], that there are yet no definite answers on how exporting paper (Part‐II), together the paper (Part‐I) [1], is to the answer a few powerthis to the upstream network orwith VRPF [1]companion can be accomplished. Therefore, aim of thisimportant paper (Part-II), questions related to this issue. together with the companion paper (Part-I) [1], is to answer a few important questions related to this issue. VRPFVRPF depends on many factors (e.g., the location and size of WSs, demand level, energy prices etc.), depends on many factors (e.g., the location and size of WSs, demand level, energy prices etc.), and therefore, to extract relationships between them by investigating these factors is not trivial. and therefore, to extract relationships between them by investigating these factors is not trivial. For this For this reason, we consider here a simplified WS model, as shown in Figure 2, inserted in the reason, we consider here a simplified WS model, as shown in Figure 2, inserted in the extended extended A‐R‐OPF model presented in Part‐I [1]. A-R-OPF The optimization problem to be solved in this paper contains a multi‐objective function F (1) [1] model presented in Part-I [1]. The optimization problem to be solved in this paper contains a multi-objective function F (1) [1] with reactive power of WSs connected to the MV‐ADN as shown in Figure 1: with reactive power of WSs connected to the MV-ADN as shown in Figure 1: max F F1 F2 F3 F4 F5
β c.w , Qdisp.w
Tfinal βc.w ,Qdisp.w
F1 “
h 1
i 1
Cpr.p phq T
Nil ÿ
final
h “1
(1)
N
F1 Cpr.p (h) Pw (i,h) β c.w (i,h)
Tÿ final
(1)
F “ F1 ´ F2 ´ F3 ´ F4 ´ F5
max
Pw pi, hqβc.w pi, hq
F2 C pr.p i“ 1 (h) Ploss (h) h 1
(2)
(2) (3)
i Pl
Tfinal
FT3final Cpr.q (h) Qloss (h)
F2 “
ÿ h 1 Cpr.p phq Ploss phq
(4)
(3)
h “1
F3 “
Tÿ final h “1
2
Cpr.q phq Qloss phq
(4)
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F4 “
Tÿ final
Cpr.p phq PS1 p1, hq
(5)
h“1Tfinal
FT4 Cpr.p ( h) PS1 (1, h)
(5)
final ÿ h 1 Cpr.q phq QS1 p1, hq F5 “
(6)
Tfinal
F5 Cpr.q (h) QS1 (1, h) h “1
(6)
1 Here, F1 (2) is the total revenue from the hinjected wind active energy with Pw as the generated w as the generated Here, F wind power of a1 (2) is the total revenue from the injected wind active energy with P wind turbine (WT), F2 (3) is the total cost of active energy losses with Ploss as the 2 (3) is the total cost of active energy losses with P lossQ as the activewind power of a wind turbine (WT), F power losses in the MV-ADN, F3 (4) is the total cost of reactive energy losses with loss as the active power losses in the MV‐ADN, F loss as the reactive power losses in the MV-ADN, F34 (4) is the total cost of reactive energy losses with Q (5) is the total cost/revenue of importing/exporting active reactive power losses in the MV‐ADN, F 4 (5) is the total cost/revenue of importing/exporting active energy at slack bus S1 with PS1 as the active power produced/absorbed at slack bus S1 , and F5 (6) is energy at slack bus S1 with PS1 as the active power produced/absorbed at slack bus S1, and F5 (6) is the the total cost/revenue of importing/exporting reactive energy at slack bus S1 with QS1 as the reactive total cost/revenue of importing/exporting reactive energy at slack bus S1 with QS1 as the reactive power produced/absorbed at slack bus S1 , as seen in Figure 1, respectively.
power produced/absorbed at slack bus S1, as seen in Figure 1, respectively.
Figure 2. Simplified model of a WS [1]. Here, M stands for electrical meter and the wind turbine (WT)
Figure 2. Simplified model of a WS [1]. Here, M stands for electrical meter and the wind turbine (WT) is connected to the grid through a full scale power converter or power conditioning system (PCS) as is connected to the grid through a full scale power converter or power conditioning system (PCS) as in [17] while the wind speed is converted to wind power P w as in [5]. in [17] while the wind speed is converted to wind power Pw as in [5].
The above objective function is subject to equality and inequality constraints as given in Part‐I [1]. Here, two control variables are is considered. the and curtailment factor βc.w (0 ≤ as βc.wgiven ≤ 1) at WS [1]. The above objective function subject toFirst, equality inequality constraints ina Part-I connected to the MV‐ADN at a specific location or bus, see Figure 2. This factor is used for curtailing Here, two control variables are considered. First, the curtailment factor βc.w (0 ď βc.w ď 1) at a WS the wind active power generation to prevent violations of system constraints (detailed mathematical connected to the MV-ADN at a specific location or bus, see Figure 2. This factor is used for curtailing formulation is given in Part‐I [1]). Second, the reactive power dispatch (Qdisp.w) of the WS, see Figure 2, the wind active power generation to prevent violations of system constraints (detailed mathematical which is to be optimized to minimize energy losses in the MV‐ADN and meanwhile minimize the formulation is given in Part-I [1]). Second, the reactive power dispatch (Qdisp.w ) of the WS, see Figure 2, reactive energy import from the HV‐TN [19,20]. More precisely, the curtailment factor and reactive which is to be optimized to minimize energy losses in the MV-ADN and meanwhile minimize the power dispatch are used to balance all the terms in the objective function F (1) using an active energy reactive energy import from the HV-TN [19,20]. More precisely, the curtailment factor and reactive price model C pr.p and a reactive energy price model Cpr.q based on a meter‐based A‐R‐OPF method [5]. power dispatch are used to balance all the terms in the objective function F (1) using an active energy The data of prices are given in Table A1 in the Appendix. price model C and a reactive energy price modelproblem Cpr.q based on a meter-based A-R-OPF method [5]. In this the optimization formulated above under the operating pr.ppaper, we solve conditions defined in [1]. inParticularly, investigate the effect of varying upper bound of active The data of prices are given Table A1 inwe the Appendix. power in reverse direction at slack bus S P1.rev (0 ≤ α P1.rev ≤ 1), the lower power factors In this paper, we solve the optimization1 denoted by α problem formulated above under the operating conditions (PFs) of WSs denoted by PF min.w (0 ≤ PFmin.w ≤ 1) under different WS‐sizes and WS‐locations. Detailed defined in [1]. Particularly, we investigate the effect of varying upper bound of active power in reverse data of the WS are given in Table A2 in the Appendix. After solving the problem different operating direction at slack bus S1 denoted by αP1.rev (0 ď αP1.rev ď 1), the lower power factors (PFs) of WSs points can be obtained and their features distinguished: denoted by PFmin.w (0 ď PFmin.w ď 1) under different WS-sizes and WS-locations. Detailed data of the given An operating green quadrant (see Figure 1) means different that both operating active and points reactive WS are in Table point A2 in in thethe Appendix. After 1 solving the problem can be energies are being imported from the HV‐TN to the MV‐ADN. obtained and their features distinguished:
‚ ‚ ‚
An operating point in the red quadrant 2 means that only active power is being exported from the
MV‐ADN to the HV‐TN, while reactive energy is still imported [1]. An operating point in the green quadrant 1 (see Figure 1) means that both active and reactive In this paper, consider the situation that point in the gray quadrants (i.e., energies are beingwe imported from the HV-TN toan theoperating MV-ADN. quadrants 3 and 4) should be avoided to minimize charging costs for reverse reactive energy [3]. An operating point in the red quadrant 2 means that only active power is being exported from the However, if reverse reactive energy is being remunerated, as in the practice in some countries, a MV-ADN to the HV-TN, while reactive energy is still imported [1]. huge amount of reverse reactive energy could be observed as shown in [21]. In this paper, we consider the situation that an operating point in the gray quadrants (i.e., 3 quadrants 3 and 4) should be avoided to minimize charging costs for reverse reactive energy [3].
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2. Electricity Market Model The market model in is this paper is defined as agreements between inthe MV‐ADN However, ifelectricity reverse reactive energy being remunerated, as in the practice some countries, a (operator/company) and the HV‐TN (operator/company) for both active and reactive energies [5]. It huge amount of reverse reactive energy could be observed as shown in [21].
is to note here that the user of this method is the MV‐ADN company/operator considering the operating and market conditions defined in Part‐I [1]. Note that in an electricity market locational 2. Electricity Market Model marginal prices (LMPs) can include many terms, e.g., system marginal energy cost, marginal cost of Thecongestion and marginal cost of losses [5], and therefore, fixed active and reactive energy prices are electricity market model in this paper is defined as agreements between the MV-ADN used in this paper for clarity and simplicity. (operator/company) and the HV-TN (operator/company) for both active and reactive energies [5]. It is
to note here that the user of this method is the MV-ADN company/operator considering the operating 2.1. Active Energy and market conditions defined in Part-I [1]. Note that in an electricity market locational marginal The forward active energy from the HV‐TN to the MV‐ADN is to be minimized based on an prices (LMPs) can include many terms, e.g., system marginal energy cost, marginal cost of congestion active energy price model Cpr.p, while the reverse active energy is either not allowed (i.e., αP1.rev = 0) in and marginal cost of losses [5], and therefore, fixed active and reactive energy prices are used in this order to avoid any possible active power rejection as shown in [18], or allowed (i.e., 0
