<PAGE>

                                                                    EXHIBIT 4.4

 
             AMENDED AND RESTATED AGREEMENT OF LIMITED PARTNERSHIP
                            OF DUQUESNE CAPITAL L.P.


     This AMENDED AND RESTATED AGREEMENT OF LIMITED PARTNERSHIP OF DUQUESNE
CAPITAL L.P. dated as of May 14, 1996 is entered into by and among Duquesne
Light Company, a Pennsylvania corporation ("Duquesne Light"), as the General
Partner, and Susan Fields (the "Initial Limited Partner"), together with the
other Persons who become Limited Partners of the Partnership as provided herein.

     WHEREAS, Duquesne Light and the Initial Limited Partner have heretofore
formed a limited partnership pursuant to (S) 17-201 of the Delaware Revised
Uniform Limited Partnership Act, 6 Del. C. (S) 17-101, et seq., as amended from
                                   ---  -              -------                 
time to time (the "Act"), by filing a Certificate of Limited Partnership with
the office of the Secretary of State of the State of Delaware on April 27, 1994,
and entering into an Agreement of Limited Partnership of Duquesne Light L.P.,
dated as of April 27, 1994, and Duquesne Light and the Initial Limited Partner
have agreed pursuant to an Amended and Restated Agreement of Limited Partnership
of Duquesne Capital L.P. dated as of May 9, 1994 to change the name of the
Partnership from Duquesne Light L.P. to Duquesne Capital L.P. (the "Original
Limited Partnership Agreement") and such name change has been reflected by
filing an Amended and Restated Certificate of Limited Partnership with the
office of the Secretary of State of the State of Delaware on May 9, 1994; and

     WHEREAS, the Partners desire to continue the Partnership as a limited
partnership under the Act and to amend and restate the Original Limited
Partnership Agreement in its entirety;

     NOW, THEREFORE, in consideration of the agreements and obligations set
forth herein and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties hereto hereby agree as
follows:


                                   ARTICLE I

                                 DEFINED TERMS

     Unless the context otherwise requires, the terms defined in this Article I
shall, for the purposes of this Agreement, have the meanings herein specified.
<PAGE>
 
     "Act" shall mean the Delaware Revised Uniform Limited Partnership Act, 6
Del. C. (S) 17-101, et seq., as the same may be amended from time to time, and
---  -              -------                                                   
any successor to such Act.

     "Affiliate" shall mean, with respect to a specified Person, any Person that
directly or indirectly controls, is controlled by, or is under common control
with, the specified Person.  For purposes of this definition, the term "control"
when used with respect to any specified Person, means the power to direct the
management and policies of such Person, directly or indirectly, whether through
the ownership of voting securities, by contract or otherwise.

     "Agreement" shall mean this Amended and Restated Agreement of Limited
Partnership of the Partnership, as amended, supplemented or restated and in
effect from time to time.

     "Bankruptcy" shall mean any events specified in (S)(S) 17-402(a)(4) and (5)
of the Act.

     "Book-Entry Interest" shall mean a beneficial interest in an LP
Certificate, ownership and transfers of which shall be made through book entries
by the Depository as described in Section 14.4.

     "Certificate" shall mean the Certificate of Limited Partnership and any and
all amendments thereto and restatements thereof filed on behalf of the
Partnership with the office of the Secretary of State of the State of Delaware
pursuant to the Act.

     "Code" shall mean the Internal Revenue Code of 1986, as amended from time
to time, or any corresponding federal tax statute enacted after the date of this
Agreement.  A reference to a specific section ((S)) of the Code refers not only
to such specific section but also to any corresponding provision of any federal
tax statute enacted after the date of this Agreement, as such specific section
or corresponding provision is in effect on the date of application of the
provisions of this Agreement containing such reference.

     "Covered Person" shall mean the General Partner, any Affiliate of the
General Partner or any officers, directors, shareholders, partners, employees,
representatives or agents of the General Partner or their respective Affiliates,
or any employee or agent of the Partnership or its Affiliates.

     "Debentures" shall mean the subordinated debentures of Duquesne Light
issued in one or more series under the Indenture and having certain payment
terms that correspond to the terms of the related series of Preferred
Securities.

     "Depository" shall mean The Depository Trust Company, New York, New York,
or its successors and assigns and any other securities depository for the
Preferred Securities in accordance with this Agreement.

                                      -2-
<PAGE>
 
     "Dividends" shall mean the distributions paid or payable to any Limited
Partner who is a Preferred Security Holder pursuant to the terms of the
Preferred Securities held by such Limited Partner.

     "Duquesne Light" means Duquesne Light Company, a Pennsylvania corporation,
and any successor thereto permitted under the Indenture.

     "Exchange Act" shall mean the Securities Exchange Act of 1934, as amended,
and any successor to such statute.

     "Fiscal Year" shall mean (i) the period commencing upon the formation of
the Partnership and ending on December 31, 1996, (ii) any subsequent twelve (12)
month period commencing on January 1 and ending on December 31.

     "General Partner" shall mean Duquesne Light, in its capacity as general
partner of the Partnership, together with any successor thereto that becomes a
general partner of the Partnership pursuant to the terms of this Agreement.

     "General Partner Interests" shall mean the Interests of the General Partner
in the Partnership.

     "Guarantee" shall mean the Payment and Guarantee Agreement of Duquesne
Light dated as of May 14, 1996 relating to the Preferred Securities.

     "Guarantor" means Duquesne Light.

     "Holder" or "Preferred Security Holder" means a Person in whose name an LP
Certificate is registered on the books and records of the Partnership; provided,
however, that in determining whether the Holders of the requisite percentage of
Preferred Securities have given any request, notice, consent or waiver
hereunder, "Holder" shall not include Duquesne Light or any Affiliate of
Duquesne Light.

     "Indemnified Person" shall mean each Limited Partner, any Affiliate of the
General Partner or any officers, directors, shareholders, partners, employees,
representatives or agents of the General Partner or of any Affiliate of the
General Partner, or any employee or agent of the Partnership or its Affiliates.

     "Indenture" shall mean the Indenture of Duquesne Light dated as of May 1,
1996 between Duquesne Light and The First National Bank of Chicago, as trustee.

     "Initial Limited Partner" shall mean Susan Fields.

                                      -3-
<PAGE>
 
     "Interest" shall mean the entire interest of a Partner in the Partnership
at any particular time, including the right of such Partner to any and all
benefits to which a Partner may be entitled as provided in this Agreement,
together with the obligations of such Partner to comply with all of the terms
and provisions of this Agreement.

     "Limited Partners" shall mean any Person who is admitted to the Partnership
as a limited partner of the Partnership in accordance with the terms of this
Agreement, including the Preferred Security Holders, together with any
successors thereto, in each such Person's capacity as a limited partner of the
Partnership.

     "LP Certificate" shall mean a certificate substantially in the form
attached hereto as Exhibit A, evidencing the Preferred Securities held by a
Limited Partner.

     "Partners" shall mean the General Partner and the Limited Partners,
collectively, and a "Partner" shall mean any one of the Partners.

     "Partnership" shall mean the limited partnership heretofore formed and
continued pursuant to this Agreement, and any successor thereto.

     "Person" shall mean any individual, corporation, association, partnership
(general or limited), joint venture, trust, estate, limited liability company,
or other legal entity or organization.

     "Preferred Securities" shall have the meaning set forth in Section 10.2 of
this Agreement.

     "Preferred Security Owner" shall mean, with respect to a Book-Entry
Interest, a Person who is the beneficial owner of such Book-Entry Interest, as
reflected on the books of the Depository, or on the books of a Person
maintaining an account with such Depository (directly as a participant or as an
indirect participant in the Depository, in each case in accordance with the
rules of such Depository).

     "Purchase Price" shall mean the amount paid for each Preferred Security in
the initial offering thereof.

     "Securities Act" shall mean the Securities Act of 1933, as amended, and any
successor to such statute.

     "Tax Matters Partner" means the General Partner designated as such in
Section 12.1 hereof.

                                      -4-
<PAGE>
 
     "Treasury Regulations" means the income tax regulations, including
temporary regulations, promulgated under the Code, as such regulations may be
amended from time to time (including corresponding provisions of succeeding
regulations).

     "Underwriting Agreement" means an Underwriting Agreement among the
Partnership, Duquesne Light and the underwriters named therein relating to the
issuance and sale of one or more series of Preferred Securities.


                                   ARTICLE II

                             CONTINUATION AND TERM

     Section 2.1  Formation.  The General Partner and the Initial Limited
                  ---------
Partner have previously formed the Partnership as a limited partnership pursuant
to the provisions of the Act and hereby amend and restate the Original Limited
Partnership Agreement in its entirety.

     Section 2.2  Continuation.
                  ------------ 

     (a)  The Partners hereby agree to continue the Partnership under and
pursuant to the provisions of the Act and agree that the rights, duties and
liabilities of the Partners shall be as provided in the Act, except as otherwise
provided herein.

     (b)  Upon the execution of this Agreement or a counterpart of this
Agreement, Duquesne Light shall continue as the General Partner and Susan Fields
shall continue as the Initial Limited Partner. Pursuant to Section 2.2(c) of
this Agreement, the Holders of Preferred Securities from time to time shall be
admitted to the Partnership as Limited Partners. Following the admission of any
Holder of Preferred Securities to the Partnership as a Limited Partner, the
Initial Limited Partner shall withdraw from the Partnership and shall receive
the return of her capital contribution without interest or deduction, and the
remaining Partners hereby agree to continue the business of the Partnership
without dissolution.

     (c)  Without execution of this Agreement, upon receipt by a Person of an LP
Certificate and payment for the Preferred Security being acquired by such
Person, which shall be deemed to constitute a request by such Person that the
books and records of the Partnership reflect its admission as a Limited Partner,
such Person shall be admitted to the Partnership as a Limited Partner and shall
become bound by this Agreement.

      (d) The name and mailing address of each Partner and the amount
contributed by such Partner to the capital of the Partnership shall be listed on
the books and records of the Partnership. The General Partner shall be required
to update the books and records from time to time as necessary to accurately
reflect the information therein.

                                      -5-
<PAGE>
 
     (e) The General Partner shall execute, deliver and file any and all
amendments to and restatements of the Certificate.

          Section 2.3  Name.  The name of the Partnership heretofore formed and
                       ----                                                    
continued hereby is Duquesne Capital L.P., unless and until the name of the
Partnership is changed by the General Partner, in its sole discretion, and an
appropriate amendment to the Certificate is filed as required by the Act.

          Section 2.4  Duration.  The Partnership commenced on the date the
                       --------                                            
Certificate was filed in the office of the Secretary of State of the State of
Delaware and shall continue until December 31, 2049 unless sooner dissolved
before such date in accordance with the provisions of this Agreement.

          Section 2.5  Registered Agent and Office.  The Partnership's
                       --------------------------- 
registered agent and office in the State of Delaware is The Corporation Trust
Company, Corporation Trust Center, 1209 Orange Street, Wilmington, New Castle
County, Delaware 19801. At any time, the General Partner may designate another
registered agent and/or registered office.

          Section 2.6  Principal Place of Business.  The principal place of
                       ---------------------------                         
business of the Partnership shall be c/o Duquesne Light Company, 411 Seventh
Avenue, P.O. Box 1930, Pittsburgh, Pennsylvania 15230-1930.  The General Partner
may change the location of the Partnership's principal place of business in its
sole and absolute discretion.

          Section 2.7  Statutory Compliance.  The General Partner shall
                       --------------------
execute and file on behalf and at the expense of the Partnership all
appropriate certificates required by law to be filed in connection with the
formation and existence of the Partnership, and the General Partner shall
execute and so file such other documents, applications and instruments as it may
be deemed necessary or appropriate with respect to the formation of and the
conduct of business by the Partnership, including, without limitation, the
conduct of business, if any, of the Partnership in Pennsylvania.


                                  ARTICLE III

                     PURPOSE AND POWERS OF THE PARTNERSHIP

          Section 3.1  Purpose.  The sole purpose of the Partnership is to issue
                       ------- 
interests in the Partnership, including, without limitation, General Partner
Interests and Preferred Securities, and to lend the proceeds thereof to Duquesne
Light in return for Debentures of Duquesne Light, and to engage in any and all
activities necessary, advisable or incidental thereto.

                                      -6-
<PAGE>
 
          Section 3.2  Powers of the Partnership.
                       ------------------------- 

         (a) The Partnership shall have the power and authority to take any and
all actions necessary, appropriate, proper, advisable, incidental or convenient
to or for the furtherance of the purpose set forth in Section 3.1., including
all of the powers that may be exercised by the General Partner on behalf of the
Partnership pursuant to this Agreement.

         (b)  The Partnership, and the General Partner on behalf of the
Partnership, may enter into and execute, deliver, acknowledge and perform one or
more Underwriting Agreements, registration statements, applications and filings
to list Preferred Securities on one or more national securities exchanges or
qualify the Preferred Securities for sale in various jurisdictions, and any
other contracts, applications, certificates or agreements contemplated thereby
or specifically described therein, and make loans to Duquesne Light in return
for Debentures of Duquesne Light, all without any further act, vote or approval
of any Partner notwithstanding any other provision of this Agreement, the Act or
other applicable law. The General Partner is hereby authorized to enter into and
perform on behalf of the Partnership all such contracts, applications, filings,
certificates and agreements, but such authorization shall not be deemed a
restriction on the power of the General Partner to enter into other documents on
behalf of the Partnership to the extent specifically provided for in this
Agreement.

          Section 3.3  Limitations on Partnership Powers.  Notwithstanding the
                       ---------------------------------                      
foregoing provisions of Section 3.2, neither the Partnership nor the General
Partner on behalf of the Partnership shall have the power or authority to (a)
borrow money or to become liable for the borrowings of any third party or (b)
except as expressly provided in Section 3.1, to engage in any financial or other
trade or business.  The Partnership shall not do business in any jurisdiction
other than Delaware or Pennsylvania, it being understood that the issuance and
sale of Preferred Securities may be consummated in New York.


                                  ARTICLE IV

                       CAPITAL CONTRIBUTIONS, SECURITIES
                              AND CAPITAL ACCOUNTS

          Section 4.1  Capital Contributions.
                       --------------------- 

         (a) The General Partner has contributed the amount of $1,515,175.00 to
the capital of the Partnership and shall make such further contributions as are
necessary to satisfy its obligations under Section 6.4.

                                      -7-
<PAGE>
 
         (b) The Initial Limited Partner has contributed the amount of $1 to the
capital of the Partnership, which amount shall be returned to the Initial
Limited Partner upon her withdrawal from the Partnership.

         (c) With respect to each Limited Partner, there shall be contributed to
the capital of the Partnership the amount of the Purchase Price for the
Preferred Securities acquired by it (such amount being such Limited Partner's
capital contribution to the Partnership).  No Limited Partner shall be required
to make any additional capital contribution to the Partnership in respect of the
Preferred Securities held by it.

          Section 4.2  Securities.
                       ---------- 

         (a) The Preferred Securities held by a Preferred Security Holder
shall be registered in its name on the books and records of the Partnership. A
Preferred Security Holder's Interests shall be represented by the Preferred
Securities so registered in its name. Each Limited Partner and Holder of
Preferred Securities hereby agrees that its Interests and any Preferred
Securities held by it shall for all purposes be personal property. No Limited
Partner or Holder of Preferred Securities shall have any interest in specific
Partnership property.

          (b) The General Partner Interests shall be set forth on the books and
records of the Partnership.  The General Partner hereby agrees that the General
Partner Interests shall for all purposes be personal property.  The General
Partner shall have no interest in specific Partnership property.

          Section 4.3  Capital Accounts.  An individual capital account (a
                       ----------------                                   
"Capital Account") shall be established and maintained for each Partner which
shall be credited with the capital contributions made and the profits allocated
to the Partner (or predecessor in interest) and debited by the distributions
made and losses allocated to the Partner (or predecessor thereof).  Any
syndication expenses incurred by the Partnership shall be allocated exclusively
to the Capital Account of the General Partner.  All provisions of this Agreement
relating to the maintenance of Capital Accounts are intended to comply with the
Treasury Regulations promulgated under Code (S) 704(b), and shall be interpreted
and applied in a manner consistent with such Treasury Regulations.


                                   ARTICLE V

                                    PARTNERS

          Section 5.1  Powers of Partners.  The Partners shall have the power to
                       ------------------                                       
exercise any and all rights or powers granted to the Partners pursuant to the
express terms of this Agreement.

                                      -8-
<PAGE>
 
          Section 5.2  Partition.  Each Partner waives any and all rights that
                       ---------
it may have to maintain an action for partition of the Partnership's property.

          Section 5.3  Withdrawal.  A Partner (other than the Initial Limited
                       ----------                                            
Partner) may not withdraw from the Partnership prior to the dissolution and
winding up of the Partnership except upon the assignment of its Interests
(including any redemption, repurchase or other acquisition by the Partnership or
Duquesne Light, as the case may be), in accordance with the provisions of this
Agreement.  A withdrawing Partner shall not be entitled to receive any
distribution and shall not otherwise be entitled to receive the fair value of
its Interests except as otherwise expressly provided in this Agreement.


                                  ARTICLE VI

                                  MANAGEMENT

          Section 6.1  Management of the Partnership.  The General Partner shall
                       -----------------------------                            
have full, exclusive and complete discretion to manage and control the business
and affairs of the Partnership, to make all decisions affecting the business and
affairs of the Partnership and to take all such actions as it deems necessary,
appropriate or convenient to accomplish the purpose of the Partnership as set
forth herein, all subject, however, to the provisions of Section 16.12 hereof.

          Section 6.2  Expenses.  The General Partner shall pay for all, and the
                       --------                                                 
Partnership shall not be obligated to pay, directly or indirectly, any, of the
costs and expenses of the Partnership (including, without limitation, costs and
expenses relating to the organization of, and offering of limited partner
interests in, the Partnership and costs and expenses relating to the operation
of the Partnership, including without limitation, costs and expenses of
accountants, attorneys, statistical or bookkeeping services and computing or
accounting equipment, any paying agents, registrars, transfer agents,
duplicating, travel and telephone).

          Section 6.3  Powers of the General Partner.  The General Partner shall
                       -----------------------------                            
have the right, power and authority in the management of the business and
affairs of the Partnership to do or cause to be done any and all acts deemed by
the General Partner to be necessary, appropriate or convenient to effectuate the
business, purposes and objectives of the Partnership, all subject, however, to
the provisions of Section 16.12 hereof.  Without limiting the generality of the
foregoing, the General Partner shall have the power and authority without any
further act, vote or approval of any Partner to:

         (a) issue Interests, including the General Partner Interests, and the
Preferred Securities in accordance with this Agreement;

         (b) act as registrar and transfer agent for the Preferred Securities;

                                      -9-
<PAGE>
 
         (c) establish a record date with respect to all actions to be taken
hereunder that require a record date be established, including with respect to
Dividends and voting rights and pay Dividends and make all other required
payments and distributions on General Partner Interests and Preferred Securities
as the Partnership's paying agent;

         (d) bring and defend on behalf of the Partnership actions and
proceedings at law or in equity before any court or governmental, administrative
or other regulatory agency, body or commission or otherwise;

         (e) employ or otherwise engage employees and agents (who may be
designated as officers with titles) and managers, contractors, advisors and
consultants and pay reasonable compensation for such services; and

         (f) execute all documents or instruments, perform all duties and powers
and do all things for and on behalf of the Partnership in all matters necessary
or desirable or incidental to the foregoing.

         The expression of any power or authority of the General Partner in
this Agreement shall not in any way limit or exclude any other power or
authority which is not specifically or expressly set forth in this Agreement.

          Notwithstanding the foregoing, the General Partner shall not have the
power to permit or cause the Partnership to file a voluntary petition in
bankruptcy without the affirmative vote of the Holders of 66-2/3% in aggregate
liquidation preference of the outstanding Preferred Securities.

          Section 6.4  Ownership by the General Partner.  The capital
                       --------------------------------
contributions made by the General Partner to the Partnership shall be at least
equal to 1% of the total contributions made by all Partners to the Partnership,
and except as otherwise provided in this Agreement, at all times at least 1% of
all income, gain, loss, deduction and credit of the Partnership shall be
allocated to the General Partner.

          Section 6.5  No Management by the Limited Partners.  Except as
                       -------------------------------------
otherwise expressly provided herein, no Limited Partner, in its capacity as
such, shall take part in the day-to-day management, operation or control of the
business and affairs of the Partnership. The Limited Partners shall not be
agents of the Partnership and shall not have any right, power or authority to
transact any business in the name of the Partnership or to act for or on behalf
of or to bind the Partnership.

          Section 6.6  Limitation of Liability.  Except as otherwise expressly
                       -----------------------                                
required by law, a Limited Partner, in its capacity as such, shall have no
liability in excess of (a) the amount of its capital contributions, (b) its
share of any assets and undistributed profits of the Partnership, and (c) the
amount of any distributions wrongfully distributed to it.  The Limited Partners
and the

                                      -10-
<PAGE>
 
Initial Limited Partner shall have no liability under this Agreement except as
expressly provided in this Agreement or the Act.


                                  ARTICLE VII

                            AMENDMENTS AND MEETINGS

          Section 7.1  Amendments.  Except as otherwise provided in this
                       ----------
Agreement or by any applicable terms of any Action (as hereinafter defined)
establishing a series of Preferred Securities, this Agreement may be amended by,
and only by, a written instrument executed by the General Partner; provided,
however, that (i) no amendment shall be made, and any such purported amendment
shall be void and ineffective, to the extent the result thereof would be to
cause the Partnership to be treated as anything other than a partnership for
purposes of United States income taxation and (ii) any amendment which would
adversely affect the powers, preferences or special rights of any series of
Preferred Securities may be effected only as permitted by the terms of such
series of Preferred Securities.

          Section 7.2  Meetings of the Partners.
                       ------------------------ 

         (a) Meetings of the Partners may be called at any time by the General
Partner or as provided in any Action establishing a series of Preferred
Securities.  Except to the extent otherwise provided in any such Action, the
following provisions shall apply to meetings of Partners.

         (b) Notice of any such meeting shall be given to all Partners not less
than thirty (30) business days nor more than sixty (60) days prior to the date
of such meeting.  Partners may vote in person or by proxy at such meeting.
Whenever a vote, consent or approval of Partners is permitted or required under
this Agreement, such vote, consent or approval may be given at a meeting of
Partners or by written consent.

         (c) Each Partner may authorize any Person to act for it by proxy on all
matters in which a Partner is entitled to participate, including waiving notice
of any meeting, or voting or participating at a meeting.  Every proxy must be
signed by the Partner or its attorney-in-fact.  No proxy shall be valid after
the expiration of eleven (11) months from the date thereof unless otherwise
provided in the proxy.  Every proxy shall be revocable at the pleasure of the
Partner executing it.

         (d) Each meeting of Partners shall be conducted by the General
Partner or by such other Person as the General Partner may designate.

         (e) The General Partner, in its sole discretion, shall establish all
other provisions relating to meetings of Partners, including notice of the time,
place or purpose of any meeting at

                                      -11-
<PAGE>
 
which any matter is to be voted on by any Partners, waiver of any such notice,
action by consent without a meeting, the establishment of a record date, quorum
requirements, voting in person or by proxy or any other matter with respect to
the exercise of any such right to vote; provided however, that unless the
General Partner has established a lower percentage, a majority of the Partners
entitled to vote thereat shall constitute a quorum at all meetings of the
Partners.

                                 ARTICLE VIII

                                  ALLOCATIONS

          Section 8.1  Profits.  Each fiscal period, the net profits of the
                       -------                                             
Partnership will be allocated (i) first, to the Preferred Security Holders, in
proportion to the number of Preferred Securities held by each such Holder, in an
amount equal to the excess of (a) the Dividends accrued on the Preferred
Securities since their date of issuance through and including the close of the
current fiscal period (whether or not paid) over (b) the amount of profits
allocated to the Preferred Security Holders pursuant to this Section 8.1(i) in
all prior fiscal periods and (ii) thereafter, to the General Partner.

          Section 8.2  Losses.  Except in connection with a dissolution and
                       ------                                              
liquidation of the Partnership, the net losses of the Partnership shall be
allocated each year to the General Partner.  Upon a dissolution and liquidation
of the Partnership, net losses shall be allocated to each Preferred Security
Holder in an amount equal to the excess of (a) such Preferred Security Holder's
Capital Account over (b) such Preferred Security Holder's Liquidation
Distribution (as defined with respect to each Preferred Security in the Action
establishing such Preferred Security), with any remaining net losses being
allocated to the General Partner.

          Section 8.3  Allocation Rules.
                       ---------------- 

         (a) For purposes of determining the profits, losses or any other items
allocable to any period, profits, losses and any such other items shall be
determined on a daily, monthly or other basis, as determined by the General
Partner using any method that is permissible under (S) 706 of the Code and the
Treasury Regulations thereunder.

         (b)  The Partners are aware of the income tax consequences of the
allocations made by this Article VIII and hereby agree to be bound by the
provisions of this Article VIII in reporting their shares of Partnership income
and loss for income tax purposes.


                                  ARTICLE IX

                                   DIVIDENDS

                                      -12-
<PAGE>
 
          Section 9.1  Dividends.  Limited Partners shall receive periodic
                       ---------                                          
Dividends, if any, redemption payments and Liquidation Distributions in
accordance with the applicable terms of the Preferred Securities.  Subject to
the rights of the Preferred Securities, all remaining cash shall be distributed
to the General Partner at such time as the General Partner shall determine.

          Section 9.2  Limitations on Distributions.  Notwithstanding any
                       ----------------------------
provision to the contrary contained in this Agreement, the Partnership shall not
make a distribution (including a Dividend) to any Partner on account of its
interest in the Partnership if such distribution (including a Dividend) would
violate (S)17-607 of the Act or other applicable law.

          Section 9.3  Withholding.  The Partnership shall comply with all
                       -----------                                        
withholding requirements under federal, state and local law.  The Partnership
shall request, and the Partners shall provide to the Partnership, such forms or
certificates as are necessary to establish an exemption from withholding with
respect to each Partner, and any representations and forms as shall reasonably
be requested by the Partnership to assist it in determining the extent of, and
in fulfilling, its withholding obligations.   The Partnership shall file
required forms with applicable jurisdictions and, unless an exemption from
withholding is properly established by a Partner, shall remit amounts withheld
with respect to the Partners to applicable jurisdictions.  To the extent that
the Partnership is required to withhold and pay over any amounts to any
authority with respect to distributions or allocations to any Partner, the
amount withheld shall be deemed to be a distribution in the amount of the
withholding to the Partner.  In the event of any claimed overwitholding,
Partners shall be limited to an action against the applicable jurisdiction.  If
the amount withheld was not withheld from actual distributions, the Partnership
may reduce subsequent distributions by the amount of such withholding.


                                   ARTICLE X

            THE GENERAL PARTNER INTERESTS AND PREFERRED SECURITIES

         Section 10.1  Interests of the Partners.
                       ------------------------- 

         (a) Duquesne Light shall be the sole general partner of the Partnership
and shall hold all of the General Partner Interests of the Partnership.

         (b) The aggregate number of Preferred Securities which the Partnership
shall have authority to issue is unlimited.

         Section 10.2  Preferred Securities.  (a) The General Partner on behalf
                       --------------------  
of the Partnership is authorized to issue limited partner interests (the
"Preferred Securities"), in one or more series, having such designations,
rights, privileges, restrictions, preferences and other terms and provisions as
may from time to time be established in a written action or actions (each, an
"Action") of the General Partner providing for issue of such series. In
connection with the

                                      -13-
<PAGE>
 
foregoing, the General Partner is expressly authorized, prior to issuance, to
set forth in an Action or Actions providing for the issue of such series, the
following:

                (i) the distinctive designation of such series which shall
distinguish it from other series;

               (ii) the number of Preferred Securities included in such series;

              (iii) the annual Dividend rate (or method of determining such
rate) for Preferred Securities of such series and the date or dates upon which
such Dividends shall be payable;

               (iv) whether Dividends on the Preferred Securities of such
series shall be cumulative, and, in the case of Preferred Securities of any
series having cumulative Dividend rights, the date or dates or method of
determining the date or dates from which Dividends on the Preferred Securities
of such series shall be cumulative;

                (v) the amount or amounts which shall be paid out of the assets 
of the Partnership to the Holders of the Preferred Securities of such series
upon voluntary or involuntary dissolution, liquidation or winding up of the
Partnership;

               (vi) the price or prices at which, the period or periods within
which and the terms and conditions upon which the Preferred Securities of such
series may be redeemed or purchased, in whole or in part, at the option of the
Partnership;

              (vii) the obligation, if any, of the Partnership to purchase or
redeem Preferred Securities of such series pursuant to a sinking fund or
otherwise and the price or prices at which, the period or periods within which
and the terms and conditions upon which the Preferred Securities of such series
shall be redeemed, in whole or in part, pursuant to such obligation;

             (viii) the period or periods within which and the terms and
conditions, if any, including the price or prices or the rate or rates of
conversion or exchange and the terms and conditions of any adjustments thereof,
upon which the Preferred Securities of such series shall be convertible or
exchangeable at the option of the Preferred Security Holder, the Partnership or
Duquesne Light into any other Interests or securities or other property or cash
or into any other series of Preferred Securities;

               (ix) the voting rights, if any, of the Preferred Securities of
such series in addition to those required by law, including the number of votes
per Preferred Security and any requirement for the approval by the Holders of
Preferred Securities, or of the Preferred Securities of one or more series, or
of both, as a condition to specified Action or amendments to this Agreement;

                                      -14-
<PAGE>
 
                (x) the ranking of the Preferred Securities of the series as
compared with Preferred Securities of other series in respect of the right to
receive Dividends and the right to receive payments out of the assets of the
Partnership upon voluntary or involuntary dissolution, winding up or termination
of the Partnership;

               (xi) the nature and terms of the Debentures and any other backup
undertakings of Duquesne Light and/or another subsidiary of Duquesne Light to be
provided to Holders of the Preferred Securities of such series; and

              (xii) any other relative rights, powers and duties of the
Preferred Securities of the series not inconsistent with this Agreement or with
applicable law;

provided that the proceeds of the issuance of each such series of Preferred
Securities, together with the proceeds of any related capital contribution of
the General Partner, shall be loaned to Duquesne Light in return for a
concurrently issued series of Debentures in aggregate principal amount equal to
the aggregate liquidation preference of the Preferred Securities of such series
and the related capital contribution, bearing interest at an annual rate equal
to the annual Dividend rate on such Preferred Securities payable at such times
as the Dividends on such Preferred Securities, and having certain redemption
provisions which correspond to the redemption provisions for such Preferred
Securities.

          (b) In connection with the foregoing and without limiting the
generality thereof, the General Partner is hereby expressly authorized, without
the vote or approval of any Partner or Holder of Preferred Securities, to take
any Action to create under the provisions of this Agreement a series of
Preferred Securities that was not previously outstanding, including a series
ranking junior to other series of Preferred Securities in respect of the right
to receive Dividends and the right to receive payments out of assets of the
Partnership upon voluntary or involuntary dissolution, liquidation or winding up
of the Partnership.  Without the vote or approval of any Partner or Holder of
Preferred Securities, the General Partner may execute, swear to, acknowledge,
deliver, file and record whatever documents may be required in connection with
the issue from time to time of Preferred Securities in one or more series as
shall be necessary, convenient or desirable to reflect the issue of such series.
The General Partner shall do all things it deems to be appropriate or necessary
to comply with the Act and is authorized and directed to do all things it deems
to be necessary or permissible in connection with any future issuance, including
compliance with any statute, rule, regulation or guideline of any federal, state
or other governmental agency or any securities exchange.

          (c)  Any Action or Actions taken by the General Partner pursuant to
the provisions of this Section 10.2 shall be deemed an amendment and supplement
to and part of this Agreement.

          (d)  All Preferred Securities shall rank senior to the General Partner
Interests in respect of the right to receive Dividends or other property
distributions and the right to receive payments out of the assets of the
Partnership upon voluntary or involuntary dissolution, liquidation

                                      -15-
<PAGE>
 
or winding up of the Partnership.  All Preferred Securities redeemed, purchased
or otherwise acquired by the Partnership (including Preferred Securities
surrendered for conversion or exchange) shall be cancelled and thereupon
restored to the status of authorized but unissued Preferred Securities
undesignated as to series.

          (e)  No Holder of Preferred Securities shall be entitled as a matter
of right to subscribe for or purchase, or have any preemptive right with respect
to, any part of any new series or additional issue of an existing series of
Preferred Securities, or of interests or securities convertible into any
Preferred Securities, whether now or hereafter authorized and whether issued for
cash or other consideration or by way of Dividend or distribution.

          (f)  Except as otherwise provided in this Agreement or by the General
Partner in accordance with Section 10.2(a) above in respect of any series of
Preferred Securities and as otherwise required by law, all management of the
Partnership shall be vested exclusively in the General Partner.

          (g)  Any Person acquiring Preferred Securities shall be admitted to
the Partnership as a Limited Partner upon compliance with Section 2.2.

          (h)  If any action is, by the terms of the Indenture, not permitted to
be taken by the Partnership without the consent of holders of Preferred
Securities or any representative appointed with respect to any series of
Preferred Securities, the General Partner shall not, without such requisite
consent, take any such action.

          (i)  The General Partner shall notify holders of Preferred Securities
of each series of any notice of default received from the trustee under the
Indenture with respect to the related series of Debentures within 20 days of
receipt of such notice; provided, however, in the event that the General Partner
receives notice from the Trustee that an Event of Default under the Indenture
has occurred and the Preferred Securities are then held by the Depository, then
the General Partner shall notify the holders of Preferred Securities of such
Event of Default within 5 Business Days (as defined in the Indenture) of receipt
of such notice.


                                  ARTICLE XI

                               BOOKS AND RECORDS

          Section 11.1  Books, Records and Financial Statements.
                        --------------------------------------- 

         (a) At all times during the continuance of the Partnership, the
Partnership shall maintain, at its principal place of business, separate books
of account for the Partnership that shall show a true and accurate record of all
costs and expenses incurred, all charges made, all credits made and received and
all income derived in connection with the operation of the Partnership's

                                      -16-
<PAGE>
 
business in accordance with generally accepted accounting principles
consistently applied, and, to the extent inconsistent therewith, in accordance
with this Agreement.  Such books of account, together with a copy of this
Agreement and a certified copy of the Certificate, shall at all times be
maintained at the principal place of business of the Partnership and shall be
open to inspection and examination at reasonable times by each Limited Partner
or its duly authorized representative for any purpose reasonably related to such
Limited Partner's interest in the Partnership.

         (b) Notwithstanding any other provision of this Agreement, the General
Partner may, to the maximum extent permitted by applicable law, keep
confidential from the Limited Partners any information the disclosure of which
the General Partner reasonably believes is not in the best interests of the
Partnership or is adverse to the interests of the Partnership or which the
Partnership or the General Partner is required by law or by an agreement with
any Person to keep confidential.

          (c) The General Partner shall prepare and maintain, or cause to be
prepared and maintained, the books of account of the Partnership and within
three (3) months after the close of each Fiscal Year the General Partner shall
transmit to each Partner a statement indicating such Partner's share of each
item of Partnership income, gain, loss, deduction or credit for such Fiscal Year
for Federal income tax purposes.

          Section 11.2  Accounting Method.  For both financial and tax reporting
                        -----------------
purposes and for purposes of determining profits and losses, the books and
records of the Partnership shall be kept on the accrual method of accounting
applied in a consistent manner and shall reflect all Partnership transactions
and be appropriate and adequate for the Partnership's business.


                                  ARTICLE XII

                                  TAX MATTERS

          Section 12.1  Tax Matters Partner.  The General Partner is hereby
                        -------------------                                
designated as "Tax Matters Partner" of the Partnership for purposes of (S)
6231(a)(7) of the Code and shall have the power to manage and control, on behalf
of the Partnership, any administrative proceeding at the Partnership level with
the Internal Revenue Service relating to the determination of any item of
Partnership income, gain, loss, deduction or credit for Federal income tax
purposes.

          Section 12.2  No Right to Make Section 754 Election.  The General
                        -------------------------------------
Partner shall not make an election in accordance with (S) 754 of the Code.

          Section 12.3  Taxation as Partnership.  The General Partner and the
                        -----------------------                              
Preferred Security Holders acknowledge that they intend, for Federal income tax
purposes, that the Partnership shall be treated as a partnership and that the
General Partner and the Holders of Preferred Securities shall be treated as
Partners of such Partnership for such purposes.

                                      -17-
<PAGE>
 
                                 ARTICLE XIII

                        EXCULPATION AND INDEMNIFICATION

          Section 13.1  Exculpation.
                        ----------- 

         (a) No Covered Person shall be liable to the Partnership or any
Indemnified Person for any loss, damage or claim incurred by reason of any act
or omission performed or omitted by such Covered Person in good faith on behalf
of the Partnership and in a manner reasonably believed to be within the scope of
authority conferred on such Covered Person by this Agreement, except that a
Covered Person shall be liable for any such loss, damage or claim incurred by
reason of such Covered Person's gross negligence, bad faith, recklessness or
willful misconduct.

         (b) Each Covered Person shall be fully protected in relying in good
faith upon the records of the Partnership and upon such information, opinions,
reports or statements presented to the Partnership by any Person as to matters
such Covered Person reasonably believes are within such other Person's
professional or expert competence and who has been selected with reasonable care
by or on behalf of the Partnership, including information, opinions, reports or
statements as to the value and amount of the assets, liabilities, profits,
losses, or any other facts pertinent to the existence and amount of assets from
which distributions to Partners might properly be paid.

          Section 13.2  Duties.
                        ------ 

         (a) To the extent that, at law or in equity, a Covered Person has
duties (including fiduciary duties) and liabilities relating thereto to the
Partnership or to any Indemnified Person, such Covered Person acting under this
Agreement shall not be liable to the Partnership or to any other Indemnified
Person for its good faith reliance on the provisions of this Agreement. The
provisions of this Agreement, to the extent that they restrict the duties and
liabilities of a Covered Person otherwise existing at law or in equity, are
agreed by the parties hereto to replace such other duties and liabilities of
such Covered Person.

         (b) Unless otherwise expressly provided herein, (a) whenever a
conflict of interest exists or arises between a Covered Person, on the one hand,
and the Partnership or a Limited Partner, on the other hand, or (b) whenever
this Agreement or any other agreement contemplated herein or therein provides
that a Covered Person shall act in a manner that is, or provide terms that are,
fair and reasonable to the Partnership or any Partner, such Covered Person shall
resolve such conflict of interest, take such action or provide such terms,
considering in each case the relative interest of each party (including its own
interest) to such conflict, agreement, transaction or situation and the benefits
and burdens relating to such interests, any customary or accepted industry
practices, and any applicable generally accepted accounting practices or
principles. In the absence of gross negligence, recklessness, bad faith or
willful misconduct by the Covered Person, the resolution, action or term so
made, taken or provided by such Covered Person shall

                                      -18-
<PAGE>
 
not constitute a breach of this Agreement or any other agreement contemplated
herein or of any duty or obligation of such Covered Person at law or in equity
or otherwise.

         (c) Whenever in this Agreement the General Partner or an Indemnified
Person is permitted or required to make a decision (i) in its "discretion" or
under a grant of similar authority, the General Partner or such Indemnified
Person shall be entitled to consider only such interests and factors as it
desires, including its own interests, and shall have no duty or obligation to
give any consideration to any interest of or factors affecting the Partnership
or any other Person, or (ii) in its "good faith" or under another express
standard, the General Partner or such Indemnified Person shall act under such
express standard and shall not be subject to any other or different standard
imposed by this Agreement or other applicable law.

          Section 13.3  Indemnification.  To the fullest extent permitted by
                        ---------------                                     
applicable law, an Indemnified Person shall be entitled to indemnification from
the Partnership for any loss, damage or claim incurred by such Indemnified
Person by reason of any act or omission performed or omitted by such Indemnified
Person in good faith on behalf of the Partnership and in a manner reasonably
believed to be within the scope of authority conferred on such Indemnified
Person by this Agreement, except that no Indemnified Person shall be entitled to
be indemnified in respect of any loss, damage or claim incurred by such
Indemnified Person by reason of gross negligence, recklessness, bad faith or
willful misconduct with respect to such acts or omissions; provided, however,
                                                           --------  ------- 
that any indemnity under this Section 13.3 shall be provided out of and to the
extent of Partnership assets only, and no Covered Person shall have any personal
liability on account thereof.

          Section 13.4  Expenses.  To the fullest extent permitted by applicable
                        --------                                                
law, expenses (including legal fees) incurred by an Indemnified Person in
defending any claim, demand, action, suit or proceeding may, from time to time,
be advanced by the Partnership prior to the final disposition of such claim,
demand, action, suit or proceeding upon receipt by the Partnership of an
undertaking by or on behalf of the Indemnified Person to repay such amount if it
shall be determined that the Indemnified Person is not entitled to be
indemnified as authorized in Section 13.3 hereof.

          Section 13.5  Outside Businesses.  Any Partner or Affiliate thereof
                        ------------------
may engage in or possess an interest in other business ventures of any nature or
description, independently or with others, similar or dissimilar to the business
of the Partnership, and the Partnership and the Partners shall have no rights by
virtue of this Agreement in and to such independent ventures or the income or
profits derived therefrom, and the pursuit of any such venture, even if
competitive with the business of the Partnership, shall not be deemed wrongful
or improper. No Partner or Affiliate thereof shall be obligated to present any
particular investment opportunity to the Partnership even if such opportunity is
of a character that, if presented to the Partnership, could be taken by the
Partnership, and any Partner or Affiliate thereof shall have the right to take
for its own account (individually or as a partner or fiduciary) or to recommend
to others any such particular investment opportunity.

                                      -19-
<PAGE>
 
          Section 13.6  Liability of the General Partner.  Except as otherwise
                        --------------------------------                      
provided in the Act, the General Partner shall have the liabilities of a partner
in a partnership without limited partners to any Person other than the
Partnership and the Limited Partners.  Except as otherwise provided in this
Agreement or the Act, the General Partner shall have the liabilities of a
partner in a partnership without limited partners to the Partnership and each
Limited Partner.

          Section 13.7  Waiver by General Partner; Indemnification of
                        ---------------------------------------------
Partnership by General Partner.  The General Partner hereby waives all rights of
------------------------------                                                  
indemnification which it may have against the Partnership under this Agreement
or otherwise.  The General Partner also hereby agrees to indemnify and hold
harmless the Partnership for (i) any payments made by it under this Article
XIII, and (ii) any indemnity payments the Partnership may otherwise be required
to make under applicable law.


                                  ARTICLE XIV

                                   TRANSFERS

          Section 14.1  Transfer of Interests. (a) Preferred Securities shall be
                        ---------------------                                  
freely transferable by a Preferred Security Holder.

         (b) The General Partner may not assign its interest in the Partnership
in whole or in part under any circumstances, except to a successor of Duquesne
Light under the Indenture. Any such assignee of all or a part of the Interest of
a General Partner in the Partnership shall be admitted to the Partnership as a
general partner of the Partnership immediately prior to the effective date of
such assignment, and such additional or successor General Partner is hereby
authorized to and shall continue the business of the Partnership without
dissolution.

         (c) No Interest shall be transferred, in whole or in part, except in
accordance with the terms and conditions set forth in this Agreement.  Any
transfer or purported transfer of any Interest not made in accordance with this
Agreement shall be null and void.

          Section 14.2  Transfer of LP Certificates.  The General Partner shall
                        ---------------------------                            
provide for the registration of LP Certificates and of transfers of LP
Certificates without charge by or on behalf of the Partnership, but upon payment
in respect of any tax or other governmental charges which may be imposed in
relation to it, together with the giving of such indemnity as the General
Partner may require.  Upon surrender for registration of transfer of any LP
Certificate, the General Partner shall cause one or more new LP Certificates to
be issued in the name of the designated transferee or transferees.  Every LP
Certificate surrendered for registration of transfer shall be accompanied by a
written instrument of transfer in form satisfactory to the General Partner duly
executed by the Preferred Security Holder or his or her attorney duly authorized
in writing.  Each LP Certificate surrendered for registration of transfer shall
be cancelled by the General Partner.  A transferee of an LP Certificate shall be
admitted to the Partnership as a

                                      -20-
<PAGE>
 
Limited Partner and shall be entitled to the rights and subject to the
obligations of a Preferred Security Holder hereunder upon the receipt by such
transferee of an LP Certificate.  The transferor of an LP Certificate shall
cease to be a limited partner of the Partnership at the time that the transferee
of the LP Certificate is admitted to the Partnership as a Limited Partner in
accordance with this Section 14.2.

          Section 14.3  Persons Deemed Preferred Security Holders.  The
                        -----------------------------------------
Partnership may treat the Person in whose name any LP Certificate shall be
registered on the books and records of the Partnership as the Preferred Security
Holder and the sole holder of such LP Certificate for purposes of receiving
Dividends and for all other purposes whatsoever and, accordingly, shall not be
bound to recognize any equitable or other claim to or interest in such LP
Certificate on the part of any other Person, whether or not the Partnership
shall have actual or other notice thereof.

          Section 14.4  Book-Entry Interests.  The LP Certificates, on original
                        --------------------                                   
issuance, will be issued in the form of a global LP Certificate or LP
Certificates representing Book-Entry Interests, to be delivered to the
Depository, by, or on behalf of, the Partnership.  Such LP Certificate or LP
Certificates shall initially be registered on the books and records of the
Partnership in the name of the Depository or its nominee, and no Preferred
Security Owner will receive a definitive LP Certificate representing such
Preferred Security Owner's interests in such LP Certificate, except as provided
in Section 14.6.  Unless and until definitive, fully registered LP Certificates
(the "Definitive LP Certificates") have been issued to the Preferred Security
Owners pursuant to Section 14.6:

          (a) The provisions of this Section shall be in full force and effect;

          (b) The Partnership and the General Partner shall be entitled to
deal with the Depository for all purposes of this Agreement (including the
payment of Dividends on the LP Certificates and receiving approvals, votes or
consents hereunder) as the Preferred Security Holder and the sole holder of the
LP Certificates and shall have no obligation to the Preferred Security Owners;

          (c) To the extent that the provisions of this Section conflict with
any other provisions of this Agreement, the provisions of this Section shall
control; and

          (d) The rights of the Preferred Security Owners shall be exercised
only through the Depository and shall be limited to those established by law and
agreements between such Preferred Security Owners and the Depository and/or the
Depository participants. Unless and until the Definitive LP Certificates are
issued pursuant to Section 14.6, the Depository will be responsible for making
book-entry transfers among its participants and accepting and transmitting
payments of Dividends on the LP Certificates to such participants.

          Section 14.5  Notices to the Depository.  Whenever a notice or other
                        -------------------------                             
communication to the Preferred Security Holders is required under this
Agreement, unless and

                                      -21-
<PAGE>
 
until Definitive LP Certificates shall have been issued to the Preferred
Security Owners pursuant to Section 14.6, the General Partner shall give all
such notices and communications specified herein to be given to the Preferred
Security Holders to the Depository, and shall have no obligations to the
Preferred Security Owners.

          Section 14.6  Definitive LP Certificates.  If (a) the Depository
                        --------------------------
elects to discontinue its services as securities depository and gives reasonable
notice to the Partnership, or (b) the Partnership elects to terminate the book-
entry system through the Depository then the Partnership shall either (i)
appoint a successor Depository or (ii) cause Definitive LP Certificates to be
prepared by the Partnership. Upon surrender of the global LP Certificate or LP
Certificates representing the Book-Entry Interests by the Depository,
accompanied by registration instructions, the General Partner shall cause
Definitive LP Certificates to be delivered to Preferred Security Owners in
accordance with the instructions of the Depository. Neither the General Partner
nor the Partnership shall be liable for any delay in delivery of such
instructions and may conclusively rely on, and shall be protected in relying on,
such instructions. Any Person receiving a Definitive LP Certificate in
accordance with this Article XIV shall be admitted to the Partnership as a
Limited Partner upon receipt of such Definitive LP Certificate. The Depository
or the nominee of the Depository, as the case may be, shall cease to be a
limited partner of the Partnership under this Section 14.6 at the time that at
least one additional Person is admitted to the Partnership as a Limited Partner
in accordance with this Section 14.6. The Definitive LP Certificates shall be
printed, lithographed or engraved or may be produced in any other manner as is
reasonably acceptable to the General Partner, as evidenced by its execution
thereof.

          Section 14.7  Surrender of Preferred Securities by General Partner.
                        ---------------------------------------------------- 
If at any time Duquesne Light shall surrender any Preferred Securities of a
particular series to the Partnership, the Partnership shall surrender to or upon
the order of Duquesne Light Debentures of the series issued concurrently with
the Preferred Securities so surrendered, in aggregate principal amount equal to
the aggregate liquidation preference of such Preferred Securities so
surrendered.


                                  ARTICLE XV

                   DISSOLUTION, LIQUIDATION AND TERMINATION

          Section 15.1  No Dissolution.  The Partnership shall not be
                        --------------
dissolved by the admission of additional or successor Partners in accordance
with the terms of this Agreement. The death, withdrawal, incompetency,
Bankruptcy, dissolution or other cessation to exist as a legal entity of a
Limited Partner, or the occurrence of any other event which terminates the
Interest of a Limited Partner in the Partnership, shall not in and of itself
cause the Partnership to be dissolved and its affairs wound up. To the fullest
extent permitted by applicable law, upon the occurrence of any such event, the
General Partner may, without any further act, vote or approval of any Partner,
admit any Person to the Partnership as an additional or substitute Limited
Partner, which

                                      -22-
<PAGE>
 
admission shall be effective as of the date of the occurrence of such event, and
the business of the Partnership shall be continued without dissolution.

          Section 15.2  Events Causing Dissolution.  The Partnership shall be
                        --------------------------                           
dissolved and its affairs shall be wound up upon the occurrence of any of the
following events:

          (a) the expiration of the term of the Partnership, as provided in
Section 2.4 hereof;

          (b) the withdrawal, removal or Bankruptcy of the General Partner or
assignment by the General Partner of its entire Interest in the Partnership when
the assignee is not admitted to the Partnership as an additional or successor
General Partner in accordance with Section 14.1(b), or the occurrence of any
other event that results in the General Partner ceasing to be a general partner
of the Partnership under the Act, unless, in any such case, the business of the
Partnership is continued in accordance with the Act;

           (c) the entry of a decree of judicial dissolution under (S)17-802
of the Act; or

           (d) the written consent of all Partners.

          Section 15.3  Notice of Dissolution.  Upon the dissolution of the
                        ---------------------                              
Partnership, the General Partner, as liquidating trustee, shall promptly notify
the Partners of such dissolution.

          Section 15.4  Liquidation.  Upon dissolution of the Partnership, the
                        -----------                                           
General Partner, as liquidating trustee, shall immediately commence to wind up
the Partnership's affairs; provided, however, that a reasonable time shall be
                           --------  -------                                 
allowed for the orderly liquidation of the assets of the Partnership and the
satisfaction of liabilities to creditors so as to enable the Partners to
minimize the normal losses attendant upon a liquidation.  The Preferred Security
Holders shall continue to share profits and losses during liquidation in the
same proportions, as specified in Article VIII hereof, as before liquidation.
The proceeds of liquidation shall be distributed, as realized, in the following
order and priority:

         (a) to creditors of the Partnership, including Partners who are
creditors, to the extent permitted by law, in satisfaction of the liabilities of
the Partnership (whether by payment or the making of reasonable provision for
payment thereof), other than liabilities for distributions (including Dividends)
to Partners;

         (b) to the Preferred Security Holders of each series then outstanding
in accordance with their respective interests and in the amount of their
respective Liquidation Distributions; and

         (c) the balance to the General Partner.

                                      -23-
<PAGE>
 
          Section 15.5  Termination.  The Partnership shall terminate when all
                        -----------
of the assets of the Partnership shall have been distributed in the manner
provided for in this Article XV, and the Certificate shall have been cancelled
in the manner required by the Act.


                                  ARTICLE XVI

                                 MISCELLANEOUS

          Section 16.1  Notices.  All notices provided for in this Agreement
                        -------
shall be in writing, duly signed by the party giving such notice.

         (a) All notices provided for in this Agreement to the Partnership or
General Partner shall be delivered, telecopied or mailed by registered or
certified mail, as follows:

               (i) if given to the Partnership, in care of the General Partner
at the Partnership's mailing address set forth below:

                       c/o Duquesne Light Company
                       411 Seventh Avenue
                       P.O. Box 1930
                       Pittsburgh, Pennsylvania 15230-1930
                       Telecopy: (412) 393-6004
                       Telephone: (412) 393-6230
                       Attention: Treasurer


               (ii) if given to the General Partner, at its mailing address
set forth below:

                       Duquesne Light Company
                       411 Seventh Avenue
                       P.O. Box 1930
                       Pittsburgh, Pennsylvania 15230-1930
                       Telecopy: (412) 393-6004
                       Telephone: (412) 393-6000
                       Attention: Treasurer

          All such notices shall be deemed to have been given when received.

          (b)  All notices provided for in this Agreement to any other Partner
shall be given at the address set forth on the books and records of the
Partnership, by mail, first-class postage prepaid, and shall be deemed given
when so mailed.

                                      -24-
<PAGE>
 
          Section 16.2  Failure to Pursue Remedies.  The failure of any party to
                        --------------------------                              
seek redress for violation of, or to insist upon the strict performance of, any
provision of this Agreement shall not prevent a subsequent act, which would have
originally constituted a violation, from having the effect of an original
violation.

          Section 16.3  Cumulative Remedies.  The rights and remedies provided
                        -------------------
by this Agreement are cumulative and the use of any one right or remedy by any
party shall not preclude or waive its right to use any or all other remedies.
Said rights and remedies are given in addition to any other rights the parties
may have by law, statute, ordinance or otherwise.

          Section 16.4  Binding Effect.  This Agreement shall be binding upon
                        -------------- 
and inure to the benefit of all of the parties and, to the extent permitted by
this Agreement, their successors, legal representatives and assigns.

          Section 16.5  Interpretation.  Throughout this Agreement, nouns,
                        --------------
pronouns and verbs shall be construed as singular or plural, whichever shall be
applicable. All references herein to "Articles", "Sections" and "paragraphs"
shall refer to corresponding provisions of this Agreement.

          Section 16.6  Severability.  The invalidity or unenforceability of any
                        ------------                                            
particular provision of this Agreement shall not affect the other provisions
hereof, and this Agreement shall be construed in all respects as if such invalid
or unenforceable provision were omitted.

          Section 16.7  Counterparts.  This Agreement may be executed in any
                        ------------ 
number of counterparts with the same effect as if all parties hereto had signed
the same document. All counterparts shall be construed together and shall
constitute one instrument.

          Section 16.8  Integration.  This Agreement constitutes the entire
                        -----------                                        
agreement among the parties hereto pertaining to the subject matter hereof and
supersedes all prior agreements and understandings pertaining thereto.

          Section 16.9  Governing Law.  This Agreement and the rights of the
                        -------------
parties hereunder shall be interpreted in accordance with the laws of the State
of Delaware, and all rights and remedies shall be governed by such laws without
regard to principles of conflict of laws.

          Section 16.10  Headings.  The headings and subheadings in this
                         --------
Agreement are included for convenience and identification only and are in no way
intended to describe, interpret, define or limit the scope, extent or intent of
this Agreement or any provision hereof.

                                      -25-
<PAGE>
 
          Section 16.11  Power of Attorney.  Appointment of General Partner. 
                         -----------------   ------------------------------
(a) Each Limited Partner hereby irrevocably constitutes and appoints the General
Partner as its true and lawful attorney in fact, in its name, place, and stead,
to make, execute, acknowledge, and file the following documents, to the extent
consistent with the other provisions of this Agreement:

                (i) This Agreement, and, to the extent required by law, the
Certificate;

               (ii) Any fictitious or assumed-name certificates required to be
filed on behalf of the Partnership;

              (iii) Any application or registration to do business in any State
other than, or in addition to, the State of Delaware;

               (iv) Deeds, notes, mortgages, pledges, security instruments of
any kind and nature, leases, and such other instruments as may be necessary to
carry on the business of the Partnership; provided that no such instrument shall
increase the personal liability of the Limited Partners;

                (v) All certificates and other instruments that the General
Partner deems appropriate or necessary to form and qualify, or continue the
qualification of, the Partnership as a limited partnership in the State of
Delaware and all jurisdictions in which the Partnership may intend to conduct
business or own property;

               (vi) Any duly adopted amendment to or restatement of this
Agreement or the Certificate;

              (vii) All conveyances and other instruments or documents that
the General Partner deems appropriate or necessary to effect or reflect the
dissolution, liquidation and termination of the Partnership pursuant to the
terms of this Agreement (including a certificate of cancellation); and

              (viii) All other instruments as the attorneys-in-fact or any of
them may deem necessary or advisable to carry out fully the provisions of this
Agreement in accordance with its terms.

          (b)  It is expressly intended by each Limited Partner that the power
of attorney granted by Section 16.11(a) is coupled with an interest, shall be
irrevocable, and shall survive and not be affected by the subsequent disability
or incapacity of such Limited Partner (or if such Limited Partner is a
corporation, partnership, trust, association, limited liability company or other
legal entity, by the dissolution or termination thereof).

                                      -26-
<PAGE>
 
          Section 16.12  Enforcement of the Indenture by Limited Partners.  Any
                         ------------------------------------------------      
provision of this Agreement to the contrary notwithstanding, any request,
demand, authorization, direction, notice, consent, election, waiver or other
action provided by the Indenture to be made, given or taken by holders of
Debentures, including without limitation any of the foregoing to be made, given
or taken by holders of Debentures in connection with the enforcement of the
obligations of Duquesne Light under the Indenture or on the Debentures, may be
made, given or taken by the Holders of Preferred Securities having a liquidation
preference equal to the principal amount of Debentures required to be held in
order for holders of Debentures to take such action or, if so provided in the
Action with respect to such Preferred Securities, by one or more special
representatives appointed by such Holders of Preferred Securities ("Special
Representative").  For purposes of the preceding sentence and Section 104 of the
Indenture, upon the reasonable request of the Trustee to provide the identities
of Holders of Preferred Securities or any of their Special Representatives, the
General Partner, at its own cost, shall promptly provide copies of the
applicable excerpts of the books and records of the Partnership to the Trustee.
If any such action shall be taken by holders of Debentures, and by Holders of
Preferred Securities or Special Representatives thereof as contemplated above,
the action taken by Holders of Preferred Securities or by one or more Special
Representatives, as the case may be, shall control.  Without limiting the
generality of the foregoing, registered Holders of Preferred Securities of each
series, or the Special Representative(s) appointed by such Holders of Preferred
Securities, shall be entitled to enforce, to the fullest extent permitted by
applicable law, Duquesne Light's obligations under the Indenture and the
Debentures that were issued concurrently with such Preferred Securities to the
extent provided in Sections 111 and 610 of the Indenture.

                                      -27-
<PAGE>
 
          IN WITNESS WHEREOF, the parties hereto have executed this Agreement as
of the date first above stated.


                         GENERAL PARTNER:

                         DUQUESNE LIGHT COMPANY


                         By:   /s/ Donald J. Clayton
                            ------------------------------------
                            Name:   Donald J. Clayton
                            Title:     Treasurer



                         INITIAL LIMITED PARTNER:

                         SUSAN FIELDS


                         By:    /s/ Susan Fields
                             --------------------------------------
 
<PAGE>
 
                                                                       Exhibit A


=============================================================================== 
           Certificate Number                Number of Preferred Securities
                  R-1
================================================================================



                                                            CUSIP NO.

                  Certificate Evidencing Preferred Securities

                                       of

                             Duquesne Capital L.P.

           % Cumulative Monthly Income Preferred Securities, Series 
         --                                                        --
                   (liquidation preference $25 per security)

          Duquesne Capital L.P., a limited partnership formed under the laws of
the State of Delaware (the "Partnership"), hereby certifies that           (the
                                                                ----------- 
"Preferred Security Holder") is the registered owner of         (         )
                                                        -------  ---------
preferred securities of the Partnership representing Interests in the
Partnership of a series designated the   % Cumulative Monthly Income Preferred
                                       -- 
Securities, Series    (liquidation preference $25 per security) (the "Series 
                   --                                                        --
Preferred Securities").  The Series    Preferred Securities are fully paid and
                                    --
nonassessable Interests in the Partnership, as to which the limited partners of
the Partnership who hold the Series    Preferred Securities, in their capacities
                                    --
as limited partners of the Partnership, will have no liability solely by reason
of being Preferred Security Holders in excess of their obligations to make
payments provided for in the Limited Partnership Agreement (as defined below)
and their share of the Partnership's assets and undistributed profits (subject
to the obligation of a Preferred Security Holder to repay any funds wrongfully
distributed to it). The Series    Preferred Securities are transferable on the
                               -- 
books and records of the Partnership, in person or by a duly authorized
attorney, upon surrender of this certificate duly endorsed and in proper form
for transfer.  The powers, preferences and special rights and limitations of the
Series    Preferred Securities are established pursuant to, and this certificate
       --
and the Series    Preferred Securities represented hereby are issued and shall
               --
in all respects be subject to the terms and provisions of, the Amended and
Restated Agreement of Limited Partnership of the Partnership dated as of May 14,
1996, as the same may, from time to time, be amended (the "Limited Partnership
Agreement") authorizing the issuance of the Series    Preferred Securities and
                                                   --
determining the powers, preferences, and other special rights and limitations,
regarding Dividends, voting, return of capital and otherwise, and other matters
relating to the Series    Preferred Securities.  Capitalized terms used herein
                       -- 
but not defined shall have the meaning given them in the Limited Partnership
Agreement.  The Preferred Security Holder is entitled to the benefits of the
Payment and Guarantee Agreement of Duquesne Light Company, a Pennsylvania
corporation, dated as of May 14, 1996 (the "Guarantee") and the   % Subordinated
                                                                --
Deferrable Interest Debentures, Series    of Duquesne Light Company (the
                                       --
"Debentures") issued pursuant to the Indenture dated as of May 1, 1996 between
Duquesne Light Company and The First National Bank of Chicago, as Trustee, in
each case to the extent provided therein and in the Limited Partnership
Agreement.  The Partnership will furnish a copy of the Limited Partnership
Agreement, the Guarantee and the Debentures to the Preferred Security Holder
without charge upon written request to the Partnership at its principal place of
business or registered office.

          The Preferred Security Holder, by accepting this certificate, is
deemed to have agreed that the Debentures and the Guarantee are subordinate and
junior in right of payment to all Senior Indebtedness of Duquesne Light Company
as and to the extent provided in the Indenture and the Guarantee.  Upon receipt
of this certificate,
<PAGE>
 
the Preferred Security Holder is admitted to the Partnership as a Limited
Partner, is bound by the Limited Partnership Agreement and is entitled to the
benefits thereunder and to the benefits of the aforesaid Indenture.

       IN WITNESS WHEREOF,
the Partnership has executed this certificate this     day of          , 199 .
                                                   ---        ---------     -

                                 DUQUESNE CAPITAL L.P.

                                 By: Duquesne Light Company, its General Partner
                                 
                                 By:
                                     -----------------------------------------


                                      A-2