Power-based distribution locational marginal pricing under high-penetration of distributed energy resources
Introduction
Recent environmental concerns due to pollutant emissions in transportation sector, looming fossil fuel crisis, and also technological improvements in new energy resources have expedited a vast penetration of distributed energy resources (DERs) in distribution systems, specifically the photovoltaic (PV) energy, and application of electric vehicles (EVs) in transportation [1]. As the distribution networks are traditionally planned for vertical and unidirectional power transfer without the presence of DERs, an increased penetration of these resources, PV, and EVs puts forward two main challenges ahead of distribution system operators (DSOs). The first one is that the PV systems generally inject the maximum power to the grid at midday hours with lower energy demand. Accordingly, the generation-consumption imbalance ends in reverse power flow toward the upstream network and hence, voltage rise is seen at PV-adjacent buses [2], [3], [4]. The second challenge is the congestion happening in distribution lines due to concurrent and uncontrolled charging/discharging of EVs. These issues not only limit the broader utilization of PVs and EVs, but also could jeopardize the security of distribution network.
As the penetration of EVs increases, further infrastructures say as parking lots (PLs) are required to handle the charging requirements of EVs and end in a proper integration of these emergent loads to the distribution grid. These stations not only provide a charging platform for EVs, but also could play in vehicle-to-grid (V2G) mode due to sensibly long-time presence of EVs. Accordingly, the PLs could be modeled as an aggregated flexible load in distribution networks [5]. Moreover, at the hours that the EVs depart the PLs, the charging infrastructures including off-board chargers and DC-link are still present and could take part in vehicle-to-grid reactive power support (V2GQ) programs. Within this program they inject or absorb reactive power and affect the Volt/VAr control of distribution system [2], [6].
The PLs owners take into account the constraints of EVs charge/discharge preferences and determine their own active/reactive power transfer strategies with the distribution grid in maximizing their net saving. Accordingly, in market-based approaches, it is possible for the DSO to send properly determined price signals to PLs to indirectly participate in load control programs by smart charging/discharging of EVs. By this way, the congestion happening in distribution feeders is handled effectively. Besides, through dedicated financial incentives for reactive power participation, the PLs could provide suitable Volt/VAr support and avert voltage rise due to maximum generation of PVs at midday hours. By this way, the penetration of PVs increases without any technical bottlenecks.
There are different studies conducted in determination of price signals for indirect control of DERs in distribution networks which fall in two main categories. The first type has recommended to form market structure in distribution level within which the DSO plays a similar role of independent system operator (ISO) at transmission level markets [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18]. The second category [19], [20], [21], [22], [23] proposes the deployment of dynamic tariff (DT) which includes the congestion and loss components of DLMP. This approach is not a market clearing approach and performs well beside the upstream transmission market. The authors in [7] have proposed an active power pricing scheme based on LMP to entice the energy storage systems (ESSs) to reduce the distribution system congestion. Reference [8] deals with DLMP calculation to increase the social welfare of distribution network players considering non-linear power flow equations and inter-temporal energy requirements. The authors in [9] have developed an approach for local distribution level market and have cleared it in a daily manner in the smart context of the grid. In [11], [12], energy management of buildings is investigated based on DLMP price signal to avert congestion happening. A pricing scheme based on game theory is developed by DSO for privately-owned DGs with the objective of active power losses and green-house gases minimization [14], [15]. In the proposed approach, the active and reactive powers of DGs are priced based on their contributions in power losses and emission minimization. The established approach does not model the inter-temporal characteristics of the ESSs and flexible loads and hence is only suitable for DGs without ramp constraints. Reference [16] have proposed real-time pricing in the multiseller–multibuyer smart distribution grid, based on dual decomposition to implement demand response. Reference [17] presents a transmission and distribution locational marginal pricing along with a co-optimization model of energy and reserves in transmission and distribution markets with centralized generation and distributed energy resources (DERs). In [18], to preserve the privacy of different network layers, concept of generalized bid functions (GBF) is proposed. The GBFs are calculated by approximating the true cost function of a network (cost of local network dispatch as a function of its hourly total power generation) by a series of affine functions. Therefore, inter-temporal energy requirements of DERs and ramp rate constraints of DGs can’t be regarded as constraints in the proposed model in [18].
The second category deals with the congestion management of distribution networks based on DT application to the aggregators. In [19], an optimal DT is determined in the presence of EVs and heat pumps (HPs). Also, to avert the multiple solution issue faced in linear programming, the quadratic programming approach is deployed for DT calculation based on price sensitivity factor. References [20], [21] have addressed the uncertainties in DT calculation and have proposed some countermeasures. Application of distributed optimization-based DT (DDT) for congestion management purposes is explored in the networks by vast penetration of EVs and HPs [22], [23]. In this view, the DSO does not afford any optimization task and accordingly there is not any need to be made informed of cost functions and energy requirements of aggregators. As well, in [23], to relax the need for the application of price sensitivity factor represented in [19], a new concept called as dynamic power tariff (DPT) is introduced. A precise overview of the investigated literature demonstrates the following shortcomings:
- (1)
Application of DC optimal power flow approach [11], [12], [19], [20], [21], [22], [23] which is not a rational assumption due to the greater ratio of R/X in distribution networks;
- (2)
Calculation of price signal based on centralized approach in [7], [8], [9], which does not consider privacy issue of DERs and also is faced with greater computational burden;
- (3)
Making no any specific use of V2G and V2GQ capabilities of PLs to improve the operational metrics of the distribution network [19], [20], [21], [22], [23];
- (4)
Ignoring the multiple solution issue in the DER optimization which occurs due to the nature of the linear programming (LP) formulation [9].
In order to alleviate the existing shortcomings and improve the surveyed literatures, this study develops a new and efficient market model for day-ahead operation of distribution network. In the proposed model, DSO acts as an independent entity to minimize the total operation cost and satisfy the running technical and economic constraints. In order to manage the DERs, a power-based distribution locational marginal pricing (PDLMP) scheme is proposed, within which price signals are in the form of linear expressions of active and reactive powers. The main contributions of the proposed approach are as follows:
- •
The concept of power based DT is extended to DLMP, namely PDLMP which to the author’s best knowledge is the first study on this type.
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Based on dual decomposition approach, a decentralized and iterative optimization approach is proposed for PDLMP calculation. In each of the iterations, only the price signals and the corresponding scheduling of DERs are exchanged between the DSO and the DERs’ owners. Therefore, in contradiction to the available pricing methods, in the proposed approach, there is not any need for the DSO to consider the DERs cost functions and constraints. Accordingly, the privacy issue is satisfied, the uncertainty level is reduced, and the computational burden of the DSO is lessened, significantly.
- •
An accurate modeling of distribution network and DERs is launched. To avoid the duality gap problem seen in dual decomposition approaches, the non-linear equations are accurately converted to linear expressions.
The remainder of this paper is organized as follows. Section 2 talks about the distribution system and DERs modeling. Section 3 intended to launch the proposed day-ahead pricing mechanism. For numerical evaluations, Section 4 organizes extensive simulation studies. Eventually, the concluding remarks are reported in Section 5.
Section snippets
Distribution system modeling
The investigated distribution network is a balanced radial medium voltage (MV) network equipped with smart grid infrastructures. In this network, besides the constant loads, a set of DERs are considered including PLs, PVs, and DGs. These DERs could provide a bidirectional data flow with DSO to receive the control commands and hence establish an optimally-controlled operation scheduling and power transfer. The network is connected to the transmission network through grid supply point (GSP) in
DSO operation model
DSO as an independent entity, should consider the distribution network limitations and control the DERs power such that the total operation cost is minimized. The cost terms include the cost of active and reactive powers purchase and also the cost of active and reactive power scheduling. To this end, the DSO should execute the following optimization model to determine the DERs optimal scheduling pattern and the optimal power exchange with the external whole-sale market. Although in this study,
Numerical analysis and results
The proposed pricing method is evaluated on standard 38-bus, 12.66 kV distribution system [30] with a high penetration level of DERs. The one-line diagram of the system is illustrated in Fig. 3. As it can be seen in this figure, the system is modified by adding 4 PV-based DGs, 2 Diesel-based generators, and 2 EV-parking lots. The nominal power rating of the PVs is assumed to be 1 MW for those installed at buses 34, 35, and 36, and 2 MW for the one installed at bus 37. The operational cost of
Conclusion
In this paper, an innovative PDLMP approach was proposed which is a decentralized and iterative one. Accordingly, the privacy of technical and economic data of DERs is preserved and the computational burden of the DSO decreases, remarkably. The conducted numerical studies reveal that:
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The proposed PDLMP approach impacts the optimal scheduling of active and reactive powers of DERs and by this way, the congestion and over-voltage issues are suppressed. Also, by motivating the DERs to participate
CRediT authorship contribution statement
Razi Rezvanfar: Conceptualization, Methodology, Software, Formal analysis, Investigation, Resources, Data curation, Writing - original draft, Writing - review & editing, Project administration. Mehrdad Tarafdar Hagh: Conceptualization, Writing - review & editing, Software, Formal analysis, Methodology, Supervision. Kazem Zare: Conceptualization, Writing - review & editing, Formal analysis, Supervision, Software, Methodology.
Declaration of Competing Interest
The authors declared that there is no conflict of interest.
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